microeconomics i - module

MODULE FOR

MICROECONOMICS I (ECON 111)

BY:

WODAJO WOLDEGIORGIS (PHD)

WONDAFERAHU MULUGETA (MSC)

TSEGA WONDIMAGEGNEHU (MA)

HASSEN ABDA (MSC)

ORGANIZED BY:

FACULTY OF BUSINESS AND ECONOMICS

JIMMA UNIVERSITY

SEPTEMBER, 2008

JIMMA

Table of Contents Page

CHAPTER ONE: INTRODUCTION ............................................................................. 1

1.1 Introduction............................................................................................................... 1

1.2 Chapter Objectives.................................................................................................... 2

1.3 Definitions, Scope and Nature of Economics ........................................................... 2

1.4 The Fundamental Economic Problems and the Alternative Economic Systems...... 7

1.5 Scarcity, Opportunity Cost and Efficiency ............................................................. 13

1.6 Decision Making Units and the Circular Flow of Economic Activities ................. 15

1.7 The Concept of Market Structure ........................................................................... 18

1.8 Microeconomic Theory and the Price System........................................................ 18

1.9 Lesson Summary..................................................................................................... 19

1.10 Review Questions ................................................................................................. 21

CHAPTER TWO: THE THEORY OF CONSUMER BEHAVIOR ......................... 24

2.1 Introduction............................................................................................................. 24

2.2 Chapter Objectives.................................................................................................. 26

2.3 What Is the Theory of Consumer Behavior? .......................................................... 27

2.4 The Rational for the Theory of Consumer Behavior .............................................. 27

2.5 Methods of Comparing Utility................................................................................ 28

2.5.1 The Cardinal Utility Theory......................................................................... 28

2.5.2 The Ordinal Utility Theory .......................................................................... 35

2.6 The Market Demand for a Commodity................................................................... 71

2.7 Elasticity of Demand............................................................................................... 75

2.8 Choice under Uncertainty ....................................................................................... 89

2.9 Lesson Summary..................................................................................................... 96


CHAPTER THREE: THEORY OF PRODUCTION ............................................... 103

3.1 Introduction........................................................................................................... 103

3.2 Chapter Objectives................................................................................................ 103

3.3 The Production Function....................................................................................... 104

3.4 The Short Run Production Function and Stages of Production ............................ 109

3.5 Laws of Production............................................................................................... 121

3.6 Returns to Scale and Homogeneity of the Production Function........................... 123

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3.7 Equilibrium of the Firm: Choice of Optimal Combination of

Factors of Production.......................................................................................... 125

3.8 Lesson Summary................................................................................................... 133


CHAPTER FOUR: THE THEORY OF COST ......................................................... 137

4.1 Introduction........................................................................................................... 137


4.3 Short-Run Costs .................................................................................................... 138

4.4 The Relationship between Product Curves and Cost Curves in the Short Run .... 149

4. 5 Long-Run Costs ................................................................................................... 152

4.6 The Relationship between Short-Run and Long-Run

Average and Marginal Costs............................................................................... 154

4.7 Derivation of Cost Function from Production Function ....................................... 158

4.8 Dynamic Changes in Costs – The Learning Curve............................................... 161

4.9 Lesson Summary................................................................................................... 163

4.10 Review Questions ............................................................................................... 164

CHAPTER FIVE: PERFECT COMPETITION ....................................................... 168

5.1 Introduction........................................................................................................... 168


5.3 Characteristics of Pure and Perfect Competition .................................................. 169

5.4 Market Equilibrium............................................................................................... 173

5.4.1 The Market Period Equilibrium................................................................. 173

5.4.2 The Short Run Equilibrium of a Firm and Industry/Market ...................... 174

5.4.3 The Long Run Equilibrium........................................................................ 184

5.5 Perfect Competition and Consumers' Welfare...................................................... 187

5.6 Lesson Summary................................................................................................... 188


CHAPTER SIX: PURE MONOPOLY ....................................................................... 192

6.1 Introduction........................................................................................................... 192


6.3 The Characteristic Features of Pure Monopoly .................................................... 193

6.4 Origins of Monopoly Power ................................................................................. 196

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6.5 Short Run Equilibrium of a Pure Monopolist ....................................................... 199

6.6 The Long Run Equilibrium of a Pure Monopolist ................................................ 207

6.7 Price Discrimination ............................................................................................. 213

6.7.1 Definition and Necessary Conditions ........................................................ 213

6.7.2 Types of Price Discrimination ................................................................... 214

6.8 A Multi-Plant Monopolist..................................................................................... 221

6.9 The Social Cost of Monopoly ............................................................................... 226

6.10 Lesson Summary................................................................................................. 234

6.11 Review Questions ............................................................................................... 236

References …………………………………………………………………………..…239

Answers to Selected Review Questions ……………………………………….……..240

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CHAPTER ONE

INTRODUCTION

LESSON STRUCTURE

1.1 Introduction

1.2 Chapter Objectives

1.3 Definitions, Scope and Nature of Economics

1.4 The Fundamental Economic Problems and the Alternative Economic Systems

1.5 Scarcity, Opportunity Cost and Efficiency

1.6 Decision Making Units and the Circular Flow of Economic Activities

1.7 The Concept of Market Structure

1.8 Microeconomic Theory and the Price System

1.9 Lesson Summary

1.10 Review Questions

1.1 INTRODUCTION

This lesson tries to acquaint students with basic economic concepts and terminologies,

which are necessary to understand any subject of economics (particularly this one –

microeconomics). It attempts to present some reasons why you as a student learn

economics. The two fundamental facts, limited resources and unlimited wants, which

provide a reason for the existence of the subject of economics, are also briefly explained.

The lesson will present the fundamental economic problems, which are common to all

countries, and how they are solved in different economic systems in some detail. The

lesson will also provide an illumination of some basic concepts like scarcity of economic

resources, opportunity cost and efficiency. The circular flow of economic activities

presents how decision-making units interact in the market economy system. Towards its

end, the chapter describes the concern of microeconomics.

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1.2 CHAPTER OBJECTIVES

After working through this lesson, you should be able to:

• Define economics;

• Explain the nature and scope of economics in general and microeconomics in

particular;

• Understand different methods of economic analysis;

• Explain what economic resources are, and the issue of scarcity;

• Understand the different economic systems and how each of them answer the

basic economic problems;

• Understand the concept of opportunity cost and efficiency;

• Have an overview of the different types of market structure;

1.3 DEFINITIONS, SCOPE AND NATURE OF ECONOMICS

Why Do You Study Economics?

Economics is a word commonly used in our daily conversation. What is economics and

why do you need to learn economics? Before defining economics first let us try to see the

reasons why people want to study economics. Many people study economics for various

reasons. Some people want to study economics because they hope to make money. Some,

on the other hand, need to study economics because they feel illiterate if they cannot

know and understand the law of demand and supply. Many want to learn economics

because they want to know and understand how inflation and budget deficit will affect

their future life.

Generally, knowledge about economics is important because each one of us faces

economic problems at different levels and makes economic decision throughout his/her

life knowingly or unknowingly. For instance, on a personal level, we often make some

personal decisions on issues like: Which job should we take? How can we best spend our

income? Shall we buy or rent a house? And so on.

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If someone enters into business, he/she will face many economic decisions like: what to

produce or what type of service to provide? How and in what quantity to produce? And

so on. Also in politics, we face many economic decisions like how much the nation

should spend on defense, on health care and environment, on education and on different

physical infrastructure? Even as a voter, we evaluate candidates partly on the basis of

their economic view. That is, on the basis of their view on unemployment, on inflation

and over all on their socio-economic programs.

In short, economic literacy is important because economic issues facing government and

individuals shape the future of the nation and affect the well being of its citizens.

Therefore, for these and the like reasons, it is essential that economics be made accessible

to everyone.

What is Economics?

Before defining economics, again, we better first introduce some terminologies which are

necessary for better understanding of the definition of economics.

A. Resources

Resource is anything that can be used to produce goods and services. Resources are also

called inputs or factors of production. Resources (factors or inputs of production) are

divided into four categories, namely:

i. Land

ii. Labor

iii. Capital

iv. Entrepreneurship

i. Land: is a natural gift, which includes all natural resources which are found inside and

on the surface of the land. These are like:

• Different minerals

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• Soil, river, lake pond

• Timber or forest resources and other natural materials necessary to produce goods

and services.

ii. Labor: is mental and physical human effort (ability) used in the production process.

The skill and amount of labor will be important in determining level and quality of

production.

iii. Capital: capital is a man-made means of production used in the production process.

Here belong resources like:

• Machineries, equipments, tools used in the production process.

• Buildings and materials attached to it, and

• Financial capital

iv. Entrepreneurship: it is managerial skill of organizing and combining the above three

resources for production purposes. The above resources cannot be productive and be

changed into goods and services without the creative effort of entrepreneur.

Entrepreneur is an individual who organizes resources for production, introduces new

products or techniques of production.

The principal role of entrepreneur includes:

• Introducing new product and new methods of production

• Setting the overall direction of the firm

• Being a risk taker

Factors of production are combined differently by entrepreneur in the production process

and will be converted into goods and services.

Inputs (Resources) Output

Land, Labor, Capital, (production process) (Goods and Services)

Entrepreneurship
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B. Goods versus Services

The distinction between goods and services is based on whether the output (product) is

tangible or intangible. Tangible Outputs (Goods) are those like clothes, shoes, beverage,

automobile and the like. These goods are feasible and their existence can be sensed.

Intangibles Outputs (Services) are those like haircut, computer repairs, teaching and

consultation, and so on.

C. The Fundamental Economic Facts

There are two fundamental facts, which constitute the economizing problems and provide

foundation for the subject economics. These are unlimited wants and limited economic

resources.

Society's wants for material goods and services are unlimited: Our needs for goods and

services are insatiable or can not be fully satisfied because,

i. Wants are multiplicative. Introduction of a new commodity creates need for

many other commodities. For example, purchasing of a car creates needs for

parking place, fuel, oil and so on.

ii. Wants are recurrent. Even if a specific want is satisfied at a particular time, it

may recur. Take for instance food consumption. Need for food may reoccur

several times a day. The same thing is true for clothing. In short, people will

consume most of the commodity many times throughout their life.

iii. Wants multiply endlessly. If one want is satisfied, the need for another arises. If

we satisfy our need for food in a particular period of time, need for cloth arises and

if we satisfy our need for it, need for shelter comes. In such manner, human wants

multiply continuously.

iv. Human nature is accumulative. People accumulate things beyond their present

need. Even if all needs were satisfied at a particular period of time, people would

like to keep it more for consumption sometimes in the future.

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In general, people have insatiable desires for goods and services to raise their standard of

living.

Limited economic resources: Economic resources like various types of labor, natural

resources, capital and entrepreneurial ability we use to produce goods and services are

limited.

If economic resources are not sufficient to produce all goods and services needed by a

society, then we have to make choice as to which good to produce first.

Thus, unlimited wants and limited resources will give us the problem of scarcity.

Because of scarcity, economic resources must be allocated efficiently. Scarcity implies

that resources are insufficient to produce all goods and services desired by consumers or

society as a whole. To solve this and related issues we have a discipline called

Economics. Therefore, economics is the study of how scarce resources are allocated

among alternative and competing ends or uses in order to maximize the consumption of

material goods and services.

In addition to the above concepts, there are others which are very important in

understanding this course. Some of them are given below.

I. Microeconomics versus Macroeconomics

Economics is typically divided into two parts: microeconomics and macroeconomics.

Microeconomics is the part of economics which studies the decision making process by

individuals (households) and by firms. It studies the behavior of individual components

of the economy like households and business firms.

Macroeconomics, on the other hand, is the part of economics which studies the behavior

of the economy taken as a whole. It deals with phenomenon at overall economy level

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like: unemployment, inflation and national income. It studies the function of the economy

taken as a whole.

II. Positive Economics versus Normative Economics

Positive Economics is that part of economic science which deals with specific statements

that are capable of verification, by reference to the facts about economic behavior. That

is, it is concerned with describing and analyzing the economy as it is. It is an economic

analysis strictly limited to make purely descriptive statements of scientific prediction. For

example, if the price of oil increases relative to all other prices, then the amount that

people will buy will fall. Here economics will tell us what will happen if some action is

taken.

Normative Economics, on the other hand, is analysis involving value judgment. It is that

part of economic science which involves someone’s value judgments about what the

economy should be like or what particular policy action should be recommended to solve

economic problems based on a given economic generalization or relationship. Here the

economics will tell us what should be done. For example, if the price of oil goes up,

people will buy less of it, therefore, we should not allow the price to go up. Such

statement is a normative economic statement.

1.4 THE FUNDAMENTAL ECONOMIC PROBLEMS AND THE

ALTERNATIVE ECONOMIC SYSTEM

Economic system is the set of organizational arrangement and institutions established to

solve the fundamental economic problems, what, how and for whom to produce.

Economic systems are different from each other on the basis of the ownership of

economic resources and the method by which economic activities are coordinated.

Economic system is a basic means of achieving economic goals that are inherent in the

economic structure of a society.

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The fundamental role of an economic system in any society is to provide a set of rules for

allocating resources and/or consumption among individuals who can't satisfy their wants,

given limited resources. The rules that each economic system provides function within a

framework of formal institutions (e.g., laws) and informal institutions (e.g., customs).

As we have mentioned earlier, because of scarcity, there must be a choice in the use of

economic resources. The important characteristics of economic resources are that they

can be put into alternative uses. Society, therefore, must choose the best ways of using

scarce resources. Nations, be it rich or poor, developed or underdeveloped, will all face

the problem of choice.

In every nation, no matter what the form of government, what the type of economic

system, who controls the government, or how rich or poor the country is, three basic

economic questions must be answered. They are:

i. What to produce?

ii. How to produce?

iii. For whom to produce?

What and how much will be produced? Literally, billions of different outputs could be

produced with society's scarce resources. Some mechanism must exist that differentiates

between products to be produced and others that remain as either unexploited inventions

or as individuals' unfulfilled desires.

How will it be produced? There are many ways to produce a desired item. It may be

possible to use more labor and less capital, or vice versa. It may be possible to use more

unskilled labor to substitute for fewer units of skilled labor. Choices must be made about

the particular input mix, the way the inputs should be organized, how they are brought

together, and where the production is to take place.

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For whom will it be produced? Once a commodity is produced, some mechanism must

exist that distributes finished products to the ultimate consumers of the product. The

mechanism of distribution for these commodities differs by economic system.

Historically, four different types of economic systems are observed. These are:

1. Pure Capitalism (Free Market Economy)

2. Pure Socialism (Command Economy)

3. Mixed Economy (Hybrid Economy)

4. Traditional Economy (Customary Economy)

Market versus Command Economic Systems

One way to define economic systems is to classify them according to whether they are

market systems or command systems. In a market system, individuals own the factors of

production and individually decide how to use them. The cumulative decisions of these

individuals are reflected in constantly changing prices, which result from the supply and

demand for different commodities and, in turn, impact that supply and demand. The

prices of those commodities are signals to everyone within the system indicating relative

scarcity and abundance. Indeed, it is the signaling aspect of the price system that provides

the information to buyers and sellers about what should be bought and what should be

produced.

In a market system the interaction of supply and demand for each good determines what

and how much to produce. For example, if the highest price that consumers are willing to

pay is less than the lowest cost at which a good can be produced, output will be zero.

That doesn't mean that the market system has failed. It merely implies that the demand is

not high enough in relation to supply to create a market; however, it might be someday.

In a market economy the efficient use of scarce inputs determines how output will be

produced. Specifically, in a market system, the least-cost production method will have to

be used. If any other method was used, firms would be sacrificing potential profit. Any

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firm that fails to employ the least-cost technique will find that other firms can undercut

its price. That is, other firms can choose the least-cost or any lower-cost production

method and be able to offer the product at a lower price, while still making a profit. This

lower price will induce consumers to shift purchases from the higher-priced firm to the

lower-priced firm, and inefficient firms will be forced out of business.

In a market system, individuals make the choice about what is purchased; however,

ability to pay, as well as the consumer's willingness to purchase the good or service,

determine that choice. Who gets what is determined by the distribution of money income.

In a market system, a consumer's ability to pay for consumer products is based on the

consumer's money income. Money income in turn depends on the quantities, qualities,

and types of the various human and non-human resources that the individual owns and

supplies to the resource market. It also depends on the prices, or payments, for those

resources. When you are selling your human resources as labor services, your money

income is based on the wages you can earn in the labor market. If you own non-human

resources – capital and land, for example – the level of interest and rents that you are paid

for your resources will influence the size of your money income, and thus your ability to

buy consumer products.

Critics commonly argue that in a market system the rich, who begin with a

disproportionately large share of resources, tend to become richer while the poor, who

begin with a disproportionately small share of resources, tend to become poorer. They

further argue that a government, which is designed to protect private-property rights, will

tend to be exploited by those in power, which tends to be the economically wealthy.

These critics argue that a market economy leads to selfish behavior rather than socially

desirable outcomes.

In contrast, a command system is one in which decision making is centralized. In a

command system, the government controls the factors of production and makes all

decisions about their use and about the consumption of output. The central planning unit

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takes the inputs of the economy and directs them into outputs in a socially desirable

manner. This requires a careful balancing between output goals and available resources.

In a command system the central planners determine what and how much will be

produced by first forecasting an optimal level of consumption for a future period and then

specifically allocating resources projected to be sufficient to support that level of

production. The "optimal" level of production in a command economy is determined by

the central planners and is consistent with government objectives rather than being a

function of consumer desires.

As a part of the resource allocation process, the central planners also determine how

production will take place. This process could focus on low-cost production or high

quality production or full-employment of relatively inefficient resources or any number

of other governmental objectives.

Finally, the command system will determine for whom the product is produced. Again,

the focus is on socially-desirable objectives. The product can be allocated based on class,

on a queuing process, on a reward system for outstanding or loyal performance, or on any

other socially-desirable basis for the economy.

Critics commonly argue that because planned economies cannot effectively process as

much relevant information as a market does, command economic systems cannot

coordinate economic activity or satisfy consumer demand as well as market forces do.

For example, consider an economic planning board of twenty people that must decide

how many coats, apartment buildings, cars, trains, museums, jets, grocery stores, and so

forth should be built in the next five years. Where should these planners begin? How

would they forecast the future need for each of these?

Critics argue that, at best, planners would make a guess about what goods and services

would be needed. If they guess wrong, resources would be misallocated and too much or

too little production would take place. These critics argue that private individuals, guided

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by rising and falling prices and by the desire to earn profits, are better at satisfying

consumer demand.

The Mixed Economic System

In practice, most economies blend some elements of both market and command

economies in answering the three fundamental economic questions: What and how much

will be produced? How will it be produced? For whom will it be produced? Furthermore,

within any economy, the degree of the mix will vary.

The economy of the United States is generally considered to be a free market or capitalist

economic system. However, even in the United States the government has determined a

"minimum wage", has set rules and regulations for environmental protection, has

provided price supports for agricultural products, restricts the imports of items that might

compete with local production, restricts the exports of sensitive output, provides for

public goods such as a park system, and provides health and retirement services through

Medicaid and Medicare. All of these detract/depart from the essential nature of a

capitalist economy. However, most decisions continue to be left to free markets, leaving

the United States as a mixed economy that leans heavily toward the capitalist economic

system.

In contrast, the economy of the former Soviet Union is generally considered to be

communist. However, the strict controls of the central planning unit of the country tended

to be more intensely focused on heavy industry, including the defense and aerospace

industries, than on agricultural industries. Farmers often had significant freedom to

produce and sell (or barter) what they wished. The former Soviet Union is thus an

example of a mixed economy that leans heavily toward the socialist economic system.

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1.5 SCARCITY, OPPORTUNITY COST AND EFFICIENCY

If human desire were fully satisfied, we don't need to worry about the efficient use of

resources. Because all of us could have as much as we please and no one would care

about the distribution of income among people. But, the reality is somewhat different.

Because, we cannot have all we want from nature with out sacrifices. The law of scarcity

states that goods are scarce because there are no enough resources to produce all the

goods that people want to consume. This implies that there is always a tradeoff between

alternative choices.

As we have mentioned it earlier, because of scarcity, there must be a choice in the use of

economic resources. The important characteristics of economic resources are that they

can be put into alternative uses. Societies or individuals, therefore, must choose the best

ways of using scarce resources. Nations be it rich or poor, developed or under developed,

will all face the problem of choice. Tradeoff here implies the economy can only produce

more of one item if it gives up the production of some other good(s). The value of trade

off is called opportunity cost. Opportunity Cost is the value (amount) that must be

sacrificed to attend something.

That is,

goodother of obtainedamount the good one of sacrificedamount theCost y Opportunit =

Although opportunity cost can be hard to quantify, the effect of opportunity cost is

universal and very real on the individual level. In fact, this principle applies to all

decisions, not just economic ones. Since the work of the Austrian economist Friedrich

von Wieser, opportunity cost has been seen as the foundation of the marginal theory of

value.

Opportunity cost is one way to measure the cost of something. Rather than merely

identifying and adding the costs of a project, one may also identify the next best

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alternative way to spend the same amount of money. The forgone profit of this next best

alternative is the opportunity cost of the original choice. A common example is a farmer

that chooses to farm his land rather than rent it to neighbors, wherein the opportunity cost

is the forgone profit from renting. In this case, the farmer may expect to generate more

profit himself. Similarly, the opportunity cost of attending university is the lost wages a

student could have earned in the workforce, rather than the cost of tuition, books, and

other requisite items (whose sum makes up the total cost of attendance).

Note that opportunity cost is not the sum of the available alternatives, but rather the

benefit of the single, best alternative. Possible opportunity costs of the city's decision to

build the hospital on its vacant land are the loss of the land for a sporting center, or the

inability to use the land for a parking lot, or the money that could have been made from

selling the land, or the loss of any of the various other possible uses—but not all of these

in aggregate. The true opportunity cost would be the forgone profit of the most lucrative

of those listed.

One question that arises here is how to assess the benefit of dissimilar alternatives. We

must determine a dollar value associated with each alternative to facilitate comparison

and assess opportunity cost, which may be more or less difficult depending on the things

we are trying to compare. For example, many decisions involve environmental impacts

whose dollar value is difficult to assess because of scientific uncertainty. Valuing a

human life or the economic impact of an Arctic oil spill involves making subjective

choices with ethical implications.

Efficiency occurs when the economy is using its resources so well that producing more of

one good results in less of other goods, i.e., no resources are being wasted. Note that the

employment of all available resources is insufficient to achieve efficiency. Full

production must also be realized. Full production implies two kinds of efficiency:

allocative efficiency and productive efficiency. Allocative efficiency means that

resources are being devoted to those combinations of goods and services most wanted by

society. In addition, productive efficiency is realized when the desired goods and services

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are produced in the least costly ways. Thus, full production means producing the “right

goods” (allocative efficiency) in the “right way” (productive efficiency).

Check Your Progress

1. What are resources? Explain how resources are classified?

2. What are the principal roles of Entrepreneur?

3. Society’s want for material goods and services is unlimited. Explain!

4. What are the two fundamental facts of economics? How do these fundamental

facts lay ground for the foundation of economics?

5. Compare and contrast microeconomics and macroeconomics?

6. What are fundamental (basic) problems of economics? And how are these

problems solved under the alternative economic systems?

1.6 DECISION MAKING UNITS AND THE CIRCULAR FLOW OF

ECONOMIC ACTIVITIES

What are the major decision making units in the economy?

The major decision-making units in the economy are households, business firms and

government.

Households: Households are consumers of final goods and services produced in the

economy. Consumers are the owners of economic resources (land, labor, and capital and

entrepreneurship). They earn income from their labor and from the property they own.

Households are generally assumed to maximize their well-being or what economists call

"utility”.

Business Firms: Business firms are the producing unit in the economy. They hire

workers and pay for the use of various property owned by households. They use

economic resources to produce goods and services needed by households and other firms.

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Firms come in all size and forms. However, regardless of their size all firms share

common objective, i.e. profit maximization.

Government: The term government used to broadly include all government and quasi-

government bodies at the federal, state and local levels. Unlike the households and

business firms, government is not assumed to have a single goal. In a pure market

economy, the role of the government is limited to such activities as law entertainment.

Generally, how the market economic system functions can be shown using the simple

model called circular flow diagram depicted in Figure 1.1 below.

The Circular Flow of Economic Activities

The circular flow diagram tries to illustrate how an economic system works and how

solutions to the basic economic problems are made. It also captures the interrelationship

between resource markets and product markets. Households need goods and services on

which they spend their income. Business firms need economic resources (owned by

households) to produce goods and services needed by households.

To buy goods and services, households will sell their economic resources (labor, capital,

land and entrepreneur skill) and generate income which will be spent on goods and

services produced by business firms as shown in Figure 1.1 below.

Business firms will pay for the resources in the resource market in the form of wage (for

the labor resource), interest rate (for capital) and rent (for land), and use these resources

to produce goods and services demanded by households. There are two different markets

in the diagram: resource market and product market.

In the resource market economic resources are traded. From the resource market, money

in the form of consumers' income flow to households and economic resources flow to

business firms. Similarly in the product market, money income in the form of revenue

flow to business firms and goods and services flow to households. Generally, both

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households and firms participate in both markets but on different side of each, once as a

demander then as a supplier. Households are suppliers in the resource market and

demanders in the product market; firms are demanders in the resource market and

suppliers in the product market.

Firms’ Expenditure on

Economic Resources Income to Resource Owners

Flow of Resources Flow of Resources

Resource Market

Business

Firms Households

Product

Markets

Flow of Goods and Services

Revenue of Firms Consumption Expenditure

Flow of Goods and Services

Figure 1.1: The Circular Flow Model

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1.7 THE CONCEPT OF MARKET STRUCTURE

Market is a place or condition in which buyers and sellers meet to exchange goods and

services for the price they agree on. In the theory of the firm we are concerned with the

question: “How are prices of commodities determined in the market?” The determination

of price of a commodity depends on the number of sellers and buyer in the market. The

number of buyers and sellers determine the nature and degree of competition in the

market.

The nature and degree of competition makes or creates the structure of the market. Thus,

the market structure is determined or defined by the nature and degree of competition in

market.

Depending on the number of sellers and the degree of competition, the market structure is

broadly classified as follows.

1. Perfect competition (competitive market), and

2. Imperfect markets (noncompetitive markets). Here belong market structures of:

a. Monopoly,

b. Monopolistic competition, and

c. Oligopoly.

This particular course gives focus only to the perfectly competitive and monopoly

markets and how prices of goods and services are determined in these market structures.

1.8 MICROECONOMIC THEORY AND THE PRICE SYSTEM

Microeconomics (or price theory) is a branch of economics that studies how individuals,

households, and firms make decisions to allocate limited resources in consumption and/or

production.

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One of the goals of microeconomics is to analyze the market mechanisms that establish

relative prices amongst goods and services, and the allocation of limited resources

amongst many alternative uses. Microeconomics also analyzes market failure, where

markets fail to produce efficient results, as well as describing the theoretical conditions

needed for perfect competition. Significant fields of study in microeconomics include

general equilibrium, markets under asymmetric information, choice under uncertainty

and economic applications of game theory. Also considered is the elasticity of products

within the market system.

This course (Microeconomics I) deals with the price theory, where the price system plays

the fundamental role of determining what to produce, how to produce, and for whom to

produce. In the chapters to follow, we will analyze the behaviors of consumers (chapter

two) and firms (chapters three and four) separately. Chapters five and six bring the two

economic units, consumers and producers, in perfectly competitive and purely

monopolistic market structures.

Check Your Progress

1. What do you understand by opportunity cost?

2. What are the decision-making units in an economy and what are their objectives?

3. Explain the difference between product market and resources market.

4. What are payments for labor, land, capital and entrepreneurial skill?

1.9 LESSON SUMMARY

Though different people have different motives to study economics, knowledge

about economics in general is essential because everyone faces economic problems

at different levels, and makes economic decision throughout his/her life knowingly

or unknowingly. Therefore, economic literacy is important because economic

issues facing government and individuals shape the future of the nation and affect

the well being of its citizens.

19

Limited economic resources and unlimited societal wants for material goods and

services are the two fundamental facts, which lay foundation for the economizing

problem and economics as discipline. Economic resources like, different types of

labor, land, capital and entrepreneurial skill are limited. Whereas society’s need for

goods and services are unlimited as wants are multiplicative, recurrent and as

human nature is accumulative. The limited availability of resources and the

unlimited wants give rise to the problem of scarcity. Scarcity forces us to make

choices. Making a choice, in turn, implies the need for the efficient utilization of

resources.

Economics is, therefore, the study of how scarce resources are allocated among

alternative and competing ends in order to maximize the consumption of goods and

services.

The basic divisions in economics are microeconomics and macroeconomics.

Microeconomics studies the behavior of individual components of the economy:

households and business firms. Macroeconomics, on the other hand, deals with

issues at the overall economic level like unemployment, inflation and national

income. Economics can be positive or normative. Positive economics is limited to

making purely descriptive statements of scientific prediction. Normative economics

involves value judgments and it tells us what should be done.

The three major or fundamental problems of economics are what to produce, how to

produce, and for whom to produce. These problems are universal to all countries

regardless of their level of development. However, different countries having

different economic system use different approach to solve them. Economic systems

are different from each other on the basis of the ownership of economic resources

and the method by which economic activities are coordinated. The four economic

systems are free market economy, command economy, mixed economy and

traditional economy system.

Opportunity cost is the amount of one product, which must be given up to obtain

additional unit of another product. Efficiency occurs when the economy is using its

resources so well that producing more of one good results in less of other goods,

i.e., no resources are being wasted. But full production must also be realized. Full

20

production means producing the “right goods” (allocative efficiency) in the “right

way” (productive efficiency).

Households, business and government are the major decision-making units of an

economy. While households attempt to maximize their utility, firms seek to

maximize their profits. The link between them is shown by the circular flow

diagram.

1.10 REVIEW QUESTIONS

I. Multiple Choice Questions

1. Which of the following is addressed by microeconomics?

a. How tax and price controls affect consumers and producers

b. The extent to which the economy’s resources are employed

c. Overseas trade

d. ‘a’ and ‘b’

2. Ceteris paribus means,

a. Other things positively sloped

b. Supply is positively sloped

c. Demand is positively sloped

d. Other things remaining constant

e. None of the above

3. In a free market economy, the fundamental problems of the economy are solved by:

a. The agreement among economists

b. Individuals who make price in a market

c. The planning committee of the country

d. Intervention of the government in every aspect of the economy

e. the price mechanism

4. Economic resources are also called

a. Capital goods

b. Consumption goods

21

c. Free goods

d. Factors of production

e. None

5. The dual role of firms comprises of:

a. providing resources and using goods and services

b. providing resources and producing goods and services

c. employing resources and producing goods and services

d. All of the above

e. None of the above

6. Which of the following is not true about the roles of entrepreneur?

a. Determines the price of the commodity

b. Takes risk

c. Introduces new technology

d. Introduces new product

e. None

7. If the amount of a commodity available at zero price could fully satisfy the human

need, then this good is a/an:

a. Free good

b. Economic good

c. Scarce good

d. Efficient good

e. None

8. Macroeconomics is a branch of economics which deals with:

a. Price determination of the individual sellers/firms

b. The level of total output in the economy as a whole

c. Movements in the overall price level (inflation)

d. ‘b’ and ‘c’

e. ‘a’ and ‘b’

22

II. True or False Questions

1. Scarcity is ever present because every economy faces the problem of not having

enough resources to produce all the goods and services that people want.

2. A market system always produces the combination and amounts of goods that are

best for society.

III. Discussion Questions

1. What are the fundamental (basic) problems of economies? How are these problems

solved?

2. How do you relate the concepts of scarcity, opportunity cost and efficiency to one

another and to the discipline of economics?

23

CHAPTER TWO

THE THEORY OF CONSUMER BEHAVIOR

LESSON STRUCTURE

2.1 Introduction


2.3 What is the Theory of Consumer Behavior?

2.4 The Rational for the Theory of Consumer Behavior

2.5 Methods of Comparing Utility

2.5.1 The Cardinal Utility Theory

2.5.2 The Ordinal Utility Theory

2.6 Market Demand

2.7 Elasticity of Demand

2.8 Choice under Uncertainty

2.9 Lesson Summary


2.1 INTRODUCTION As it has been mentioned in the first chapter, there are three decision making units in

economics and they are households (the primary consuming units), firms (the primary

producing units) and government. As you recall from the topic “Alternative Economic

Systems” of chapter one, the decision making units in a pure market economy are

households and firms. Hence, in order to understand the pure market system it is better to

analyze the behavior of households and firms. Thus, in this chapter we will study the

behavior of households (consumers) under the “Theory of Consumer Behavior “and in

the next two chapters we will be concerned with the behavior of firms under “The

Theories of Production and Costs”.

24

In a given economy it is a must to find a market for a commodity. And in any market we

find the demanders as well as the suppliers. Hence, there is a need to study about the

markets so as to know the behavior of the economy; and, in order to know about the

market, it is necessary to deal with the components of the market i.e. demanders and

suppliers.

The analysis of the demand side and the supply side of the market involves the study of

the behaviors of households (demanders of final goods and services in the product

market) and firms (suppliers of final goods and services in the product market). Thus, the

rational for studying the theory of consumer behavior is the fact that it is the basis for the

theory of demand. This is because the market demand is assumed to be the horizontal

summation of the demand of the individual consumers. That means, we first analyze the

behavior of a consumer to determine the individual demand, and then stepping on the

demand of an individual consumer we will develop the market demand.

However, in our attempt to study the behavior of the consumer, we deal with the

traditional demand theory which has the following important features.

The traditional theory of demand examines only the final consumer’s demand for

durables and non- durables. It deals only with consumers’ demand, i.e., it does not

deal with the demand for investment good, nor with the demand for intermediate

products.

It examines the demand in one market in isolation without considering the

conditions of demand in other markets (what is referred to as partial equilibrium

analysis).

It also assumes that firms sell their product directly to the final consumers.

In order to determine the various factors that affect demand we need to deal with the

theory of demand. As demand is a multivariate relationship determined by many factors

simultaneously, we need to go beyond the law of demand which states that there is

negative relationship between market demand and price under the assumption of ceteris

25

paribus (other things remaining constant). All those important determinants of demand

are related with the behavior of the consumer. Thus, the traditional theory of demand

starts with the behavior of a consumer.

Under the theory of consumer behavior, the following important assumptions are made:

1. The consumer is assumed to be rational. Given his/her income and the market

prices of the commodities, he/she spends his/her income on the basket of goods and

services that give the highest possible satisfaction or utility. This is the

axiom/postulate of utility maximization.

2. It is also assumed that the consumer has all relevant information important for

his/her decision. This means that the consumer has perfect knowledge about his/her

income, complete knowledge of the available commodities in the market, and exact

knowledge of the prices of all available commodities in the market.

At this point it is important to mention that the theory of consumer behavior in this

chapter will be dealt with in two parts. The first part is in line with the second assumption

which considers that the consumer has full knowledge of all the information relevant to

his/her decision. The second part relaxes this assumption and tries to involve the

possibility of the existence of uncertainties in the market. In short, the first part deals with

the behavior of the consumer under the condition of certain information (Choice under

certainty), while the second part is concerned with choice under uncertainty.


This chapter has a general objective of enabling the students know how consumers decide

on baskets of goods and services to maximize their satisfaction. The specific objectives of

the chapter are:

Help students know the basis of the theory of demand;

Enable students derive a consumer’s demand under some alternative sets of

information;

Enable students know the concepts of utility and preferences;

26

Help students understand different types of utility functions;

Help students understand the determinants of individual and market demands, and

the concept of elasticity.

2.3 WHAT IS THE THEORY OF CONSUMER BEHAVIOR?

Before looking at what the theory of consumer behavior is all about, let’s first see what a

consumer is.

A consumer is an individual or a household who uses/consumes final goods and services

with a primary objective of maximizing utility.

The theory of consumer behavior is a description of how consumers allocate income

among different goods and services to maximize their well-being. It answers the

question: “How can a consumer with a limited income decide which goods and services

to buy with the objective of maximizing their utility?” It deals with how consumers

allocate their income across various goods and services and explain how these allocation

decisions determine the demands for the various goods and services.

2.4 THE RATIONAL FOR THE THEORY OF CONSUMER

BEHAVIOR

Understanding the consumers’ purchasing decisions will help us understand how changes

in income and prices affect demands for goods and services, and why the demands for

some products are more sensitive than others to changes in prices and income. In general,

as it has been mentioned above, we study the theory of consumer behavior since it is the

basis for the theory of demand.

We have said that consumers are the primary consuming units with an objective of

maximizing their utility/satisfaction. In order to attain this objective, the consumer must

27

be able to compare the utility/satisfaction of the various baskets of goods and services

which he/she can buy with his/her income.

2.5 METHODS OF COMPARING UTILITY

Utility is the level of satisfaction/pleasure that the consumer can derive from

consumption of goods and services or by undertaking a certain activity. It is the power of

a good or service to satisfy a certain human need.

There are two basic approaches to the problem of comparison of utilities. These

approaches are:

1. The Cardinalist Approach, and

2. The Ordinalist Approach.

In the next section, we will examine the two approaches one by one. In each case, we first

state the assumptions underlying the approach, and then derive the equilibrium of the

consumer.

From this equilibrium of the consumer, we will determine the demand for individual

products which will help us establish the market demand for the commodity.

Finally, we will point out the critics of each approach. Let’s first see the Cardinalist

Approach.

2.5.1 The Cardinal Utility Theory

There are some theories of utility that attach significance to the magnitude of utility.

These are known as Cardinal Utility Theories.

The cardinalist school postulates that utility can be measured. The advocates of this

school have given various suggestions for the measurement of utility. With the

28

assumption of complete knowledge of market conditions and income levels over the

planning period i.e. under certainty, some economists have suggested that utility can be

measured in monetary units, say, by the amount of money the consumer is willing to

sacrifice for another unit of a commodity. And others suggested the measurement of

utility in subjective units, called Utils.

Thus, in a theory of cardinal utility, the size of the utility difference between two bundles

of goods and services is supposed to have some sort of significance.

In its attempt to reach at the equilibrium of the consumer, the cardinal utility approach

makes the following assumptions.

Assumptions of the Cardinal Utility Theory

1. Rationality: The consumer is rational. He/she aims at the maximization of his/her

utility subject to the constraint imposed by his/her given income. This means that

the consumer is able to allocate his/her limited income first on the good that gives

him/her the highest possible level of satisfaction, and then move to the next best,

and so on.

2. Cardinal Utility: The utility of each commodity is measurable. It is assumed that

utility is a cardinal concept. The most convenient measure of utility is money: the

utility is measured by the monetary units that the consumer is willing to pay for

another unit of the commodity.

3. Constant Marginal Utility of Money: This assumption is necessary if the monetary

unit is used as the measure of utility. The essential feature of a standard unit of

measurement is that it is constant. If the marginal utility of money changes as

income changes (increase or decrease) the measuring rod for utility becomes, like

an elastic ruler, inappropriate for measurement.

4. Diminishing Marginal Utility of Commodities: The utility gained from successive

units of a commodity diminishes. In other words, the marginal utility of a

29

commodity diminishes as the consumer consumes larger quantities of it. This is

what is referred to as the axiom of diminishing marginal utility.

5. The Total Utility of a Basket of Goods and Services Depends on the Quantities of

the Individual Commodities. For example , if there are n commodities in the bundle

with quantities x1, x2,…………,xn, the total utility is given by:

U = f(x1, x2,…………,xn)

6. Additivity of Utility: In very early version of the theory of consumer behavior, it

was assumed that the total utility is additive. This means, if there are n commodities

in the bundle with quantities x1, x2,…………,xn, the total utility is:

U = u1(x1) + u2(x2) + ………+un (xn)

However, the additivity assumption is dropped in later versions of the cardinal

utility theory because additivity implies independent utilities of the various

commodities in the bundle, and this is an assumption which is clearly unrealistic

and unnecessary for the cardinal utility theory.

Equilibrium of the Consumer under the Cardinal Utility Theory

Let’s begin our analysis of the equilibrium of the consumer with a simple model of a

single commodity, X. The consumer has two alternatives for the use of his/her income:

either to buy X or retain the money income, Y. Under this condition, the consumer is in

equilibrium (at the highest possible level of satisfaction) when the marginal utility of X is

equal to its market price (Px). Marginal utility of a commodity is the extra satisfaction

that one can derive from one additional unit of the commodity.

Symbolically, the equilibrium of the consumer can be represented as:

MUx = Px

Where: MUx is the marginal utility of the commodity (X), and

Px is the price of the commodity (X)

If the marginal utility of X is greater than its price (MUx > Px), the consumer can

increase his/her welfare by purchasing more units of the commodity X. Similarly, if the

30

marginal utility of the commodity is less than its price, the consumer can increase his/her

total satisfaction by cutting down the quantity of the commodity X and keeping more of

his/her income unspent. Therefore, the consumer attains the maximum level of

satisfaction (utility) when MUx = Px.

So far, for the sake of simplicity we have been assuming that there is only one

commodity. However, in reality, since the consumer may consume more than one

commodity, we can extend our analysis of the consumer into the case of many

commodities. If there are more commodities, the condition for the equilibrium of the

consumer is the equality of the ratios of the marginal utilities for the individual

commodities to their prices.

Symbolically, assuming that there are N commodities: X, Y, Z, ………..N, the

equilibrium is attained when:

= Y

Y

PMU

= Z

Z

PMU

= … = N

N

PMU

X

X

PMU

Mathematically, we can derive the equilibrium of the consumer as follows:

Suppose the utility function in a simple model of single commodity X is given by:

U= f (Qx) where U is total utility measured in monetary units and Qx is quantity of the

commodity X.

If price of the commodity is Px and the consumer buys Qx units of commodity X, the

expenditure of the consumer will be the product, PxQx. Hence, the consumer wants to

maximize the difference between his/her utility and his/her expenditure.

i.e, Maximize (U- PxQx)

In order to maximize the above mentioned difference there is necessary condition as well

as sufficient condition. The necessary condition is that the partial derivative of the

function with respect to Qx be equal to zero.

31

Thus,

XQU

∂∂ –

X

XX

QQP

∂∂ )(

= 0

By rearranging the above expression we obtain:

XQU

∂∂ =

X

XX

QQP

∂∂ )(

, but since price is constant we can factor it out and find

XQU

∂∂ =

X

XX

QQP

∂∂ 1

XQU

∂∂ = XP

XMU = XP

In the case of several commodities, the utility derived from spending an additional unit of

money must be the same for all commodities. If the consumer derives greater utility from

any one commodity, he/she can increase his/her welfare by spending more on that

commodity and less on the others, until the above equilibrium condition is fulfilled.

Derivation of the Demand of the Consumer

The derivation of demand is based on the axiom of diminishing marginal utility. As it has

been mentioned above, the marginal utility of a commodity (MUx) is the slope of the

total utility of the commodity (U=f(Qx)). Total utility is the total amount of satisfaction

that one can derive from the use of a certain bundle of goods and services or by

undertaking a certain activity.

Total utility of a commodity (X), TUx, increases, but at a decreasing rate initially up to a

certain level of quantity, let’s say X1, and then starts declining. Thus, this implies that

TUx is at its maximum point at X1 units of quantity (See Figure 2.1). Accordingly, the

1

X

X

QQ∂∂ = 1 and only Px will be remaining on the right hand side, and

XQU

∂∂ is marginal

utility of the commodity (X) which is the slope of total utility.

32

marginal utility of the commodity (MUx) declines continuously when TUx increases at a

decreasing rate, and becomes negative beyond quantity X1 i.e MUx is zero at the

maximum point of TUx. Thus, the marginal utility of a commodity is depicted by a

negatively sloped line (See Figure 2.2).

Geometrically, marginal utility of a commodity is the slope of the total utility function

U = f (X). That means, marginal utility of a commodity is an extra satisfaction as a result

of one unit increase in the consumption of the commodity.

Mathematically, given total utility function U = f (X), Marginal utility of the function is

given by:

)(

)(Xd

TUd X=MU Where: MUx is the marginal utility of commodity

X, d(TUx) is change in the total utility of commodity X, and d(X) is change in the

quantity of X consumed.

MUx

TUx

X1

Figure 2.1: Total Utility Function

TUx

X

MUx

X1 X

Figure 2.2: Marginal Utility Function

33

NB. The slope of a tangent line to total utility function gives marginal utility of the

commodity at that point. Hence, as can be seen on Figure 2.1 above the tangent lines on

the total utility function are becoming flatter and flatter with increase in consumption of

X. This implies that the slopes of the tangent lines, which are the slope of the total utility

function, are declining with increase in consumption of the commodity.

If the marginal utility is measured in monetary units the demand curve for commodity X

is identical to the positive segment of the marginal utility curve since marginal utility of

the commodity is equal to price of the commodity (MUx = Px). As depicted in Figure

2.3a below, at quantity level X1 the marginal utility is MU1 which is equal to the price

level P1 by definition. Hence, at the price level P1 the consumer demands X1 units of he

commodity (Figure 2.3b). Similarly, at X2 the marginal utility of the commodity is MU2,

which is equal to P2. Hence, at P2 the consumer will buy X2 units of the commodity, and

so on. Thus, we can observe that Figure 2.3b shows the demand curve which is derived

from the marginal utility function of a commodity (Figure 2.3a)

MUX1

MUX2 MUX3

X

P1

P2

P3

Demand Curve

P

O X1 X2 X3O X1 X2 X3

X

MUx

MUx

Figure 2.3a: Marginal Utility of X Figure 2.3b: Demand Curve for X

34

NB. The negative section of the MUx curve does not form part of the demand curve since

negative prices do not make sense in economics.

Critiques of the Cardinal Utility Approach

There are three basic weaknesses in the cardinal utility approach.

a) The assumption of cardinal utility is extremely doubtful. This is because the

satisfaction derived from various commodities can not be measured objectively.

The attempt by Walras to use subjective units (Utils) for the measurement of utility

does not provide any satisfactory solution.

b) The assumption of constant utility of money is also unrealistic. As income increases

the marginal utility of money changes. Thus, money can not be used as a measuring

rod for utility since its own utility changes.

c) The additivivty of utility is questionable since there is no objective measure of

utility.

Check Your Progress

1. Explain why we study the theory of consumer behaviour.

2. What does it mean by: the marginal utility of a commodity is diminishing?

3. Explain the meaning of MUx = 4.

4. Derive the demand curve using the approach you studied above.

2.5.2 The Ordinal Utility Theory

The ordinalist school postulates that utility is not measurable, but is an ordinal

magnitude. The consumer need not know in specific the utility of various commodities to

make his/her choice. Under this approach, it suffices for the consumer to be able to rank

the various baskets of goods and services according to the satisfaction that each bundle

35

gives him/her. The consumer must be able to determine his/her order of preference

among the different bundles of goods and services.

There are two main ordinal utility theories, which are:

1. The Indifference Curves Theory

2. The Revealed Preference Hypothesis

1. The Indifference Curves Theory

The indifference curves theory is one of the theories which argues that utility is not

cardinally measured rather it is ordinally measured. This theory tries to show the

equilibrium of the consumer using the concept of indifference curves as the name

suggests.

Assumptions of the Indifference Curves Theory

1) Rationality: The consumer is assumed to be rational – he/she aims at the

maximization of his/her utility, given his/her income and the market prices. It is

also assumed that the consumer has full knowledge (certainty) of relevant

information.

2) Utility is Ordinal. It is taken as axiomatically true that the consumer can rank

his/her preferences (orders the various baskets of goods and services) according to

the satisfaction of each basket. Unlike the cardinal utility theory, he/she need not

know perfectly the amount of satisfaction. It suffices that he/she expresses his/her

preference for the various bundles of commodities. That means it is not necessary to

assume that utility is cardinally measurable, but only ordinal measurement is

required.

3) Diminishing Marginal Rate of Substitution: Preferences are ranked in terms of

indifference curves which are assumed to be convex to the origin. This implies that

the slope of the indifference curves decreases with increase in consumption of the

commodity. The slope of the indifference curves is called the marginal rate of

36

substitution of the commodities. Thus, the indifference curve theory is based on the

axiom of diminishing marginal rate of substitution. (More will be said on marginal

rate of substitution later in the chapter.)

4) The Total Utility of the Consumer Depends on the Quantities of the Commodity

Consumed:

U = f(X1, X2, …, Xn)

5) Consistency and Transitivity of Choice: It is assumed that the consumer is

consistent in his/her choice, that is, if he/she chooses bundle A over B in one

period, he/she will not use B over A in another period if both bundle are available to

him/her, under exactly the same conditions. The consistency assumption may be

symbolically written as follows:

If A > B, then B ≯A.

Similarly, it is assumed that consumer’s choices are characterized by transitivity: if

bundle A is preferred to B and B is preferred to C, then bundle A is preferred to C.

Symbolically, we may write the transitivity assumption as follows:

If A > B and B > C, then A > C.

Equilibrium of the Consumer under the Indifference Curves Theory

To define the equilibrium of the consumer (that is his/her choice of the bundle that

maximises his/her utility) we must introduce two concepts:

the indifference curve and its slope which is the marginal rate of substitution, and

the budget line.

These are the basic tools of the indifference curves theory.

The Indifference Curve

An Indifference Curve is a curve representing all combinations of market baskets that

provide a consumer with the same level of satisfaction. Hence, all points along the same

indifference curve give the consumer the same level of satisfaction. The consumer is,

37

therefore, indifferent among different combinations of goods represented by the points

graphed on a curve.

Y

Indifference

Curve

X O

Figure 2.4: An Indifference Curve

An Indifference Map shows a set of indifference curves which rank the preferences of

the consumer. Combinations of goods situated on an indifference curve yield the same

level of satisfaction for the consumer.

However, combinations of goods lying on a higher indifference curve yield higher level

of satisfaction and are preferred. Combinations of goods on a lower (close to the origin)

indifference curve yield lower level of satisfaction.

I3

I2

I1

Y

X

Figure 2.5: An Indifference Map

O

38

An indifference curve is shown in Figure 2.4 and an indifference map is depicted in

Figure 2.5. It is assumed that the commodities Y and X are can substitute one another to a

certain extent but are not perfect substitutes.

Symbolically, an indifference curve is given by the equation:

U = f(X1, X2……..Xn) = K Where K is a constant.

Given the above utility function, an indifference map can be derived by assigning every

possible value to K in such a way that as we move away from the origin the level of

satisfaction increases (Higher K).

The negative of the slope of indifference curve at any one point measures the rate of

change of commodity Y as a result of change in commodity X, and is called the marginal

rate of substitution of the two commodities.

Geometrically, the marginal rate of substitution is given by the slope of the tangent line at

that point:

Curve ceIndifferen theof Slope , −=−=dXdYMRS YX

The marginal rate of substitution of X for Y is defined as the number of units of

commodity Y that must be given up in exchange for an extra unit of commodity X so that

the consumer maintains the same level of satisfaction.

For example, MRSX,Y = 5 can be interpreted as: five units of Y must be sacrificed in

order to increase the consumption of X by one unit and leave the consumer on the same

level of satisfaction. Similarly, MRSY,X = 3 can be interpreted as: three units of

commodity X must be sacrificed in order to increase the consumption of commodity Y by

one unit and leave the consumer on the same level of satisfaction. With this definition,

the proponents of the indifference curves approach thought that they could avoid the non-

operational concept of marginal utility.

39

Marginal Utility (MU) and Marginal Rate of Substitution (MRS)

The concept of marginal utility (MU) is implicit in the definition of the marginal rate of

substitution (MRS), since it can be proved that the marginal rate of substitution (the slope

of the indifference curve) is equal to the ratio of the marginal utilities of the commodities

involved in the utility function:

Symbolically:

Y

XYX MU

MUMRS =,X

YXY MU

MUMRS =, or

Where, MRSx,y is marginal rate of substitution of x for y

MRSy,x is marginal rate of substitution of y for x

MUx is marginal utility of commodity x

MUy is marginal utility of commodity y

We can prove the above relationship between MRS and MU

Proof:

The slope of any curve at any one point is measured by the slope of the tangent line at

that point. For example the slope of the curve f(x) at point a in the figure below (figure

2.6) is the slope of line one (L1) and the slope of the curve at point b is the slope of line

two (L2). The equation of a tangent line is given by the total derivative2, which shows the

total change of the function as its determinant changes.

2 The total derivative of a function is change in the dependent variable as a result of change in the

independent variable. For example, if the function is given by Y= f(X), Y being the dependent variable

and X the independent variable, then the total derivative of the function is dXdY

, where dY is change in Y

and dX is change in X.

40

X O

b

a

f(x)

L2

L1

Y

Figure 2.6: Slope of a Curve

The total utility function in the case of two commodities x and y (assuming that the

consumer is consuming only two commodities x and y) is: U = f(x,y).

The equation of an indifference curve is: U = f (x,y) = K, where K is a constant.

The total differential of the utility function is measured by dU. dU shows the total

change in utility as the quantities of both commodities change.

dYYUdX

XUdU

∂∂

+∂∂

=

YX MUYUMU

XU

=∂∂

=∂∂ and [ ]

l utility

nsumer derives the same level of satisfaction

ndifference curve.

dYMUdXMUdU YX )()( +=

In words, the total change in utility (dU) caused by changes in X and Y is

approximately equal to the change in X (dX) multiplied by its margina

(MUx) plus the change in Y (dY) multiplied by its marginal utility (MUy).

By definition, along any particular indifference, the total change (differential) in

utility is equal to zero since the co

along the same i

41

Hence, dU = 0

By rearranging the above equation we obtain:

()( += = 0

dYMUdXMUdU YX )()( += = 0

)dYMUdXMUdU YX

dYMUdXMU YX )()( −=

MUYMUXdY

=− . dX

[But, recall that MRSX,YdXdY

−= ]

Y

XYX MU

MUdXdYMRS =−=,

Similarly, X

YXY MU

MUdYdXMRS =−=, .

The indifference curves theorists substitute the assumption of diminishing marginal

tility of commodities with the assumption of diminishing MRS of commodities since the

indifference curves solute value from

left to right, i.e., declining MRSx,y).

u

are convex to the origin (with declining slope in ab

Properties of Well-Behaved Indifference Curves

a) Well-behaved indifference curves are negatively sloped. This denotes that if the

quantity of one commodity (X) decreases, the quantity of the other commodity (Y)

must increase, if the consumer is to stay on the same level of satisfaction.

b) The further away from the origin an indifference curve lies, the higher the level of

utility it denotes. Bundles of goods on a higher indifference curve are preferred by

the rational consumer.

42

c) h other. If they did, the point of their

intersection would imply two different levels of satisfaction, which is impossible.

That means if indifference curves intersect to each other, they will violate the

assumption of transitivity and consistency.

I1

I2

I3

Y

O X

I3 > I2 > I1

Figure 2.7: A Higher Indifference Curves Denote Higher Level of Utility

Indifference curves do not intersect to eac

X

Y

O

I

I2

1

Figure 2.8: Intersecting Indifference Curves, Which Is Not Possible

43

d)

ng the curve from the left downwards to

t along

the indifference curve. The case of convex indifference curves implies that the

nds of

difference curves which violate some of the above mentioned behaviors of an

ing different types of indifference curves.

goods which can serve similar needs of the consumer. For example,

oca Cola and Pepsi, Tea and coffee, Bread and ‘Injera’ may be considered as examples

to substitute one good for the other at a constant rate. The simplest

ase of perfect substitutes occurs when the consumer is willing to substitute the goods on

Indifference curves are convex to the origin: The slope of the indifference curves

decline (in absolute terms) as we move alo

the right. This implies that the marginal rate of substitution of the commodity X for

commodity Y (= MRSx,y) is diminishing.

The axiom of decreasing marginal rate of substitution expresses the observed

behavioral rule that the number of units of X that the consumer is willing to sacrifice

in order to obtain an additional unit of Y increases as the quantity of Y decreases. It

becomes increasingly difficult to substitute X for Y as we move to the righ

commodities are substitutes for one another, but are not perfect substitutes.

However, depending on the type of the commodities there are different ki

in

indifference curve. Consider the follow

1. The Case of Perfect Substitutes

Substitute goods are

C

of substitute goods.

If the two goods X and Y are perfect substitutes to each other, the indifference curves

will be downward sloping straight line. Hence, the marginal rate of substitution between

the two goods will be constant. In other words, two goods are perfect substitutes if the

consumer is willing

c

a one-to-one basis.

For example, let us consider a choice between red pencil and blue pencil, and the

consumer involved like pencils, but doesn’t care about colours at all. Pick a consumption

bundle, say (10, 10). Then for this consumer, any other consumption bundle that has 20

44

pencils in it is just as good as (10, 10). Mathematically speaking, any consumption

bundle (X, Y) such that X + Y = 20 will be on the consumer’s indifference curves.

Hence, the indifference curves for this consumer are parallel downward sloping straight

lines.

ed with fixed proportions.

hus if the two goods are perfect complements to each other, the indifference curves will

X O

Figure 2.9: Indifference Curves for Perfectly Substitute Goods

Y

2. The Case of Perfect Complements

Complement goods are goods which are consumed together to serve a single need of the

consumer. Perfect complements are goods that are always consumed together in fixed

proportions. For instance, Sugar and Tea, Photo camera and Film, Car and Fuel can be

considered as examples of perfect complementary goods. This means that one good

cannot be consumed without the other as the goods are consum

T

be L-Shaped (right angled) as depicted in Figure 2.10 below.

A good example of perfect complements is the case of right shoe and left shoe. The

consumer likes shoes but always wear right shoe with left shoe together. Having many of

left shoes and one right shoe doest allow the consumer to wear more than one pair of

shoes, meaning, having only one out of a pair of shoes does not do a consumer a bit of

45

good. The consumption bundle (10, 10), i.e., 10 units of left and 10 units right shoes,

gives the consumer the same level of satisfaction for the consumer as a bundle which is

composed of (11, 10) or (10, 11). Hence, the consumer always consume at the vertex of

e ference curves where the number of the two goods are the same or the proportion

of the two perfectly complementary goods are the same.

creasing both the number of left shoes and right shoes at the same time will move the

e curves will still be L shaped. In

is case the corners of the indifference curves will occur at (2 teaspoons of sugar, 1 cup

on.

th indif

X

Y

O

Figure 2.10: Indifference Curve for Perfect Complements

In

consumer to a higher indifference curve, or to a more preferred position.

The important thing about perfect complement goods is that the consumer consumes the

goods in fixed proportions, not necessarily that the proportion is one-to-one. For

example, if the consumer always uses two teaspoons of sugar in his/her cup of tea and

doesn’t use sugar for anything else, then the indifferenc

th

of tea), (4 teaspoons of sugar, 2 cup of tea), and so

3. The Case of ‘bad’ and ‘good’ Commodities

If one of the two commodities is ‘good’ and the other is ‘bad’ (for example, alcohol

(‘bad’) and milk (‘good’)), the consumer needs some compensation for every unit of the

46

‘bad’ commodity he consumes. A bad is a commodity that the consumer doesn’t like to

consume. And this compensation is by extra unit consumption of the ‘good’ commodity.

This implies that the consumer increases his consumption of the ‘good’ commodity for

increase in consumption of the ‘bad’ commodity. In such a case, the indifference curve

will be upward sloping. The level of satisfaction increases as we move closer to the axis

of the ‘good’ commodity.

doesn’t care about it one way or another. Let’s

say that the consumer is neutral about good Y and likes good X. Then in this case, the

diff ves will be vertical lines.

4. The Case of Neutrals

A good is a neutral good if the consumer

X (Good)

Y (Bad)

O

Figure 2.11: Indifference Curves for ‘good’ and ‘bad’ Commodities

in erence cur

Y

(Neutral)

O

X

Figure 2.12: Indifference Curves for a Neutral Good

47

The Budget Constraint of the Consumer

Economists assume that consumers choose the best bundle of goods and services they can

afford. Suppose that there is some set of goods from which the consumer can choose. In

real life there are many goods to consume, but for the sake of simplicity it is enough to

consider the case of only two goods X and Y so that we can depict the consumer’s choice

behavior graphically. Consider that the prices of the two commodities are given by Px

en the budget

X

Qy is the quantity of commodity Y, and

/ her income. In

ther words, the consumer has a given income which sets limits to his/her maximizing

nd Y

xQx + PyQy) is equal to I (Income of the consumer) as it is assumed that the consumer

commodity

and Py, and that the amount of money the consumer has to spend is I. Th

constraint of the consumer can be written as:

Px Qx + PyQy ≤ I where: Px is the price of commodity X

Py is the price of commodity Y

Qx is the quantity of commodity

I is the income of the consumer

The consumer maximizes his/her satisfaction given his/her income. That means the

consumer’s utility maximization objective is constrained or limited by his

o

behavior. Income acts as a constraint for utility maximization.

In the above equation which shows the budget constraint of the consumer, PxQx gives

the total amount of income that the consumer spends on commodity X and PyQy gives

the total amount of income that the consumer spends on commodity Y. Hence, the total

amount of spending of the consumer on the two goods, X and Y, is PxQx + PyQy. It is

considered that this total amount of spending of the consumer on commodities X a

(P

spends all of his/her income on the consumption of the two commodities X and Y.

Thus, if the consumer spends all of his/her income on the consumption of the two

commodities, X and Y, the proportion of income spent on commodity X and

48

Y is determined by dividing the total spending o n X (= PxQx) by total income (I) and

er, respectively.

total spending on Y (= PyQy) by total income of the consum

Proportion of income spent on commodity X = I

Proportion of income spent on commodity Y =

QP XX

IQP YY

The budget constraint of the consumer requires that the amount of money spent on the

o goods be no more than the total amount of the consumer’s income. Hence, the

consumer’s affordable consu o not cost any more than I.

he set of all affordable consumption bundles at prices Px and Py, and income I is called

get Line

tw

mption bundles are those that d

T

the budget set of the consumer.

Properties of the Bud

f goods that just exhaust the consumer’s income.

PxQx + PyQy = I --------------------------------------------------- Budget Line

y solving for Qy from the general

budget equation. From the general budget equation we know that PxQx + PyQy = I.

PyQy = I – PxQx Bringing PxQx to the right

The budget line can be defined as the locus of points of all the combinations of the two

commodities that cost exactly the consumer income. The budget line includes the bundles

o

In the case of two commodities the general budget line equation can be given by:

We can present the income constraint graphically b

By solving for Qy we obtain:

Y

YY

PQP

= Y

XX

Y PQP

PI− Dividing both the right hand side and the left hand side by Py

49

Qy = Y

XX

Y PQP

PI− …………………………………………………….. Budget line

Given the prices of the two commodities, Px and Py, and income of the consumer, I, we

may find the corresponding values of Qy by assuming various values of Qx.

hus, if Qx = 0 (that is, if the consumer spends all his/her income on commodity Y), the T

consumer can buy YPI units of Y. Mathematically, this will give us the vertical intercept

of t

on commodity X), the consumer can buy

he budget line. Similarly, if Qy = 0 (that is, if the consumer spends all his/her income

XPI units of X, and this will give us the

Let’s consider that we measure commodity Y on the y-axis and commodity X on the x-

axi

et line: when the consumer consumes commodity Y

horizontal intercept of the budget line.

s. Hence:

Vertical intercept of the budg

Y

XX

Y PQP

PI− only (0, Y) Qy =

Qy = )0XPI− , Since Qx = 0 (

YY PP

YPI Qy =

Horizontal intercept of the budget line: when the consumer consumes commodity

X only (X, 0) Qy = Y

XX

Y PQP

PI−

Y

XX

Y PQP

PI− 0 = , since Qy = 0

YY PP

, bringing XX QPI=

YPI to the left hand side to solve for Qx

50

XPI , multiplying both sides by

X

Y

PP

Qx = to solve for Qx

we join the vertical and the horizontal intercepts on the X–Y set of axis, then we will

btain the budget line shown Figure 2.13.

If

o

The area below the budget line is the budget set, which includes all affordable bundles by

the consumer.

Geometrically, the slope of the budget line is

I/Py

O

Y

X

Budget Line A

B

Budget set

I/Px

Figure 2.13: Budget Line and Budget Set of the Consumer

Y

XY PPIOA−=−=− .

X PPIOB

athematically, the slope of the budget line is the derivativeY

X

X

Y

PP

QQ

−=∂∂

. M

The slope of the budget line has a nice economic interpretation. It measures the rate at

which the market is willing to substitute commodity X for commodity Y. The negative

sign is there since the change in X and change in Y must always have opposite signs. If

ou consume more of commodity X, you have to consume less of commodity Y and vice

omists sometimes say that the

lope of the budget line measures the opportunity cost of consuming commodity X. This

y

versa if you continue to satisfy the budget constraint. Econ

s

51

is because in order to consume more of commodity X you have to give up some

consumption of commodity Y.

Changes in the Budget Line

is because in order to consume more of commodity X you have to give up some

consumption of commodity Y.

Changes in the Budget Line

W

I2/Py

I1/Py

I2/Py

I1/Py

hen prices and/or income change, the set of goods that a consumer can afford changes

s well. How do these changes affect the budg et? Let us first consider changes in

. The Effect of Change in Income on the B dget Line

n increase in income, assuming that Px and Py are constant, will increase the vertical

tercept and the horizontal intercept, and does not affect the slope of the budget line.

hus, an increase in income will result in a parallel outward shift of the budget line.

imilarly, a decrease in income will reduce both the vertical and the horizontal intercepts

nd as a result it will cause a parallel inward hift of the bud

a et s

inc . ome

a u

A

in

T

S

a s get line.

X

Figure 2.14a: Effect of Increase in

Income from I1 to I2 on the Budget Line

Y

O X I1/Px I2/Px

Y

I /P

I /P

1 y

I2/Px I1/Px

Figure 2.14b: Effect of Decrease in

Income from I to I on the Budget Line 1 2

2 y

52

b. The Effect of Changes in Price on the Budget Line

Let us first consider an increase in price of X while holding price of Y and income

constant.

Accor to the budge line equation, increase in Px will not change the vertical intercept

/Py), since I and Py are constant. But it will make the budget line steeper since Px/Py

h of the budget line in absolute terms) will become larger. That means, increase

Px shifts the horizontal intercept inward, a lt the budget line rotates inward with

constant vertical intercept and a steeper slope.

imilarly, if we consider the effect of decline in Px while holding Py and I constant, the

ertical intercept remains constant but the slope becomes flatter and the horizontal

tercept increases and shift outward, as a result the budget line rotates outward with a

onstant vertical intercept and a flatter slop

ding

(I

(t e slope

in s a resu

a

S

v

in

c e.

Figure 2.15a: Effect of Increase in Px from Px1 to Px2 on the Budget Line

Figure 2.15b: Effect of Decrease in Px from Px1 to Px2 on theBudget Line

Y

X

I/Px2 I/Px1

Y

I/Py

O O

I/Py

I/Px1 I/Px2

X

53

Not

1.

2.

oice of the consumer from the budget set doesn’t change

either.

3. T es in

market conditions (demand and/or supply conditions) or because of government

is good increases

from PX to PX + 0.05PX = (1 + 0.05)PX = 1.05PX. If the price of the other commodity

e:

If both prices Px and Py increase in the same proportion, both the vertical and the

horizontal intercepts shift inward by half of increase in prices. Thus, the budget line

will shift inward. The opposite is true for proportionate decline in price of X and Y.

The budget set does not change when we multiply all prices and income by a positive

number, the optimal ch

he changes in commodities prices could be either the result of natural chang

policies (because of taxes imposed on or subsidies granted for the consumption of a

particular commodity). For instance, if government imposes a value (an ad valorem),

tax on the consumption of good X, at a rate of 5%, then the price th

(PY) and income (I) are kept constant, the effect of this tax on the budget line will be

similar to the one shown in Figure 2.15a. Similarly, if a value subsidy of 10% is

granted on the consumption of X, the budget line is affected in a way similar to that

shown in Figure 2.15b.

The Equilibrium of the Consumer under the Indifference Curves Theory

Th er is at equilibrium when he/she maximizes his/her utility his/her

income and the market pri

e consum , given

ces of the commodities. Under the indifference curves theory,

o conditions must be fulfilled for the consumer to be in equilibrium.

he first condition is that the marginal rate of substitution be equal to the ratio of

ommodity prices.

tw

T

Y

X

Y

XXY P

PMUMUMRS == . This is a necessary but not sufficient

ondition for equilibrium. The second condition is that the indifference curves be convex

the origin. This is the sufficient condition for equilib um.

c

c

to ri

54

This means that at equilibrium the consumer’s budget line is tangent to the highest

ossible indifference curve and at the tangency point the slope of the indifference curve (

) is equal to the slope of the budget line (=

p

XYMRS−Y

X

PP

− ). That is, = XYMRSY

X

PP

= at

quilibrium.

The e

and t of commodity Y and X* units of

c

indiff

not c sume more given his/her

in

e

quilibrium of the consumer is attained at the tangency point of the budget line (BL)

he indifference curve (I2), consuming Y* units

ommodity X (Figure 2.16). This is because, the consumer cannot consume on the third

erence I3 curve as it is not attainable given his/her income. And, the consumer does

onsume on the first indifference curve (I1) as he/she can con

come.

Check Your Progress

1. Explain the difference between the equilibrium conditions of the consumer under

cardinal utility approach and ordinal utility (indifference curves) approach.

Figure 2.16: Equilibrium of the Consumer

Y

E I3

I2

B

O X

Y*

I1

X* L

55

2. Suppose the total utility function of a consumer is given by TU(x) = 2x2. What is

the marginal utility

3. Assuming the income of the consumer to be constant, what will be the effect of a

d the

onstant.

b. The effect of decrease in price of Y on the budget line when price of X and

of X?

decline in price of both commodity X and commodity Y by the same proportion?

Explain your answer with the help of graph(s).

4. If the price of commodity X is 10 Birr per unit and the price of commodity of Y is 8

Birr per unit, write the budget line equation assuming that the consumer spends all

of his 500 Birr income on the two commodities, X and Y.

5. Mention at least one assumption which is common for both the cardinal an

ordinal utility approaches.

6. Graphically explain:

a. The effect of increase in price of Y on the budget line when price of X and

income are c

income of the consumer remain constant.

Income Offer Curve and Engel Curve

Previously when we were discussing the behavior of a budget line, we were able to

identify that the budget line changes with changes in income of the consumer (I) and

prices of the commodities (Px and Py). When the budget line changes due to change in

income or prices or both, the equilibrium of the consumer will also change since the most

preferred attainable indifference curve of the consumer also changes with the new budget

line. With the new equilibrium there are also new levels of equilibrium quantities.

Hence, in this section we see the effect of changes in income of the consumer on the

quilibrium of the consumer. And in the next section we will see the effect of a change in

th

e

the price of a commodity on the equilibrium of the consumer and on the level of the

quantity consumed.

In analysing the effect of a change in income on the equilibrium of the consumer, we use

e concepts of Income Offer Curve and Engel Curve.

56

Suppose that the initial income of the consumer is I1 with the budget line BL and the

initial indifference curve is IC1. Thus, the initial equilibrium point of the consumer is E1

here the consumer consumes X1 units of commodity X (See Figure 2. 17). Given these

rence curve, IC2.

successive

uilibrium points which result from changes in income, we will find an Income Offer

urve. Income offer curve is also called income consumption curve or income expansion

th.

r a normal good, incom curve is pos ively sloped as the new equilibr ts

e to the right of the or es. On the er hand, the income offer cu

ferior good is negativ ed since the new successive equilibrium points of the

onsumer (caused by increases in income) lie to the left of the original equilibrium point.

w

initial conditions, suppose that the consumer’s income rises, ceteris paribus. If the income

of the consumer increases, say, from I1 to I2, the budget line will shift upward from BL to

B’L’ in a parallel manner and the consumer will be able to consume on a higher level of

indifference curve, IC2. Thus, the equilibrium of the consumer will also change from E1

to E2 at the tangency point of the new budget line B’L’ and the now affordable

indiffe

Here, when the equilibrium changes from E1 to E2, E2 will be to the right of E1 if the

good is normal3. In this case, the consumption of commodity X increases from X1 to X2.

But, if the good is inferior good E2 will be to the left of E1 and the level of consumption

will decline from X1 to X2.

If income continues to increase, there will be successive equilibrium points with the

changed budget lines and higher indifference curves, and the quantities of the commodity

will also be changed. As can be seen from Figure 2.17, if we connect those

eq

C

pa

Fo e offer

iginal on

ely slop

it ium poin

rve for an li oth

in

c

od ormal’ when its demand changes in the same direction as income, i.e., the

reases with increase in incom the commodity mmodity is called an inferior good. That is, for an inferior good d with an increase in income an

3 Ad

comm ity is defined as ‘Nemand of the commodity inc

changes inversely with income, the coemand for the commodity decreases

e and vice versa. However, if the demand for

d vice versa.

57

For each level of income, I, there will be some optimal/equilibrium choice for each of the

oods, X and Y. Let us focus on good X and consider the optimal choice at each set of

rices and income (Px, Py, I). This is simply the demand function for good X.

look at the how demand for X changes as we

hange income, we generate a curve which is known as the Engel Curve. That means,

g

p

Y

B’ B

X

I

Y

B’ B

E1

E2 Income Offer Curve for normal good

E2 E1

O X

X1 X2 L L’ Figure 2.17a: Income Offer

Curve for a Normal Good X

O X1 X2 L L’

Income offer curve for inferior good

IC2

IC2

e Offer

Good X

IC1 IC1

Figure 2.17b: Incom

Curve for an Inferior

If we hold the prices of X and Y fixed and

c

2

I

1

Engel Curve for an Inferior Good

X

I

X

IEngel Curve

I1

I2

for Normal Good

X X O 1 2O X1 X2

Figure 2.17c: Engel Curve

for a Normal Good X

Figure 2.17d: Engel Curve

for an Inferior Good X

58

depicting the relationship between changes in income and changes in the quantity

consumed of a commodity while all commodity prices are held constant, will give as

what is called Engel curve of the commodity. An Engle curve is a graph of the demand

for one of the commodities as a function of income, with all prices held constant.

The Engel curve is positively sloped for normal goods since consumption of the good

increases with increase in income or since it decreases with a decrease in income. On the

ther hand, the Engel curve for an inferior good is negatively sloped since consumption o

of the good decreases with an increase in income or increases with a decrease in income.

Derivation of the Demand Curve using the Indifference Curves Theory: Price Offer

Curve and the Demand Curve

From the equilibrium of the consumer under the indifference curves theory, we can

derive the demand for a good graphically.

As the price of a commodity (Px) falls, assuming that Py and I are constant, the budget

line of the consumer rotates upward from its initial position to a new position (from BL

to BL’ in Figure 2.18a) with a constant vertical intercept. This is due to the increase in

the purchasing power of the given money income of the consumer. With more purchasing

in his/her possession, the consumer can buy more of X and/or more of Y. This

L’) is now tangent to a new indifference curve (I2)

hich is higher than the original indifference curve (I1).

we allow the price of the commodity (Px) to fall continuously and join the points of

ngencies of the successive budget lines and higher indifference curves (equilibrium

oints with the changed prices), we form the so call Curve.

he price consumption curve is also referred to the price offer curve.

rom the price consumption curve due to change in price of commodity X, we can derive

e demand curve for commodity X. In the figure 2.18a below, at point E1, the consumer

power

means that the new budget line (B

w

If

ta

ed the Price Consumptionp

T us

F

th

59

buys X1 units of commodity X at the original level of price (say P1). At point E2, price has

duced from P1 to P2, thus the quantity demanded of commodity X has increased from

1 to X2, and so on. Now we can plot the price quantity pairs defined by the points of

quilibrium (on the price consumption curve) to obtain a demand curve for commodity X

ee Figure 2.18b below).

re

X

e

(S

Y

E2E3

B

E1

I1

I2

I3

O X X1 X2 X3 L’ L’’

Price- consumption curve

L

Figure 2.18a: Price Consumption/Offer Curve

P

P1

P2 P3

X O X1 X2 X3

Demand Curve

Figure 2.18b: The Demand Curve

60

The demand curves for normal goods always have negative slope, denoting the ‘law of

demand’. The law of demand states that price and quantity demanded are

oppositely/negatively related, i.e. the quantity bought increases as the price falls.

Substitution and Income Effects of a Change in Price

So far we have seen that a fall in price of X (say, from P1 to P2) results in an increase in

the quantity demanded (say, from X1 to X2). This is the total effect which can be split in

to two separate effects, a substitution effect and the income effect.

In the indifference curves theory, the ‘law of demand’ is derived from what is known as

iation can

e shown graphically by a parallel shift of the new budget line until it becomes tangent to

2 to the right of the original tangency (equilibrium E1), because this line

parallel to new budget line which is less steep than the original one when the price

f X falls.

the Slutsky’s Theorem, which states that the substitution effect of a price change (relative

to the price) is always negative; if the price increases, the quantity demanded decreases

and vice versa.

The substitution effect is due to the tendency of the consumer to consume more of a

relatively cheaper good. Thus, it is assumed that the consumer will increase the

consumption of the good whose price has declined by reducing the consumption of the

other commodity and remain on the same level of satisfaction. Substitution effect is the

increase in the quantity bought as the price of the commodity falls, after ‘adjusting’

income so as to keep the real purchasing power of the consumer the same as before. This

adjustment in income is called compensating variation. The compensating var

b

the initial indifference curve (See Figure 2.19). The purpose of the compensating

variation is to allow the consumer to remain on the same level of satisfaction as before

the price change. The compensated budget line will be tangent to the original indifference

curve I1 at point E

is the

o

61

62

pensated Budget line Com

hus, the movement from E1 to E2 shows the substitution effect of the price change, i.e.

ecause of decline in price of X, the consumer buys more of X which is now cheaper,

bstituting X for Y (movement from X1 to X2).

owever, the compensating variation is a device which makes possible the isolation of

e substitution effect, but does not show the final equilibrium of the consumer. The final

quilibrium of the consumer after the price decline is defined by point E3 at the tangency

oint of the new budget line and a higher indifference curve I2. Since the consumer’s

urchasing power has now increased due to the decline in price of X he/she will spend

me of his/her increased real income on X, if the commodity (X) is normal. Thus, the

onsumer moves from X2 to X3. This is the income effect of the price change.

T

b

su

H

th

e

p

p

so

c

The income effect of a price change for normal goods is negative; when purchasing

power increases due to a decline in price, quantity consumed increases and when

purchasing power decreases due to an increase in price, quantity consumed declines if the

good is normal.

Y

O

X

B

X1 X2 L X3 L’’ L’

B’

E3

E2

E1

I1I2

New budget line

Original budget line

Substitution Effect

Income Effect

Total Price Effect Figure 2.19a: Substitution and Income Effect for a Normal Good X

If, however, the commodity is inferior, the income effect of the price change is positive

.e., for an increase in price, the quantity demanded of an inferior good will also increase

ue to the decline in purchasing power; and conversely, for a decrease in price, the

uantity demanded of an inferior good will also decline due to the increase in purchasing

ower). But the substitution effect of a price change is negative for normal goods as well

s inferior goods – for price rise quantity will decline, and for price decline quantity will

or normal goods, the negative substitution effect reinforces the negative income effect

negative. Similar to the case of normal goods,

e substitution effect is negative for inferior goods as well. However, unlike the case of

ormal goods, the income effect is positive for inferior goods. Nevertheless, since the

substitution effect is stronger than the income effect for most of the inferior goods, the

(i

d

q

p

a

rise.

Y

O

X

B

X1 X3 X2 L L’’ L’

B’

E3

E2

E1

I1

I2

New budget line

Original budget line

Substitution Effect

Income Effect

Total Price Effect

Figure 2.19b: Substitution and Income Effects for an Inferior Good X

Compensated Budget line

F

and as a result the total price effect is also

th

n

63

total effect is also negative. Thus, the negative substitution effect is in most cases

dequate to establish the law of demand (the negative relationship between price and

uantity demanded/consumed). It is when the income effect is positive and stronger than

e substitution effect that the law of demand does not hold. This is the case of the Giffen

Goods giffen

goods, like the case of inferior goods, the substitution effect is negative and the income

sitive. But the positive ng iv

e case of giffen goods otal i

e for e, an

ncome Effects of a Fall in the Price of X

a

q

th

, which are inferior goods with a positive sloping demand curves4. Thus, for

effect is po income effect is stro er than the negat e substitution

effect in th . As a result, the t price effect for g ffen goods is

positive (quantity will increas an increase in pric d vice versa).

Summary of Substitution and I

Type of Good Substitution Effect Income Effect Total Effect

Nor ) mal Good Negative (X ) Negative (X ) Negative (X

Infe ) Positive (X ) Negative (X ) rior Good (that is not giffen) Negative (X

Giffen Good Negative (X ) Positive (X ) Positive (X )

4 Giffen goods are very rare in practice.

E3

Y

B

B

IC2 ’

E1

E2

X

IC1

X3 X1 X2 L’ L’’ L

Figure 2.19c: Substitution and Income Effects for a Giffen Good X

O

64

Check Your Progress

ferior one

2. Explain the difference between the Engel curves for normal and inferior goods.

regardless of

whether the good is normal or inferior?

p sated budget line represent?

Mathematical

1. Explain the difference between the income offer curves for a normal good and for

an in .

3. Why is the substitution effect of a price change always negative

4. What does the com en

Derivation of Individual’s Demand for a Commodity

rived from the

ave seen previously, the equilibrium condition of the consumer is given by the

ta r. At this

al. Thus

The demand (function) of a consumer for a commodity can be de

equilibrium condition of the consumer.

As we h

ngency point of the indifference curve and the budget line of the consume

point, the slope of the two curves is equ ,

NYX PPP

=== ... NYX MUMUMU .

And, the budget line is given by:

I =∑=

N

iiiQP

1

.

For Example, consider the case of two goods, X and Y. If the total utility function is

given by: XYU4

= ; where U is total Utility, X1 is quantity of good X and Y is quantity of

he demand functions for the two goods as follows. good Y, we can derive t

Y

X

Y

XYX P

PMUMUMRS ==, . Step 1: At equilibrium,

65

Given the total utility function, the marginal utilities of X and Y are5:

Y XU

=∂∂

= ………………….……..……… (1) MU X 41 ………………………………

XYUMUY 4

1=

∂∂

= …………………………….…………………….……..……… (2)

By substituting the marginal utilities into the equilibrium conditionYY

obtain:

XX

PP

MUMU

= , we

YPX41

XPY=4

1…………………………………………………………………………..… (3)

Y

X

PP

XY

=Rearranging the above equation gives: .

ss multip

PxX = PyY ………………………………………………………………….………….(4)

ends on the specific form of the utility function.

Step 2

By criss-cro lying we obtain:

Note that the equality of the expenditures on the two commodities is not a general rule

rather it dep

: Now we c X by substituting

quation number (4) above into the budget line equation.

PxX + PxX = I since PyY = PxX from (4)

an derive the demand function for commodity

e

(Recall that the budget line is PxX + PyY = I).

PxX + PyY = I

2PxX = I

XX

X

PI

PXP

222

= dividing both sides by 2Px.

XP2

IX = Or XP

IX 5.0= → Demand for X

e use the derivative 1−=∂∂ nnXXY

. 5 W rule, i.e., if Y = Xn, then

66

Thus, the demand for X is negatively related to its own price, Px, and positively related to

me, I. inco

the

since PyY = PxX from (4).

2PyY = I

Similarly, we can derive the demand for commodity Y by substituting equation (4) into

budget line equation PxX + PyY = I.

PxX + PyY = I

PyY + PyY = I

Dividing both sides by 2Py gives:

YP2

IY = Or YP

Thus, the demand for Y is negatively related to its own price, P

IY 5.0= → Demand for Y

y, and positively related to

income, I.

Critiques of the Indifference Curves Approach

Although the advantages of the indifference curves approach are important, the theory

s indeed its own severe limitations.

. The main weakness of this theory is its axiomatic assumption of the existence and the

e ndifference curves

2. F

p references of

t der the influence of various factors, so that any

lid for the

3. T

w

d

ha

1

convexity of the indifference curves. The theory does not establish either the

xistence or the shape of the indifference curves. It assumes that i

exist and have the required shape of convexity.

urthermore, it is questionable whether the consumer is able to order his/her

references as precisely and rationally as the theory implies. Also the p

he consumer changes continuously un

ordering of these preferences, even if possible, should be considered as va

very short run.

he theory has also retained some of the weaknesses of the cardinal utility theory

ith the strong assumption of rationality and the marginal utility implicit in the

efinition of the marginal rate of substitution.

67

4. A

ef

in ce of preferences among consumers which lead to behavior that would

b

is is considered as a major breakthrough in the theory

f demand because it has made possible the establishment of the ‘law of demand’ directly

the advantage over the existence and convexity of the

difference curves as it does not accept them axiomatically. However, the indifference

urves are redundant in the derivation of the demand curve.

Assumptions of the Approach

nother defect of the indifference curves approach is that it does not analyze the

fects of advertising, the effect of past behavior (habit persistence), and effect of

terdependen

e considered as irrational.

2. The Revealed Preference Hypothesis

The revealed preference hypothes

o

(on the basis of the revealed preference axiom) without the use of indifference curves and

all their restrictive assumptions. Regarding the ordering of consumers’ preferences, the

revealed preference hypothesis has

in

c

1. Rationality: The consumer is assumed to behave rationally, in that he/she prefers

bundles of goods that include more quantities of the commodity.

2. Consistency: The consumer behaves consistently, that is, if he/she chooses bundle

A in a situation in which bundle B was also available to him/her, he/she will not

choose B in an identical situation in which A is also available.

Symbolically, if A > B, then B ≯ A.

3. Transitivity: If in any particular situation A > B and B > C, then A > C.

4. The Revealed Preference Axiom: The consumer, by choosing a collection of goods

in any one budget situation, reveals his/her preference for that particular collection.

That is, the chosen bundle is revealed to be preferred among all other alternative

maximizes the utility of the consumer. The revealed preference for a particular

collection of goods implies (axiomatically) the maximization of the utility of the

consumer.

bundles available under the budget constraint. Thus, the chosen ‘basket of goods’

68

Derivation of the Demand Curve Using the Revealed Preference Hypothesis

ssume that the consumer has the budget line BL as shown in Figure 2.20a below. If we

new batch will include a larger quantity of X

ith the help of the figure below.

A

assume that he/she chooses the collection of goods denoted by point A, this reveals

his/her preference for this batch.

Now, suppose that the price of X falls so that the new budget line facing the consumer is

BL’ (Figure 2.20a). We will show that the

w

Y

B B’

A

O X1 X2 L X3 L’’ L’ X

Figure 2.20a: Equilibrium of the Consumer

under the Revealed Preference Hypothesis

CD

Px

P1

P2

O X1 X2

X

Figure 2.20b: Demand Curve for a Normal Good

Derived Using the Revealed Preference Hypothesis

Demand Curve

69

Firstl

reduc sumer will have just enough income to enable him/her

continue purchasing bundle ‘A’ if he/she so wishes. The compensating variation is

hat the compensated

udget line B’L’’ passes through point A.

ice would be

consistent, given that all the batches on segment B’A were revealed inferior to A in the

original situation. Hence, uy A (in which case the

ubstitution effect is zero) or he/she will choose a batch on the segment AL’, such as C,

as a negative income effect). The new revealed

quilibrium position (D) contains a larger quantity of X (i.e. X3) which results from the

fall in its price. Thu tency of

choice open a direct way to the derivation of the demand curve: as price falls, more of X

is purchas

y, we make a ‘compensating variation’ in the income, which consists of the

tion of income so that the con

to

shown in Figure 2.20a, by a parallel shift of the new budget line so t

b

Since the collection A is still available to him/her, the consumer will not choose any

bundle to the left of A on the segment B’A. This is because his/her cho

in

the consumer will either continue to b

s

which includes a larger quantity of X (namely X2).

Secondly, if we remove the (fabricated) reduction in income and allow the consumer to

move onto the new budget line BL’, he/she will choose a batch (such as D) to the right of

C (if the commodity is normal – h

e

s, the revealed preference axiom and the implied consis

ed.

Check Yo

What are the differences and the simila s between the indifference curves

approac d the revealed ference hypo s?

Suppose that the total utility function of a consumer is given by TU(x,y) Y, and the prices of X and Y are 1 Birr and 2 per unit, res ively. If the income

of the consumer is 600 B nd if he spen ll of his inco on the cons on

of commodities of X and Y, find the optimu mount of X and Y that the consumer

will consume at equilibriu

ur Progress

1. ritie

h an pre thesi

2. = 3X2

Birr pect

irr a ds a me umpti

m a

m.

70

2 HE M KET DEM D FOR A MMODITY

he market demand for a given commodity is the horizontal summation of the demands

.6 T AR AN CO

T

of the individual consumers. In other words, the quantity demanded in the market at each

price is the sum of the quantities demanded by all consumers at that price.

Derivation of the Market Demand

In the real world, there may be millions of individual consumers in a market, but for

simplicity, let us consider the case of only four individual consumers in a given market.

Table 2.1 we show the quantity demanded by four consumers at various prices of a In

certain commodity and the total (market) quantity demanded. These data are also

presented graphically in Figure 2.21.

Table 2.1: Individual and Market Demands

Price

Quantity

demanded by

consumer A

(DA)

Quantity

demanded by

consumer B

(DB)

Quantity

demanded by

consumer C

(DC)

Quantity

demanded by

consumer D

(DD)

Market

Quantity

Demanded

(QM)

2 90 45 20 110 265

4 80 40 30 100 250

6 70 35 40 90 235

8 60 30 50 80 220

10 50 25 60 40 175

12 40 20 70 20 150

14 30 15 80 10 135

16 20 10 90 5 125

71

From the table, we observe that the market demand is negatively sloped as the individual

demands are. Sometimes, one or two of the individual demands may be positively slo

if the good is giffen for those individuals.6 For example, the demand for individual C

positively sloped implying that the good is giffen for consumer C. Although the

commodity is giffen and the demand is positively sloped for consumer C, the ma

demand has the normal positive slope, because the demands of other consumer more than

offset the giffen case of consumer C.

Economic theory does not define any particular form of the demand curve. In textbooks,

market demand is sometimes shown as a straight line (liner demand curve) and

sometimes as a curve convex to the origin. The linear demand curve may be written in

the form: Q = a – bP. This linear form implies a constant slope but with a changing

elasticity at various prices. [We will see elasticity later on].

ped

is

rket

iffen for another.

Figure 2.21: Individual and Market Demand Curves

0

250

300

2 4 6 8 10 12 14 16

100

150

200

50

Price

DA DB

DCDD DM

QD

6 The classification of goods as normal, inferior or giffen depends on the individual consumer. That is, depending on the income, attitude, and preferences of the consumer, what is normal for one consumer may be inferior or g

72

Determinants of Demand

Deman te variable; it is determined by many variables. Traditionally the

most im terminants of the market demand are considered to be the price of the

e prices of other commodities, consumer’s income and

tastes.

1. Own Price (Price of the Commodity)

The law of demand states that the quantity demanded of a commodity increases when

ere is a decline in the price of the commodity (and vice versa), for an ordinary good7.

his results in movement along the same demand curve as shown in Figure 2.22 below.

. Price of Other Commodities

d is a multivaria

portant de

commodity under consideration, th

th

T

P

Qx O

P1

P2

X1 X2

Figure 2.22: Movement along the Demand Curve as the

A

B

Price of X Changes

2

A change in the price of another related commodity, which could be either a substitute or

a complement, is also a factor that affects the demand for a commodity. When the price

7 An ordinary good is a good which is either normal or inferior but not giffen. If the good is giffen the

demand curve will be upward sloping as there is direct relationship between quantity demanded and price of the commodity.

73

of a substitute good increases, the quantity demanded of the commodity under

conside n will also increase. Thus, this change shifts the market demand curve

outward. For instance, if the price Coca Cola rises, the quantity demand of Pepsi is

expected to rise at the prevailing price. When the price of a complementary good

increases, the quantity demanded of the commodity under consideration will decline, and

thus it will make the demand curve shift upward. As an example, if the price of petroleum

rises, the quantity demanded of car falls.

. Income of the Consumer

s income of the consumer increases, the quantity demanded of a good will increase if

e good is normal, and thus the demand curve will shift outward. However, if the good is

bility, etc.

ratio

3

A

th

inferior the quantity demanded of the commodity declines with an increase in income,

and the demand curve will shift downward.

P

Qx

Apart from the above determinants, market demand is also affected by numerous other

factors, such as tastes and preferences, the distribution of income, the size of total

population and its compositions, wealth, credit availa

O

Figure 2.23: Shift of the Demand Curve as, for example, Income Increases

P1

X1 X2

74

As can be seen from the above two figures, Figure 2.22 and Figure 2.23, the result of a

change in the price of the commodity itself is shown by a movement from one point to

anot the effect of changes in other determinants is

show e other factors are considered as the shift

fact

ssumption; the shift factors (factors other than the price of the commodity) are assumed

2.7 ELASTICITY OF DE

many elasticities of demand as its determinants. The most important of these

and.

Price Elasticity of Demand

her on the same demand curve, while

n by a shift of the demand curve. Thus, thes

ors of the demand curve. The demand curve is thus drawn under the ceteris paribus

a

to remain constant in drawing the demand curve.

MAND

Elasticity can be defined as the responsiveness of a variable for a change in one of its

determinants, holding the other factors constant. Thus, elasticity of demand is the

measure of responsiveness of quantity demanded as a result of a change in one of its

determinants, holding all the other factors constant.

There are as

elasticities are:

a) The Price Elasticity of Demand,

b) The Income Elasticity of Demand , and

c) The Cross- Price Elasticity of Dem

Let us start with the first one: the price elasticity of demand

asticity of demand is the relative measure of the responsiveness of quantity

an d o changes in the commodity’s own price. If the changes in price are very

small, we use the point elasticity of demand as a measure of the responsiveness of

emand. If the changes in price are not small, we use the arc elasticity of demand as the

The price el

dem de t

d

relevant measure.

75

At e h poac int on the market demand curve, the price elasticity of demand is defined as

the percentage change in the quantity demanded resulting from a one percent change in

price of the commodity. In other words, it is the sensitivity of the quantity demanded to

changes in price.

Symbolically, the point elasticity of demand is given by the proportional/percentage

change in quantity demanded divided by the proportional/percentage change in price.

dpε = commodity theof Pricein change %age

demandedQuantity in change %age

P/P Q/Q

dd =

dpε =

P Q

dd .

Q P

If, for instance, the demand curve is linear with an equation of the form Q = a – bP, its

slope will be P Q

dd = -b

Substituting this into the elasticity formula we obtain:

= -bdpε Q

P .

his implies that the price elasticity of demand differs at the various points of the linear

emand curve. That is, even though a linear demand has a constant slope, the price

lasticity of demand is not constant.

bove formula for the price elasticity is applicable only for infinitesimal (very small)

hanges in price. If the price changes appreciably (significantly), we use the following

rmula which measures the arc elasticity of demand:

T

d

e

The a

c

fo

dpε =

P Q

dd )

QQ PP

(21

21

++ .

The arc elasticity of demand measures the average elasticity, that is, the elasticity at the

id point of the chord that connects two points, lets say A and B, on the demand curve.

hese two points are defined by the initial and the new price levels. It should be clear that

m

T

76

the measure of the arc elasticity is an approximation of the true elasticity of the section

om A to B on the demand curve. It is used when we know only the two points A and B

ut not the intermediate ones.

For a

the rat nd curve and above the point. For

fr

b

We can also estimate the price elasticity of demand graphically. Suppose that we want to

estimate the price elasticity of demand plotted in Figure 2.25 below.

P

Q O

A

B

Arc Elasticity

Figure 2.24: Arc Elasticity of Demand

a linear demand curve, price elasticity of dem nd can be determined geometrically by

io of a segment below the point on the dema

P

A

QxOB

C

Figure 2.25: Geometrical Dem nstratioo n of the Price Elasticity of Demand

(/ε / = ∞) dp

(/ dpε / = 1)

(/ dpε / = 0)

(0 < / dpε / < 1)

(1 < / dpε / < ∞)

77

exa

above i

ence, if point C is the midpoint of the demand curve (i.e., if CB = AC), the price

f demand would be one at this point; and, at this point demand is said to be

uni

greater gment

abo

coefficient of the price elasticity of demand is less than one (in absolute value) as the

segmen t a , u p ine s .

t the two extreme points of the demand curve, point A and point B, price elasticity of

dem rf hat means,

. At point A, demand is perfectly elastic (/ / = ∞)

. Between points A and C, demand is elastic (1 < / / < ∞) (a small change in

price induces a more than proportionate change in quantity demanded).

At point C, demand is unitary elastic (/ / =1) (a change in price results in a

proportionate change in quantity demanded).

<

induces a less than proportionate change in quantity demanded).

5. At point B, demand is perfectly inelastic ( / = 0)

ote that:

Price elasticity of demand is always negative due to the inverse relationship

between price and quantity dem mand).

mple, the price elasticity of demand at point C on the demand curve in Figure 2.25

s the ratio of the segment CB to the segment AC, i.e., CB/AC.

H

elasticity o

tary elastic. To the left of point C, the coefficient of price elasticity of demand is

than one (in absolute value) as the segment below is greater than the se

ve, and thus demand is price elastic. To the contrary, to the right of point C, the

t below is less than the segmen bove th s demand is rice la tic

A

and is perfectly elastic and pe ectly inelastic respectively. Tdpε1

dpε2

dpε3.

4. Between point C and B, demand is inelastic (0 < / dpε 1) (a change in price /

/ dpε

N

anded (i.e., because of the law of de

We usually talk of the coefficient ignoring the sign; or equivalently, we

sometimes define elasticity as dpε = –

P Q

dd .

Q P instead of d

pε = P Q

dd .

Q P .

78

P P P

Q Q Q

/ dp / = 0: Perfectly

Inelastic Demand ε

/ d

pε / = ∞: Perfectly Elastic Demand

0< / dpε / <1, / d

pε

or / dpε / =

/ > 1

1

Figure 2.26: Examples of Demand Curves with Different Elasticities

Factors Affecting Price Elasticity of Demand

and is elastic or inelastic is an important consideration, especially for

ent policy in individua

Whether dem

governm l commodity markets. For example, suppose the demand

for wheat were high

result in a proportionately greater redu

expenditures on wheat decline. Now, suppos

wheat price above the market equilibrium

would farmers’ incom

sales guaran

Price e

of de

1.

ubstitutes for a specific good are, the greater its price

ple,

ticity of demand. Goods with

many and very close substitutes will have higher elasticities.

ly price elastic. An increase in the price of wheat would accordingly

ction in quantity demanded. Thus, total

e the government established a minimum

price. Wheat sales would be reduced, and so

es be, unless the price support were accompanied by a minimum

tee.

lasticities range quite widely. The major factors that determine the price elasticity

mand are:

The availability and closeness of substitute goods:

The more and closer the s

elasticity of demand tends to be. Goods with few and poor substitutes, for exam

foods and fuel, will always tend to have low price elas

2. The nature of the need that the commodity satisfies:

79

Goods can be either luxuries or necessities in satisfying human needs. Thus, the price

elasticity of demand is more elastic for luxurious goods and less elastic for necessity

goods.8

3. The proportion of income the good have in the total income of the consumer:

is spent on a commodity, the price elasticity of demand

would be less elastic. For example, the price elasticity of demand for salt may be less

elastic for most individual consumers as it has a small share in the budget of many

run, the price elasticity of demand is less

elastic.

If large proportion of the income of the consumer is spent on a commodity, the price

elasticity of demand for the commodity would be more elastic. On the other hand, if

small proportion of income

individuals.

4. The available time for the consumer:

In the long run, the price elasticity of demand is more elastic as the consumer has

enough time to respond to the price change by adjusting his/her consumption pattern

and finding new substitutes. In the short

5. The number of uses to which a commodity can be put:

The more the possible uses of a commodity, the greater its price elasticity will be.

Income Elasticity of Demand

income elasticity of demand is defined as the proportionate change in the quantity

anded resulting from a proportionate change in income. Symbolically, we may write:

The

dem

dIε =

I Qd .

Q I

d

he income elasticity of demand is positive ( > 0) for normal goods and negative (

< 0) for inferior goods. So city for classifying goods

to luxuries and necessities. A commodity is considered to be luxury if the income

dIε

dIε T

me writers have used income elasti

in

8 The classification of goods as luxuries and necessities depends on the income and preferences of the

consumer; what is luxury for one individual may be necessity for the other.

80

elasticity for its demand is greater than unity ( dIε > 1). A commodity is a necessity if the

income elasticity for its demand is less than one (0 < ε dI < 1).

The main determinates of income elasticity of demand are:

1. The nature of the need that the commodity covers. Generally, luxurious goods have

t is a luxury good in an underdeveloped,

poor country while it is a necessity in a country with higher per capita income.

Cross Price Elastic f Demand

greater income elasticity than necessity goods.

2. The initial level of income of a consumer or a country: The percentage of income

spent on food declines as income increases (this is known as Engel’s Law and has

sometimes been used as a measure of welfare and of the development stage of an

economy). As another example, a TV se

3. The time period: Because consumption patterns adjust with a time lag to changes in

income, demand income tends to be elastic in the long run.

ity o

emand for a given commodity is determined not only by price of the commodity but

a

defined as the proportionate change in the quantity demanded of X resulting from a

p

D

lso by prices of other related commodities. The cross price elasticity of demand is

roportionate change in the price of Y. Symbolically,

YX , dε = X

YPdQx . QdPy

The s

g

relate ther, the cross price elasticity of demand is zero. The higher the value of

e cross price elasticity, the stronger will be the degree of substitutability or

complementarily of the

ign of the cross price elasticity of demand is negative if X and Y are complementary

oods and positive if X and Y are substitutes. If the two commodities X and Y are not

d to each o

th

two goods, X and Y.

81

The main determinant of the cross price elasticity of demand is the nature of the

com odities relative to their uses. If two commodities can satisfy the same need equally

well, the cross price elasticity is high, and vice versa.

m

Check Your Progress

Price Elasticity and Total Expenditure

1. Graphically show the effect of an increase in price of Coca Cola on the demand of

Pepsi Cola.

2. If the price elasticity of a commodity is -5, what will be the change in the quantity

demanded of the commodity as a result of a 4 % rise in the price of this

commodity?

3. Interpret the expression: "The cross price elasticity of demand between two

commodities A and B is equal to 3". What can you say about the two commodities?

4. Explain the difference between arc elasticity of demand and point elasticity of

demand.

he total amount spent on a good (Total Expenditure) varies directly with the change in

t l expenditure. However, if demand is inelastic (if < 1), an increase in price raises

esult is straight forward. A price increase means that more is

spe ount spent.

Off gher price. If

the If the quantity

ffect outweighs the price effect, then total expenditure falls. Elasticity is the measure of

the relative strengths of the two effects.

T

price when price elasticity of demand is less than one, and inversely related to the price

when price elasticity of demand is greater than one. In other words, if demand is elastic

(if dPε > 1), an increase in price reduces total expenditure and a decline in price increases

a dPεto

total expenditure and a decrease in price reduces total expenditure.

The intuition behind this r

nt on each unit of the good purchased, which tends to increase the am

setting this is the fact that fewer units of the good are purchased at the hi

price effect outweighs the quantity effect, then total expenditure rises.

e

82

If the price elasticity of demand is less than one (if dPε < 1), then a one percent increase

in price induces a less than one percent decrease in quantity demanded. Thus, the price

effect swamps (more than offsets) the quantity effect, and thus total expenditure rises.

But, when price elasticity of demand exceeds one (if dε > 1), a small increase in price

induces a larger decrease in quantity, so the quantity effect dominates and consequently

al expenditure falls.

Note: Since total expenditure and total revenue are two sides of the same coin, the effect

of change in price o

P

tot

n total revue is the same as its effect on total expenditure when

emand is elastic and inelastic. The total expenditure of a consumer (the buyer) is the

total

An important relationship exists between t e price elasticity of demand and the total

expenditure o on ( d n

the price of a commodity:

results in an increase in total expenditures if dem d is price elastic;

leaves total expenditure unchanged if demand is unitary elastic; and

results in ine in total expenditure if dema rice inelastic.

Specifically, when he price of t ommodity falls, total expenditure (price times

uantity) increases if demand is price elastic > 1 because the percentage increase in

e

to an inc ease in the quantity demanded

f the commodity that is smaller than the percentage reduction in price, and so total

d

revenue for the producer (the seller).

h

f consumers the commodity total revenue of pro ucers). A decline i

an

a decl nd is p

t he cdPεq

quantity (which by itself tends to increase total expenditure) exceeds the percentage

decline in price (which, by itself, tends to decrease total expenditure). Total expenditures

is at its maximum when dPε = 1, and d cline thereafter as d

Pε falls below 1. That is, when dPε < 1, a reduction in the commodity price leads r

o

expenditure on the commodity declines. The hypothetical data in Table 2.2 below

illuminate this point.

83

Table 2.2: The Relationship between Price Elasticity of Demand and Total

Expenditure

Price of X

(Px)

Quantity of X

(Qx)

Total Expenditure

(TE

Absolute Value of

Point ) (/ /) d

Pε

A 2.00 0 0 ∞

C 1.50 3 4.50 3

E 1.00 6 6.00 1

F 0.50 9 4.50 1/3

H 0 12 0 0

rom the above table, we see that between points A and E, / / > 1 and total expenditure

total

re and the price elasticity of demand as follows:

When demand is price elastic ( > 1): when demand is elastic, a small increase in

price results in a large declin uantity demanded, then total revenue and total

expenditure decline (↑P (↑P.Q↓) = ↓TE = ↓TR). Price and total

s if > 1.

large increase in

ll

dF Pε

on the commodity increases as the commodity price declines. The opposite is true

between points E and F over which / dPε / < 1. Total expenditure is maximized at point E

(the geometric mid-point of the demand curve).

Given that total revenue or total expenditure is the product of price and quantity

demanded (i.e., TE = TR = P.Q; where TE is total expenditure, TR is total revenue, P is

price and Q is quantity demanded), we can summarize the relationship between

expenditudPε

e in q

Q↓

dPεexpenditure change in opposite direction

When demand is inelastic (ε d < 1): when demand is inelastic, aP

price results in a sma decline in quantity demanded, then total revenue and total

84

expenditure increase (↑P Q↓ (↑P.Q↓) = ↑TE = ↑TR). Price and total

expenditure move in the same direction if < 1.

Market Demand, Total Revenue (TR) and Marginal Revenue (MR)

dPε

e can derive the total expenditure of consumers (or the total revenue of firms selling

e particular product) from the market demand curve. As seen earlier, total revenue is

e product of the quantity sold and the price, i.e., TR = P.Q.

the market demand is linear, the TR curve will be a curve which initially slopes

pwards, subsequently reaches a maximum, and then starts declining. We can prove this

om our previous discussion of the relationship between elasticity and TR (or TE).

e third and fourth

ue (MR). The marginal revenue is the

W

th

th

If

u

fr

Another important point in the theory of firm (to be discussed in th

chapters in some detail) is the marginal reven

change in total revenue resulting from selling an additional unit of the commodity.

O Q1 Q* Q2 Q O Q* Q

A

C

B

D

D’

/ dPε / = 1

P

P1

P* P2

85

TR

TRmax

TR

Figure 2.27: Price Elasticity of Demand and Total Revenue

D

P

raphically, MR at any one point is the slope of total revenue curve at that particular

point. If the nd curve.

vative of the TR f ction:

G

demand curve is linear, the MR curve is twice as steep as the dema

This can be proved mathematically as follows:

MR is the deri un

)()(

QdTRdMR =

)(Qd

= ).( QPd

)()( PdQd)()( QdQd

QP +=

)(Qd

QPMR += )(Pd

If the demand curve is linear, its equation in terms of price is:

Substituting P into the TR function, we find:

The MR is then:

P = a – bQ

TR = PQ = (a – bQ)Q = aQ – bQ2

)(Q)(

dTRdMR =

86

)(

)bQ-a( Q 2

QddMR =

= a – 2bQ.

that the MR curve starts from emand curve, and

that the MR is a straight line with a negative slope (-2b) twice as steep as the demand

urve (with a slope of -b).

The Relationship between MR and Price Elasticity of Demand

This proves the same point (a) as the d

c

The MR is related to the price elasticity of demand with the formula

)//

1( dPMRε

−=

Proof

1

p

:

Assume that the demand function is P = f(Q)

The

Above, just before a moment, we have shown that

total revenue is TR = PQ = [f(Q)]Q

)()(

QdPdQPMR +=

We o o als kn w that the price elasticity of demand could be defined as: dpε =

P Q

dd .

Q P

ing this definition of elasticity, we obtaRearrang in:

dpε .

P Q =

P Qd (criss-cross m tion).

d ultiplica

dpεQ.

= PdQd P (taking reciprocal).

Substituting dQd P = dε

P into the expression of the MR, we find: pQ.

)()(

QdPdQPMR +=

dp

QPMRεQ. P

+=

87

)Q.

Q1( dp

PMRε

+=

) 11(MR dpε

P +=

)//

11( dp

PMRε

−= (Since is negative, = – / /)

Total Revenue, Marginal Revenue and the Price Elasticity of Demand

dpε d

pεdpε

t its slope, the MR, is equal to zero. That is,

We said that if the demand curve is falling linearly, the total revenue (TR) curve initially

increases, subsequently reaches its maximum, and then starts declining. We can use the

relationship among the marginal revenue (MR), price (P) and dPε derived earlier to

establish the shape of the total revenue curve.

The total revenue curve reaches its maximum at the point where / dε / = 1, because

at this poin

P

)1

1( −= PMR = P(0) = 0.

If / dPε / > 1, the TR curve has a positive slope, that is, it is still increasing and

hence has not reached its maximum point.

1

If / dPε / > 1, then

// dpε

< 1 implying that1 0)//

1( >− dpε

. Given that P > 0, then 1

)//

11(PMR −= dε > 0.

p

If / dPε / < 1, the TR curve has a negative slope, that is, it is falling.

If / dPε / < 1, then

//1

d > 1 implying that 0)11( <− d . Given that P > 0, then // pε

pε

)// d

pε11(PMR − < 0. =

88

Check Your Progress

1. What will happen to the total expenditure of a consumer as a result of a rise in the

2. oint

of a linear demand curve?

amined so far implicitly assumed a risk free world. It

as mplete certainty as to the results of the choices they

ake. Clearly, this is not the case in most instances. In contrary to our earlier

A

b

price of a commodity if the demand for this commodity is highly price elastic?

Why?

What is the value of the price elasticity of demand for a commodity at the mid p

2.8 CHOICE UNDER UNCERTAINTY

The traditional theory of demand ex

sumed that consumers face co

m

assumptions of price, income and other variables to be known with certainty, many of the

choices that people make involve considerable degree of uncertainty.

lthough risk and uncertainty are usually used interchangeably, some people distinguish

etween the two.

(I) Uncertainty: refers to a situation when there are more than one possible outcomes

to a decision-maker and where the probability of each specific outcome is not

(I

known. This may be due to insufficient past information or instability in the

structure of the variables.

I) Risk: refers to a situation where there are more than one possible outcomes to a

decision-maker and the probability of each specific outcome is known or can be

estimated.

(III) Certainty: refers to a situation where there is only one possible outcome to a

decision and this outcome is known precisely. For example, investing on treasury

bills leads to only one outcome (i.e. the amount of the yield), and this is known

with certainty.

89

Expected Value and Variation of Risky Choices

We usually need two measures to describe and compare risky choices. These measures

are: expected value and variation.

1. Expected value: is the weighted average of all possible payoffs/outcomes that can

result from a decision the probability of those

payoffs used as weights. It measures the value that we would expect on average.

en by P1

nd P2, then the expected value is:

under the various states of nature, with

If we multiply each possible outcome or payoff by its probability of occurrence and add

up these products, we get the expected value. If, for instance, there are two possible

outcomes having payoffs X1 and X2 and if the probability of each outcome is giv

a

E(X) = P1X1 + P2X2

Example: If the probability that an oil exploration project will be successful is ¼ and the

probability that it will be unsuccessful is ¾, and if success yields a payoff of 40 Birr per

share while failure yields a payoff of 20 Birr per share, the expected value is:

E(X) = P(success)(yield from success) + P(failure)(yield from failure)

. Variability:

= ¼ (40 Birr/share) + ¾ (20 Birr/share)

= (10 + 15) Birr/share

= 25 Birr/share

is the extent to which the possible outcomes of an uncertain event may

differ. We measure variability by recognizing that large differences between the

actual and expected value imply greater risk.

tandard deviation is the often used measure of variability. Standard deviation measures

e dispersion of the possible outcomes from the expected value. The smaller the value of

e standard deviation (σ), the tighter or less dispersed the distribution is and thus the

wer would be the risk attached to it, and vice versa.

2

S

th

th

lo

90

Standard deviation (σ) = 2222

2111 )]([)]([ XEXPXEXP −+−

two alternatives to choose from have the same expected value, the one with the

aller standard deviation is less risky and is hence the preferred one. If, however,

but is much riskier than the other one and

ice versa, the preference depends on the individual – whether he/she is a risk averse, a

tral, or a risk loving person.

Different Preferences towards Risk

If

lower/sm

one alternative offers a higher expected value

v

risk neu

A Risk Averse Person:

1. is a person preferring a certain income to a risky income with

e expected value. For a risk averse person, losses are more important (in terms of

I

have a certain income of 20 Birr, or an

come of 30 Birr with probability of 0.5 and an income

ed income from this second alternative (A2) is:

) = 0.5(30) + 0.5(10) = (15 + 5) Birr = 20 Birr. This is the same as the income

ers to consume the risk free 20 Birr to trying

the sam

the change in utility) than gains. Losses hurt him/her more seriously than gains benefit

him/her. Thus, the marginal utility of income (MU ) diminishes as income rises.

To illustrate, assume that a person can either

alternative decision yielding an in

of 10 Birr with probability 0.5. The expect

E(A2

earned without risk (from the first alternative – A1).

A risk averse person facing this situation pref

the alternative in which he/she could have consumed 30 Birr if successful or 10 Birr if

unsuccessful. The figure below makes this point more clear.

91

Figure 2.29: Utility Function for a Risk Averse Individual

18

16

14

10

E

C

B

A

D

Utility

0 10 16 20 30 Income

From the figure, we see that utility at point B is greater than utility at point C. The utility

of this risk averse person from the risk free income of 20 Birr is 16 (point B) and the

expected utility from the risky alternative is:

E(U) = 0.5U(10 Birr) + 0.5U(30 Birr)

ote that the expected utility, E(U), is the sum of the utilities associated with all possible

Birr) to avoid taking risk. The

aximum amount of money (4 Birr in our case) that a risk averse person will pay to

void taking a risk is called a risk premium.

= 0.5(10) + 0.5(18)

= 14 (point C).

N

outcomes weighted by the probability that each outcome will occur.

The risk averse person achieves the expected utility of 14 at a lower, but a risk free,

income of 16 Birr. That is, a risk free income of 16 Birr gives the same level of

satisfaction as a risky alternative with an expected income of 20 Birr. Thus, he/she is

willing to pay or forgo 4 Birr (20 Birr – 16 Birr = 4

m

a

92

2

Figure 2.30: Utility Function for a Risk Neutral Individual

18

12

E

C

Utility

6 A

0 10 20 30 Income

. A Risk Neutral Person: is a person who is indifferent between a certain income and an

ncertain income with the same expected value. For this person, the marginal utility of

come is constant.

he utility of this risk neutral person from the risk free income of 20 Birr is 12 (point C)

same point C).

As 12 = 12, the risk neutral person is indifferent between the risky and the risk free

alternatives.

u

in

T

and the expected utility from the risky alternative is:

E(U) = 0.5U(10 Birr) + 0.5U(30 Birr)

= 0.5(6) + 0.5(18)

= 12 (the

3. A Risk Loving Person: is a person who prefers a risky income to a certain income

given that the risky alternative has the same expected value as the certain income. This

person may prefer an uncertain income to a certain one even if the expected value of the

uncertain income is less than that of the certain income. The expected utility of the

uncertain income is greater than the utility of a certain income for a risk loving person

and thus their utility of income curve is upward bending.

93

Figure 2.31: Utility Function for a Risk Loving Individual

18

Utility

3

E

B

A

10.5

8

C

0 10 20 30 Income

The utility of this risk loving person from the risk free income of 20 Birr is 8 (point B)

nd the expected utility from the risky alternative is:

E(U) = 0.5U(10 Birr) + 0.5U(30 Birr)

(18)

(point C).

s 10.5 > 8, the risk loving person prefers the risky alternative to the risk free alternative.

Risk loving people prefer alternat xpected value and high standard

eviation (risk) to a lower paying but less risky alternative (unlike the risk averse people).

Risk Aversion and Indifference Curves

a

= 0.5(3) + 0.5

= 10.5

A

ives with high e

d

However, risk loving people are few at least with respect to major purchases or large

amounts of income or wealth.

curves

at relate the expected income to the variability of income, the latter being measured by

the standard deviation.

We also describe the extent of a person’s risk aversion in terms of indifference

th

94

An indifference curve shows the combinations of the expected value and the standard

deviation of income that give the individual the same level/amount of utility. Indifference

curves are upward sloping. This is because risk is undesirable (a ‘bad’) so that the greater

the amount of risk, the greater the amount of income needed to make the individual

equally well-off. An increase in the standard deviation (a higher variability of income)

ust be compensated by a higher expected value of income so as to a leave a person on

a large increase in the standard

eviation of income (σ).

m

the same level of utility.

As opposed to the case of a highly risk avert person, a slightly risk avert person requires

only a small increase in expected income, E(I) for

d

E(I) U3

U2

U1

O σ O σ

Panel (a): Indifference Curves of Person A Panel (b): Indifference

Curves of Person B

U3

U2

U1

E(I)

Figure 2.32: Person A is more Risk Averse than Person B

Reducing Risk

e face of a broad variety of risky situations, people are generally risk averse.

umers and managers commonly reduc ris

In th

Cons e k using various ways. The major ones are:

d

iversification, insurance and obtaining more information.

95

1. Diversification: refers to reducing risk by allocating resources to a variety of activities

e outcomes are not closely related –“Don’t put all your eggs in one basket.” whos

2. Insurance: If the cost of insurance is equal to the expected loss, risk averse people will

nough insurance to recover fully from any losses they might suffer. For a risk averse

mer, the guarantee of the same income regardless of the actual outcome generates

utility than would be the case if that person had a high income when there was no

nd a low income when a loss occurred.

e value of information

buy e

consu

more

loss a

3. Th : People often make decisions based on limited information. If

information were available, one could make better predimore ctions and reduce risk.

E

study

2.9 L

f utility: Cardinal Utility and

Under the cardinal utility approach, the consumer reaches equilibrium when the

marginal utility of the commodity is equal to its price in the case of one commodity

(MUx = Px), and when the ratio of the marginal utilities of the commodities to their

ven though forecasting is inevitably imperfect, it may be worth investing in a marketing

that provides a reasonable forecast for the future.

ESSON SUMMARY

The theory of consumer behavior is the basis for the theory of demand.

There are two approaches for the measurement o

Ordinal utility approaches. The cardinal utility approach argues that utility is

measurable and quantifiable with a unit of measurement of utils while the ordinal

utility approach argues that utility has ordinal value and could only be ordered and

ranked.

PnMUn

PyMUy

PxMUx

=== ...............prices is equal for all commodities ( ).

lity approach, using the indifference curve theory, the

consumer reaches equilibrium at the tangency point of the indifference curve and

Under the ordinal uti

96

the b the

same as the slope of the budget line (

udget line. At the tangency point, the slope of the indifference curve is

Y

XPMRS = ). XY P

The i v curve is derived from the equilibrium of the consumer, and

ndividual demand curves.

By using the revealed preference axioms, the revealed preference hypothesis allows

the derivation of the equilibrium of the consumer without the use of the indifference

curve

The total effect of a change in price of a commodity, while income and price of

other m nstant, can be decomposed into substitution and income

negative substitution effect is

stronger than the positive income effect, and as a result the total price effect is

negative. In the case of giffen goods, the positive income effect is stronger than the

negat ion effect, and the total effect is positive.

Elasticity of demand measures the responsiveness of quantity demanded to a change

in on f terminants of demand. In this module, we have tried to see three

to a change in income), and the cross price

elasti uantity demanded of a good to a

chang ty).

The s nd/or other variables is different

from other variables; hence, the optimum

decision of the consumer is depends on the expected value and variation of income

ndi idual demand

then the market demand is derived from the individual demand curves, as the

horizontal summation of the i

s.

co modities is co

effects. For normal goods, both the substitution and income effects are negative;

and for inferior and giffen goods, the substitution effect is negative but the income

effect is positive. In the case of the inferior goods, the

ive substitut

e o the de

types of elasticities: the price elasticity of demand which is the responsiveness of

quantity demanded to a change in price), the income elasticity of demand (the

responsiveness of quantity demanded

city of demand (the responsiveness of q

e in the price of another related commodi

con umer’s decision with certain income a

the decision with uncertain income and/or

and the resulting expected utility of the consumer.

97


I. Choose the Best Answer

1. For norm

nd is positive and greater than one.

offer curve and the demand curve are negatively sloped.

he income offer curve are positively sloped.

are true.

2. price elasticity of demand between two commodities X and Y is

negat ,

lements

goods

ed is twice the marginal utility of the last unit of Y consumed,

the c

al good,

a. the income elasticity of dema

b. both the price

c. both the Engel curve and t

d. b and c

e. All are true.

If the cross

ive then X and Y are:

a. substitutes

b. giffen goods

c. normal goods

d. comp

e. inferior

3. Assume a budget line is drawn for two commodities: X on the x-axis and Y on the

y-axis. If the income of the consumer is 100 Birr, the y-intercept is 4, and the slope

of the budget line is -2, the price of commodity X is:

a. 25 Birr

b. 12.5 Birr

c. 50 Birr

d. 8 Birr

e. None

4. Assume that there are only two commodities, X and Y. If the marginal utility of the

last unit of X consum

onsumer is in equilibrium when:

a. the price of Y is twice the price of X.

b. the price of Y equals the price of X.

c. the price of Y is half of the price of X.

98

d. the consumer can’t reach equilibrium.

5. An indifference curve will be L-shaped when the two goods are:

t substitutes

complements

ect substitutes

ed

d good commodities

alled:

e

7. One

commodi

a. er

c.

d.

f.

8. If the dem is given by Q = 16 – 2P, where Q is

the qu t

is the pric

a.

c.

d. astic

e. Elastic

e. None

a. perfec

b. perfect

c. imperf

d. unrelat

e. bad an

6. The line joining the different points of consumer’s equilibrium resulting from the

change only in the price of the commodity is c

a. demand curve

b. income consumption curve

c. Engel curve

d. price consumption curv

e. None

of the following is not a shift factor of the demand curve for a given

ty.

Income of the consum

b. Price of other related commodities

Tastes and preferences

Price of the commodity

e. All

None

and function for a certain commodity

an ity demanded of the commodity and P is the price of the commodity, what

e elasticity of demand when price is equal to 4 Birr per unit?

Inelastic

b. Perfectly elastic

Perfectly inelastic

Unitary el

99

9. One of the following is not true about the characteristics of well-behaved

indifference curves.

Indifference curves farther from the origin represent higher utility

10. ility function of a consumer is given by U = X2Y2, what is the MRSxy?

X/Y2

f. X/Y3

consumption of different commodities as

1st , 2nd and 3rd etc, we are measuring utility:

y

12. If price of an inferior good (which is not giffen) is rising,

fect increases the

result the total effect is a

effects increase the quantity

as a result the total effect is an increase

modity.

e quantity

total effect is a decrease in the

quantity demanded of the commodity.

a. Indifference curves do not intersect

b. Indifference curves have negative slope

c. Indifference curves are concave from the origin

d.

e. None

If the ut

a. Y/X

b. X/Y

c.

d. Y2/X

e. X2/Y

11. When we rank the utility gained from the

a. ordinally

b. cardinall

c. in both approaches

d. traditionally

a. the substitution effect decreases but the income ef

quantity consumed of the commodity, and as a

decrease in quantity.

b. both the substitution and the income

consumed of the commodity, and

in the quantity demanded of the com

c. both the substitution and the income effects increase th

consumed of the commodity, but the

100

d. both the substitution and the income effects decrease quantity consumed

of the commodity, and as a result the total effect is an increase in the

quantity demanded of the commodity.

e

II. True or Fa

e. the substitution effect increases but the income effect decreases th

quantity consumed of the commodity, but the total effect is an increase in

quantity.

lse Questions

1.

e consumer

2. n is the same for a consumer along the same indifference

3. sticity of demand for a good is always positive

5.

III. S

The revealed preference hypothesis is different from the indifference curves theory

as the revealed preference hypothesis determines the equilibrium of th

without the use of the indifference curves, unlike that of the indifference curves

theory.

The level of satisfactio

curve.

Income ela

4. For a normal good, both the Engel curve and the demand curve are positively

sloped.

The firm’s total revenue decreases for an increase in price of the commodity if

demand is price inelastic.

hort Answer and Workout Questions

1. Defin

c. Marginal Rate of Substitution

d. Engel Curve

2. Distinguish between the following pairs of economic concepts:

a. An indifference curve and an indifference map

b. Budget line and budget set

e the following terms:

a. Utility

b. Marginal Utility

101

c. Income offer cu

d. Normal good and inferior good

e. Ordinal

f. Indifference curve theory and revealed preference hypothesis

MRSy,x is 12.

4. Suppose that the consumer is asked to contemplate a gamble with a probability of

ing Birr 10,000 with a utility of 10 utils, and a 40% probability of

12 utils.

cted income and expected utility of the consumer?

tive which gives him

come of the risky alternative given

risk averse? Why?

Y = 4Y, Price of X is 3 Birr per unit and price of Y is also 3

e of the consumer is 1200 Birr, find the amounts of X and

Y that the consumer chooses to consume so as to maximize his utility.

tion P = 20 – 5Q, find the price elasticity of demand when

Birr per unit. Mention if the demand is price elastic or

inelastic at this point.

rve and price offer curve

utility and cardinal utility

3. Explain the interpretation of

60% of winn

winning Birr 15,000 with a utility of

a. What will be the expe

b. If the utility of this consumer from a risk free alterna

an income equal to the expected in

above is equal to 11 utils, is this consumer risk lover or

Illustrate your answer with the help of a diagram.

5. Given MUx = X, MU

Birr per unit. If the incom

6. Given the demand func

price of the commodity is 5

7. Explain the substitution and income effects of a price rise for a normal good using a

diagram.

8. Suppose Martha earns an of income 400 Birr currently, and her utility function is

given by: U(m) = 4m, where m represents income. She has two options:

Option 1: to buy a share. If she is successful her income will be 700 Birr and if she

is not successful her income will be 100 Birr.

Option 2: to do nothing and keep on earning 400 Birr.

are equally likely,

a. What would be her expected income if she buys the share?

the share?

Assuming that success and failure

b. What would be her expected utility of buying

c. Would Martha buy the share? Why?

d. Is Martha risk averse, risk lover or risk neutral?

102

CHAPTER THREE

THEORY OF PRODUCTION

ESSON STRUCTURE

.1 Introduction

of the Production Function

.7 Equilibrium of the Firm: Choice of Optimal Combination of Factors of Production

N

Production is the process of conversion of

consumable form (goods and services). In this regard, in the production process or

activity, firms turn inputs Th on o rs of

production) into output is defined at a particular time period and at a given technology.

By technology we mean the state of knowledge about the various methods that might be

used to to outpu and it is described by a production function.

.2 CHAPTER OBJECTIVES

illustrate the short-run production function and stages of production

L

3


3.3 The Production Function

3.4 The Short Run Production Function and Stages of Production

3.5 Laws of Production

3.6 Returns to Scale and Homogeneity

3

3.8 Lesson Summary


3.1 INTRODUCTIO

inputs (factors of production) into a

into output. is transformati f inputs (facto

transform inputs in ts,

3

After studying this lesson thoroughly, you would be able to:

understand the context of the production function

103

understand and explain the laws of production

explain the returns to scale and homogeneity of the production function

ge of equilibrium theory of firms and optimum combination of

ction.

DUCTION FUNCTION

function is a function that shows the highest output that a firm can

roduce for every specified combination of inputs. It is a purely technical relation which

onnects factor inputs to outputs. Assuming labor (L) and capital (K) as the only inputs,

e production func here Q stands for the total

uantity produced

produced by

e following processes:

have a edknowl

factors produof

3.3 THE PRO

The production

p

c

th tion can be written as: Q = f(L, K); w

q of an output/product.

The production function allows inputs to be combined in varying proportions so that

output can be produced in many ways (say, using either more capital and less labor, or

more labor and less capital). For example, a unit of commodity X may be

th

Table 3.1: Three Processes for Producing a Unit of X

Process 1 (P1) Process 2 (P2) Process 3 (P3)

Units of Labor 1 2 3

Units of Capital 3 2 4

These activities or methods of production can be shown by lines from the origin to the

point determined by the labor and capital inputs combination.

104

method of production ‘A’ is technically efficient if it uses less of at least one input and

no more of the other facto mpared with any

ther method ‘B’. For example, suppose commodity Y can be produced by two methods

method of production ‘A’ is technically efficient if it uses less of at least one input and

no more of the other facto mpared with any

ther method ‘B’. For example, suppose commodity Y can be produced by two methods

0 2 3 4 L

2

1 P3

K

3

P2

P1

The production function, which is a purely technical relationship that connects factor

inputs and outputs, includes all the technically efficient methods of production. The

technically inefficient methods are not included in the production function.

The production function, which is a purely technical relationship that connects factor

inputs and outputs, includes all the technically efficient methods of production. The

technically inefficient methods are not included in the production function.

Figure 3.1: Alternative Production Processes

AA

rs to produce a given level of output as cors to produce a given level of output as co

oo

(Method A and Method B) as shown below:

Method A Method B

(Method A and Method B) as shown below:

Method A Method B

Labor 2 3

Capital 3 3

If these are considered to be the only methods of production, method A is considered as

technically the efficient method. This is because the two methods, A and B, use the same

amount of capital (3 each), but method A uses less units of labor (2) than B does (3).

105

The basic theory of production concentrates only on the efficient methods, and thus

inefficient methods are excluded as a rational producer will not used them. If a process A

uses less of one factor (say, L) and more of another (say, K) as compared to B, then A

nd B cannot be directly compared on the criterion of technical efficiency. For example, a

the two activities in the table below are not directly comparable.

Method A Method B

Labor 2 1

Capital 3 4

In such cases, both processes are considered as technically efficient and included in the

production function. Which one of them will be chosen at any particular time depends on

the price of factors (inputs). The choice of any particular technique among the set of

chnically efficient processes is an economic one, which is based on the price of factors

ap

te

of production. Note that a technically efficient method is not necessarily economically

efficient.

Isoquants and an Isoquant M

two inputs used to produce an item, the output

chievable for various combinations of inputs can be shown by using isoquants.

n isoquant:

In addition to defining the production function mathematically, it is also common to

depict the technically efficient production processes with the help of isoquants. Assuming

that labor (L) and capital (K) are the only

a

A is the locus of all the technically efficient methods (or all the technically

fficient combinations of factors of production) for producing a given level of output. It

a curve showing all the possible combinations of inputs that yield the same level of

utput. Isoquants may assume different shapes depending on the degree of substitutability

etween the factors of production. The following are the common ones:

e

is

o

b

106

1. Linear isoquant: this type assumes perfect substitutability of factors: a given output

ay be produced by using only labor, or only capital, or by an infinite number of

ombinations of K and L. See Panel (A) of Figure 3.2 below.

uant

m

c

2. Input-output isoq : this assumes strict complementarily (i.e., zero substitutability)

f production. There is only one method of production for producing any

articular level of a commodity. The isoquant takes the shape of a right-angle. This type

f isoquant is also called “Leontief Isoquant” after the name Leontief who invented the

put output analysis. Panel (B) of the figure below depicts such isoquants.

ant

of the factors o

p

o

in

3. Kinked isoqu : this assumes limited substitutability between factors of production,

processes of a

omm y. Substitutability of the factors is possible only at the kinks. See Panel (C) of

.

. Smo or c nvex isoquant

say K and L, and that there are only few for producing a particular amount

c dito

Figure 3.2 be wlo

4 oth o : this form assumes a continuous (and a less than perfect)

bstitutability between factors (K and L) only over a certain range, beyond which factors

nnot substitute each other. The isoquant is a smooth curve which is convex to the

rigin. This is depicted in Panel (D) of the figure below.

ven though the kinked isoquant is more realistic, most of the time the smooth or convex

oquant mic the ly simpler

hand

su

ca

o

E

is is used in the traditional econo ory because it is mathematical

to le by the simple rules of calculus.

107

An Isoq of several isoquants. An isoquant map is another way of

describing a production function, just as an indifference map (discussed in Chapter Two)

ove upward

n isoquant (See points A, B and C in the

An Isoq of several isoquants. An isoquant map is another way of

describing a production function, just as an indifference map (discussed in Chapter Two)

ove upward

n isoquant (See points A, B and C in the

uant map: is simply a set

uant map: is simply a set

is a way of describing a utility function. The level of output increases as we mis a way of describing a utility function. The level of output increases as we m

to the right where as it remains constant along ato the right where as it remains constant along a

O L

K

O L

Panel (A): A Leontief Isoquant

P1

X (Level of Output)

X

K

A Linear Isoquant Panel (B):

P2

P3 X

X

P4

O L O L

K

Figure 3.2: Isoquants of Different Shapes

Panel (C): A Kinked Isoquant Panel (D): A Convex Isoquant

108

figure below; 100 units of good X are produced both at A and C while 50 units are

produced at B).

K

X = 100

B

A

C

O L

X = 50

Figure 3.3: Movement on an Isoquant versus Movement from an

Isoquant to Another

Check Your Progress

n? What is the use of production function in

production analysis?

2. Explain some important/common types of production function.

4. W ves?

itional theory generally assumes the form:

1. What is meant by production functio

3. What are isoquants? Explain their main properties.

hat are the differences between isoquant curves and indifference cur

5. What is the reason behind an isoquant curve that is convex to the origin? When

will an isoquant be straight-line, and when will it be right-angled?

3.4 THE SHORT RUN PRODUCTION FUNCTION AND STAGES

OF PRODUCTION

The production function in the trad

X = f(L, K, r, y)

109

Where L is labor, K is capital, r is returns to scale which refers to the long run analysis of

the laws of production since it assumes change in the plant, and y is the efficiency

parameter related to the organizational and entrepreneurial aspect of the production.

e long run) can be shown graphically, as follows:

the production function shifts upwards. If, for instance, the levels of

e three fixed inputs rise from (k1, r1 and y1) to (k2, r2 and y2), the curve X shifts upward

We usually abstract from the availability of many factors of production to two factors of

production (L and K) only in order to simplify things. In this simplified case, any change

in the amount of factors other than L and K is considered to shift a production function.

The short run production function and its behavior for a change in amount of the fixed

factors (as time goes to th

In Figure 3.4, the quantity of output X produced is drawn as a function of the amount of

labor, for fixed amounts of the other factors. For a given curve (X), as labor increases,

ceteris paribus (the others factors fixed at k1, r1 and y1), output increases and we move

along the curve depicting the production function. If any one or all of the fixed factors

(K, r, y) increases,

th

to X’’, and so on.

O L

X X’’ = f(L)k3,r3,y3

X’ = f(L)k2,r2,y2

Figure 3.4: The Short Run Production Function and How It Shifts as the Amount

X = f(L)k1,r1,y1

of Fixed Factors of Production Change with the Passage of Time

110

The time period for which we assume that some factors are fixed in amount is called the

short run. Thus, curve X in the figure above is drawn for the short run. If we could

increase (or change in general) the amount of all factors, then we are in a long run.

The slope of the production function (say, X = f(L)) is the marginal product of the factor

function X = f(K) is the

m

chan

facto

of production L (MPL) . Similarly, the slope of the production

arginal product of capital (MPK). The marginal product of a factor is defined as the

ge in output resulting from the change in the factor by a unit, keeping all other

rs constant. That is:

LXMPL ∂∂

= andKXMPK ∂∂

= .

G he

PK is shown by the slope of the production function X = f(K). As you remember from

hapter two, the slope of a curve at any one point is the slope of a tangent line at that

oint.

he average product of an input is the total product divided by the units of the input used

produce it. Graphically, the average product of a factor at a given point is given by the

ope of a straight line from the origin to the point.

et’s derive the average product and marginal product of labor from the total product of

bor graphically. By doing so, we will also distinguish among three stages of production.

s shown in Panel (A) of Figure 3.5, as the units of labor used in the production process

oes on increasing, the output initially increases at an increasing rate (up to point A), then

ses at a decreasing rate (from point A to point C), reaches a maximum (at point C), and

en starts falling.

s a result, since marginal product is the slope of the total product curve, the marginal

roduct of labor initially increases, reaches maximum, and then starts declining. The

arginal product of labor (MPL) is even negative when the total product declines (beyond

raphically, the MPL is shown by the slope of the production function X = f(L) and t

M

c

p

T

to

sl

L

la

A

g

ri

th

A

p

m

111

point C). The average product of labor (APL), which is the slope of the line drawn from

e origin t e corresponding point on e total product (TPL) curve, initially increases,

aches maximum (at point Z) and then starts d ing. The APL and MPL curves are

own in Panel (B) of the sam

he following points are clearly reflected in Figure 3.5 below:

Before point Z is ched, in Panel A of the figure, the slope of a tangent line at a

point on the TPL curve is greater than the slope of a line from the origin to the point.

In other words, the MPL is above the APL.

At point Z, where the APL reaches its maximum, the slope of a tangent line at a

point on the TPL curve is greater than the slope of a line from the origin to the point.

PL are equal at the maximum of the APL (Panel B of Figure 3.5).

When TPL curve reaches its maximum (point C in Panel A), the MPL equals zero.

th o th th

re eclin

sh e figure.

T

rea

That is, APL and M

112

Now, let us study the three stages of production. Figure 3.6 below is partly reproduced

from Panel B of the above figure to assist us to this end.

Accordingly, we divide this production function into three stages as: Stage I (from zero

TPL up to the maximum of APL), Stage II (from the maximum of APL to zero MPL), and

Stage III (from zero MPL onwards).

A

B

C

D

Z

X

O LA LZ LB LC LD L

TP = f(L)

MPL

AP

MPL

AP

Panel (A): The TPL Curve

L

A’

C’

Z’

O LZ’ LC’ L

L

Panel (A): The MPL and APL Curves

Figure 3.5: The Relationship among TPL, MPL and APL

113

ile MPL falls latter on.

ince each additional unit of labor is coming up with a contribution larger than the

tion is negative).

Thus, it is in the second stage that a rational firm operates. Here each additional labor

tes positively to the production but less than the average. Where exactly in this

ces.

riable input (labor) increases with other inputs (like capital)

t (MPL) will eventually decrease. This manner

as the law of variable proportions or the law of

At stage I, MPL > APL, and both of them are rising initially wh

S

average (MPL > APL), it is rational to hire more labor and produce more output. Thus, it

is not reasonable to produce at this stage. A rational producer (firm) observes that using

more labor is preferred to the existing situation and thus moves out of this stage.

At the third stage, where both APL and MPL are declining and MPL < APL, it is not

rational to produce at all because each additional unit of labor makes the total product to

decline (i.e. its contribu

contribu

stage does a rational firm produce? The answer is, it depends on factor pri

At this stage as the use of a va

being fixed, the resulting additions to outpu

is captured by a principle known

diminishing marginal returns.

MPL

APL

APL

C’

O LZ’ LC’ L MPL

Z’

Stage I

Stage II

Stage III

Figure 3.6: The Three Stages of Production

114

In summary, the p ficient part of the

roduction function, that is, on the ranges of output over which the marginal

l

ge

roduction theories concentrate only on the ef

p

productivities are positive but declining. The second stage of production in the above

analysis corresponds to this efficient stage in the short run. No rational firm wou d

employ labor less than OLZ’ or beyond OLC’ (in Figure 3.6). This means over the ran

where MPL > 0 but L∂

MPL∂ )( < 0

In the long run, where all factors of production (L and K for simplicity) are variable, we

s to define the rational/efficient stage of production. In this case, the

ex to the origin. In the figure

elow, the production function is depicted by a set of isoquants.

s of points of isoquants where the marginal products of the factors are zero

e ridge line. At points a, b and c, the MPK is zero. This forms the upper ridge

rl the lower ridge line shows the path along which the MPL is zero (points d,

. Outside the ridge lines the marginal product of the factors is negative and the

f output. Thus, production techniques are efficient only

side the ridge lines.

use isoquant

traditional theory of production defines the rational stage of production as the range of

the isoquants over which their slopes are negative and conv

b

The locu

forms th

line. Simila y,

e and f)

methods of productions are inefficient, since they require more quantities of both factors

for producing a given level o

in

Upper Ridge Line (MPK = 0) b

a

c K

Lower Ridge Line (MPL = 0)

e

f

O L

Figure 3.7: The Ridge Lines and the Region of Efficient Production

d

115

The Marginal Rate of Technical Substitution

solute value) defines the degree of substitutability of the

f roduction. As we move downwards along the isoquant, the slope (

The slope of the isoquant (in ab

dLdK

−=factors o p )

tion,

or the marginal rate of technical substitution (MRTS) of factors:

decreases in absolute terms, showing the increasing difficulty in substituting L for K.

The absolute value of the slope of the isoquant is called the rate of technical substitu

isoquantan of slope −==dLdKMRTSLK

is defined as the amount of K that the firm must sacrifice in order to use one

can be proved that the MRTSLK is equal to the ratio of the marginal products of the

factors.

hat is,

MRTSLK

more unit of L so that it produces the same level of output.

It

T

K

LLK MP

MP

KX

LX

dLdKMRTS =

∂∂

∂∂

==

Proof:

The production function can be written as X = f(K,L) = C. It is equal to C because the TP

is constant along an isoquant.

is defined by the total differential. The total differential (dX) is zero along an isoquant

The slope of a curve is the slope of a tangent line at that point. The slope of a tangent line

since the TP is constant. Thus,

0)()( =∂∂

+∂∂

= dLLXdK

KXdX

0)()( =+ dLMPdKMP LK

dLMPdKMP LK )()( =−

116

K

L

MPMP

dLdK

=− which is the definition of the MRTSLK

long the upper ridge line, we have: A

∞==⇒=K

LLKK MP

MPMRTSMP 0

the lower ridge line,

And along

00 ==⇒=K

LLKL MP

MPMRTSMP

The MRTS as a measure of the degree of substitutability of factors has a serious defect

since it depends on the units of measurement of the factors. A better measure of factor

substitutability is provided by the elasticity of factor substitution (σ). It is given by:

LKMRTSinChangePercentage

LKinhangePercentage

=σ

C

)()(

)()d( LK

LKMRTSMd

LK

he elasticity of su t nit of measurement of

h the numerator and the denominator are measured in the same unit.

=σLKRTS

T bsti ution is a pure number independent of the u

K and L since bot

Factor Intensity

Factor intensity refers to a measure of the intensity of a method of production in the sense

that it measures whether a given method of production is labor intensive (uses more labor

tensive (uses mo capital and less labor). It can be measured

by the slope of the line from the origin to a particular point on the isoquant representing a

s r equivalently, it is measured by the capital labor ratio at a particular

and less capital) or capital in re

particular proces . O

point.

117

In the figure belo itw, process P1 is more cap al intensive than process P2 because the slope

of line OP is higher than the slope of line OP or the ratio 1 21L1K is greater than

2L

lies t at the upper part of the isoquant includes more capital intensive techniques

2K . This

imp h

Exa

where as the lower part includes more labor intensive techniques.

mple:

us illustrate the above concepts with a specific form of production function, namely

Cobb-Douglas production function. This form is the most popular in applied research,

ause it is easier to handle mathematically. It is of the form:

cb

Let

the

bec

KALX =

he marginal product of factors: 1. T

cbL KbAL

LXMP 1−=∂∂

=

1)( −= LKALb cb

)(APbL

=

)( Xb=

)( 1LXb= −

P1

P2

K1

K

O L L L

K2

1 2

Figure 3.8: Factor Intensity

L

118

Similarly, )()(1K

cbK APc

KXcKcAL

KXMP ===∂∂

= −

e marginal rate of substitution of labor for capital: 2. Th

cLbKL

Xb

KXcK

XMRTSLK ==L

X

∂∂

=)(

.

3

∂∂ )(

. The elasticity of substitution:

)()(

)( LK=σ

)d( LK

LK

LKMRTS

MRTSd

)()(

)()d(

LKLK

=σ

cLbKcLbKd

)(

)(.)()d(

cLbKdcLbK

LKLK

=σ

)().(

)).(()()d(

LKdcbLKcb

LKLK

•=σ

.1)(

)((

)d(=

LKK

LKσ)

=•LKdL

. Factor intensity: In a Cobb-Douglas function factor intensity is measured by the

ratio

4

cb . The higher the r chnique is and vice atio, the more labor intensive the te

versa.

Given that )(LXbMPL = , we can rearrange to find that )(

LMPXbL = .

Similarly, )(KXcMPK = gives us )(

KMPXcK =

Then, )(

)(

K

L

MPXc

MPXb

KL=

)()( K

MPcMPb

= L

119

LKMRTScb

=

c

The higher the

b= since MRTSLK = 1 (as shown above).

cb ratio means the higher the

KL ratio, and hence the technique is labor-

intensive.

5. The efficiency of production. The effici

production is measured by the coefficient A. It

ency in the organization of factors of

is clear that if two firms have the same

K, L, b and c, and still produce different quantities of output, the difference can be

efficient firm will have a higher A than the less efficient one.

the Cobb-Douglas production function, the returns to scale are

due to the superior organizational and entrepreneurial quality of one firm. The more

6. The returns to scale. In

measured by the sum of the coefficients b + c. This point will be discussed latter on.

Check Your Progress

(c) the upper and the lower ridge lines

2. Define and distinguish between marginal product and average product. Draw the

al product and average product curves from your own hypothetical data. And

check whether there is any relation between them.

nsity? When do we say a technique of production is labor

is capital intensive?

of factor substitution?

1. Distinguish between the following and show their importance in production theory:

(a) short run and long run

(b) variable input and fixed input

margin

3. Define marginal rate of technical substitution. Why does it decrease along the

isoquant?

4. What is factor inte

intensive? When

5. What is elasticity

120

3.5

The

production. This can be done in various ways. Output can be increased by changing all

, output can be increased by changing only the variable input

fixed inputs constant, which is possible in the short run. Let us see

LAWS OF PRODUCTION

laws of production describe the technically possible ways of increasing the level of

factors of production which is possible in the long run. This is called the law of returns to

scale. On the other hand

while keeping the

these laws one by one.

The Law of Variable Proportions

This is a law for the case of short run where there is at least one fixed input. The MP of

the ctor are

ombined with the fixed amounts of other factors. This is known as the law of variable

d stages of

ariable input and capital as a fixed input. From

at graph, what we can understand is that as the use of a variable input (labor) increases

variable factor will decline eventually as more and more quantities of this fa

c

proportions. In our earlier discussion of the short run production function an

production, we have assumed labor as a v

th

with other inputs (capital) fixed, the resulting addition to output will eventually

decreases. This is shown by a downward sloping MPL curve after its maximum point.

This principle is known as the law of variable proportion or the law of Diminishing

returns.

The Law of Returns to Scale

The law of returns to scale refers to the long run analysis of production. In the long run,

here all inputs are variable, output can be increased by changing all factors by the same

w

proportion. The rate at which output increases as inputs are increased by the same

proportion is called returns to scale. We have three cases of returns to scale: increasing,

constant and decreasing returns to scale.

121

Increasing returns to scale: this is the case where increasing all factors by the same

roportion, say m, leads to an increase in output by more than m scale. p

Constant returns to scale: if we increase all inputs by some factor m and output is

incr is called constant returns to

sca ect the productivity of its

fact .

sing returns to scale

eases by the same proportion as inputs, m, and then it

le. In this case the size of the firm’s operation doesn’t aff

ors

Decrea : if scaling up all inputs by m scales output up by less than m,

may be difficulties in organizing

eration leads to decreased productivity of both labor and

it is called decreasing returns to scale. This is because,

and running a large scale op

capital.

Examples:

1. Suppose Q = 2K + 3L. To tell the returns to scale, we will increase both K and L by a

factor m and create a new production function Q*. Then we will compare Q* and Q.

Q* = 2(mK) + 3(mL)

, we can replace (2K + 3L) by Q, as we were given that from the start.

Since doing so gives Q* = mQ, we note that by increasing all of our inputs by the

r multipliers and create our new production function.

Q* = 0.5(mK)( mL)

n m2 > m. Th r new production has

y more than m. so we have increasing returns to scale.

. Q = K0.3L0.2. Again we put in our multipliers and create our new production function.

= 2mK + 3mL

= m(2K + 3L)

= mQ.

After factoring

multiplier m, we have increased production exactly by a factor of m. So we have

constant returns to scale.

2. Q = 0.5KL. Again we put in ou

= 0.5KLm2

= Qm2. Since m > 1, the is implies that ou

increased b

3

122

Q* = (mK)0.3(mL)0.2

= K0.3L0.2m0.5

= Qm0.5. Since m > 1, then m0.5 < m. So we have decreasing returns to scale.

.6 RETURNS TO SCALE AND HOMOGENEITY OF THE

PRODUCTION FUNCTION

uppose we increase both factors of production in the function X = f(L,K) by the same

roportion m, and we observe the resulting new level of output X* as X* = f(mK,mL). If

can be factored out (that is, can be taken out of the bracket as a common factor), then

tions since m can be

ctored out in each case.

hus, a homogeneous function is a function such that if each of the inputs is multiplied

b

the degree of homogeneity and is a measure of the returns to scale.

urns to scale.

If n > 1, we have an increasing returns to scale.

e is measured by

e sum of the powers of the factors. That is,

3

S

p

m

the new level of output can be expressed as a function of m (to the power n) and the

initial level of output X as follows: X* = mnf(L,K) or X* = mnX. If so, the function is

called homogeneous. If m cannot be factored out, the production function is called non-

homogeneous. The above three examples are homogeneous func

fa

T

y m, then m can be completely factored out of the function. The power n of m is called

If n = 1, we have a constant returns to scale.

If n < 1, we have a decreasing ret

Given a Cobb-Douglas production function X = ALbKc, returns to scal

th

If b + c = 1, then there is a constant returns to scale.

If b + c > 1, then there is an increasing returns to scale.

If b + c < 1, then there is a decreasing returns to scale.

Proof

L and K increases by m. The new level of output iLet s

123

Thi

sca um.

duct curve passes thro h the origin if both factors are variable. But if only one

factor is variable (the other being kept constant), the product line is a straight line parallel

X* = A(mL)b(mK)c

= AmbLbmcKc

= Amb+cLbKc

= mb+c(ALbKc)

X* = mb+c(X)

s implies the function is homogeneous of degree b+c and the type of the returns to

le depends on the s

Product Line: It shows a physical movement from one isoquant to another as we change

either both factors and a single factor. It describes the technically possible alternative

paths of expanding output. What path will actually chosen by the firm will depend on the

prices of factors.

The pro ug

to the axis of the variable factor.

124

Product Lines Product Lines Product Line

O L O L O L

K K K

Panel (A): Product Lines Panel (B): Product Lines for Panel (C): A Product Line

where K is Fixed

K

for a Homogenous Function a Non-Homogenous Function

erent Kinds of Product Lines Figure 3.9: Diff

A special type of product line which is the locus of points of different isoquants at which

e MRTS of factors is constant is called an isocline. For homogeneous production

nctions, the isoclines are straight lines through the origin. In such a case, the K/L ratio

constant along any isocline (refer to the Panel A of Figure 3.9).

th

fu

is

Check Your Progress

1. What is the law of variable proportions? How does it differ from the laws of returns

2. How is the degree of homogeneity of a production function related to the returns to

TIMAL

BINATION OF FACTORS OF PRODUCTION

Max . In this case, total cost and prices are

given and the problem may be stated as follows:

Max П = R – C = PxX – C

П (profit) is achieved in this case if X (quantity of output) is

maximized, since C (cost) and Px (price of the product) are constants.

II. Maximize profit for a given level of output.

П = R – C = PxX – C

Clearly in this case maximization of profit is achieved by minimizing cost, since X

and Px are given.

of the firm graphically, we will use the isoquant map and the

isocost lines. As discussed earlier, an isoquant is a curve that shows the various

to scale?

scale of the production function?

3.7 EQUILIBRIUM OF THE FIRM: CHOICE OF OP

COM

A firm is said to be in equilibrium when it employs those levels of inputs that will

maximize its profit. This means the goal of the firm is profit maximization (maximizing

the difference between revenue and cost). Thus the problem facing the firm is that of

constrained profit maximization, which may take one of the following forms:

imizing profit subject to a cost constraintI.

Clearly maximization of

Max

To derive the equilibrium

125

combinations of K and L that will give the same level of output. It is convex to the origin

whose slope is defined as:

KMPLMP

KX

LXdK

dL=

∂∂

∂∂

=−

The

C = rK + wL;

where w = wage rate, and r = price of capital services.

ors of production in absolute terms,

isocost line is defined by the cost equation:

The isocost line is the locus of all combinations of factors that the firm can purchase with

a given monetary cost or outlay. The slope of the isocost line is equal to the ratio of the

prices of the factrw

− .

From the isocost equation given by: C = wL + rK

=>

=> rK = C - wL

Lrw

rCK −= .

From this the slope is r

− w

Now, let us see how the equilibrium of the firm is determined in the two cases mentioned

above.

KrC

O L wC

Figure 3.10: An Isocost Line

126

Case 1: Maximization of Out Subject to a Cost Constraintput

Given le will be in

utput it prod e . This is at the point of

tangency of the isocost line to the highest possible isoquant curve.

) are desirable but not attainable due to the cost constraint. Other

oints below the isocost line lie on a lower isoquant than X2. Hence X2 is the maximum

d given the above a umptions (C, w, r and Px being constant).

the vel of cost and the price of the factors and output, the firm

equilibrium when it maximizes the quantity of o uc s

In the following graph (Figure 3.11), the equilibrium of the firm is obtained at point e,

where the firm produces X2 with K1 and L1 units of the two inputs. Higher levels of

output (to the right of e

p

output that can be achieve ss

At the point of tangency:

a. Slope of isoquant = slope of isocost

rw

− LKK

L MRTSMP

== . This is a necessary condition for profit maximization.

b. The isoquant is convex to the origin. This is the sufficient condition for profit

maximization.

MP

K

K1

L L O

X

1

X2

e X3

1

Figure 3.11: Maximizing Output subject to Cost

127

The mathematical derivation of the above equilibrium condition is as follows. A rational

roducer seeks the maximization of its output, given total cost outlay and the prices of

ctors. That is,

Maximize X = f (K, L) subject to C = wL + rK

his is a constrained optimization which can be solved by using the Lagrangean method.

he steps are:

a. Rewrite the constraint in the form:

wL + rK – C = 0

b. Multiply the constraint by a constant λwhich is the Lagrangean multiplier:

λ(wL + rK – C) = 0

c. Form the composite function:

Z = X – λ(wL + rK – C)

d. Partially d

multiplier, and then equate to zero.

p

fa

T

T

ifferentiate the function with respect to each factor as well as the

* 0=−∂∂

=∂∂ w

LX

LZ λ

wMPL λ=

w

=λ …………………………………………………………………… (1) MPL

* 0=−∂

=∂ rXZ λ

∂∂ KK

rMPK λ=

rMPK=λ …………………………………………………………………… (2)

* 0=−+=∂∂ CrKwLZ

……………………………………………………………… (3)

λ

CrKwL =+

From e ioquat ns (1) and (2) we understand that: rw

MPMP KL = or LKKMPr

L MRTSMPw==

128

This sh s e marginal

shown that e econd order conditions

for the equilibrium of the firm require that the marginal product curves of the two factors

ow that the firm is in equilibrium when it equates the ratio of th

productivity of each factor to its price. It can be th s

have a negative slope.

,0)(2

2

<∂∂

=∂

∂LX

LMPL Slope of the MPL =

and ,0) Slope of the MPK = (2

2

<∂∂

=∂

∂K

XK

K MP

.).

(. 22

2

2

2

2

KLX

LX

LX

∂∂∂

<∂∂

∂∂

Case 2: Minimization of Cost for a Given Level of Output

quant and the lowest possible isocost line, and the

i u

the desired level of output, but we have a set of isocost lines.

Curv a lower total cost outlay. Since isocosts are drawn on the

ssumption of constant prices of factors, they are parallel to each other and their slopes

The condition for the equilibrium of the firm is formally the same as in case 1. That is,

there must be tangency of the given iso

soq ant must be convex. However, in this case we have a single isoquant which denotes

es closer to the origin show

a

(rw

− ) are equal.

Thus, the firm minimizes its cost by employing the combination of K and L determined

by e isocost li e. Points below

e in Figure 3.12 below are desirable because they show lower cost but are unattainable

o t X. Points above e show higher costs. Hence, point e is the least cost point.

the point of tangency of X isoquant with the lowest possibl n

for utpu

129

In this case also, the Lagrangean method can be followed to derive the equilibrium

condition mathematically. But the problem is different. That is,

Minim

a. The Lagrangean function will be:

Z

b. Partially differentiate Z with respect to L, K and λ and equate to zero.

*

K

ize C = wL + rK subject to X* = f(K,L)

= (wL + rK) + λ[X*- f(K,L)]

0),(=

∂∂

−=∂∂

LKLfw

LZ λ

LMPw .λ=

LMP

w=λ …………………………………………………………………… (1)

* 0),(=

∂∂ KK

KMPr .

∂−=

KLfrZ λ ∂

λ=

KMP

r=λ …………………………………………………………………… (2)

* 0 ),(* =−=∂∂ KLfXZλ

…………….………………………………………………… (3) ),(* KLfX =

K1

X

L

Figure 3.12: Minimizing Cost for a Given Level of Output

1 L O

e

130

From equations (1) and (2) we understand that: KL MP

rMP

w= or LK

K

L MRTSMPMP

rw

==

s is the same as the conThi dition in case one. In a similar way, the second condition will

e: b

Slope of the MPL = ,0)(2

2

<∂∂

=∂ L

XL

∂ MPL

Slope of the MPK = and ,0)(2

2

<∂∂

=∂

∂K

XK

MPK

.).

(. 22

2

2

2

2

KLX

LX

LX

∂∂∂

<∂∂

∂∂

Th

discussed above.

E

are r

a. the level of output for a total

b. inimize the cost of the firm for producing

53,747,712 units of output.

olution:

. Maximize subject to

e following numerical example clarifies the optimization of a firm for the two cases

xample: If the production function of a firm is given by ,32 LKQ = and the input prices

= Birr 8 per unit and w = Birr 2 per unit,

Find the levels of labor and capital that maximize

outlay of Birr 240.

Find the units of labor and capital that m

S

a 32 LKQ = KL 82240 += , with respect to L and K.

The equilibrium condition (from case 1 above) is given by: .K

L

MPMP

rw=

,3 22 LKLL ∂QMP =∂

= and .2 31LKKQMPK =∂∂

=

Thus, KMPrLMPw

= .28

323

22

KLLK

=⇒

131

L24K31

=⇒ .62

22

12212 KLLKLK =⇒=⇒=⇒

Substitute KL 6= into the budget constraint: KL 82240 += and solve.

12 =⇒ 20

20

240 8122408)6(224082 +=⇒+=⇒+= KKKKKL

20240 =⇒

20240 =⇒

K

K

Sinc

K

e L = 6K, we also have 6 =⇒= LKL .72)12(6 =

The p ital under the given constraints (or, the

optim or and capital) are L = 72 units and K = 6 units.

b. Mini h respect to L and K.

The

out ut maximizing levels of labor and cap

um combination of lab

mize KLC 82 += subject to 712,747,5332 == LKQ , wit

equilibrium condition (from case 2 above) is given by: .K

L

MPrw=

MP

,3 22 LKL

PL =∂

= and QM ∂ .2 31LKK

MPK =∂Q∂

=

Thus, K

L

MPr=

MPw .28 3KL

=⇒ 32 22 LK

L24

=⇒K31 .6

2212 LK

2212 LK ⇒=⇒ KL =⇒=

S and solve. ubstitute KL 6= into the output constraint: 712,747,5332 == LKQ

122488325 =

248832

2

63

=

⇒

⇒

⇒

⇒

=

K

K

KK

LQ

=L

The evels of labor and capital under the given constraints (or, the

o and capital) are L = 72 units and K = 6 units.

712,747,53)(712,747,53

32 =KK 32 =

712,747,5316 5 =K 712,747,5365 =

216==

712,747,535

Hence, .72)12(66 == K

cost minimizing l

ptimum combination of labor

132

Verify that the second order conditions are fulfilled in both cases!

Check Your Progress

1. ze production given a fixed total

outlay? sary condition required for minimizing cost for a

giv e

3.8 LESS

Firms produce outputs by combining inputs. The

en profit private sector

a n profit

fi the

P u elationship between factors of production and

o

In e g-run, all factors are variable.

In the short-run, as variable factors are added to the fixed factor, the firm may

tput but eventually will incur

d levels of output.

F s on to maximize output

su

What is the necessary condition for a firm to maximi

Is this the same as the neces

en l vel of output?

ON SUMMARY

are organized by entrepreneurs to

trepreneur does this in such away as to maximize profit. Non-

nd on-profit governmental enterprises face different incentives than for-

rms. We are concerned with for-profit firms. The single proprietorships are

dominant form of business organization by number.

rod ction function is the technical r

utputs.

th short-run, some factors are fixed; but in the lon

experience increasing returns at low levels of ou

iminishing returns at some higher

irm choose their input mix from the production functi

bject to cost constraints.

133

3.9 RE I

I. Choose the Best Answer

V EW QUESTIONS

1. :

ly of certain inputs is perfectly inelastic

c. in which supply of all inputs is perfectly inelastic

d. None of the above

2. Long run is period:

a. which is longer than three years

b. in which supply of labor is elastic

c. in which supply of all inputs is elastic


3. When total production increases at a constant rate, then

a. average and marginal output increase at the same rate

b. average product increases faster than the marginal product

c. marginal product increases faster than the average product

d. marginal product equals average product

4. When total production increases at increasing rates, then

a. average and marginal output increase at the same rate

b. average product increases faster than the marginal product

c. marginal product increases faster than the average product

d. marginal product equals average product

5. In case of a convex isoquant, as we move from left to right, MRTSLK:

a. decreases at a decreasing rate,

b. decreases at increasing rate,

c. neither increases nor increases,

d. increases along the isoquant.

6. When an isoquant is L-shaped, then

a. MRTSLK = 0

Short run is a period

a. less than one year

b. in which supp

134

b. MRTSLK > 1

c. MRTSLK < 1

d. MRTSLK = 1

7. When MRTSLK = 1, then

b. MPL / MPK = 1

PK =0

proportion are associated with:

ts

input is decreasing.

input is increasing but at a decreasing rate.

c. quantity of output is either decreasing or increasing at a decreasing rate

is either decreasing or increasing at an increasing rate

10. The law of diminishing returns comes into force because of:

ale apply only when there is:

a. a change in one input only.

a. MPL / MPK = 2

c. MPL / M

d. MPL / MPK = ∞

8. Laws of variable

a. change in the variable input

b. change in all the inpu

c. change in return to scale


9. The law of diminishing returns implies that:

a. quantity of an

b. quantity of an

d. quantity of output

a. indivisibility of variable input

b. indivisibility of fixed factors

c. indivisibility of both variable and fixed factors

d. indivisibility of products

11. Laws of returns to sc

b. proportionate and simultaneous changes in all inputs.

c. disproportionate change in inputs

d. more than proportionate changes in outputs

12. A Cobb-Douglas production function shows:

a. A constant returns to scale,

b. An increasing returns to scale,

135

c. A decreasing returns to scale

d. One of the three returns to scale

13. The laws of variable proportions and the laws of returns to scale:

a. Are exactly the same

c. Of any form

b. Are different and have no similarity

c. Are similar but not exactly identical.

d. No answer

14. Expansion path is a strait line when production function is:

a. Homogeneous

b. Non-homogeneous

136

CHAPTER FOUR

THE THEORY OF COST

duct Curves and Cost Curves in the Short Run

Long-Run Costs

Questions

In the previous chapter, we saw the laws of

the amounts of input(s) are changed. The laws s of

physical quantities, e.g., labor as num

achinery, and output as unit or some other measurements of output, e.g., tones or

rding price and production are taken on the basis of money

r we go beyond the technical analysis of the

– theories of production – and look at the economic analysis in firms’

aking process. The two chapters (chapter three and four) together make up a

plete discussion of the behavior of business firms. Do you recall that, in the theory of

consumer behavior of Chapter Two, we derived the demand for a commodity? As you

LESSON STRUCTURE

4.1 Introduction


4.3 Short-Run Costs

4.4 The Relationship between Pro

4.5

4.6 The Relationship between Short-Run and Long-Run Average and Marginal Costs

4.7 Derivation of the Cost Function from the Production Function

4.8 Dynamic Changes in Costs – The Learning Curve

4.9 Lesson Summary

4.10 Review

4.1 INTRODUCTION

production, i.e., how output is changed when

of production are expressed in term

ber of workers, capital as unit of plants or

m

quintals of wheat.

However, most decisions rega

value of inputs and outputs. In this chapte

theory of the firm

decision m

com

137

complete this chapter, you would be ready to derive the other component of a market –

e s commodity, and to bring together the two sides (the demand and supply

des) of a market in the subsequent chapters.

ost functions are derived functions (derived from production functions). Economic

eory distinguishes between short-run and long-run costs. Both in the short-run and in

e long-run, total cost is a multivariate functio otal cost is determined by many

ctors such as output, technology, prices of variable and fixed factors. To simplify the

nalysis, we consider cost as a function of output [C = f(X)] on a ceteris paribus

ssumption. Thus, determinants of costs, other than output, are called shift factors.

.2 CHAP R OBJECTIVES

fter studying this lesson thoroughly, you would be able to:

understand the theory of cost;

product curves and cost curves

d marginal costs; and

4.3 SHORT-RUN COSTS

In t

at least one input (factor of production) cannot be changed. Practically, this is a time

eriod that is so short that the firm cannot alter its current plant size. In other words,

th upply of a

si

C

th

th n, i.e., t

fa

a

a

4 TE

A

differentiate between short-run costs and long-run costs;

know the details of the relationship between the following pair of concepts:

average total cost and average variable cost

marginal cost and average total cost

marginal cost and average total cost

short-run and long-run average an

derive the cost function from the production function.

heory of the firm, the short run is defined as any time period in which the quantity of

p

during the short run, a firm works with whatever heavy equipment and factory size it

already has. No matter how much more it wants to produce, say because of an increase in

138

the demand for its product, it cannot change its plant size in the short run. However, it

may change the amount of other inputs like labor. Thus, in the short run, we have two

types of inputs – fixed inputs and variable inputs.

The following are the types of cost a firm incur to produce a given good in the short run:

Total Costs (TC): are all costs of a firm incurred to produce goods and services. The

total cost (TC) includes both implicit costs (sacrifices) and explicit (out of pocket) costs.

The total cost can be divided into two: the Total Fixed Cost (TFC) and the Total Variable

Cost (TVC), i.e., TC = TFC + TVC

Total Fixed Costs (TFC): are those costs that must be incurred by the firm whether or

ot production takes place, or whether the firm produces less or more quantity of a given

nchanged.

xamples of the fixed cost include:

Property tax,

Fire insurance

Salaries of the administrative staff, say, salaries of a secretary and a guard,

Payments for the land (rent) and expenses for land maintenance,

s for depreciation and repairs (of machinery, building, etc).

raphically, the total fixed cost can be depicted as follows:

n

product. In other words, these are costs that do not fluctuate/vary with the level of output;

whether the firm changes (increases or decreases) its production level or not, they remain

u

E

Expense

G

139

C= Cost

TTotal Variable Costs (TVC): are the costs of production th

140

otal Variable Costs (TVC): are the costs of production that vary with the level of

utput the firm produces. Unlike the total fixed costs, these costs depend on the level

mount) of output produced. If the firm wants to increase its production, it must use

ore of the variables inputs and incur more variable costs. If there is no production, there

ill be no va le input used, and thus, there won’t be any variable cost incurred.

xamples of the total variable costs include:

n agriculture

Electricity bills,

Wage payments for direct labor,

Q

TFC

O

Figure 4.1: The Total Fixed Cost

o

(a

m

w riab

E

Payments for raw materials used for production (like cotton in textile factory,

seed i , etc.),

The running expenses of fixed capital, such as fuel, ordinary repairs and routine

maintenance.

The total variable cost has usually an inverse-S shape, which reflects the law of variable

proportions. According to this law, at the initial stage of production with a given plant

140

size, as more of the variable factor is employed, its productivity increases and thus total

variable cost(TVC) increases at a decreasing rate. For example, to increase the level of

output by one unit may require one more worker, and if the price of this additional

worker (the wage rate) is 10 Birr (per given period of time), the TVC increases by 10

s the pr ivity of the variable input (labor) falls, larger and larger units of the

ill be needed to increase output by the same unit. To continue with our

ypothetical example, two more workers may be needed to increase output by a unit in

ses by 2x10 = 20 Birr. Thus, the total variable cost (TVC) first

creases at a slower rate and then increasing rate because of the law of variable

a ter Three).

ince the TC is the sum of the TFC and the TVC, and as the TFC doesn’t change, the TC

ehaves just like the TVC. Figure 4.2 below shows the TC, TFC, and TVC curves a firm.

Birr.

A oduct

variable input w

h

which case the TVC increa

in at an

proportions (discussed pin Ch

S

b

Cos TC

TVC

TFC

Output (X) O

t

Figure 4.2: The TC, TVC and TFC Curves

141

From the total fixed cost, the total variable cost and the total cost curves, we obtain the

average fixed cost, the average variable cost and the average (total) cost curves

respectively.

Average F eix d Cost (AFC): is the total fixed cost divided by the amount of output, i.e.,

X

TFCAFC = .

n increase in X reduces the ratioX

TFCSince TFC is constant, a , and thus the AFC

approaches the quantity (output) axis as output rises. This is depicted in Figure 4.3 below.

Average Variable Cost (AVC): is the total variable cost divided by the level of output,

Cost

O X

AFC

Figure 4.3: The Average Fixed Cost (AFC) Curve

i.e., X

raphica e AVC at a given level of output is equal to the sl line drawn from

e origin to the point on the TVC curve corresponding to the particular level of output.

or example, in Figure 4.4 below, the AVC at X is the slope of the ray OA; and

milarly, the AVC at X2 is the slope of the ray OB; and so on. It is clear from the figure

that the slope of a ray through the origin de es continuously until the ray becomes

TVCAVC = .

G lly, th ope of a

th

F 1

si

clin

142

tangent to the TVC curve at point C. To the right of this point the slope of ray through the

falls initially as the productivity of the

erated optimally and

he graphical derivation of the ATC curv e way as the derivation of

e AVC curve. That is, the ATC at any on

origin starts increasing. Thus, the AVC curve

variable factor increases, reaches a minimum when the plant is op

ses beyond that point. ri

O X1 X2 X3 X4 X

A B

C

D

Cost TVC

($)

O X1 X2 X3 X4 X

AVC Cost ($)

Figure 4.4: Deriving the AVC Curve from the TVC Curve

C

A

B D

T e is done in the sam

e level of output is the slope of a line from the th

143

origin to the point on the TC curve corresponding to the level of output. Like the AVC

urve, the average (total) cost (AC or ATC) curve is also U-shaped, reflecting the law of

ariable proportions.

c

v

Note that: AVCAFCX

TVCX

TFCX

TVCTFCX

TCATCorAC +=+=+

==

arginal Cost (MC): is the additional/extra cost incurred in order to produce one more

nit of output. That is,

M

u

)()(

XdTCdMC =

It is straight forward to prove that marginal cost could be defined as the change in the

total variable cost for a unit increase in output, i.e.,)()(TVCdMC = .

Xd

Proof:

)()(

XdTCdMC = (As defined earlier)

.)()(MC

cost) fixedin ange)(

TVCdXd

=

l of production is the slope of the TC curve

hich of course is the same at any point as the slope of the TVC). The slope of the TC

comes flatter and flatter as

output expands up to X3 level of output, and then becomes steeper and steeper as the

output goes on increasing. This means that the slope of the TC (or TVC) curve (MC)

ch no is there(Since )(0

)()(

)()(

)()(

TVCdXd

TVCdXd

TFCdXd

TVCTFCdMC

+=

+=

+=

Xd

Graphically, the marginal cost at a given leve

(w

curve at any one point is the slope of a tangent line at that point. As we can see from the

following graph (Figure 4.5), the tangent line initially be

144

initially decreases, reaches a minimum, and then starts increasing. Thus, the MC curve is

also U-shaped.

In summary, the traditional theory of cost postulates that in the short run the average and

arginal cost (AVC, ATC and MC) curves are U-shaped, reflecting the law of variable

proportions. In the short run with a fixed plant there is a phase of increasing productivity

(falling unit costs) and a phase of decreasing productivity (increasing unit costs) of the

variable factor. Between these two phases of plant operation, there is a single point at

hich unit costs are at a minimum. In general, these short run cost curves are as shown

Cost ($)

c

d

m

w

in Figure 4.6 below.

O X1 X2 X3 X4 X

a

b

MC

d

TVC

Cost ($)

a

b

c

O X X2 X3 X4 X

Figure 4.5: Deriving the MC Curve from the TVC Curve

1

145

Fig tween the following pairs: AVC and

AT d below.

(A) The Relationship between AVC and ATC

Cost ($) AC

MC

AVC

AFC

c

a

b

O XM XV XT X

Figure 4.6: The Short Run Unit Cost Curves

ure 4.6 above also shows various relationships be

C; ATC and MC; and AVC and MC. These relationships are discusse

The AV AVC and ATC are U-shaped,

flecting the law of variable proportions. However, the minimum point of the ATC

ATC declines. But later on, the rise in the

VC more than offsets the fall in the AFC and thus the ATC will start rising. The AVC

be

elationship between MC and ATC

C is a part of the ATC: ATC = AFC + AVC. Both

re

occurs to the right of the minimum point of the AVC. This is due to the fact that ATC

includes AFC which falls continuously with increase in output. Initially, the fall in the

AFC offsets the rise in the AVC and thus the

A

approaches the ATC asymptotically as X increases since the AFC, which is the difference

tween the two, declines continuously.

(B) The R

146

Th

producing an extra unit of output. To illustrate the relationship, assume that we start from

a l

If

production of the (Xn+1)th unit. That is, MC = TCn+1 – TCn.

Th

of Xn

e MC cuts the ATC at its minimum point. We said that MC is the change in TC for

evel of Xn units of output.

we increase the output by one unit the MC is the change in TC resulting from the

e AC at each level of output is found by dividing TC by X. Thus, the ATC at the level

is:

n

nn X

TCATC =

And at the level of Xn+1:

1

11

+

++ =

n

nn X

TCATC .

Clearly, from the first relationship above, TCn+1 = TCn + MC.

n+1 will be smaller than the ATCn. On the other hand, if the MC of the

(Xnth unit is higher than ous Xn units), the ATCn+1 will

be higher than the ATCn.

far as the MC is below the ATC (i.e., MC < ATC), it pulls the ATC

downward; and, whenever the MC is above the ATC (i.e., MC > ATC), it pulls the latter

upward. From this, it follows that the MC curve intersects the ATC at the minimum point

TC.

b tween the ATC and the MC can also be proofed by using a simple

Thus, if the MC of the (Xn+1)th unit is less than the ATCn (the ATC of the previous Xn

units), the ATC

+1) the ATCn (the ATC of the previ

In general, as

of the A

This relationship e

calculus:

XATCTCX

TCATC •=⇒= )( , and From

)()(TCdMC = by definition.

Xd

147

ATC) theof (SlopeX MC )(

)()()(

)()(

)()(

•+=

•+•=

•=

=⇒

ATCXd

ATCdXXdXdATC

XdXATCd

XdTCdMC

Given that X and ATC are positive, the last line above shows that:

MC < ATC if the slope of ATC is negative.

MC = ATC if slope of ATC = 0, (at the minimum of the ATC).

MC > ATC if slope of ATC > 0.

(C) The Relationship between MC and AVC

s similar to the relationship between MC and

TC seen above; the MC curve intersects the AVC curve at the minimum point of the

tter one.

The relationship between MC and AVC i

A

la

From XAVCTVCX

TVC•=⇒= )( , and

AVC

TFC.in change no is therebecause )()(

)()(

)()(

XdTVCd

XdTVCTFCd

XdTCdMC =

+==

AVC) theof (SlopeX MC )(

)()()(

)()(

)()(

•+=

•+•=

•=

=⇒

AVCXd

AVCdXXdXdAVC

XdXAVCd

XdTVCdMC

Given that X and AVC are positive line above shows that:

MC < AVC if the slope of AVC is negative.

, the last

148

MC = AVC if slope of AVC = 0, (at the minimum of the AVC).

MC > AVC if slope of AVC > 0.

.4 THE RELATIONSHIP BETWEEN PRODUCT CURVES AND

COST CURVES IN THE SHORT RUN

short, assuming that there is only one variable factor of production, the average

va oduct; and similarly, the marginal cost

is product.

That is, if :

e f labor (APL) rises, the average variable cost of

e product of labor (APL) falls, the average variable cost of

rises;

product of labor (APL) is at its maximum, the average variable

AVC) is at its minimum;

when the marginal product of labor (MPL) rises, the marginal cost of production

when the marginal product of labor (MPL) falls, the marginal cost of production

he mathematical proofs of the above inverse relationships between average product and

4

In

riable cost is the mirror image of the average pr

the mirror image of the marginal

labor is the only variable factor of production, the following relationships hold

wh n the average product o

production (AVC) falls;

wh n the average

production (AVC)

when the average

cost of production (

(MC) falls;

(MC) rises; and

when the marginal product of labor (MPL) is at its maximum, the marginal cost of

production (MC) is at its minimum.

T

marginal product of labor on the one hand and the average variable cost and marginal

cost on the other hand are as follows.

Given TVC = w.L, where w = the market wage rate (assumed fixed) and L = the quantity

of labor input.

149

QLw

QTVCAVC .

==1. , where Q is the level of output

LAPw

QLw

1.

.

=

=

AVC⇒

LAP

wAVC =⇒

2. Q

TVCQ

TCMC∂

∂=

∂∂

=)()( ,

Q

wQ

MC∂

=∂

=⇒ . because w is a constant (fixed).

LLw ∂∂ ).(

LMPw 1.=

LMP

C =

he same set of relationships is shown graphically:

wM⇒

Below, t

150

APL MPL

A B

Check Your Progress

1. Why is the cost function a derived function?

2. Distinguish between/among:

a. The short run total fixed cost, total variable cost and total cost.

The short run average fixed cost, average variable cost and average total cost.

Implicit and explicit costs

3. Discuss the relationship between each of the following pairs (in the short run).

b.

c.

151

a. MC and AVC

b. MC and ATC

c. MC and MPL

d. AVC and APL

. 5 LONG-RUN COSTS

he long-run is a period of time of such length that all inputs are variable. It is a planning

orizon in the sense that economic agents can plan ahead and choose many aspects of the

), doubling

utput requires doubling of inputs, which implies doubling of total output (cost) for given

we consider the case where total cost first increases at a deceasing rate due to

creasing returns to scale (which implies economies of scale), and then increases at an

creasing rate attributed to decreasing returns to scale after the optimum size, the long-

4

T

h

“short-run” in which they will operate in the future. Thus, the long-run consists of all

possible short-run situations among which an economic agent may choose.

If a production technology is characterized by constant returns to scale (CRS

o

factor prices. Hence, the long-run total cost curve in this case is a straight line through the

origin. This implies that the long-run average and marginal cost curves are horizontal

lines and are identical (i.e., LAC = LMC).

LT

LMC = LAC

O Q O Q

Figure 4.8: The Long-Run Total, Average and Marginal Cost Curves under CRS

C LTC LMC

If

in

in

152

run total cost curve will look like the following. Consequently, the LAC and LMC curves

ill be U-shaped.

scale, which means output can be doubled for less than doubling of cost.

he range to the right of the minimum point of the LAC curve is called the range of

ant size. With this plant size all

ossible economies of scale are fully exploited. If the firm expands production further

are

verworked and the decision making process becomes less efficient.

w

LTC

LTCLAC LMC LMC

LAC

The range to the left of the minimum point of the LAC curve is called the range of

economies of

O Q O Q

Figure 4.9: The Long-Run Total, Average and Marginal Cost Curves

T

diseconomies of scale, because a doubling of output requires more than a doubling of

cost.

The traditional theory of the firm assumes that economies of scale exist only up to a

certain plant size, which is known as the optimum pl

p

than this optimum size, there are diseconomies of scale arising from managerial

inefficiencies. It is argued that management becomes highly complex, managers

o

When a firm is producing an output level along the falling part of the LAC curve, the

LMC is less than the LAC. Conversely, when the LAC curve is rising, the LMC is greater

153

than the LAC. The two curves intersect at the point where the LAC curve achieves its

minimum.

Like the short run average cost (SAC) and short run marginal cost (SMC) curves, the

LAC and the LMC curves are also U-shaped. But the reason behind the U-shape of the

long run curves is different from the reason behind the U-shape of the short run curves. In

the long-run, the source of the U-shape is increasing and decreasing returns to scale,

ther than diminishing returns to a factor of production which is the source of the U-

ape fro the short run.

.6 THE RELATIONSHIP BETWEEN SHORT-RUN AND LONG-

RUN AVERAGE AND MARGINAL COSTS

ssume that a firm is uncertain about the future demand for its product and is considering

ree alternatives plant sizes: Small, Medium and Large. The short-run average cost

urves are SAC1, SAC2 and SAC3 as shown in the figure below.

ra

sh

4

A

th

c

If the firm expects that the demand will expand further than Q1, it will install the medium

plant, because with this plant outputs larger than Q1 are produced with a lower cost. For

O Q1 Q1* Q2 Q2

* Q

Cost ($)

AC1

AC2

AC1*

AC2*

Figure 4.10: Short Run Average Cost Curves and the Long Run Average Cost

SAC1

SAC2 SAC3

154

instance, the average cost of producing Q1* units with the medium plant (AC1

*) is less

than the average cost of producing the same units with the small plant (AC1).

Similar considerations apply for the decision of the firm once the level production passes

Q2. For instance, the average c with the large plant (AC2*) is

ss than the average cost of producing the same units with the medium plant (AC2).

Thus, the firm follows the path which is drawn in bold in the figure above. This bold

e

If we relax the assumption of the existence of only three plant sizes and assume that there

i v tain a continuous curve, which is

e planning LAC curve of the firm.

oducing various

lanning curve because the firm decides what plant size to set up

um cost on the basis

aped and it is often called the envelop curve because

ost of producing Q2* units

le

nvelope is thus the long run average cost curve for the case of three plant sizes assumed.

s a ery large (an infinite) number of plant sizes, we ob

th

Cost ($)

SAC4

SAC7 LAC

SAC1SAC2

SAC5

SAC6

SAC3

The LAC curve is the locus of points denoting the least cost ways of pr

levels of output. It is a p

in order to produce optimally the expected level of output at minim

of this curve. The LAC curve is U-sh

it envelopes the short run curves.

O Q* Q

Figure 4.11: The LAC Curve as an Envelope of Var

M

ious SAC Curves

155

Because there are economies of scale and diseconomies of scale in the long-run, the

minimum points of the short run average cost curves (plants 1 up to 3, and 5 up to 7 in

the figure above) do not lie on the long-run average cost curve. For example, a plant size

of 2 op ing at its m

advantage of increasing returns to scale to produce the same level of output at a lower

averag o

Each p o curve.

The point of tangency occurs on the falling part of the SAC curves for points lying to the

left of M, i.e., for the plant sizes such as 1, 2 and 3. Since the slope of the LAC is

negativ cause at the

lope.

um.

t the falling part of the LAC curve the plants are not worked to full capacity. To the

The LMC is derived from the SMC curves but does not envelop them. The LMC is

formed from points of intersections of the SMC curves with vertical lines drawn from the

points of tangency of the corresponding SAC and the LAC curve. Figure 4.12 below

erat inimum average cost is not efficient because a larger plant can take

e c st.

oint f the LAC curve is a point of tangency with some corresponding SAC

e up to M, the slope of these SAC curves must also be negative, be

point of tangency the two curves have the same s

By the same logic, the points of tangency of the LAC curve and the SAC curves for

outputs larger than Q* (to the right of M) occur on the rising part of the SAC curves.

Only at the minimum point (M) of the LAC is the corresponding SAC also at a minim

A

rising part of the LAC curve the plants are overworked. Only at the minimum point M is

the plant optimally utilized.

illustrates how this is done.

156

SMC1

SMC2

SAC1

SAC2

SAC3

SMC3

LAC

LMC Cost ($)

a

To the left of a, SAC1 is greater than LAC so that SAC1 declines at a faster rate than the

LAC. As the larger (SAC1) is falling at a faster speed than the smaller (LAC), the two

ill be equalized at some point – at point a in the figure above. This implies the LMC is

ental cost is added to the short-run cost than to the

g-run cost). At the minimum point of the LAC, the LMC intersects the LAC. At this

= SMC = LAC = LMC.

w

greater than SMC1 to the left of a. At a, LMC = SMC1 (the same amount of additional

costs accrue to both the short-run and the long-run costs so that SAC1 = LAC). To the

right of a, LMC < SMC1 (more increm

lo

point, SAC

Check Your Progress

1. Are the short run and the long run cost curves similar in shape? If so, do you see any

difference between the two?

2. The long run average cost curve is an envelope curve. What does this mean?

Explain.

3. Why don’t we have a long run average fixed cost?

157

4.7 DERIVATION OF COST FUNCTION FROM PRODUCTION

Cost curves are derived functions in that they are derived from the production function.

Costs are not incurred for their own sake but only to produce output.

Graphically, the total cost curve is determined by the locus of points of tangency of

successive isocost lines with the corresponding highest isoquants.

Mathematically, the cost function can be derived as follows. As usual, we use the Cobb-

FUNCTION

cbKALX = Douglas production function:

rKwLC +=Given this production function and the cost function , we want to derive the

cost function, that is, cost as function of output: C = f(X).

e begin by solving the constrained output maximization problem: W

Maximize cbKALX = subject to rKwLC +=

Form the composite function:

)( CrKwLXZ −+−= λ

Partially differentiate Z with respect to L, K, λ and equate each to zero.

* 0=−∂

=∂ wXZ λ

∂∂ LL

wMPL λ=

w

MPL=λ …………………………………………………………………… (1)

* 0=−∂∂

=∂∂ r

KX

KZ λ

rMPK λ=

r

MPK=λ …………………………………………………………………… (2)

158

* 0=−+=∂∂ CrKwLZλ

CrKwL =+ ……………………………………………………………… (3)

equations (1) anFrom d (2) we understand that: rw

MPMP KL = orKMPr

g the Cob-Douglas production function given above,

LMPw=

Usin

XKc

KKcALKcALMP

LLcb

cbL

L

=== −1similarly, and

XbKbALKbALPcb

cb === −1

sing the equilibrium condition and these marginal products, solve for K in terms of L,

r for L in terms of K. Let us solve for L in terms of K.

M

U

o

XKc

XLb

rw=

cLbK

rw= ⇒

)4...(..............................................................................................................wc

rbKL

rbKwcL

=⇒

=

ubstitute this term for L into the production function and solve for K in terms of X:

⇒

S

....(*)................................................................................])([

)

1

Kwc

KrbA

cbb

cbb

=

=

+

+(

)(

)(

X

KrbAX

Kwc

rbKAX

cbb

cb

⇒

⇒

=

=

+

we know tha

⇒

wcXwc

rbA

twc

rbKL = . From equation (4) above,

159

cbb

rbwc

AX

wcrb

wcrbKL +==

1

])([ Then,

*)........(*......................................................................][)(1

cbcbc

AX

wcrbL ++=⇒

rKwLC += As a final step, substitute (*) and (**) into the isocost equation:

cbcbcbcbcb XAwc

r +++++ ]})([bbb

cbcbc

cbc

cbb

cbcbcbb

cbb

cbb

cbcbcbc

cbc

cbb

cbbcbcbc

bAcbrwC

XAwcbrXA

cbrwC

rbwc

AXr

AX

wcrbw

−−−+−

+++

++−

++−

+−

++−

+++

+++

+=⇒

+=

+=

1111

11111

11

])({[

])([])([

}])([{}][)({

C

⇒

constan a is which )([])([ v where;}{ cbcbcbcbcbcbcbcb AwcbrA

cbrwcbXvC ++++++++ +=+= t

1111 bbbccb −−−−

⇒

Don

eas

’t worry if you find the above derivation cumbersome. A numerical example makes it

31

32

ier. Suppose we have a production function given by KLX = , w = 2 Birr per unit

nd r = 4 Birr per unit. Derive the cost function. a

Solution:

The steps that are involved to derive the cost function are:

Step 1: Solve for L in terms of K or K in terms of L from the optimality

32

32

31

31

132

42

−

−

=⇒KL

KL condition

K

L

MPMP

rw= .

3

31

32

32

31

32

32

31

31

2

+

+

−

−

=L

K

KL

KL

41

21

⇒

=⇒

160

KLLK

= 4

41

=⇒

⇒

Step 2: Substitute the result from step 1 into the production function and solve for L and

s of Q from the production function. K in term

31

32

K

3

3

333

16

16

4

XK

KX

=

=

= 122

31

32

)4( KK=

+

K

X

X

LX

⇒

⇒

⇒

⇒

=

XL

Because L = 4K, XL3

3144

=⇒

=⇒

X

2

4

16−

KL3

44 ==⇒

Step 3: Substitute the results from step 2 into the cost constraint.

rKwLC +=

C KL

XXC )16

(4)4(23

3 += 142 +=⇒

⇒

⇒

XC )]1(4)4(2[ 3 +=163

XC ]22[ 32

35

+= . ⇒

4.8 DYNAMIC CHANGES IN COSTS – THE LEARNING CURVE

A l e average cost than a smaller firm because of

implies that growing firms with

incr i me.

arg firm may have a lower long run

increasing returns to scale in production, which

eas ng returns to scale enjoy lower average costs over ti

161

Bu is e firms, long-run average cost may

dec technological information as

wit cost (MC) and average cost (AC) of producing a

given level of output fall for four reasons:

1. s me more adapted to a given task, their speed increases.

2. schedule the production process more effectively.

3. o are initially cautious in their product designs may gain enough

t organization may

4. earn how to process materials required more effectively

is advantage in the form of lower materials cost.

gra

amount of inputs needed to produce each unit of output is known as the learning curve.

t th may not be necessarily the case. In som

line overtime because workers and managers absorb new

they become more experienced at their jobs. As management and labor gain experience

h production, the firm’s marginal

A workers beco

Managers learn to

Engineers wh

experience to be able to allow for tolerances in design that save cost without

increasing defects. Better and more specialized tools and plan

also lower cost.

Suppliers of materials may l

and may pass on some of th

As a consequence of this, a firm “learns” overtime as cumulative output increases. The

ph (curve) that describes the relationship between a firm’s cumulative output and the

Am

ount

of i

nput

s ne

per

Cumulative output

Learnin

eded

unit

of o

utpu

t

g Curve

Figure 4.13: The Learning Curve

162

Overtim oduction can decline because of:

from A to B in

igure).

e, a firm’s average cost of pr

a. Growth of sales when increasing returns are present (movement

the figure below), or

b. The existence of learning curve/effect (movement from A to C in the f

A

B

AC1

AC2

Q

4: Economies of Scale versus Learning Effect

AC

C

O Figure 4.1

Check Your Progress

ing the cost function from the production

m that has been in business for long could

d learning effect?

4.9

– derived from the production function.

rt and the long run, economists calculate implicit as well as explicit

o hose costs implied by the alternatives given

iture or bookkeeping costs.

1. Outline the steps to be followed for deriv

function

2. Discuss the reasons for which a fir

experience low average unit cost of production.

3. What is the difference between economies of scale an

LESSON SUMMARY

The cost function is a derived function

In both the sho

c sts of production. Implicit costs are t

up, and explicit costs are direct expend

163

n ri le factor(s) are added to the

i ing returns to the variable

owever, eventually the firm reaches a point (some higher level of output) at

egin to increase at an increasing rate. Such increasing and

returns to the variable factor of production (the law of variable

e short-run average and marginal cost

u

Except that we don’t have a fixed cost in the long run, the short and the long run

ver, the U-shape of the long-run average and

marginal cost curves is due to economies and diseconomies of large-scale

f increasing returns to scale (economies of scale) in

ore

I. M

I the short run, as more and more units of the va ab

f xed factor, the firm may initially experience increas

factor and thus total costs of production rise slowly at lower levels of output.

H

which total costs b

diminishing

proportions) account for the U- shape of th

c rves.

cost follow similar patterns. Howe

production.

There a predictable relationship between short run cost functions and production

functions as well between short run and long run cost functions.

A large firm may have a lower long run average cost than a smaller firm because of

two reasons: because o

production, and/or because of the learning effects (as workers and managers of a

large firm could easily absorb new technological information as they become m

experienced at their jobs).


ultiple Choice Questions

If we have a linear cost function of the firm C = a +

1. bQ, then the average cost will:

a. remain constant as prod

b. decrease continuously as production expands.

c. increase with in

d. first increase and then decrease with increases in output.

eases beyond its minimum, the average cost,

a. increases

uction expands.

creases in output

2. When the marginal cost incr

164

b. decreases

c. remains constant

d. first decreases and then increases

3. Which of the following is the general sequence?

a. nomies end

b.

c. ies begin

ether

incurs in purchasing or hiring any factor of production from

ferred to as:

a. explicit cost

c. variable cost

d

b. rise at a decreasing rate

Economies of scale begin when diseco

Diseconomies begin where economies end.

Diseconomies end where econom

d. Economies and diseconomies of scale go tog

4. The cost that a firm

outside the firm is re

b. implicit cost

d. fixed cost

5. An entrepreneur running a business earns $20,000 per year as his/her salary from the

total receipts of the firm; the implicit cost of this entrepreneur is:

a. $20,000/year

b. more than $20,000/year

c. less than $20,000/year

d. any of the above is possible

6. If only part of the labor force employed by a firm can be dismissed at any time an

without pay, the total wages and salaries paid out by the firm must be considered:

a. a fixed cost

b. variable cost

c. partly fixed and partly variable cost

d. any of the above

7. When the law of diminishing returns begins to operate, the TVC begins to:

a. fall at an increasing rate

c. fall at a decreasing rate

d. rise at an increasing rate

165

8. All the following curves are “U” shaped except:

a. the AVC curve

b. the AFC curve

d. the MC curve

c. curve, but not by the slope of the TVC curve

10. The its minimum point before the AVC and the ATC curves do so.

the MC curve intersects both the AVC and the AC curves at their lowest

a. always

d. sometimes

from the origin is tangent to the TC curve, the ATC

is:

2. The LAC curve is tangent to the SAC curve at the lowest point of the latter when the

statement is true:

a. always

is due to:

a. economics of scale

c. the ATC curve

9. MC is given by:

a. the slope of the TFC curve

b. the slope of the TVC curve, but not by the slope of the TC curve

the slope of the TC

d. either by the slope of the TC curve or by the slope of the TVC curve

MC curve reaches

In addition,

points. The above statements are both true:

b. never

c. often

11. At the point where a straight line

a. at its minimum

b. equal to MC

c. equal to AVC plus AFC

d. all of the above

1

LAC curve is falling. This

b. never

c. sometimes

d. cannot say

13. If the LAC curve falls as output expands, this

166

b. the law of diminishing returns

c. diseconomies of scale

d. any of the above

14. The LAC curve:

a. falls only when the LMC curve falls

b. rises whenever the LMC curve rises

t point of the LMC curve

d. falls when LMC < LAC and rises when LMC > LAC

n the long run total cost. This statement

is:

a. always true

b. often true

c. sometimes true

d. never true

I

c. goes through the lowes

15. The short run total cost can never be less tha

I. Discussion and Workout Questions

1. Distinguish between: (a) short-run and long-run costs, (b) explicit and implicit costs.

2. Explain the relationship between the marginal and average cost curves. Show the

relationship between marginal cost, average variable cost and average total cost.

3. Explain why the average total cost and the average variable cost become closer and

closer as output increases.

. Show the circumstances when the marginal cost is constant throughout but the

int: think of the geometric derivations of the two costs.)

from the short run average cost curves.

curve.

that at the output where SAC = LAC, SMC also equals LMC?

+ re a cost

TVC, TC, AFC, AVC, MC, and ATC. Is this cost

function? Why? Draw the cost curves on the

4

average cost is falling. (H

5. Derive the long run average cost curve

6. Write a short note on the derivation of long run marginal cost

7. Why is it

8. Suppose the cost function is given as C = 135 + 75Q – 15Q2 Q3. Prepa

schedule (table) showing the TFC,

function a short run or a long run cost

basis of cost data obtained from the cost function.

167

CHAPTER FIVE

PERFECT COMPETITION

LESSON STRUCTURE

5.1 Introduction

bjectives

.3 Characteristics of Pure and Perfect Competition

um

5.4.1 Equilibrium in the Market Period

son Summary

.7 Review Questions

.1 INTRODUCTION

The type (or

ature) of competition firms face from competitors, which in turn determines the degree

f power of a firm over the price of its product, is the basis for categorizing markets into

n is the only type of competition firms

perating in perfectly competitive markets will face from competitors both price and non-

5.2 Chapter O

5

5.4 Market Equilibri

5.4.2 The Short Run Equilibrium of a Firm and Industry/Market

5.4.3 The Long Run Equilibrium

5.5 Perfect Competition and Consumers’ Welfare

5.6 Les

5

5

The market in which an individual firm operates or sells its product (good or service) to

consumers can be categorized broadly into perfect and imperfect market9.

n

o

perfect and imperfect. While price competitio

o

price competitions are common in imperfect markets. In short, Perfect Competition is a

market structure characterized by complete absence of rivalry among individual firms.

9 Markets dominated by one firm (monopoly), very few firms (oligopoly), and relatively large numbers of

firms selling closely substitutable products (monopolistic competition) are the three common types of imperfect markets in which firms use different means of deterring other firms from entering into the market or the means of influencing their market share. The later two are characterized by rivalry among individual firms.

168

In neoclassical economics and microeconomics, perfect competition describes a market

in which no buyer or seller has market power or where all buyers and sellers are price-

takers; that is, perfect competition is a market structure in which firms treat price as a

arameter. It is this distinction which differentiates perfectly competitive markets from

petitive markets are characterized by

llocative and productive efficiency. In general, a perfectly competitive market is

CTIVES

Distinguish between pure and perfect competition

.3 CHARACTERISTICS OF PURE AND PERFECT COMPETITION

perfectly competitive market has several distinguishing characteristics. The main

1. Many Buyers and Many Sellers

ingness and ability to buy the product at a certain

rice and many producers with the willingness and ability to supply the product at a

p

imperfectly competitive ones. Perfectly com

a

characterized by the fact that no single firm has influence on the price of the product it

sells. Because the conditions for perfect competition are very strict, there are few

perfectly competitive markets in the real world.

5.2 CHAPTER OBJE

After completing this chapter, you will be able to:

Determine the short and long run equilibrium output and price of a competitive

firm and industry.

Describe why perfect competitive market is an ideal market in terms of ensuring

consumer welfare.

5

A

features include:

There are many consumers with the will

p

certain price. Since each firm supplies only small part of the total market supply any firm

cannot affect the market price by altering (increasing or decreasing) its output.

169

2. Homogeneous Products

The industry or market is defined as group of firms supplying homogeneous products

(goods or services). That is, products supplied by the different firms are exactly the same.

Example, salt supplied by two sellers are identical to the extent that buyers are unable to

differentiate which firm supplied which product.

The assumption of large number of sellers and product homogeneity together imply that

ectly competitive market is a price taker. Thus, a

a completely horizontal or perfectly elastic demand curve for its

it can sell any amount of output only at the ongoing market price

an individual firm operating in a perf

competitive firm faces

product indicating that

( P ). Moreover, the demand curve is also the average revenue (AR) and marginal

venue (MR) curve.

quality of the ongoing market price (

re

P

Figure 5.1: The Demand Curve Faced by a Firm under Perfectly Competitive Market

The reason for the e P ) and the demand curve is that

ny firm receives, for any unit of output sells, the price which is determined by the

igure 5.2 below.

a

intersection of market demand and market supply. This is depicted in F

O Q

MRARDDP === P

170

SS

P MC

−

P ME −

P FE MCDDP ==−

DD

irm

Q FQ Q MQ

(a) Industry/Market (b) F

Figure 5.2: Determination of Equilibrium Price under Perfect Competition

Why do the relationships ARP = and MRP = hold? Let us show these mathematically.

QQPTRAR .

== )().( dQPPQddTRMR === Q dQdQdQ

PAR =⇒ PMR =⇒

3. Free Entry/Exit

Unl im rf t ma ets, ry to an xit fr a business is not blocked in a perfectly

t m t w f a e f

arrier that restricts firms from entry into and/or exit out of a perfectly competitive

arket.

t a point where the marginal cost of production meets the

arginal revenue from sales. More on this will be discussed in Section 5.4.

ike pe ec rk ent in d e om

competi ive arket. In o her ords, irms h ve fre dom o movement or there is no

b

m

4. Firms Aim to Maximize Profit

The objective of firms in perfect competition is profit maximization. To this end firms

operate (produce and sell) a

m

171

5. Absence of Government Intervention

This is to say the no er nt regulation or intervention in th arket in any way,

say through imposing tariffs, granting subsidies, rationing, etc., which are considered as

disturbances to the ma . notion is based on the argum of sical

economists led by Adam Smith who regard the government intervention as unnecessary.

A m et t ful on he a ve f cha is c u p Pure

com tio nd petition are diff o t ui e f ent of

the w additional charac istic um s.

6. P ct bil f F tors Pro tio

This implies that all factors of odu n, s a al free to

move from e se to othe r fro ne o r is e change

their jobs without any restriction for labor is not unionized and the supply of raw

mat s ot no ized ithe o ir h o es full

employme re ce

7. P ct rm n Bo Con er P r

and buyers have

omplete information and knowledge of the market. The implication is that the current

er a perfectly competitive market.

re is gov

rket

nme

This

e m

ent the clas

ark tha fils ly t bo ive racter tics is alled p re com etition.

peti n a perfect com erent f r the la er req res th ulfillm

follo ing ter s/ass ption

erfe Mo ity o ac of duc n

pr ctio such a labor nd raw materi s, are

on ctor an r o m o firm t anothe . That , work rs can

erial is n mo pol e r by ne or few f ms. T is als impli

nt of sour s.

erfe Info atio for th sum s and roduce s.

It is assumed that in a perfectively competitive market both sellers

c

and future price of products, quality of products supplied by different firms, etc., are

certainly known. In other words, information is costless: there is no uncertainty about

future prices, and no non-price competition exists und

Check Your Progress

1. Distinguish between pure competition and perfect competition.

172

2. Discuss the implication of the notion that there is no barrier to entry and exit under

equilibrium of a perfectly competitive firm as well as that of industry

erent cases: the market period, the short run and the long run equilibria.

ket Period Equilibrium

market period refers to a very short period in which supply is absolutely fixed. For

D3

ctly Competitive Market

r that different level of demand gives different equilibrium

ut equilibrium output remains the same. This implies that, at any market period demand

alone determines the equilibrium price. A market period is thus different from short run

perfect competition.

5.4 MARKET EQUILIBRIUM

We will see the

under three diff

5.4.1 The Mar

A

instance, the quantity of agricultural products available in the market cannot be increased

instantly with demand as production is seasonal. Put it differently, though different levels

of demand give rise to different prices, supply will remain the same for it cannot be

increased until the next harvest.

P S

D2

D1

Figure 5.3: Market Period Equilibrium under Perfe

3P

2P

1P

From the above figure it is clea

b

O SQ Q

173

and long run in which both the supply and demand conditions determine the equilibrium

price and quantity.

5.4.2 The Short Run Equilibrium of a Firm and Industry/Market

The Short Run Equilibrium of a Firm

Shot run is a production period in which the amount of one or more of the inputs a firm

uses is fixed or constant. In other words, in the short run, the quantity of output produced

by a competitive firm can be increased (decreased) only by increasing (decreasing) the

ariable inputs. The short run equilibrium of a firm or an industry (a market) is thus the

hat maximizes profit or minimizes loss under such conditions. This profit-

using any of the two

al R r ch

s in equilibrium when total revenue less total cost is the

aximum. That is, the firm maximizes profit when the difference between total revenue

ollowing hypothetical example for a competitive firm

ow we determine the equilibrium output and maximum profit using the TR –

C approach.

t run output (Q)

w.

Q 3 4 5 6 7 8 9 10 11 12

v

output level t

maximizing level of output and the profit level can be determined

approaches discussed below.

1. The Tot evenue – Total Cost (TR – TC) App oa

Using this approach, a firm i

m

and total cost is the greatest. The f

clarifies h

T

Example 1: Suppose the short run market price is $5. Moreover, the shor

and associated total cost of a competitive firm as are shown in the table belo

0 1 2

TC 5 19.5 20 2 5 24.75 27.48 32.48 38.88 46.66 55 65.2810 15 17 18. 2.2

ter Four that the total cost wh10 Recall from Chap en output is equal to zero is the short run total fixed cost

174

G the abov iniven e formation, we need to compute only TR (i.e., price multiplied by the

vel of output, Q) in order to determine the equilibrium output and maximum profit le

using the TR – TC approach. The profit/loss of the firm for each output level is computed

by subtracting TC from TR and is shown in the last column of table 5.1. Other variables

are computed for latter use.

Table 5.1: Determination of Equilibrium of a Firm Using the TR – TC Approach

) Q)

Pric

e (P

Out

put (

Q)

TR

(P.Q

)

AR

(TR

/Q)

TR

/∆Q

)

TFC

TV

C

TC

(FC

+VC

)

C/Q

)

∆TC

/∆

/Los

s

(TR

–T

C)

M (∆

AT

C (T

MC

(

Prof

it

$5 0 0 - - 15 - 15.00 - - (15.00)

$5 1 5 5 5 15 2.00 17.00 17.00 2.00 (12.00)

$5 2 10 5 5 15 3.50 18.50 9.25 1.50 (8.50)

$5 3 15 5 5 15 4.50 19.50 6.50 1.00 (4.50)

$5 4 20 5 5 15 5.00 20.00 5.00 0.50 0

$5 5 25 5 5 15 7.25 22.25 4.45 2.25 2.75

$5 6 30 5 5 15 9.75 24.75 4.13 2.50 5.25

$5 7 35 5 5 15 12.48 27.48 3.93 2.73 7.52

$5 8 40 5 5 15 17.48 32.48 4.06 5.00 7.52

$5 9 45 5 5 15 23.88 38.88 4.32 6.40 6.12

$5 10 5 50 5 15 31.66 46.66 4.67 7.78 3.34

$5 11 55 5 5 15 40.00 55.00 5.00 8.34 0

$5 12 60 5 5 15 49.20 64.20 5.35 9.20 (4.20)

$5 13 65 5 5 15 59.36 74.36 5.72 10.20 (9.36)

Note: The values o Af ATC (S C) are rounded to two decimal places.

175

176

n ormal (zero) profit or is at its break even

ut. Moreover, the firm obtains maximum

rofit when it produces either 7 or 8 units of output.

he most important points in the total revenue – total cost approach are depicted

Figure 5.4: Profit Maximization of a Firm

The profit (loss) of e (negative) distance between the

total revenue (TR) and total cost (T In the above figure, first the TC curve lies

above the TR curve until exac

the firm achieves economic

and lines gradually af

ce again, the firm breaks even at point B when it produces

ofit becomes negative beyond point B.

From Table 5.1 it is clear that the firm obtai s n

point when it produces 4 or 11 units of outp

p

T

graphically as follows.

T

The maximum profit = 7.52

TRTC

0

T

Q

B55.0 40.00 32.48 20.00

A

15.00

O 4 7 8 11

T

Depicted Using the TR – TC Approach

a firm is represented by the positiv

C) curves.

tly 4 units of output is produced at point A implying that

profit is negative (there was loss) prior to this point. Secondly, the intersection of the total

revenue and total cost curves at point A implies that the firm has reached its breakeven

ofit). Thirdly,point (no loss and no gain or obtains zero pr

(positive) profit at any level of production between point A and B. In this region, profit

increases gradually, reaches maximum towards the middle, dec ter 8

units of output is produced. On

exactly 11 units of output. Finally, pr

Therefore, profit maximizing level of output is achieved at a point where the positive

tal cost curves is the longest. At this point, the

he MC (see the TT line which is tangent to the TC curve) is equal

the slope of the total revenue curve, the MR. In other words, the short run equilibrium

f the firm is achieved when 8 units if output is produced.

2. The M

reason is that the short run equilibrium output (profit maximizing level of

utput) and the associated profit can be clearly determined by equating marginal revenue

ATC

distance between the total revenue and to

slope of the total cost, t

to

o

arginal Approach

The total revenue – total cost approach indicates only the amount of profit (or loss) at

different levels of production. In the above example, for instance, both 7 and 8 units of

output generate 7.52 units of profit and the TR – TC approach doesn’t tell us why we

choose 8 as a profit maximizing level of output (and why not 7). Hence, it does not help

for analytical interpretation of business behavior. In this regard, the marginal approach is

a useful analytical tool at least for the following reasons.

The first

o

to marginal cost, i.e., MCMR = .

Graphically:

MR MC

Profit MRP =

Figure 5.5: Short Run Equilibrium of a Firm Depicted Using the Marginal Approach

0.50

4.06

MC

ATC

5.00

4 EQ = 8 Q

177

The amount of profit )(π at any level of output could be calculated using:

QATCP )( −=π . This is derived from the TR-TC approach as follows:

TCTR −=π

QATCQP .. −=π

QATCP )( −=π .

ATCP > , there is excess profit; if ATCP = the firm gets normal (zero) profit; Thus, if

and, if ATCP < the firm incurs loss. For instance, at the equilibrium output (EQ) profit is,

8)06.45( −=π , which is

52.78)94.0( ==π .

The second reason is that comparing the value of MR and MC to the left and right of

whether to expand or reduce output. For example, to the left of E

short run equilibrium output (EQ) has an important implication for a firm’s decision on

ta nce price is greater than unit cos

to expand production. On the other

is lower than MC to the right of the equilibrium output implying that the firm

sho

Alterna

from th m.

Q (for any output level

less than 8), the MR ( = P) exceeds the MC, indicating that the sale of a unit of output

would increase total revenue more than to l cost si t

(ATC) of production. Therefore, it pays for the firm

hand, MR

uld reduce its production.

tively, the short run equilibrium of a firm can also be derived mathematically

e given level of market price and total cost function of a fir

Example 2:

Suppose the market (per unit) price a firm faces is $10 and its cost function is given by:

12 += QTC . Calculate the profit maximizing level of output and the maximum profit.

In this case,

QdQ

dTCMC 2== andQ

QQ

TCATC 12 +== .

Equating the market price to the MC will give the equilibrium output. That is,

178

MCP =

Q210 = .

us, the output level that maxim zes profit is: 5Th i =Q .

Substituting this output level into the TC and ATC equations gives the values 26 and 5.2,

respectively.

Furthermore, the profit of the firm obtains is:

TCTR −=π

1)1( 22 −−=+−= QPQQPQπ

242650)15()5(10 2 =−=+−=⇒ π .

The same result can also be obtained using: QATCP )( −=π .

245)8.4(5)2.510( ==−=π .

Check Your Progress

1. A perfectly competitive firm is faced with the following output and total cost

schedule.

Q 0 1 2 3 4 5 6 7 8 9 10

TC 9 20 30 32 39 47 60 67 77 90 109

If the market price is Birr 13,

a. Compute a table that shows the short run equilibrium of the firm using the TR –

roaches.

b. What is the equilibrium output of the firm?

c. Using the marginal approach, show the profit level graphically.

. Assume a two product firm is operating in a perfectly competitive market. The market

prices of its products are $12 and $18, respectively. Furthermore, the production cost

of the firm is given by . Based on this information:

a. Find the short run equilibrium outputs, and , that in combination maximize

profit.

b. Calculate the total profit of the firm

c. Show graphically the profit the firm arns from each market separately.

TC and marginal app

2

2221

21 22 QQQQTC ++=

1Q 2Q

.

e

179

180

MR1

P

P1

D F H P2 P3G P4

P5

O q5 q4 q3 q2 q1 Q

MR2

ATC

MR5

MC

MR3

MR4

AVC

E1

E2

E4E5

E3

A B C

K

So far we h ch. Thirdly,

is approach will provide the basis weather to shutdown a loss making firm or not. This

ilibria of a Firm for Different Market Prices

ave seen two reasons for the usefulness of the marginal approa

th

can be illustrated with the help of the figure below.

Figure 5.6: Short Run Equ

In the above figure, five short run equilibrium points are established at different market

prices. The equilibria are established at points where MCMRP == . As a result, the

quantity of output produced by a firm as well as its profit or loss varies. For example,

when the ongoing market price is 1P , the short run equilibrium is at point 1E . At this

price, the total amount of output produced by a firm operating in a perfectly competitive

market is 1Oq . On the other hand, the unit cost (ATC) of producing one unit of output is

given by the distance OF or Cq1 .Since )( 11 CqATCP > , the area CFEP 11 indicates the

excess profit the firm obtains.

to . In this case, the short run equilibrium

established at point and amount of output is supplied. Since, price is

equal to unit cost , the firm is in its breakeven point; that is it earns normal (zero)

Suppose the market price declines from 1P 2P

2E 2Oq 2OP

22 Eq

is

profit. However, for any price level below 2P , the firm will incur loss or will earn

negative profit as the market price will be less than ATC.

s that, should a loss making firm close down? The

answer to this question is that one should observe whether the market price is greater than

or equal to th

An interesting question one might ask i

e AVC at that equilibrium output in order to decide whether to close down

r not. That is, a loss making firm should stay in business by continuing production as far

the market price is greater than the AVC. This is because not all fixed costs incurred

re lost if the market price is greater than AVC. In other words, since all fixed costs will

e lost if the firm discontinues production, th rm will lose less by staying in business

osts. However, a loss making firm should shut down

hen the market price becomes less than the minimum of AVC. Recall from earlier

iscussion in Chapter Four that, graphically, AVC will be at its minimum when it is

rossed by the MC curve from below. Therefore, the point where thee minimum AVC is

qual to MC is called the shutdown point.

The reason as to w o stay in business

is established at and hence the

e cost of producing

or . Since

o

as

a

b e fi

and covering some part of the fixed c

w

d

c

e

hy it is a sensible strategy for a loss making firm t

and shutdown when the market price is greater than and less than the AVC respectively

can be justified by considering the situations at market price 3P and 4P in Figure 5.6

above.

First, consider the situation when the market price declines from P to P . When the

ongoing market price is , the short run equilibrium

2 3

3P 3E

firm produces 3Oq amount of output. At this level of production, th

one unit of output (ATC) is given by OH Bq3 BqP 33 < , or , the area

esides,

Total cost, which is equal to output multiplied by ATC, is

VC) is

OHP <3

BHEP indicates the loss incurred by this competitive firm. 33

B

BHOq3 .

AVC is OG or Kq . This implies that, total variable cost (T3 KGOq3 .

181

The difference between total cost and total variable cost gives us the total fixed

BHG .

cost (TFC), which is equal to

But the market price is greater than average variable cost, i.e.

ften less costly to

ducing at a loss than to shutdown and still be forced to bear the high fixed

aking firm should shutdown as soon as the market price falls below

i produce. The mark

ed cost by shutting down. If it were to produce at

e point where MC equals the very low market price, it would lose more than fixed cost.

herefore, it is a wise decision to shutdown the business.

he Short Run Market/Industry Equilibrium

he short run industry supply curve is the horizontal summation of the short run supply

urves of individual firms. The short run supply curve of an individual firm is derived

om the intersection of its MC curve with its successive demand (MR) curves. It is part

f the MC curve above the intersection of the MC and the AVC curve. As the market

rice increases gradually we expect that each higher demand curve (price line) cuts the

K

KqEqOP 3333 )( >=

Therefore, if the firm decides not to produce 3Oq amount of output it will lose the whole

of TFC given by area KBHG . However, by deciding to stay in business it will lose only

BHEP 33 , which is less than KBHG . This is because it has covered the part of the TFC

given by the area GPKE 33 . Profit maximizing firms may in the short run continue to

operate even though they are losing money. This is the case particularly for firms that

own great deal of capital and therefore high fixed costs, because it is o

continue pro

cost.

However, a loss m

.4P Because, when it produces 4Oq amount of output at 4E , the firm will lose all of its

TFC amounting to 44 ADPE ; and, as soon as the price falls short of 4P , it won’t even

cover its variable cos rice ( 4P ) that is equal to the

minimum of the AVC ( 44 Eq ) and the MC is the dividing line between the decision to

shut down and to continue operation. When the market price is below 4P , the firm should

shut down since it will lose only its fix

t if it dec des to et p

th

T

T

T

c

fr

o

p

182

MC curve at a s that quantity

pplied by firms will increase as price increases.

herefore, the industry supply curve is simply the horizontal summation of the individual

ibrium

ill be obtained after determining the industry demand curve which is downward

point to the right of the previous intersection. This indicate

su

Figure 5.7: The Supply Curve of a Perfectly Competitive Firm

T

firms’ supply curves. Given the industry supply curve, the short run industry equil

w

sloping. Assuming that there are 100 identical firms in the industry, the short run

equilibrium will be as shown in the figure below.

Figure 5.8: The Short Rum Equilibrium an Industry

5.4.3 The Long Run Equilibrium

P P3

100*q3 Q

The Industry Supply Curve

Market Demand Curve

q1 q2 q3 Q q1 q q2 3 Q

P1

P2

P3

MC ATC

AVC

The Supply Curve of a Firm P

183

Unlike the short run, the long run is a period of time in which a firm can vary/change the

amounts of all of its inputs. Since all inputs are variable in the long run, a firm has the

opt of adjusti

It is als o

is poo

areas/e into the industry if profit prospect is

attractive or are g s

in the i

run equ

The Long R

In the l

produc

will be

ion ng its output through adjusting its plant size to achieve maximum profit.

o p ssible some businesses can be liquidated /shutdown/ entirely if profit prospect

r. The resources are thus transferred into more profitable investment

ndeavors. Similarly, new firms will enter

reater than profits elsewhere. Hence, adjustment of the number of firm

ndustry in response to profit motives is the key element in establishing the long

ilibrium.

un Equilibrium of a Firm

ong run, firms are in equilibrium when they have adjusted their plant size so as to

e at the minimum of the long run average cost (LAC) curve. At this point the LAC

tangent to the demand curve defined by the market price. Therefore, the equality:

MRPLACSACSMC ==== is the long run equilibrium condition of a

itive firm.

LMC =

compet The implication is that competitive firms will earn only normal profit in

e long run.

Assume for simplicity that there are 100 identical firms that are supplying the same

th

SMCSACLMC

LAC

Lq Q

DD = MRP

Figure 5.9: The Long Run Equilibrium of a Firm

amount of output in the short run. Further assume that the business they engaged in is

184

profit

each

able. The short run market/industry supply is thus 100 multiplied by the supply of

firm or simply 100(q1) indicated on the industry supply curve, ∑ 1q . As m d

r, we can now expect that the short run excess profit enjoyed by the firms in the

try will attract new firms into the industry.

∑ 1q

∑ 2q

DSMC SAC

185

q2 q1 100(q1) 180(q2)

D

D P

P1

A MR

ES

2

B

C MR

1

2

EL

entione

earlie

indus

Firm

Figure 5.10: Derivation

supplies

indus

ti

curve

curve

busin

mark

The L

The i

firms inimum p

LAC

Market

of Long Run equilibrium of Firms from the Short Run

Equilibrium

As shown in Figure 5.10, the individual firms are in the short run equilibrium when each

1q units of output. It cannot be the long run equilibrium because each firm in the

try earns excess profit shown by area 1ABDP in the first graph as ATCP >1 . Each

me new firms (attracted by the excess profit) enter into the market, the market supply

will shift to the right. The entry of firms will continue until the industry supply

shifts to ∑ 2q , the market price falls to P2, each firm produces q2, and firms in the

ess obtain normal profit. At this point, suppose 80 new firms have entered into the

et. Therefore, the long run industry equilibrium output will be 180(q2).

ong Run Equilibrium of the Industry/Market

ndustry is in the long run equilibrium when a price level reaches a point where all

are in equilibrium. That is, when all firms produce at the m oint of the

curve or when MRPLACSACSMCLMC ===== , and each firm just makes a

SMCSAC

LMC LACSS

normal profit. With all firms in the industry being in equilibrium and with no entry and

remains stable and given the demand curve, the price

ill be the long run equilibrium price.

e Industry

T hat although

emand equals supply in both cases, the long run equilibrium is defined at a point where

and no excess profit is obtained.

exit, then the industry supply curve

w

Figure 5.11: The Long Run Equilibrium of th

herefore, the difference between the short run and long run equilibrium is t

d

demand is equal to supply

Check Your Progress

Referring to Figure 5.10 above, what is the price elast

1) icity of supply if an individual

fi supplied 18 units of output when P s $6 12 ts w the rket e

fa to P2 3?

2) Based on the price and output information in question 1, calculate the elasticity of

3) Do r why

5.5 PERFECT COMPETITION AND CONSUMERS WELFARE

rm 1 wa and uni hen ma pric

lls = $

market demand?

you expect any of the 180 firms to exit out of the business at P2? Why o

not?

186

Perfe

resource a

When the long run equilibrium is achieved, the economy operates at the maximum

econ

level of

This that each consumer buys those quantity of goods at which the marginal rate

of su goods.

Put d

competitive equilibrium, which in turn equals the marginal cost (MC) of producing the

good

ct competition is regarded as the most ideal market from the point of view of

llocation; resource utilization; resource employment; and consumers’ welfare.

omic efficiency. This is because:

individual firms operate at the optimal plant sizes and produce optimal

output,

consumers buy different units of each output at the price equal to the minimum

attainable average cost per unit (P = LAC).

implies

bstitution (MRS) between any two goods is equal to the price ratio of the two

ifferently, the marginal utility of the consumed good (MU) equals the price (P) at

. The discussion in the following three steps show that, if MCPMU == , allocation

is eff

of satisfaction from the last

rices of goods

2. ium condition of a perfectly competitive firm is given by

plying their sweaty

g that last bit of

to produce the last unit of the good (output price/value) exactly

irm’s of producing the last unit of the good supplied11.

3. Putting these two equations together, we see that

icient or optimal.

1. MUP = : Consumers choose to purchase a good up to the amount corresponding

to MUP = . As a result, every person is gaining utils

unit of the good consumed as good as what he/she pays. Since the p

are the lowest, consumers’ welfare is maximized.

:MC= The equilibrP

.MCP = From the viewpoint of laborers, workers are sup

labor up to the point where the utils of satisfaction lost by workin

time needed

equals the f MC

MCMU = . This means that the

utils gained from the last unit of good consumed exactly equals the utils lost for

sweaty labor required to produce that last unit. It is exactly this condition – the

marginal gains of society from the last unit consumed equal the marginal costs of

11 The MC (of the firm) is the price/wage paid to the laborer for the cost they incur in terms of the utility of

leisure forgone and the disutility of the sweaty labor needed to produce the last unit of the good.

187

society for that last un guarantees that a competitive

equilibrium is efficient.

ence, both the allocation and utilization of resources are optimal under perfect

h this quality of perfect competition, as we will see in subsequent

rkets (monopoly, monopolistic competition, and oligopoly) fall

a equilibrium.

e firm is the one that can sell an amount of output it wants at

ompetitive firms are assumed to maximize their profit

mize profits, the competitive firm will choose that

e equals marginal cost of production, i.e.,

D he competitive firm’s equilibrium will come where the rising

MC curve intersects its horizontal demand curve.

) costs must be taken into account in determining firm’s

short-run decision to shutdown or to continue operation. Below some critical price

rm shuts down and produce

nothing when price falls below the shutdown price.

in the industry. So as free entry

it produced – which

H

competition.

To t e contrary of

chapters, the imperfect ma

short of reaching such an efficient and welfare-maxim

5.6 LESSON SUMMARY

A perfectly competitiv

the ongoing market price. C

(or minimize losses). To maxi

MCP = . output level at which pric

iagrammatically, t

Variable (or avoidable

(the shutdown point), the firm’s revenue will not even cover the variable cost that

could be saved completely if it shuts down. Rather than end up losing more than

fixed costs by operating, it would be better if the fi

The rising part of the MC curve of each firm above the shutdown price is its supply

curve. To obtain the supply curve of a group of independent competitive firms, we

add horizontally their separate supply curves. Hence, the supply curve of an

industry represents the marginal cost curve for the competitive industry as a whole.

In the long run when firms are free to enter and leave the industry and where no one

firm has any particular advantage of skill or location, competitors will compete and

eat away any excess profits earned by existing firms

188

means P cannot persist above th Pe breakeven point and free exit means cannot

fall below that point, all firms just earn normal profit in long-run equilibrium.

light on the efficient organization of a

h that anyone’s satisfaction or profit can

where no single

g other(s) worse off.

al conditions, a competitive economy attains allocative efficiency. This

in

market, they buy that amount for which the marginal utility just equals the price. (b)

ly goods where the marginal cost is

The analysis of competitive markets shed

society. Productive and allocative efficiency occur when there is no way of

recognizing production and distribution suc

be improved without hurting others. A different way of defining efficiency (in

production and consumption) is to say that it is a situation

individual/firm is made better off without makin

Under ide

occurs because of three step conditions: (a) First, when consumers buy goods

Secondly, competitive producers choose to supp

just equal to price. (c) Since, PMU = and PMC = , it follows that

u

5.7

I. Discu

MCMU = .

Thus, the social cost of producing a good under competition just equals its marginal

tility.

REVIEW QUESTIONS

ssion Questions

hy a competitive firm is a price taker?

1. W

2. What is the difference between market period (momentary run) and short run?

e

) It is only the excess profits that are wiped out by

competition. Managers get paid for their work; owners get a normal return on capital

in compet ive lo ru

ct competition?

3. What is the profit maximizing (or loss minimizing) condition of a competitive firm?

4. Does a firm is in its short run equilibrium necessarily mean that the firm enjoys

xcess profit?

5. Interpret this dialogue. A) “How can competitive profits be zero in the long run?

Who will work for nothing?” B

it ng n equilibrium – no more, no less.”

6. Under what condition should perfectly competitive firm supply goods at a loss?

7. What are the three conditions for the efficiency of perfe

189

II. Workout Questions

1. Suppose the market price a competitive firm faces in the short-run is Birr 10.

Moreover, its fixed cost is Birr 40. The output level (Q ) and the correspon ingd

) are as given in the table be

Q 0 5 10 15 20 25 30 35 40 45 50

variable costs (TV low. C

VC 0 30 60 80 120 170 225 287 340 410 520

(A) Compute the oss of the firm at each

results in a tab

(B) What will be the short run equilibrium output?

oach

) and

interpret the implication of the lowest point from which the supply curve

he increase in output

following the entry of the new firms has also dampened market price from Birr 10 to

n equilibrium output of a firm and the industry?

rofit do firms in th of the

profit?

(C) Derive the short run and long run supply curves of the industry.

3.

that follow.

TR, MR, TC, ATC, AVC, and profit or l

level of production and present the le similar to Table 5.1.

(C) Show the short run equilibrium and profit levels graphically using the marginal

appr

(D) Derive the short run supply curve of the firm from your graph in (C

begins.

(E) Calculate the producer’s surplus at the equilibrium.

(F) Calculate the elasticity of demand at the equilibrium price and output.

2. Suppose there were 80 identical firms operating in the industry in the short run.

Price was Birr 10. Further assume that the short run profit the existing competitive

firms enjoy attracts 80 more firms to enter the industry. T

Birr 8.

(A) What will be the long ru

(B) How much p e industry enjoy? What is the implication

(D) What happens to the consumers’ surplus?

Suppose the short run market price a competitive firm faces is Birr 9 and the total

cost of the firm is: 202.0200 QQTC ++= . Answer the questions

190

(A) Calculate the short run equilibrium output and profit of the firm.

(B) Derive the MC, ATC, and AVC and calculate the values at the short run

equilibrium output.

(C) Calculate the producers’ surplus at the equilibrium output.

(D) Find the output level that will make the profit of the firm zero.

191

CHAPTER SIX

PURE MONOPOLY

LESS

istic Features of Pure Monopoly

.4 Origins of Monopoly Power

arket structure in which there is only one supplier in the market

ince there is only one firm in the market, the demand and supply curves of a

onopoly are also the industry demand and supply curves.

hen there is only one firm in the market, the firm is unlikely to take the market price as

onopolist would recognize its influence over the market price and

nd output that will maximize its overall profit. Of course, a

rm cannot choose price and output independently. Because, for any price, the

onopoly will sell only what the market will bear. If it chooses high price, consumers

ers will

constrain the monopolist’s choice of price and quantity.

ON STRUCTURE

6.1 Introduction


6.3 The Character

6

6.5 The Short Run Equilibrium of a Pure Monopolist

6.6 The Long Run Equilibrium of a Pure Monopolist

6.7 Price Discrimination

6.8 A Multi-Plant Monopolist

6.9 The Social Cost of Monopoly

6.10 Lesson Summary


6.1 INTRODUCTION

Monopoly is a m

(industry). S

m

W

given. Instead, the m

choose that level of price a

monopoly fi

m

will demand small quantity. In other words, the demand behavior of consum

192


fter learning this chapter, you will be able to:

he main features characterizing pure monopoly are:

arrier

A

compare and contrast a purely monopolistic market to that of perfect competition;

identify the sources of monopoly power;

examine the equilibrium conditions for a single plant and multi-plant monopolist;

examine price discriminations applied by monopoly firms; and,

figure out the social cost of monopoly power.

6.3 THE CHARACTERISTIC FEATURES OF PURE MONOPOLY

T

1. The existence of a single seller and many buyers in the market.

2. The product or service of a monopolist is unique or does not have close

substitutes.

3. A monopolist is a price-maker for its product/service.

4. Entry to and exit out of the market are difficult (if not impossible). This is because

since the fixed cost (for potential entrants) will be larger while the marginal and

average costs for the existing monopolist will be smaller, this serves as a b

for new entrants. Such a situation is referred to as natural monopoly. Some other

sources of monopoly power will be discussed in Section 6.4.

As a result of these features, price will be higher and output will be lower than

competitive market. Moreover, a monopolist operates at a point where )( ARP = is greater

than MC . This is regarded as the inefficiency of monopoly in terms of resource allocation

and maximizing social welfare. The price of a monopolist is derived from the profit

maximization equation as follows.

TCTR −=π

TCPQ −= ------------------------------------------------------- (1)

The equilibrium of a monopoly is MCMR = which is similar to the equilibrium condition

of perfectly competitive market discussed in Chapter Five.

193

We know thatdQ

dTCMC = . And, MR is derived as follows:

dQ

dPQdQdTRMR == ---------------------------------------------- (2)

Since monopoly price is not constant as in the case of perfectly competitive market, price

cannot be equal to MR for a monopolist. Using the product rule of differentiation

the MR is:

dQ

QdPPdQ

QdPdQ

PdQMR +=+= ------------------------------- (3)

Alternatively, equation (3) can also be written as:

⎥⎤

⎢⎡+=

QdPPMR 1 --------------------------------------------- (4) ⎦⎣ PdQ

ecall that the price elasticity of demandPdQQdPR

QdPPdQ

P .)( =ε . Hence, the expression in

equation (4) is the reciprocal of price elasticity of demand. Thus, the above equation can

be written as:

⎥⎦

⎤⎢⎣

⎡+=

P

PMRε11 ------------------------------------------------ (5)

In equation (P

Lε1

=5), the one in the right hand side of the bracket, i.e., is known as the

rice elasticity of demand

e greater the monopoly power to increase price, and vice-versa.

Lerner Index, which measures the degree of the monopoly power. The formula indicates

that monopoly power is the reciprocal of the price elasticity of demand. Or, it implies that

the extent to which the monopolist can influence the price of its product depends upon

the elasticity of demand for its product. That is, the lower the p

th

194

Since the price elasticity of demand for normal goods is always negative12, equation (5)

can also be written as:

⎥⎦

⎢⎣ //1

P

PMRε

-------------------------------------------- (6)

The above equation will be us opolist’s price, it

⎤⎡−=

1

s MRed to obtain either the mon , or its

rice elasticity of demand (p pε ) when any two of the three variables are known. You

should note that, this form more relevant than the usual ula is ⎥⎦

⎤⎡∆ PQ⎢⎣ ∆ QP

. in terms of

yielding accurate Pε value for the monopolist’s product unlike when discrete price and

onopolist are given.

inally, the equilibrium condition of a monopoly,

output values of a m

MCMR = , is given by: F

MCPP

=⎥⎦

⎤⎢⎣

⎡−

//11ε

-------------------------------------------- (7)

We can also use the elasticity formula to express the optimal pricing policy of a

monopolist. The optimal price of a monopolist is:

⎥⎦

⎤⎢⎣

⎡−

=

//11P

MCP

ε

----------------------------------------------- (8)

Equation (8) indicates that the market price of a monopolist is a markup over its marginal

cost; where the amount of the markup also depends on the elasticity of demand. The

markup is:

⎥⎦

⎤⎢⎣

⎡−

//11Pε

---------------------------------------------------- (9)

1

12 Recall th y of demand for normal goods is always negative due to the law of demand,

which postulates an inverse relationship between price and quantity demanded. Moreover, since the

importance of elasticity is to understand the magnitude of responsiveness of consumers to changes in

at the price elasticit

price, it is conventional to use absolute value in order to make it a positive value.

195

Since a monopolist will always operate where the elasticity of demand for its product is

elastic due to barriers to entry, we know that // Pε is greater than unity. Hence, the

markup is also greater than one. That is, since ,1// >Pε .1//

1<

pε It follows that

//11

pε− – the denominator of equation (9) – is between zero and one. Finally, 1 divided

by a number between 0 and 1 (for instance, 0.5) is greater than one.

6.4 ORIGINS OF MONOPOLY POWER

T origin of monopoly power. There are barriers to

entry and exit. The four types of barriers are:

low cost production or technology;

3. contr l egic raw mat nd

4. Government may grant a firm an exclusive right to serve the market for a

particu r e

1) The Minimum Efficiency Scale (MES):

MES refers to the level of output that minimizes average cost relative to the market size

or m

The shape of ATC or MES, which is determined by the technology of production, is an

impo a m ively or

onopolistically. If the MES of a technology is very small it means that the technology

capacities but facing similar market size in two separate markets/areas are depicted.

here are several factors that lead to the

1. The minimum efficiency scale (MES);

2. Exclusive (special) knowledge of

A o over strat erials; a

la product or s rvice.

arket demand.

rtant factor that determines whether arket will operate competit

m

of production is cheaper. Hence, the smaller the MES relative to the size of the market,

the easier will it be for other firms to enter into the market and hence we might expect

that competitive condition will prevail and vice versa. Consider the following graphs

where the ATC curves and the demand curves of two monopolists with different

196

A Monopolist with Small MES A Monopoly with Large MES

Figure 6.1: Comparison of MES under Pure Monopoly

list in

arket. Therefore, we would expect that the first market might operate as a

ountry.

P

P* P*

O MES QM Q O MES QM Q

ATCATC

MC MC

P

In the first graph of Figure 6.1, there is a room for other firms to enter into the market,

each charging a price close to P* and operating at a relatively small scale since the MES

is less than the market demand, QM. In the second graph, only one firm can make positive

profit and the firm will be a monopolist. This is because, the incumbent firm (or the firm

already in the market) in the latter case has enough cost advantage to be able to

discourage other firms from entering into the industry as compared to the monopo

the first m

competitive market and the second would operate as a monopolist.

Technology may be such expensive that relatively large firms can invest and produce at a

lower cost. Another reason is, the size of the market may not allow the existence of more

than a single large plant size monopoly. Once a monopoly power is established entry will

be difficult because any new entrant must be able to produce at a relatively low cost

compared to the already established monopoly. This is likely to result in loss for these

potential firms, as it likely corresponds to a price level below the shut-down price.

Examples include electricity, telecommunication, and other utilities in our c

197

Macroeconomic policy of a country can influence the size of the market. If a country

ternational

s, people would prefer to travel through other countries Airlines or Airways and

hence EAL wo

Conversely, if a country fo s res e tra olicy se protect domestic

firms fro petitors so that the m e i d to t citiz ts own

country, then m sti es re likely to take hold.

Hence, ono ris o E ve ma iz is not

feasible ncre si m an er thr om firms,

then the ustry is liab e of ion ove i on. In

practice th r on op w ov nt intervention are costly.

Thus, from on should be weather th

In developing countries, the deadweight

Exclusive (special) knowledge of low cost production or technology:

m may develop or invent a unique product or technique of production and steps to

being copied by competitors by having patent right or copy right. Thus,

ill give a firm an exclusive right to produce a certain

follows non-restrictive foreign trade policy, domestic firms may face competition from

foreign firms and hence the domestic firms’ power to influence price will be much less. A

good example is the competition the Ethiopian Airlines (EAL) faces from foreign

Airlines (Airways) in international flights or transporting citizens and foreigners to the

outside world. The implication is that if the EAL sets higher fares for in

flight

uld lose its market share.

llow trictiv de p in the nse to

m foreign com arket siz s limite he ens of i

onopoli c practic are mo

if m poly a es due t large M S relati to the rket s e and it

to i ase the ze of the arket d/or if th e is no eat fr foreign

ind le to som form regulat or g rnment nterventi

, bo egulati of mon oly po er and g ernme

society point of view, the questi e deadweight loss of

monopoly exceeds the cost of regulation or not.

loss of monopoly is greater than the cost of regulation. Therefore, in most developing

countries, public provision of essential public services and utilities for development is

preferred to leaving them in the hand of monopolists.

2) A control over strategic raw materials:

If a firm has exclusive control over a given raw material, the firm can become a

monopoly.

3)

A fir

keep this from

patent right or copy right w

198

commodity or to use a certain production technology and as a result the firm becomes a

monopolist established due to the above factors, will have enough cost advantage to be

ble to discourage other firms from entering into the industry. The incumbent firm (or the

ive right to serve the market for a

particular product or service:

u h en by the government to serve solely a given

r ical area within its jurisdiction is called franchise. The best example

a is the National Lottery.

monopoly.

A

a

firm already in the market) may also, under certain conditions, threaten potential entrants

that it will cut prices if they attempt to enter into the industry.

4) Government may grant a firm an exclus

A monopoly established d e to t e right giv

market or geog aph

of such a monopoly in Ethiopi

Check Your Progress

e differences between a perfectly competitive firm and a pure

t?

power.

n MC, AVC, and ATC are all U-shaped while AFC

hyperbola. Wide U-shape of ATC, as in the case of the monopolist in the second

Unlike perfectly competitive market, however, a unique supply curve cannot be derived

from th curve of a monopolist. This is because since entry to and exit from the

a

of AMC = t monopo price will be equal or below the

1. What are th

monopolis

2. Discuss the different sources of monopoly

6.5 SHORT RUN EQUILIBRIUM OF A PURE MONOPOLIST

The short run cost functions confronting a monopolist are identical with those faced by a

competitive firm. That is, the short ru

is

market in Figure 6.1, implies that the capacity of the plant installed is very high.

e MC

market is difficult, the price of monopolist cannot reach the minimum point

)( VCorAVC . The probability tha ly,

199

minimum of AVC depends on the strategy o the incumbent monopolist to discourage

potential entrants by reducing its price.

f

As mentioned under Section 6.3, the profit maximization rule is the same in both perfect

competition and monopoly markets. Accordingly, a monopolist will choose to produce

in order to maximize profit. Moreover, price is equal to

enue (

MCMR =output level for which

ARP =average rev ) in both markets. Nevertheless, the marginal revenue of a

monopolist at any unit of output/production is always less than its price ( PMR < ) unlike

that of price-taker competitive firms where marginal revenue is equal to the ongoing

market price ( PMR = ).

In order to understand the short run equilibrium price and output of a monopolist it is

portant to derive the relationship between demand, price, and average and marginal

rves. The relationship can be best explained mathematically. To this end,

l mal

goods. e demand function for normal goods is

ing. If we as me a linear demand function (for simplicity), we would

unction of the form:

im

revenue cu

recal that there is an inverse relationship between price and quantity demand for nor

This law of demand implies that th

downward slop su

;PQ βα −= where alpha )(α and beta )(βhave a demand f are

ers. From this demand function, the following important points and

o the demand function:

constant numb

relationships can be derived:

β−=dPdQ 1) The slope f

QP

QP

dPdQ

P .. βε −== 2) The price elasticity of demand:

.PQPQ βαβα −=−⇒−=3) The invers de emand function: Rearranging this gives:

QPββ

α 1−= , setting ba ==

ββα 1; we get

. From this is the vertical intercept and bQaP −= a b− is the slope.

.= 4) Total revenue: QR PT

QbQaTR )( −= 2bQaQTR −=

200

PbQaQ

bQaQQTRAR =−=

−==

2

5) Average revenue:

6) Mar inal revenueg : bQadTRMR 2−== ; where a is the vertical intdQ

ercept (the level

of MR when output is equal to zero) and b2− is the slope of the MR curve.

MR13

From equation (6) above, it is also clear that the of a monopolist is a downward

sloping straight line with the same vertical intercept as the price equation or inverse

demand function but with a slope which is tw e steeper. That is, the slope of the price

and that of the MR in equation (6) is

ic

equation in equation (3) is b− b2− . Furthermore,

elasticity of demand will b unitary and that of the will be at its maximum

when [See Figure 6.2].

Figure 6.2: The Relationship among Demand,

e TR

.0=MR

pε , MR, and TR under Monopoly

You should also note that a monopolist would always operate in the short run in the

gion ty of demand in elastic. This implies that a monopolist will

ake elasticity of demand inelastic (

re where the price elastici

not set a price that will m 1// <Pε ) (i.e., below *P in

deterring potential firms from entering into

e market (by reducing price below

the above figure), unless it has a strategy of

th *P ). The reason is that the MR of a monopolist (the Note that the values of price and MR in equations (3) and (6) corresponding to give the vertical intercept equal to , and this is the only point at which P = MR for a pure monopolist.

13 ,0=Q a

P* 1// =pε

DD

TRp 1// >ε

1// <pε

MR=0 Q

P, , TR MR

201

additional revenue accrued to the monopolist due to sale of an additional unit of output)

ill be negative when the price elasticity of demand is less than one (or inelastic).

ith the short run profit maximization condition of a monopoly firm at hand, we can

price and output as well as the profit of a

onopolist. To do so, we need to have information on either (1) a serious of output sold

uantity demanded for its product) and price per unit of output (or in short unit price)

harged by a monopolist of our concern or (2) the market demand function it faces for its

roduct and its total cost function, representing the plant capacity installed, to meet the

urrent and future demand. The main procedures one should follow in order to determine

e monopolist’s short run equilibrium price, output, and profit depending on the type of

formation provided are illustrated using two examples for normal goods.

xample 1: Suppose we have information only about the amount of output supplied by a

t

d

run e list as well as its profit associated to each

am

w

W

now determine the short run equilibrium

m

(q

c

p

c

th

in

E

hypothetical ABC monopolist and the unit price consumers are charged per outpu

emanded (as shown in columns 1 and 2 of Table 6.1). Having this information, the short

quilibrium output and price of the monopo

ount of output sold are determined as shown in the same table (Table 6.1).

Table 6.1: The Short Run Equilibrium of a Monopolist

Qd Price(P) TR MR TC ATC MC Profit

5 24.80 124.00 - 214.50 42.90 - -90.50

13 23.20 301.60 22.20 228.90 17.61 1.80 72.70

23 21.20 487.60 18.60 264.90 11.52 3.60 222.70

36 18.60 669.60 14.00 341.60 9.49 5.90 328.00

50 15.80 790.00 8.60 462.00 9.24 8.60 328.00

60 13.80 828.00 3.80 572.00 9.53 11.00 256.00

66 12.60 831.60 0.60 647.46 9.81 12.58 184.14

72 11.40 820.80 -0.18 730.40 10.14 13.82 90.40

202

From the table above, the maximum profit is 328. The monopolist achieves this profit

when the demand for its product is either 36 or 50 units. Despite this, the monopolist will

pply 50 units of output in stead of 36 since the short run profit maximization condition su

or the equality of its marginal revenue and marginal cost ( 6.8== MCMR ) holds only at

this output level. Accordingly, the short run equilibrium price is Birr 15.8. Furthermore,

the equilibrium output, price, and profit of the monopolist can be depicted graphically

using the marginal approach as follows.

After determining price, the rginal revenue and marginal cost of the monopolist, we

can also calculate the price el icity o and g eq (6) of Section 6.3. That is,

price elasticity of demand is culated llow

E

15.8 9.24

50 Q

ATC

MC

P, MC, ATC Profit

8.60

ma

ast f dem usin uation

cal as fo s:

⎥⎦

⎤⎢⎣

⎡−=

//11P

PMRε

.

Substituting the values of MR and P , we get:

⎥⎦/⎤⎡

−=118.156.8Pε

.

ing es:

⎢⎣ /

Rearrang this giv ].// Pε18.8 //[ P156. ε −

=

// ε

8.15//8.5 P1

P

6.8 ε −=⇒

8.15//8.15//6.8 −=⇒ PP εε

8.15//8.15//6.8 −=−⇒ PP εε

203

.8.15//2.7 −=−⇒ Pε

Finally, we get the price elasticity of demand:

.2.2419.22.78.15//

.≈=

−−

=Pε

This implies that the price elasticity of demand for the product of this hypothetical

monopoly is elastic. The value can be interpreted as: As a result of one percent increase

the price of the monopolist’s product, consumers will decrease their consumption by

in

about 2.2 percent, and vice-versa14.

As mentioned earlier, we also know that the monopolist’s price is always greater than the

MC of producing an additional unit of output. The issue is thus to know by how much the

price of the monopolist is markup over its MC ? The markup can be determined using

equation (9) of Section 6.3 as follows:

=

⎥⎦

⎤⎢⎣

⎡−

=

//11

1

P

Markup

ε ⎥⎦⎢⎣ 419.2

=

⎥⎤

⎢⎡− .

11

1

⎥⎥⎤

⎢⎡ −

.1419.2

1

⎦⎢⎣

.419.2

=

⎥⎥⎤

⎢⎡ .

419.1

1

⎦⎢⎣

.419.2

= 84.11=

544303798.0

price, and profit of the mo

Example 2: Unlike the above example, suppose that we now have information only about

the market demand function a hypothetical XYZ monopolist faces for its product and its

total cost function. Suppose the demand and cost functions are PQ 5.060 −= and 2348 QTC += , respectively. The steps involved in order to obtain the short run output,

nopolist are given below.

Solution:

(A) The steps involved to find the short run equilibrium output and price levels are:

14 Note that the accuracy of this value of // Pε can be verified by substituting this value into equation (6)

to obtain or into equation ai 6.8=MR (7) to obt n 6.8=MC .

204

1st: Find the inverse demand function.

PQ 5.060 −=

PQ 5.060 −=−⇒

QQP 21205.05.0

60−=−=⇒

2nd: Find TR.

3rd: Find MR.

PQTR = 22120)2120( QQQQTR −=−=

QdQdTRMR 4120 −==

4th: Find MC.

QdQ

QddQ

dTCMC 6)348( 2

=+

==

5th: Equate MR to

.

6th: Substitute into the inverse demand function to obtain price.

.MC

QQ 64120 =−⇒

QQ 46120 +=⇒

Q10120 =⇒

1=⇒ Q 2

12=Q

P 96)12(21202120 =−=−= Q

and price of the monopolist are 12 and 96

respectively.

) The profit of the monopolist is calculated as:

Therefore, the short run equilibrium output

(B

TCTR −=π

]348[]2120[ 22 QQQ +−−=π .

Substitutin , we get:

+−−=π

g 12=Q

])12(348[])12(2)12(120[ 22

)]144(348[)]144(21440[ +−−=

205

]43248[)]2881440[ +−−=

.7724801152 =−=

(C) In order to show the equilibrium price, output, and profit graphically we need to

follow the following steps.

1st: Find the value of MR and t th ilibr utput, 12=QMC a e equ ium o

QdQdTRMR 4 Q120= −=

dQ=

dTCMC 6=

)12120 72(4 =−=MR 72)12(6 ==M

2nd: Find at Q

C

ATC 12=

QQ

QTCATC

23+== 48

.4012480

1243248

12)12(348 2

==+

=+

=ATC

3rd : Graphic solution:

E

96

40

72

12 30 Q

ATCMC

P, MR, MC, ATC

206

Check Your Progress

On the basis on the information given in Example 2 above, answer the questions below.

1. Calculate the price elast and and the markup at the short run equilibrium

o and price of the YZ

2. W price elasticity of demand when MR is 40 and price is

80?

akes the MR zero? What will be the price level and TR at

is output level? How about the elasticity of demand?

6.6 THE LONG RUN EQUILIBRIUM OF A PURE MONOPOLIST

g run, the monopolist wil its plant size or to use the

l nt optimally to produce output that will maximize profit. Hence, if the

opolist earns excess profit in the short run with the existing plant(s), it must

determine weather a plant of different size will earn larger profit in the long run or not.

Since entry is blocked, it is not necessary or a must for a monopolist to operate at optimal

othe ords, the is nothing that induces to install additional plant size so as to

t inimum of LAC (where LAC will be equal to the LMC) and obtain

LMC is the chang in tot sociat d with the change in output when all factors

nt size itself is changed (in the long run). To

understand how the long run m C) and long run average cost (LAC)

e that a monopolist has installed two plant sizes in the short run in order to

meet the current and future demand for its product. Furthermore, assume that the change

anded t a change in price is constant. Given the relevant information in

2 elow, Table 6.3 helps us compute the LMC and LAC.

icity of dem

utput monopolist X .

hat will be the value of the

3. What level of output m

th

In the lon l have time to expand

existing p a

mon

scale. In r w re

operate a the m

normal profit if not its own strategy.

The e al cost as e

including the plant scale vary or when the pla

arginal cost (LM

behave, assum

in quantity dem o

Table 6. b

207

208

Table 6.2: Information for Deriving LMC

Q MR TC1 TC2

0 -

1 34.5 11 14.25

2 33.5 14 15.00

3 32.5 1 9 16.25

4 31.5 26 18.00

Table 6.3: Determination of the LMC from Short Run and Long Run Plants

Q P TC2 SAC1 SAC2 SMC1 SMC2 LMC LAC ProfitTR MR TC1

1 34.5 34.5 - 11.00 14.25 11.00 14.25 - - - 11.00 23.5

2 5 34.0 68.0 33. 14.00 15.00 7.00 7.25 3 0.75 3 7.00 54.0

3 33.5 100.5 32.5 32.50 16.25 6.33 5.42 5 1.25 2.25 5.42 84.25

4 33.0 132.0 31.5 31.50 18.00 6.50 4.50 7 1.75 1.75 4.50 114.0

The problem of the monopolist is which of the two plants should be used in the short and

ng run in order to maximize profit. If the monopolist wants to produce only one unit of

ut.

ut for

diffe

and olumn of the third row of

Table 6.3, this will be equal to 2.25, which is TC2 (16.25) less TC1 (14). Furthermore,

lo

output in the long run, then the best choice would be to use plant one. This is

because 21 SACSAC < or 21 TCTC < . If the monopolist wants to produce two units of

output, it should also choose to use the first plant. Since the first plant is chosen to

produce the first and second units, the SMC of the first plant will also be the LMC up to

the second unit of outp

However, the monopolist has to choose plant 2 if it wants to produce 3 units of outp

12 SACSAC < or 12 TCTC < . In this case, the LMC of the monopolist will be the

rence between the total costs of a plant chosen to produce 3 units output (plant 2)

2 units of output (plant 1). As indicated in the eleventh c

208

since the plant 2 is the one to be chosen to produce 4 units of output, the LMC will be

(the SMC of the plant 2). 1.75

who

poin C = The corresponding unit price is P4.

It is thus clear from Figure 6.3 that the monopolist’s point of optimal operation is on the

f

e ewpoint of the society for the monopolist

is not operating at the minimum point of the LAC (envelop) curve. This is because

producing 5 units at point

i

e and implying a normal

(zero) profit. This implies that since there is output restriction or since the monopoly firm

d

l

D

onopolist may prefer to produce at point E3 only if there are firms

p

As indicated in Figure 6.3, the optimal plant of the monopolist in the long run is plant 2

se 2SAC is tangent to the LAC curve and the long run equilibrium is established at

t 2E where SMMR = .2 LMC

alling part of LAC. To the contrary, producing 4 units of output in the long run (or

quilibrium point E ) is not optimal from the vi2

3E where the LAC is at its minimum and where

pSMCLMCLAC === 2 (similar to the case of a competitive firm in the long run) will

ncrease the output of the monopolist and reduce selling price thereby eliminating the

xcess profit that could be enjoyed by producing 4 units of output

oes not produce at its full capacity, price is greater than MC in pure monopoly in the

ong run. This situation, which arises due to restriction of output, is called the

eadweight Loss (DWL) of pure monopoly. This will be discussed in detail under a latter

section.

Nevertheless, the m

lanning to enter into the market and hence the monopolist wants to discourage them or

block entry by reducing price.

209

SAC1

E1

E3

E

ow, we can obtain the monopolist’s price if the

and is given for any level of output. Once the monopolist’s price is

ine the total revenue and the associated profit (or loss) for

ow, we can obtain the monopolist’s price if the

and is given for any level of output. Once the monopolist’s price is

ine the total revenue and the associated profit (or loss) for

2

E

Given the information in the table bel

Given the information in the table bel

price elasticity of demprice elasticity of dem

known, we can also determknown, we can also determ

both the short run and long run. both the short run and long run.

Q MR TC1 TC2

1

E3

E2

Q MR TC1 TC2

0 - - -

1 18 12 17.5

2 12.5 22.8 23.8

3 4 30 26.7

4 3.6 45 30.3

For example, let us calculate the price and short and long run profit (or loss) of the

monopolist if the price elasticity of demand of producing 4 units of output is.6.1 .

SMC2

DD

P1 P2 P3 P4

1 2 3 4 5 Q

LAC

LMCSAC2

MR

SMC1

Figure 6.3: The Long Run Equilibrium of a Pure Monopolist

210

Solution:

1st: Find the unit price of the monopolist when selling 4 units of output .

)( 4P

)//

11(44P

PMRε

−=

)6.1

11(6.3 .4 −= P

)625.01(6.3 −= P 4

P=

)375.0(6.3 4

6.9375.06.3

4

4

=

=

P

P.

2nd: Find the profit of the monopolist when selling 4 units of output. Since, plant 2 is used

to produce 4 units of output we should consider the total cost15 of the second plant to

calculate profit )( 4π .

4244 QQ TCTR −= π )( 42444 QSACPQ −=π

3.304 −= PQπ OR )4

3.306.9(44 −=π

4

==

π 1.83.304.383.30)4(6.9

4

π=−

− 1.8)025.2(44 ==π

3 : Find ,, 23 PP and 1P sequentially

rd

34

3344

34

344 QQ

QPQPQQTRTRMR

−−

=−−

=

34

)3(4.386.3 3−=

P −

)3(1.386.3 3P−=

335.34 P−=−

5.113

5.34==P

3

15 The subscript at the end of the total cost indicates the plant used.

211

2

22332 QPQPTRMR

−==

323

33 QQQQ

TR−−

−

23)2()3(5.114 2

−−

=P

)2(5.344 P−= 2

225.344 P−=−

25.152

5.302 ==P

12

1122

12

122 QQ

QPQPQQTRTRMR

−−− =

−=

12

)1()2(25.155.12 1

−−

=P

15.305.12 P−=−

4 t used to produce each level of

output.

181 =P th: Find profit by considering the total cost of a plan

3233 QQ TCTR −=π

7.26−= PQ3π

8.77.26)3(5.113 = =−π

QTCTR −= 22 Q 21π

5.122 −= PQπ

7.78.22)2(25.152 =−=π

1111 QQ TCTR −=π

121 −= PQπ

612)1(181 =−=π

Ther the ab ve profit figures we can conclude that the short run equilibrium

level of output of the monopolist is 2 units for it yi

efore, from o

elds higher profit as compared to

producing and selling one unit of output (7.7 > 6). In the long run, however, as the profit

212

le ng

an roduce and sell 4

u

vel from producing and selling 4 units of output (8.1) is greater than that of produci

d selling any other level of output (1, or 2, or 3), the monopolist will p

nits of output and thus operates at a point where .6.32 === LMCSMCMR

Check Your Progress

economic profit in the long run? Why or

ndition (rule) of a monopolist the same as the

short run one?

E DISC INATION

ition and ecessary Conditions

iscrimination is the practice of selling a certain product or service of a given

s to different consumers for reasons unrelated to costs. It involves

in diffe nt prices for the same or different quantities of a given quality of a

ers, and/or in different markets based on

t ity of demand.

scrimination is workable when the following three conditions are realized:

power: or at least possess some degree of

opoly power over the commodity or service. That is, it must have some ability to

control the production of the good or service and its price.

ller must be able to segregate buyers into separate classes

li gness or ability to pay for the product or

buyers is based on the difference in elasticity of demand.

st must be able to separate (or segment) the two or more

markets and keep them separate so that it is impossible for one buyer to resale the

1. Can a pure monopolist earn a positive

why not? Discuss.

2. Is the long run profit-maximizing co

6.7 PRIC RIM

6.7.1 Defin N

Price d

quality at different price

charg g re

product or service to different class of buy

elas ic

Price di

(A) Monopoly The seller must be a monopolist

mon

(B) Market segregation: The se

where each group has a different wil n

service. This segregation of

(C) No resale: The monopoli

product to another.

213

6.7.2 Types of Price Discrimination

nsider three types of price discriminations. These are: first,

ird degree price discriminations.

egree (perfec price discrimination: This means that the monopolist sells

t at different prices and prices may differ from person to person.

e ns th t the m opolist sells each unit of output to that individual who values it

lling to pay for it. This turns out that

ut.

ce discrimination monopolist must produce an

al s

Economists usually co

second, and th

First d t)

different units of outpu

This m a a on

most highly at the maximum price that he/she is wi

perfect price discrimination produces an efficient level of outp

To prove this, note that a perfectly pri

t )( MCP =output level where price is equal to the margin co . If price is grater than

n it would mean that there is someone who is willing to pay more than what

to n unit of output; so, why not produce that extra unit and sell to

o

on is an idealized concept as the word “perfect”

ency, we refer to the situation where all the

aking someone better off without making others worse off have already

out. There are few real life ex ples of perfect price discrimination. A

t fferent prices to his/her patients based on their ability

o pay f the closest examples of perfect price discrimination. Other examples

ntial prices to different classes or ranks of train

air transportation (the payment for economic and business

ople fly in the same airplane); cinema hall; football

atch etc. Fo ple, the prices can be differentiated as first class or rank ticket-Birr

watch a football match in a stadium; a

l through train.

the MC, the

it costs produce a extra

that pers n?

However, perfect price discriminati

might suggest. But it is interesting theoretically since it gives us an example of a

resource allocation mechanism (other than perfectly competitive market) where Pareto

efficiency is achieved. By Pareto effici

possibilities of m

been carried am

small own doctor who charges di

t is one o

include, the prevailing differe

transportation; international

class are different though two pe

m r exam

60, second rank-Birr 40; and third rank-Birr 30 to

movie in a cinema hall, or to trave

214

Second degree (non-linear) price discrimination: This means that a monopolist sells

; but every individual who buys the same

goods consumed or depending how much is bought but not across people like first

ost common examples of this type of price

ination are the practice of charging diffe ption at different

bands (blocks) and bulk discounts in public utilities.

or example, the price of electricity often depends on how much is consumed. Suppose

r charges consumers a progressive rate across bands say for the first

H each at a ice of 0.2730 cents; for the next 50 KWH each at 0.2921 cents; and

KWH each at 0.4508 cents. In this case, the payment/ bill of the household

who consumed 200 KWH a month is:

different units of output for different prices

amount of output pays the same price. In other words, price differs across the quantity of

degree price discrimination. The m

discrim rent prices for consum

F

an electricity supplie

50KW pr

the next 100

[ ])4508.0100()2921.050()2730.050( xxx ++= Bill

335.7308.45605.146.13 =++ =

The above example indicates that the price charged by the hypothetical electricity

hence the decision to consume more

er.

ed by such type of monopolist is

sive because price per u es as consumption increases from one block to

another. In this case, consumers who purchase large quantities of the monopolist’s

product or service may face a price equal to MC at some level of purchase.

, since there is consumption at a price greater than

MC (at least for some consumers), there are some ways to make som mers in the

market better off without making others worse off. That is, not all the possibilities to

supplier is progressive in a sense price per unit increases as consumption increases from

one band to another. That is, any output or service consumed within the next higher

consumption band will cost higher price and

depends on the willingness and ability to pay of the consum

Contrary to the example above, sometimes monopolists offer discounts for bulk

purchases, in most cases across blocks. The price charg

regres nit decreas

From the viewpoint of social welfare

e consu

215

maximize social welfare are exhausted. Hence, second degree (non-linear) price

discrimination is Pareto inefficient.

Third degree price discrimination: This occurs when a monopolist charges different

prices for the same commodity in different markets; but every unit of output sold in a

given market is sold at the same price. For this to happen markets must be kept separate

(no resale) and the elasticity of demand of these two or more markets must be different.

Third degree price discrimination is the most common form of price discrimination. An

example of charging different prices in different markets is found in international trade

when a nation sells its commodity abroad at a lower price than in its domestic market.

g the domestic

and less elastic.

price discrimination is: “How does a monopolist determine

trate this with an example, assume that a monopolist sells its product only in two

monopolist is:

This is referred to as dumping. The reason for dumping is that the demand for a

monopolist product is more elastic abroad because substitutes are available from other

nations whereas there can be import restriction in domestic market makin

dem

The key issue of third degree

the optimal price to charge in each market?” The answer is based on the

conditions/assumptions that consumers in each market are not able to resale the good in

another market, and that there are different elasticities of demand in the two (or more)

markets.

To illus

markets. Furthermore, let )( 11 qp and )( 22 qp be the inverse demand functions of market

1(domestic) and market 2 (abroad), respectively. In addition, let )( 21 qqc + be the cost of

producing the output. Thus, the profit maximization problem of the

Max )()()( 21222111 qqcqqpqq21,qq

p +−+ ---------------------------------------- (1)

The optimal solution m

qMR ------------- (2a)

– Equilibrium in market 2 ------------------------- (2b)

ust have:

)( qqMC += – Equilibrium in market 1 -------------)( 2111

)()( 2122 qqMCqMR +=

216

Equations 2a and 2b say that the MC of producing an additional unit of output must be

qual to the MR in each market. If the MR in market 1 exceeds MC, it pays to expand

utput sale in market 1 and vice versa. Using the standard elasticity of demand formula

r MR, we can write the profit maximization condition as:

e

o

fo

)(/)(/

11)( 211

11 qqMCq

qpP

+=⎥⎦

⎤⎢⎣

⎡−

ε

)(/)(/

11)( 212

22 qqMCq

qpP

+=⎥⎦

⎤⎢⎣

⎡−

ε

hese two conditions imply that: ⎥⎦

⎤⎢⎣

⎡−=

⎤⎡−

/)(/11)(11)(

2qqpqp

Pε T ⎥

⎦⎢⎣ /)(/ 22

111 qPε

⎥⎦

⎢⎣−

/)(/1

1

22

qPε

⎤⎡⎦⎣=⇒

1)()( 211

qpqp P ----

⎥⎤

⎢⎡−

11/)(/ qε

--------------------------------------------------------- (3)

If price in the first market is greater than price in the second market )( 21 pp > , then each

ust be greater than 1 and thus we must have: side of equation (3) m

⎥⎥⎦

⎤

⎢⎢⎣

⎡−<⎥

⎦

⎤⎢⎣

⎡−

)(/11

/)(/11

21 qq pP εε------------------------------------------------ (4)

his implies that,

T

)(/

11> -------------------------------------------------- (5

/)(/ 21 qq pP εε)

Therefore, /)(/)1q(/ pp 2qεε < ------------------ ------ ------ ---------- (6)

Equation (6) says that th lower elastic dem (price insensitive)

must have the higher pri ile t ce s e m wil lower price. The

validity of this argument i ate the of a rical example below.

Example: Supp e the d fun s a olis s in et 1 and market 2

are and pq pect Furthermore, assume that its cost

function is . With this information at hand let us:

------ ------ ------

e market with a ity of and

ce wh he pri ensitiv arket l have

s illustr d with help nume

os emand ction monop t face mark

1 1 55 pq −= 2 , res2 270 −= ively.

205 += QTC

217

1) determine pq h i pro he m olist;

2) calculate the profit of the mon t fro ling duct in the two markets;

3) determine price ities man e tw rkets; and

4) show the outputs and prices of the two m s us bac ack diagram

1q 2p t, and ,, 12 at maxim ze the fit of t onop

opolis m sel its pro

the elastic of de d in th o ma

arket ing the k-to-b

Solution:

From the given cost function, the common marginal cost is: 5==dQ

dTCMC .

1. Outputs and prices of the monopolist

(a) For market 1

1st: Find the inverse demand function.

qq

: Find

11 55 pq −=

11 55 qp −=

2nd: Find 111 qpTR =

111 55(TR −= )

21155 qq −=

1

11 dq

dTRMR = 3rd

255 qMR −= 11

4th: Equate MR to MC.

MR MC=1

1 =q

1 −=q

555 − 2 2− 555

502 1 −=− q

252

501 =q

bstitute in the inverse demand function.

=−

(b) For market 2

=

5th: Su 251 =q

55 11 =−= qp 302555

218

1 : Findst the inverse demand function

p−

22 270 pq −=

70q =− 22 2

22

2 5.03522

70 q qp −=−=

2nd: Find TR.

3rd: Find MR.

222 qpTR = 222 )5.035( qqTR −=

=35q2-0.5q22

2

2dTR= 2 dq

MR

4th: Equate MR to MC.

5th: on.

2. The profit of the monopolist:

a et. Thus, total profit will be

= )( 21

22 35 qMR −=

M MCR =2

535 2 =− q

3552 −=− q

302 =q

Substitute 30=q in the inverse demand functi2

22 5.035 qp −=

)30(5.0352 −=p

=−=p 2015352

From the above solution the monopolist will sell 25 units of output in market 1 and 30 in

market 2. The price of a unit of output in market 1 is Birr 30 while it is Birr 20 in the

second m rk

TCTRTR −+π

[ ])205()( 2211 +−+= Qpqpq

Since 21 qqQ += the profit equation is also

219

[ ])20)(5()( 212211 ++−+= qqpqp qπ

[ ])20)3025(5()2030()3025( ++−+= xx

)20)55(5(600750 +−+=

20275(1350 +−=

3.

)

10552951350 =−=

Price elasticity of demand

Market 1

11 55 pq −=

Slope: 11

1 −=dpdq

1

1

1

11 //

qpx

dpdq

p =ε

25301// 1 xp −=ε

2.12 .125

// 1 −−=pε30

==

Market 2

22 270 qq −=

22

2 −=dpdq Slope:

2

222 // pxdq

p =ε 2 qdp

30202// 2 xp −=ε

33.133.13040//

.

2 =−=−=pε

220

The above result tells us that demand is more elastic in market 2 as compared to market

1. Therefore, as described in equation 4 to 6 earlier in this section, the monopolist charges

lower price in market 2 compared to market 1.

4. Back to back diagram

The relationship between output and prices in the two markets can be represented using

what is known as the Back to back diagram as follows.

o ive to price changes16.

P

q2q1

DD2MR2

DD1

MC = 5

P2=20

P1=30

MR1

q1 q2=30 =25

Market 1 Market 2

Figure 6.4: The Back to Back Diagram of Third Degree Price Discrimination

From the above figure, it is clear that the market with lower elasticity of demand

(market1) has higher price. This implies that the monopolist will charge high price in the

market in which quantity purchased is less resp ns

16 pp For further reading on this topic, see Koutsoyiannis, A. (1998). “Modern Microeconomics”. 2nd edition,

197.

221

6.8 A MULTI-PLANT MONOPOLIST

o far it has been assumed that a monopolist owns and produces by means of only one

stall more than one plant and

conditions may differ from one plant to another. Such a monopolist is called a

the allocation of production

plant 2 in the case of two plants).

opolist’s profit maximization rule is equating MR MC. However, we have only

e function and many marginal cost functions for a multi-plant

The marginal cost function of plant 1

Common or the multi-plant marginal cost function

commo

produce, and also find how much should be produced by each plant.

S

plant. Nevertheless, it is also possible for a monopolist to in

hence cost

multi-plant monopolist. The problem of such a monopolist is

among the different plants (say, between plant 1 and

The mon

one marginal revenu

monopolist. For the case of a monopolist with two plants, we have:

=1MC

=MC The marginal cost function of plant 2 2

=MC

The profit maximization rule of this multi-plant monopolist is depicted in Figure 6.5.

Example: Given the price and MC figures of two plants for each level of output,

determine the MR, the n MC, and the total output a multi-plant monopolist should

MR

MCMC1 MC2

DD

O q1 q2 Q O Q* = q1+q2 Q

Each Plant Multi-plant Figure 6.5: Short Run Equilibrium of a Multi-Plant Monopolist

222

Table 6.4: The Short Run Equilibrium of a Multi-Plant Monopolist

Q P MR MC1 MC2 MC

1 5.00 5.00 1.92 2.04 1.92

2 4.50 4.00 2.00 2.14 2.00

3 4.10 3.30 2.08 2.24 2.04

4 3.80 2.90 2.16 2.34 2.08

5 3.55 2.55 2.24 2.44 2.14

6 3.35 2.35 2.32 2.54 2.16

7 3.20 2.30 2.40 2.64 2.24

8 3.08 2.24 2.48 2.74 2.24

9 2.98 2.18 2.56 2.84 2.32

10 2.89 2.08 2.64 2.94 2.34

The common MC is obtained by arran ging the MC figures in ascending order. The profit

al to the common MC. Once the total

output to produce is determined, the monopolist will produce 5 units using plant 1 and 3

is maximized when MR = MC1 = MC2 = MC.

Mathematical Example:

maximizing level of output the multi-plant monopolist will produce is 8 units of output. It

is at this level of output that the MR will be equ

units using plant 2. This is because profit

Suppose a monopolist faces a linear demand function PQ 2200 −= for its product. Let, the

cost functions of the two plants be: 11 10qTC

= and 222 25.0 qTC = , respectively. Given the

above information, find 1q , 2q ,

P and the profit of the multi-plant monopolist.

223

Solu

1 : Find the inverse demand function, TR, and MR:

Inverse demand function

tion:

st

PQ 2200 −=

QP 5.0100 −= ;

here Q = q

W

PQ 2200 −=−

1 +q2

Total revenue

PQTR =

QQTR )5.0100( −=

25.0100 QQ

Marginal revenue

−=

dQ

MR =

Q−= 100

2

dTR

nd: Find the marginal cost of the two plants; 1MC and 2MC

10)10(

1

1

1

11 ===

dqqd

dqdTCMC

22

22

2

22 5.0)25.0( q

dqqd

dqdTCMC ===

3rd: Equate the MR to the two MCs ( 11MCMR = and 2MCMR = )

1MCMR =

10100 =−Q

10)2 =q

10100 21 =−− qq -------------------------------------------------------------

(100 1 +− q

(1)

2MCMR =

25.0100 qQ =−

221 5.0)(100 qqq =+−

224

------------------------------------------------------- (2)

tions in step 3 using simultaneous equation procedures to obtain

the output levels to be produced by each plant.

221 5.0100 qqq =−−

4th: Solve the two equa

⎩⎨⎧

−×=−−=−−

)1](5.0100[10100

221

21

qqqqq

⎨⎧

−=++−⇒ 21

5.010010100

qqqqq =−−

⎩ 221

05.010 2 =−⇒ q

205.02

10==⇒ q .

Substituting this output level into one of the two equations we found under step 3, we get the

utput that should be produced using plant 1. Let us substitut into the first

e

e 202 =qoptimal o

quation17.

10100 21 =−− qq

1020100 1 =−− q

80 − 101 =q

7010801 =−=q th l arket price by substituting 90702021 =+=+= qqQ5 : Calcu ate the m into the inverse

d one. emand function derived from the market demand in step

QP 5.0100 −=

)90(5.0100 −=P

5545100 =−=P

6th: Finally, calculate the profit of the multi-plant monopolist using the total revenue – total cost

approach. It can be calculated in two ways: either by substituting total output into the

to ining total revenue by multiplying price and total outpu as

)(Q

t )(Qtal revenue function or obta

follows:

)( 21 TCTCTR +−=π

17 Afte ether substituting them into both equations will satisfy the

equ xt step! r obtaining q1 and q2 you should check wh

ality. Do this before proceeding to the ne

225

0 221 qq +

2+−

50 +−

)25.01()5.0100( 2QQ −−=

])90(5.0)90(100[ 2−= ])20(25.0)70(10[

409000[ −= ]100700[]

[ ] 418004950 =−= 50

OR

)( TCTCPQ +− 21=π

221 qq +=

6.9 THE SOCIAL COST OF MONOPOLY

Is the existence of a monopolist evil? The answer to this question depends on the pricing

decision of the monopolist. If the monopolist charges a single price, the answer is

“YES”! If the monopolist charges different prices based on the willingness to pay (WTP)

[or if the monopolist sells each unit at the maximum price consumers are willing to pay],

i.e., if the monopolist can exercise the first degree price discrimination, the answer to the

above question would be “NO”! That is, a monopolist exercising the first degree price

discrimination produces a Pareto efficient outcome as it expands output to the level

where P = MC. If the monopolist exercises the second or the third degree price

discrimination (block pricing, bulk discount, market segregation based on differences in

price elasticity of dem e is Pareto inefficient though the inefficiency is

m onopolist charging a single price is evil; that of

a second or third degree price discriminator is less evil; and that of a first degree price

discriminator is consistent with social welfare maximization (just like a perfect

competitor).

e that a remarkable outcome of a perfectly competitive

market is an efficient resource allocation, which results in a maximum social welfare and

maximum employment. This is because the equilibrium of a competitive firm is at the

)25.010()9055( −×

])20(25.0)70(10[4950 2+−=

4150=

and), the outcom

inimal. To sum up, the existence of a m

We have seen in Chapter Fiv

226

equality of price and the MC of producing the good which implies that the marginal

utility of goods consumed is also equal to the price charged. Hence, if

cation efficiency) and

)(MU )( p

MCP = (i.e., allo PMU = (i.e., maximization of consumers’

welfare), then 18.

A t is through

using t nsumers’ surplus (CS) and producers’ surplus (PS).

Consu e difference between what consumers are willing to pay for

different levels of quantity demanded (proportional DD curve; see in the figure

below at they actually paid to consume amount of output (prorata DD

curve; see

the perceived DD curve and above the equilibrium price or (prorata DD curve) or simply

by area

willin ay a price higher than the equilibrium price or it is the savings of the

c

CS E CS E

Linear Demand and Supply Curves Non-Linear Demand and Supply Curves

PMCMU ==

n alternative way to understand the efficiency of the competitive marke

he concepts of co

mers’ surplus is th

PDD

)19 and wh EQ

ADD in the figure below). In Figure 6.6, it is shown by the area to the left of

1EPPE . In other words, it represents money not spent by consumers who have the

gness to p

onsumers from buying EQ at equilibrium price EP .

P1 P1

PS PS

D

18 ack to Chapter Two on how the equality of P = MU is derived based on the ordinalist argument.

perceived demand curve can be linear or non-linear. Because determining CS and PS from non-nowledge in integral calculus, which is discussion of consumers and producers

surpluses using linear demand and supply functions for the mathematical example in this section.

Refer b19 The

linear demand and supply functions requires some advanced kbeyond the scope of the course, we restrict ourselves to the

DDP

PEDDA

P

QE

MC=SS

QE

MC=SS

DDP

P

PE

227

Figure 6.6: Consumers’ Surplus and Producers’ Surplus

The MC of producing a good rep quating the MC or the supply

curve that passes through point E to demand (as in the above graphs) gives the producers’

surp m

pric

firms

different quantities of output). Put differently, it is the money that suppliers receive solely

beca

produce that unit. In Figure 6.6, it is shown by the area

These perfectly competitive market, the social cost of

onopoly arises due to the fact that a monopolist operates inefficiently as compared to

that price under monopol is greater than price

nder perfect competition or and the monopolist’s optimum level of

o

becau

resents the supply curve. E

lus (PS). Producers’ surplus is the area above the MC curve but below the equilibriu

e ( EP ). The PS indicates the difference between the market price (what competitive

arge per unit) and the MC (what competitive firms actually incur for producing ch

use of selling each unit of output (below QE) at a price above what they incur to

.EDPE

being the CS and PS in a

m

y )( MPperfect competition in the sense

)( CP CM PP >u

utput )( MQ is less than output under perfect competition )( CQ or CM QQ < . This is

se unlike the competitive firms that equate MCP = in order to determine

output and price, which in turn always makesequilibrium MRP = , a monopolist

mines its equilibrium output and price by equating MR MC= and hence its price is deter

gr

As a result, som

the m

surpl

(DWL)

eater than both marginal revenue and marginal cost.20

e part of the CS and PS in a perfectly competitive market are lost when

arket is monopolized by a single firm. These losses in consumers’ and producers’

uses due to monopoly power are known as the social cost or the Dead Weight Loss

of monopoly. Consider the graph below.

20 Note that P > MC implies that the value of the good measured in terms of market price is greater than the

social cost measured in terms of MC.

228

The a

comp se. As

th

area

that w by

A B EC

EM

Figure 6.7: The social Cost (Dead Weight Loss) of Monopoly

bove graph shows the change in the CS and PS when the market is changed from

etitive to monopoly or from monopoly to competitive. Consider the first ca

e market changes from perfect competition to monopoly, the CS goes down by

MCC APE [area CABE since they lose some surplus from the reduction in the units

ere used to be sold under perfect competition MC Q

P

Q − ; and area MC BAPP since

mers are now getting all the units they buy at a higher price]. Alternatively, we can

der what happens when a monopolist is replaced by a perfectly competitive firm. As

arket changes from monopoly to perfect competition, goes up by

MCC APE [area MC BAPP since consumers are now getting all the units they used to

nder mon poly at a lower price; and area CABE since they now gain some surplus

al units )( MC QQ − that are now sold in the market]. Let us continue our

ssion with the first approach – where a perfect competitor is replaced by a pure

consu

consi

the m the CS

area

buy u o

from the addition

discu

monopolist.

P

MC P F PM PC

DDC=MRC=MC

DDM

MRM

QM QC Q

D

229

The PS, on the other hand, goes up by area due to the higher price on the units

at were already being sold; and goes down by due to the loss from the decline

elling

MC BAPP

CM BEEth

)( MC QQ −in the level output as the firm is not s now.

ers to the monopolist, and hence one

de of t rket (the producer) is made better off while the other side (consumers) is

d

How BE and represent the Dead Weight Loss (DWL) due to

monopolist’s price than paying the completive price. The DWL due to monopoly like

at of the DWL due to tax increase measures the value of the lost output by valuing each

e that people are willing to pay for a unit. In other words, as

e move from competitive to monopoly output, the sum of the distance between the

lost

(are .

Clearly, an economy is performing well when it generates much to the consumer surplus

is s em.

Nu

ndency of moving from competitive to monopoly output. If the

emand and total cost functions are Q = 100 – 2P and TC = 14Q + 2Q2 respectively,

C. Calculate the CS and PS under competitive and monopoly market structures.

The area MC BAPP is just a transfer from the consum

si he ma

ma e worse off; but, the total surplus does not change as a result of this transfer.

ever, the areas A C CM BEE

monopoly behavior.

The DWL provides a measure of how much worse off people are paying the

th

unit of lost output at a pric

w

demand curve and the MC curve generates (gives) the value of the

output )( MC QQ − due to monopoly behavior. The total area between the two curves

a CM EAE ) is the DWL when moving from competitive to monopoly output

and an inefficient situation is one in which the maximum amount of consumers’ surplus

queezed out of the syst

merical Example:

Assume that there is a te

d

A. Determine PC, QC, PM, and QM.

B. Show the equilibrium Q and P you obtained in (A) above graphically.

230

D. Calculate the part of CS transferred to the monopolist due to inefficiency

monopoly

of

.

Solution

A. E

(i

50 –

36 = 4.5Q

Q

E. Calculate the social cost (net loss or DWL) of monopoly.

:

quilibrium Q and P:

) In perfectly competitive market:

P = MC

0.5Q = 14 + 4Q

50 – 14 = 4Q + 0.5Q

C = 8 PC 0 – 0.5Q OR PC = 14 + 4Q

– 0. )

= 5

= 50 5(8) = 14 + 4(8

= 50 – 4 = 14 + 32

PC = 46 PC = 46

(ii) In monopoly market:

TR = P.Q

= (50 – 0.5Q).Q

= 50Q – 0.5Q2

QTRR −=∂

= 50 Q∂

M

QTCMC 414 +=∂

= Q∂

Equate MR MC: MR = MC

50 – 14 = 4Q + Q

6

Q

to

50 – Q = 14 + 4Q

3 = 5Q

M = 36/5 = 7.2 PM

= 50 – 0.5(7.2)

= 50 – 0.5Q

231

= 50 – 3.6

PM = 46.4

B. Graphical presentation of the results under (A)

C.

i)

Consumers’ and producers’ surplus:

( Under perfect competition:

.16)8)(4(21

==⇒ CS

)8)(4650(21

−=CS

.128)8)(32(21

2

==⇒ PS

)8)(1446(1−=PS

( ii) Under monopoly:

.96.12)2.7)(6.3(

21

==⇒ CS

)2.7)(4.4650(2

−=CS

1

232

6.12992.2568.103

)2.7)(6.3()2.7)(8.28(21

)2.7)(8.424.46()2.7)(148.42(21PS −+−=

=+=

+=⇒ PS

⇒ PS

D The amount of surplus transferred from consumers to the monopolist: .

= (46.4 – 46

.

Method (i)

(PM – PC) x QM

) x 7.2

= 0.4 x 7.2 = 2.88

E DWL due to monopoly

of

the triangle shaded is:

The DWL is represented by the shaded area in the figure under (B) above. The area

44.1)8.0)(6.3(21

)2.78)(8.424.46(21

−=DWL

==⇒

−

DWL

Method (ii)

Alternatively, DWL is the (negative) net change in consumers’ and producers’

surpluses.

Changes in CS = CS under monopoly – CS under perfect competition. That is,

(LOSS!)

Changes in PS = PS under monopoly – PS under perfect competition. That is,

(GAIN!)

e (NCh) in consumers’ and producers surpluses is:

The net change is negative – indicating an overall loss to the economy:

Method (iii)

04.31696.12 −=−=∆CS

6.11286.129 =−=∆PS

Thus, the net chang

44.16.104.3 −=+−=⇒

∆+∆=NCh

PSCSNCh

44.1=⇒ DWL

DWL Lost rs toProduceerednot transf PSCS +=

))(at (21))((

2 MPDWL =1

CMCCC QQQMCPQQP −−+−− M M

233

)2.78)(8.4246(1)2. +2

78)(464.46(21

−−−−=DWL

44.128.116.0

)8.0)(2.3(21)8.0)(4.0(

21

=+=⇒

+=

DWL

DWL

nceptually, all the three ods are the same.

Co meth

Check Yo

What are the necessary conditions fo pr ination?

Is there any relationship between the pr

price discrimination charges and nd in the segregated

markets? Discuss.

Differentiate between the concepts of discrimi ulti-plant

monopolist.

How do you compare the social welfare ects of perfectly competitive and

monopoly market structures?

LESSON SUMMARY

produ ven in then we have an

perfect market structure s the opposite of perfect

petition. Unlike a com a price maker. As a result, a

nopolist faces a downw

Economies of scale or decreasing average costs are the m ources of imperfect

competition in pure monopoly. When the minimum efficient size of plant is larger

relative to the national or onal market, the cost conditions of the monopolist

rs to entry hence monopoly power es. In addition to

eclining costs, other fo leading to market imperfections such as legal

ur Progress

r the practicability of

ices a monopolist engaged in third degree

the price elasticities of dem

ice discrim1.

2.

a

price nation and m3.

asp4.

6.10

When a single firm ces all the output in a gi

called monopoly, which i

petitive firm a monopolist is

ard sloping demand curve.

dustry

exact im

com

mo

ajor s

regi

produce barrie and emerg

d rces

234

restrictions in the form of patents or government regulat

/competition.

There is a spectrum betw and na

urs when av r succ utput so

at the industry requires a cient firm. Few industries come close to

n today - perh like telephone, water, electricity etc.

onopolist's dema y derive its total revenue. From the

hedule or urve of total easily derive its marginal revenue – the

extra revenue resulting fro it of output. For a monopolist,

enue will fa

ions are also barriers to

entry

een perfect competition

erage costs are falling fo

tural monopoly. Natural

monopoly occ essive units of o

th single most effi

aps local utilities this conditio

From a m nd curve, we can easil

sc c revenue, we can

m the sale of an extra un

marginal rev ll short of price ( PMR < ) because of the loss on all

s of output th en it is forced to drop price in order to

utput

ind ma re the last unit it sells brings in

e just equal to R

previous unit at will result wh

sell an extra unit of o

A monopolist will f

.

ximum profit position whe

its extra cost. This same Mextra revenu MC= result can be shown

the interse ves. Regardless of whether a

pl ist the equality of marginal

al cost .

o st may sell given quality to different

consumers at different pric ts. Such a practice is called

ination. The three necessary conditions that must be fulfilled for price

iscrimination to take place are: (a) monopoly power; (b) market segmentation; and

there should no be resa ne market to another. The basis for

ce discrimination are c o pay (first degree or perfect price

rimination); quantity of output consumed (second or non-linear price

crimination); and elastic gree price discrimination).

Exercise of monopoly pow omic waste when price rises above

is bec es where

graphically by ction of MR and MC cur

ant or multi-plant monopol

must hold at the equilibrium

its product or service of a

es for reasons unrelated to cos

monopolist is a single

revenue and margin

A monop li

price discrim

d

(c) le of products from o

pri onsumers’ ability t

disc

dis ity of demand (third de

er also leads to econ

marginal cost. This ause a monopolist produc MR equal and

tly produces les uals price (less than the point

f allocatio efficiency). I onopolist does not produce the optimal

level of output where the s s y ) is equal to the value of

ers or ial welfare (as measured by

MC

consequen s output than where MC eq

n other words, a mo n

ocial cost (as mea ured b MC

the good to consum soc MUP = ). Rather, the

235

236

monopolist is keeping its output a little in short supply. It does not produce up to the

point of MCP = because to do so would require lowering price to all consumers,

which would make the monopolist lose some profit. So, society does not get as

much of the monopolist’s output as it wants in terms of the good’s marginal cost

and marginal value to consumers. The losses in consumers' and producers' surpluses

due to monopoly power are known as the social cost or the Dead weight Losses

(DWL) of monopoly.


I. True or False Questions with Justification(s).

1. The lower the value of the MR of a monopolist the higher will be the degree of its

monopoly power.

2. The lower the value of the price elasticity of demand for a monopolist product the

higher will be the markup.

3. We can derive the short run supply curve for a monopolist, provided that the

minimum AVC is known.

II. Discussion Questions

1. How many price discriminations are there under pure monopoly? What are they?

2. Does the difference in payment by spectators for the same movie or football match in

a stadium represent an example of price discrimination? Why or why not?

3. Why is that it is meaningless to ask what price will a monopolist charge for its

product?

4. What kind of economic and technological conditions are conducive to the emergence

of monopoly power?

5. Why a monopolist is better off with price discrimination than without? Under what

conditions is it feasible for a monopolist to practice price discrimination?

237

III: Workout Questions

1. Suppose a hypothetical monopolist facing a linear demand function operates at an

output level where the elasticity of demand is negative 3. If the government imposes

a quantity tax of Birr 6 per unit, how much will be the new selling price of the

monopolist?

2. Given the demand function a single plant monopolist faces and its cost function as: 310 −= PQ and QTC 2= , respectively,

A. Determine the short run optimal output, price, and profit of this monopolist.

B. Calculate elasticity and mark up price at the equilibrium output and price.

C. Show your results in (A) and (B) graphically using the marginal approach.

D. Based on your graph in (C), do you think there is a room for entry into the

market in which this existing monopoly operates? Why or why not?

3. Advanced: Suppose a multi-monopolist has marginal cost functions

11 220 qMC += , and

22 510 qMC += .

Where, 1MC is the marginal cost of the first plant and 2MC is the marginal cost of

the second plant. Besides, 1q and 2q represent output to be produced using the first

and second plants, respectively. If the monopolist is maximizing its short run profit

by producing 5 units of output in the first plant, then:

A. What is the monopolist's profit maximizing level of output in the second plant?

Show the steps how you have determined 2q .

B. Prepare a schedule similar to 6.3 for both marginal costs for 1 up to 10 output

levels and show how you determine the total short run output of the monopolist.

4. Assume that a monopolist has identified two markets such that the inverse demand

functions for its product in the two markets are:

11 292 qP −= , and

22 70 qP −= .

Its total cost function is: 2240100 QQTC ++= ; Where 21 qqQ += .

238

A. How much output will the monopolist sell and what price will it charge in the

two markets with price discrimination and without price discrimination?

B. Show the short run optimal outputs and prices in the two markets with price

discrimination using back-to-back diagram.

C. Find the amount of profit the monopolists will earn with price discrimination.

What is total profit if the monopolist does not discriminate between the two

markets?

D. Based on the profit figures you obtained in “C” above, are you then convinced

that a monopolist is always better off with price discrimination than without?

Why or why not?

E. In which market is the elasticity of demand higher? What is its implication?

F. Calculate the mark up at the short run equilibrium when the monopolist

discriminates. In which market is it higher? Why?

G. Show that a monopolist charges a price higher than its marginal cost in the

two markets.

5. Assuming that the monopolist in Question 4 above has evolved from perfect

competition to monopoly.

A. What is the restricted amount of output due to monopoly power?

B. Calculate the consumers’ and producers’ surplus under perfect competition

and monopoly.

C. What is the surplus transferred from consumers to the monopolist?

D. Calculate the net social cost (or Dead weight loss-DWL) due to monopoly

power or behavior.

E. Show first, the output and price levels under perfect competition graphically

and then shade or label with number (i) consumers’ and monopoly surplus; (ii)

surplus transferred to the monopolist; and (iii) the net DWL.

6. If the marginal cost functions of a monopolist were those given for the two plants in

Question 3, but if it faces the total market demand function in Question 4,

A. How much output should the multi-plant monopolist produce in each plant?

B. What will be the price the monopolist charges?

C. Calculate the monopolist’s profit assuming that TFC of each plant is 30 Birr.

239

REFERENCES

Dwivedi, D.N. (1997). Microeconomic Theory. 3P

rdP ed. Vikas Publishing House Pvt

Ltd, New Delhi.

Ferguson, C.E. and Gould J.P. (1989). Microeconomic Theory. 6th ed. Irwin

Publications.

Henderson, M. and Quandt E. (1980). Microeconomic Theory: A Mathematical

Approach. 3P

rdP edition. McGraw Hill.

Koutsoyiannis, A. (1981). Modern Microeconomics. 2nd edition. St Martins Pr.

Mansfield, E. (1988). Microeconomics: Theory and Applications. Shorter sixth

edition. W.W. Norton & Company: New York, London.

Pindyck, R. S. and D.L. Rubinfeld (1991). Microeconomics. 8th ed. Macmillan.

Salvatore, D. (2003). Microeconomics: Theory and Applications. 4th ed. Oxford

University Press, New York.

Varian, Hal R. (2002). Intermediate Microeconomics: A Modern Approach. 6th ed.

W.W. Norton and Company.

240

ANSWERS TO SELECTED REVIEW QUESTIONS

CHAPTER ONE

Part I

1. a

2. d

3. e

4. d

5. c

6. a

7. a

8. d

Part II

1. True

2. False

CHAPTER TWO

Part I

1. c

2. d

3. c

4. c

5. b

6. d

7. d

8. d

9. c

10. a

11. a

12. a

Part II

1. True

2. True

3. False

4. False

5. False

Part III

4.

a. Expected income =

Birr 12,000; Expected

utility =10.8 utils.

b. She is risk-averse.

Because, the expected

utility from gambling

(10.8) < the utility from

the safe source of

income (11).

5. X* = 320; Y* = 80

6. 31−=d

pε . Demand

is price inelastic at the

point.

7.

a. Birr 400.

b. 1600 utils.

c. She is indifferent

between buying and not

buying the share. This is

because the expected

utility from the gamble

(= 1600) is exactly the

same as her current

utility from the safe

source (U = 4m = 4*400

= 1600).

d. risk-neutral

CHAPTER THREE

Part I

1. b

2. c

3. d

4. c

5. a

6. a

7. b

8. a

9. c

10. b

11. b

12. d

13. c

14. a

241

CHAPTER FOUR

Part I

1. b

2. d

3. b

4. a

5. d

6. c

7. d

8. b

9. d

10. a

11. d

12. b

13. a

14. d

15. a

CHAPTER FIVE

Part II

1. (B) Q* = 25.

(E) PS = ?

(F) ∞=// dpε

2.

3. (A) Q* = 200;

Π* = 600.

(B) MC = 1 + 0.04Q;

ATC = (200/Q) + 1

+ 0.02Q;

AVC = 1 + 0.02Q.

At equilibrium, MC* = 9;

ATC* = 6; AVC* = 5.

(C) PS = 800

2.373;8.26.3100200

≈≈⇒±=

QQQ

CHAPTER SIX

Part I

1. True

2. True

3. False

Part III

1.

2. (A) Q* = 10/27; P* =

3; Π* = 10/27

(B) ;3// =dpε

Markup = 3/2 = 1.5

3.

4.

(A) *With price

discrimination: q1 = 6;

p1 = 80; q2 = 1; p2 = 69.

* Without price

discrimination:

Q = 7; P = 72.67.

(B) *With price

discrimination: Π* =171

* Without price

discrimination:

Π* = 130.67

(F) Markup in market 1

= 20/17; Markup in

market 2 = 69/68. It is

higher in market 1

because consumers in

market 1 are less

sensitive to price

changes.

5. (A) output declines by

1 unit (from 8 to 7).

(B) *Under perfect

competition:

CS = 21.33; PS = 128

*Under monopoly:

CS =16.33; PS = 130.67.

(C) CS transferred to

producer = 4.67.

(D) DWL = 2.33

6.

(A) q1 = 410/29 = 14.14;

q2 = 222/29 = 7.66

(B) P = 5464/87 = 62.8.

(C) Π = 602.68

microeconomics i - module

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