“economics is the study of mankind in the ordinary business of … · microeconomics the study of...

Part 1 consists of only a single background chapter. In it we review some basic principles ofsupply and demand, which should look familiar from your introductory economics course.This review is especially important because supply and demand models serve as a startingpoint for most of the material covered later in this book.

Mathematical tools are now widely used in practically all areas of economics. Althoughthe math used in this book is not especially difficult, the appendix to Chapter 1 provides abrief summary of what you will need to know. These basic principles are usually covered inan elementary algebra course. Most important for our purposes are the relationshipsbetween algebraic functions and the representation of these functions in graphs. Becausewe will be using graphs heavily throughout the book, it is important to be sure you under-stand this basic material before proceeding.

Part 1Introduction

“Economics is the study of mankind in the ordinary business of life.”

Alfred Marshall, Principles of Economics, 1890

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3

Why do the prices of airline tickets fluctuate so wildly? A colleague has made thesame trip four times in the past year, paying as little as $203 for her flight and asmuch as $865. The other passengers on each of these flights probably also paida bewildering variety of prices. Surely the cost of carrying a passenger on a planehas not changed all that much in the past year, so how can the price variabilitybe explained?

Or, consider gas prices. During the past year, some drivers have paid as littleas $0.75 per litre for unleaded regular gasoline and as much as $1.25. Althoughwe have been warned by environmentalists about how our “wasteful” use offossil fuels must be cut back before it is too late, do such price trends really haveanything to do with geology? The amount of available crude oil just has notchanged that much over the past year. So what explains the price movements?

Bono of U2 fame has appeared on television talking about how farm subsi-dies in Western industrialized countries will hurt farmers in Ghana, West Africa.Should we be worried about that? And why do we have farm subsidies in the firstplace, for that matter? Who pays for them?

If these are the kinds of questions that interest you, this is the right place tobe. As the quotation in the introduction to this part states, economics (especiallymicroeconomics) is the study of “the ordinary business of life.” That is, econo-mists take such things as airfares, gas prices, and farm subsidies as interestingtopics, worthy of detailed study. Why? Because understanding these everyday fea-tures of our world goes a long way toward understanding the welfare of theactual people who live here. Our intention is to cut through the garble of televi-sion sound bites and the rhetoric of politicians that often obscure rather thanenlighten these issues. By developing a thorough analysis of market forces, thegoal here is to help you to understand better the many economic trends that affectall of our lives.

1

Economic Models

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WHAT IS MICROECONOMICS?

As you probably learned in your introductory course, economics can be formallydefined as the “study of the allocation of scarce resources among alternativeuses.” This definition stresses that there simply are not enough basic resources(such as land, labour, and capital equipment) in the world to produce everythingthat people want. Hence, every society must choose, either explicitly or implic-itly, how its resources will be used.1 Of course, such “choices” are not made byan all-powerful dictator who specifies every citizen’s life in minute detail. Instead,the way resources get allocated is determined by the actions of many people whoengage in a bewildering variety of economic activities. Many of these activitiesinvolve participation in some sort of market transaction. Flying in airplanes,buying gasoline, or purchasing food are just three of the practically infinitenumber of things that people do that have market consequences for them and forsociety as a whole.

Microeconomics is the study of all of these choices and of how well theresulting market outcomes meet basic human needs. At the level of an individualconsumer or producer, given the goal of the consumer or producer and given theset of feasible actions that can be taken, economists attempt to determine whichfeasible action is best in helping the agent to realize its goal. Economists describethe best action as optimal, since the Latin word for best is optimum.

Of course, any real-world economic system is far too complicated to bedescribed in detail. Just think about how many items are available in the typicalhardware store (not to mention in the typical Home Depot megastore). Surely itwould be impossible to study in detail how each hammer or screwdriver was pro-duced and how many were bought in each store. Not only would such a descrip-tion take a very long time, but also no one would care to know such trivia,especially if the information gathered could not be used elsewhere. For this reason,all economists build simple models of various activities that they wish to study.These models may not be especially realistic, at least in terms of their ability tocapture the details of how a hammer is sold; but, just as scientists use models ofthe atom or architects use models of what they want to build, so too economistsuse simplified models to describe the basic features of markets. Of course, thesemodels are “unrealistic.” But maps are unrealistic too—they do not show everyhouse or parking lot. Despite this lack of “realism,” maps help you see the overallpicture and get you where you want to go. That is precisely what a good economicmodel should do. The economic models that you will encounter in this book havea wide variety of uses, even though, at first, you may think that they are unreal-istic. The applications scattered throughout the book are intended to stress thatpoint. But they only hint at the ways in which the study of microeconomics canhelp you understand the vast number of economic events that impact your life.

4 Part 1: Introduction

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1 Microeconomics focuses on the actors of the economy—consumers, firms, governments—whilemacroeconomics examines the “big picture” relationship among such aggregate variables as themoney supply, interest rates, foreign exchange rates, inflation, and unemployment.

EconomicsThe study of the allo-cation of scarceresources amongalternative uses.

MicroeconomicsThe study of the eco-nomic choices indi-viduals and firmsmake and of howthese choices createmarkets.

ModelsSimple theoreticaldescriptions thatcapture the essen-tials of how theeconomy works.

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A FEW BASIC PRINCIPLES

Much of microeconomics consists of simply applying a few basic principles tonew situations. We can illustrate some of these by examining an economic modelwith which you already should be familiar—the production possibility frontier.To simplify matters, let us assume that only two goods can be produced in aneconomy. This graph shows the various amounts of two goods that an economycan produce during some period (say, one week). Figure 1.1, for example, showsall the combinations of two goods (food and clothing) that can be produced withthis economy’s resources. For example, 10 units of food and 3 units of clothingcan be made, or 4 units of food and 12 units of clothing. Many other combina-tions of food and clothing can also be produced, and Figure 1.1 shows all ofthem. Any combination on or inside the frontier can be produced, but combina-tions of food and clothing outside the frontier cannot be made because notenough resources are available.

Chapter 1: Economic Models 5

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FIGURE 1.1 Production Possibility Frontier The production possibility frontier shows thedifferent combinations of two goods that can be produced from a certain amount of scarceresources. It also shows the opportunity cost of producing more of one good as the quantity ofthe other good that cannot then be produced. The opportunity cost at two different levels ofproduction of a good can be seen by comparing points A and B. Inefficiency at point C isshown by comparing C with point B.

Amountof foodper week

4

9.510

A

BC

Opportunity cost of 1 unit ofclothing = 1⁄2 unit of food

Opportunity cost of1 unit of clothing =2 units of food

2

Amountof clothingper week

0 3 4 12 13

ProductionpossibilityfrontierA graph showing allpossible combina-tions of goods thatcan be producedwith a fixed amountof resources.

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This simple model of production illustrates five principles that are commonto practically every situation studied in microeconomics:

• Resources are scarce. Some combinations of food and clothing (such as 10 units of food together with 12 units of clothing) are unattainable given theresources available. We simply cannot have all of everything we might want.

• Scarcity involves opportunity costs. That is, producing more of one good necessarily involves producing less of something else. For example, if thiseconomy produces 10 units of food and 3 units of clothing per week atpoint A, producing 1 more unit of clothing would “cost” 1⁄2 unit of food. Inother words, to increase the output of clothing by 1 unit means the produc-tion of food would have to decrease by 1⁄2 unit.

• Opportunity costs are usually increasing. Expanding the output of one par-ticular good will usually entail increasing opportunity costs as diminishingreturns set in. Although the precise reasons for this will be explained later,Figure 1.1 shows this principle clearly. If clothing output were expanded to12 units per week (point B), the opportunity cost of clothing would rise from1⁄2 unit of food to 2 units of food (point A). Hence, the opportunity cost of aneconomic action is not constant but varies with the circumstances.

• Opportunity costs should be measured in real terms. The opportunity costsinvolved in producing more of something involve sacrificing some amount ofanother actual good. Although it is often convenient to talk of opportunitycosts in terms of money (dollars, yen, pesos, and so forth), this can sometimesbe misleading. Suppose, for example, that an economy operating at point Ain Figure 1.1 had a price of clothing of $10 and of food of $20. The oppor-tunity cost of clothing would be 1⁄2 unit of food (as the production possibilityfrontier shows). If prices doubled, the price of clothing would rise to $20 andthe price of food would rise to $40. But the opportunity cost of 1 unit ofclothing would remain 1⁄2 unit of food. Focusing on the change in dollar costswould be misleading since, in real terms, prices have not changed. Practicallyall of microeconomics deals only in such real terms. Issues involving the pricelevel are usually studied in macroeconomics.

• Inefficiency involves real opportunity costs. An economy operating inside itsproduction possibility frontier is said to be performing “inefficiently”—a termwe will be making far more precise later. Producing, say, 4 units of clothing and4 units of food (at point C in Figure 1.1) would involve such an inefficient useof this economy’s resources. It might also indicate that the economy is not fullyutilizing its resources. For example, there might be unemployed workers orunderutilized capital. Such a production level would involve the loss of, say,8 units of clothing that could have been produced along with the 4 units of food.

When we study why markets might produce such inefficiencies, it will beimportant to keep in mind that such losses are not purely conceptual and ofinterest only to economic researchers. These are real losses. They involve realopportunity costs. Seeking to avoid such costs should make people in societybetter off.


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Opportunity costThe cost of a goodas measured by thealternative outputthat is forgone byproducing it.

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In the next section, we show howapplying these basic concepts helps inunderstanding a number of importanteconomic topics. In Application 1.1: DoAnimals Understand Economics?, weshow how the problem of scarcity andthe opportunity costs it entails are uni-versal. It appears that these basic princi-ples can even help us to understand thechoices made by wolves, hawks, andfinches.

Consider the production possibility frontier (PPF) shownin Figure 1.1 (page 5):

1. Why would society wish to avoid producing at thelevel that is inside the PPF?

2. This curve has a “concave” shape. Would the oppor-tunity cost of clothing production increase if the shapeof the curve were convex instead?

MicroQuiz 1.1

Scarcity is a dominant feature in nature. Indeed,the effect of scarcity is easier to study in biologicalsocieties because they are less complex thanmodern human societies. In trying to understandthe pressures that scarcity imposes on actions,economists and biologists have used models withmany similarities. Charles Darwin, the founder ofmodern evolutionary biology, was well acquaintedwith the writings of the major eighteenth- andnineteenth-century economists. Their thinkinghelped to sharpen his insights in The Origin ofSpecies. Here we look at the ways in which eco-nomic principles are illustrated in the behaviour ofindividual animals and in the evolution of species.

Foraging for FoodAll animals must use time and energy in their dailysearch for food. In many ways, this poses an “eco-nomic” problem for them in deciding how to usethese resources most effectively. Biologists havedeveloped general theories of animal foragingbehaviour that draw largely on economic notionsof weighing the benefits and costs associatedwith various ways of finding food.1

Two examples help to illustrate this “eco-nomic” approach to foraging. First, in the studyof birds of prey (eagles, hawks, and so forth),

biologists have found that the length of time abird will hunt in a particular area is determinedboth by the prevalence of food in that area andby the flight time to another location. Thesehunters recognize a clear trade-off betweenspending time and energy looking in one areaand using those same resources to go some-where else. Factors such as the types of foodavailable and the mechanics of the bird’s flightcan explain observed hunting behaviour.

A second, related observation about foragingbehaviour is the fact that no animal will stay in agiven area until all of the food there is exhausted.For example, once a relatively large portion of theprey in a particular area has been consumed, ahawk will go elsewhere. Similarly, studies of honey-bees have found that they generally do not gatherall of the nectar in a particular flower before movingon. To collect the last drop of nectar is not worththe time and energy the bee must expend to get it.Such weighing of benefits and costs is preciselywhat an economist would predict.

Scarcity and EvolutionCharles Darwin’s greatest discovery was thetheory of evolution. Later research has tended toconfirm his views that species evolve biologically

APPLICATION 1.1 Do Animals Understand Economics?

1 See, for example, David W. Stephens and John R. Krebs, Foraging Theory (Princeton, NJ: Princeton University Press, 1986).

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over long periods of time in ways that adapt totheir changing natural environments. In thatprocess, scarcity plays a major role. Adaptationsthat meet the challenges of a changing environ-ment will allow species to thrive. The failure toadapt rapidly enough can, in extreme cases, causeextinction (as was the case for the dinosaurs).

Many of Darwin’s original insights were drawnfrom his visits to the Galapagos Islands, off the coastof Ecuador. Recent research on the many types offinches Darwin discovered on these islands has pro-vided data with which to test his theories.2 The envi-ronmental event that most affected the finches wasa severe drought in the early 1980s. Only thosefinches with extra strong beaks were able to survive,because of their ability to break open what fewseeds remained. Succeeding generations of finches

have tended to have larger beaks than previousgenerations. The finches evolved in ways that metthe shortage of seeds.

The reactions of economic markets to changingscarcities and to costs, benefits, and trade-offs tendto resemble these evolutionary trends. Rising pricessignal the need to economize, and market partici-pants respond by altering their behaviour.

To Think About1. Does it make sense to argue that animals con-

sciously choose an optimal strategy fordealing with the scarcity of resources?

2. Evolution selects those genetic traits that favourlong-term survival. How does this explain thefact that most animals care for their youngeven when that takes time and energy?

2 This discussion is based on the summaries contained in J. Weiner, The Beak of the Finch (New York: Knopf, 1995).

USES OF MICROECONOMICS

Microeconomics has been applied to study practically every aspect of human behav-iour. The insights gained by applying a few basic principles to new problems can befar-reaching. For example, in Chapter 10, we see how one economist’s initial fasci-nation with the way prices were set for the rides at Disneyland opened the way forunderstanding pricing in such complex areas as air travel or the bundling andpricing of cable television and Internet connections; and, in Chapter 15, we look atanother economist’s attempt to understand the pricing of used cars. The resultingmodel of the pricing of “lemons” offers surprising insights about the markets forsuch important products as health care and legal services. Hence, one must becareful in trying to list the ways in which microeconomics is used because new usesare being discovered every day. Today’s seemingly trivial discovery may aid in under-standing complex transactions that may not occur until some distant future date.

One way to categorize the uses of microeconomics might be to look at thetypes of users. At the most basic level, microeconomics has a variety of uses forpeople in their own lives. An understanding of how markets work can help youmake decisions about future jobs, about the wisdom of major purchases (such ashouses), or about important financial decisions (such as retirement). Of course,economists are not much better than anyone else in predicting the future. Thereare legendary examples of economists who in fact made disastrous decisions—notably illustrated by the financial collapse of a “hedge fund” run by two Nobel

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Prize–winning economists in 1998. But the study of microeconomics can help youto conceptualize the important economic decisions you must make in your life andthat can often lead to better decision making. For example, Application 1.2: Is ItWorth Your Time to Be Here? illustrates how notions of opportunity cost canclarify whether attending university is really a good investment. Similarly, our dis-cussion of lottery prize payment choices in Chapter 14 uses the concept of the timevalue of money.

Those of you who are studying microeconomics aspart of your university education are probablypaying quite a bit to be here. It is reasonable to askwhether this spending is somehow worth it. Ofcourse, many of the benefits of a postsecondaryeducation (such as the better appreciation of cul-ture, friendship, etc.) do not have monetary value.In this application, we ask whether the cost isworth it purely in dollar terms.

Measuring Costs CorrectlyA typical Canadian university student pays about$14,000 per year in tuition, fees, general livingexpenses (including transportation and entertain-ment), and room and board charges. So one mightconclude that the “cost” of 4 years of university isabout $56,000. But this would be incorrect for atleast three reasons—all of which derive from asimple application of the opportunity cost idea:

• Inclusion of general living expenses plus roomand board fees overstates the true cost of uni-versity because these costs would likely beincurred whether you were attending univer-sity or not;

• Including only out-of-pocket costs omits themost important opportunity cost of universityattendance—forgone earnings one mightmake on a job; and

• University costs are paid over time so onecannot simply add 4 years of costs together toget the total.

The costs of university can be adjusted forthese factors as follows. First, room and boardplus general living expenses amount to about$9,000 annually, so tuition, books, and fees alonecome to $5,000. To determine the opportunitycost of lost wages, we must make several assump-tions, one of which is that you could earn about$20,000 per year if you were not in school andcan only make back about $2,000 in odd jobs.Hence, the net opportunity cost associated withlost wages is about $18,000 per year, raising thetotal annual cost to $23,000. For reasons to bediscussed in Chapter 14, we cannot simply mul-tiply 4 × $23,000 but must allow for the fact thatthese dollar payments are made at different times.In all, this adjustment would result in a total costfigure of about $85,000.

The Earnings Gains to UniversityA number of recent studies have suggested thatuniversity graduates earn much more than thosewithout such an education. A typical finding isthat annual earnings for otherwise identicalpeople are about 50 percent higher if one hasattended university. Again, using our assumptionof $20,000 in annual earnings for someonewithout a university education, this would implythat earnings gains from graduation mightamount to $10,000 per year. Looked at as aninvestment, going to university yields almost12 percent per year (that is, 10/85 = 0.12). This isa relatively attractive real return, exceeding that

APPLICATION 1.2 Is It Worth Your Time to Be Here?

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Businesses also use the tools of microeconomics. Any firm must try to under-stand the nature of the demand for its product. A firm that stubbornly continuesto produce a good or service that no one wants will soon find itself in bankruptcy.Even when firms like Air Canada and Laidlaw produce vital services such as airand bus transportation and waste management, they may become bankrupt as aresult of poor management, as these two prominent Canadian firms actually did.

Firms must also be concerned with their costs; for this topic, too,microeconomics has found many applications. For example, in Chapter 6 we look atsome of the research on airline company costs, focusing especially on why WestJetAirlines has been able to make such extensive inroads into the Canadian market. Asanyone who has ever flown on this airline knows, the company’s attention to keepingcosts low is paramount; passengers certainly get to their destinations on time and atvery attractive prices, even though a bag of pretzels is typically served instead of ameal. Microeconomic tools can help you to understand such efficiencies. They canalso help you to explore the possible implications of introducing these efficienciesinto such notoriously high-cost markets as those for air travel within Europe.

Microeconomics is also often used to evaluate broad questions of governmentpolicy. As Application 1.3 (“Duff’s Ditch”: The Story of an Unsung CanadianHero) illustrates, embarking on a costly public project with unclear future bene-fits can leave a politician quite vulnerable to ridicule and defeat. If, however, theproject proves to be completely justified, the politician may achieve a kind ofimmortality for his or her foresight and vision, as well as for the courage to pro-ceed with the project despite many cynics and naysayers.

As we see in later chapters, economists have devised a number of imaginativeways of measuring how various government actions affect consumers, workers,


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on long-term bonds (about 3 percent) and onstocks (about 7 percent). Hence, being here doesseem worth your time.

Will the Good Times Last?These calculations are not especially surprising—most people know that postsecondary educationpays off. Indeed, university attendance in Canadahas been expanding rapidly, presumably inresponse to such rosy statistics. What is surprisingis that this large increase does not seem to havereduced the attractiveness of the investment. Itmust be the case that for some reason thedemand for university-educated workers has

managed to keep up with the supply. Possiblereasons for this have been the subject of muchinvestigation.1

To Think About1. When making the opportunity cost calcula-

tions associated with a postsecondary educa-tion, how should you take into account thepossibility that you might not be able to finda job if you were not in school?

2. The estimated earnings gains from attendinguniversity are based on averages. How mightindividual peculiarities affect the size of such gains?

1 For a discussion, see D. Acemoglu, “Technical Change, Inequality, and the Labor Market,” Journal of EconomicLiterature (March 2002): 7–72.

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and firms. These measures often play crucial roles in the political debate sur-rounding the adoption or repeal of such policies. Of course, as Application 1.4:Microsoft and Antitrust illustrates, there are often two sides to such policy ques-tions, and economists are no more immune than anyone else from the temptationto bend their arguments to fit a particular political point of view. Knowledge ofmicroeconomics does provide a basic framework—that is, a common language—in which many such discussions are conducted.


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Located in the centre of Canada where themighty Red River meets the Assiniboine River, thecity of Winnipeg had been plagued by floodssince time immemorial. The legendary flood of1826 crested at a height of more than 11 metres.Other catastrophic floods occurred in 1852, 1861,and 1950. The latter was called the “Great Floodof 1950” and caused $125 million in damage;80,000 residents had to be evacuated from theirhomes, which became submerged by floodwater.

Following a time-honoured Canadian tradi-tion, a Royal Commission on Flood Cost–Benefitwas appointed in 1956. Its research director wasClarence L. Barber, for many years the head of theDepartment of Economics at the University ofManitoba and later president of the CanadianEconomics Association. Barber compared thecosts and benefits of constructing a floodway—an enormous ditch into which the waters of theRed River could be diverted when Winnipegbecame threatened by flooding from the RedRiver overflowing its banks. The study took twoyears to complete, and on the basis of careful andwell-documented analysis, concluded that whatwould be called the “Manitoba Floodway” defi-nitely made economic sense, representing asound investment that would more than repay itscost in the future.

Armed with the persuasive economic analysisof Clarence Barber in support of the project, DuffRoblin, Manitoba’s premier at the time, tabled aproposal in the Manitoba legislature in 1959 for

the construction of a floodway at a cost of $63 million. Despite the economic analysis sup-porting the project, it became known as “Duff’sDitch” and “Duff’s Folly.” Construction began in1963 and the Manitoba Floodway was com-pleted in 1968.

The task was a monumental engineering feat:It involved dredging and hauling away more than76 million cubic metres of earth in an area thatwas almost the width of the Red River—47 kilo-metres in length and more than 9 metres deep.The volume of earth removed was equivalent tothat involved in constructing the Panama Canaland one-third more than was removed for the St.Lawrence Seaway. The gorge that the ManitobaFloodway created was visible to the Apollo astro-nauts on the moon!

The floodway allows the Red River to split intotwo forks just south of Winnipeg. When runoffcould cause the Red River to overflow its banks,the gates are opened and the excess water isdiverted away from Winnipeg into the floodway.

With Twenty–Twenty Hindsight, What’s theVerdict?The Manitoba Floodway has been a smashingsuccess—since 1968, it has been used 20 times tocontrol Red River floods. In 1997, the year of the“Flood of the Century,” the waters of the RedRiver would have crested at 10.5 metres, about1.5 metres higher than the 1950 flood and3 metres above its actual crest of 7.5 metres.

APPLICATION 1.3 “Duff’s Ditch”: The Story of an Unsung Canadian Hero

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Without the floodway, more than 80 percent ofWinnipeg would have been under water, and550,000 residents would have had to be evacu-ated. The monetary estimate of the physicaldamage that would have occurred without thefloodway exceeds $6 billion. The psychologicaland human costs from catastrophic floodingwould have raised this figure significantly.

So Who Got the Credit and Who Was theUnsung Hero? As might have been expected, the recipient of themost glory was Premier Duff Roblin, who was cel-ebrated for his vision and courage in the face ofskepticism and ridicule. The Dutch Canadianhydrological engineer Ed Kuiper was celebratedfor his design ingenuity and professional compe-tence. Who was not invited to bask in the glory ofa project that was so monumentally successful inconception and execution? The unsung hero was

the modest Canadian economist Clarence Barber(1917–2004), who spent the first 19 years of hislife growing up on a Saskatchewan farm. Now,however, we all know what an instrumental rolehe played in the birth of this project.

To Think About1. Why was the floodway built by the govern-

ment rather than by the private sector?2. Can you account for the fact that Grand

Forks, North Dakota, suffered extensive flooddamage from the Red River in 1997, or thatNew Orleans was devastated by HurricaneKatrina in 2005, by simply stating thatAmericans prefer a relatively smaller govern-ment role in the economy than Canadians?

3. Suppose that no floods had occurred to date.Would the architects of the floodway beregarded as bold visionaries or as recklesssquanderers of public funds?

In May 1998 a trial began in federal district courtin Washington, D.C., that pitted the U.S.Department of Justice and 20 states against theMicrosoft Corporation—the largest computersoftware firm in the world. At issue was whetherMicrosoft had illegally “monopolized” varioussegments of the software industry and therebyviolated the Sherman Antitrust Act.

Economic IssuesThe central issue in the Microsoft case waswhether the firm’s dominance of its industryallowed it to follow practices that were ultimatelyharmful to consumers. In particular, there was theconcern that the firm would be able to use itsdominance in operating systems for personalcomputers (Windows 2000 and its predecessors)to harm competitors in other areas. For example,

the Netscape Corporation claimed that Microsoftmade it intentionally difficult for users to installNetscape’s Navigator Web browser in place ofMicrosoft’s own Internet Explorer. Similarly, therewere fears that the firm would gain unfair advan-tages in various types of word processing andspreadsheet software.

The Consent DecreeThis was not the first time that the MicrosoftCorporation had been in the legal spotlight. In1994 it had signed a consent decree with the U.S.Department of Justice in which the companyagreed to end such practices as tying the sale ofMicrosoft Word or Excel to the licensing ofWindows. It also agreed to change the ways inwhich it charged computer makers such asCompaq (now owned by Hewlett-Packard) and

APPLICATION 1.4 Microsoft and Antitrust

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Dell for the basic Windows operating system. Butthe decree said little about Internet issues—therebyleaving cause for concern that intensified with therapid increase in Internet usage in the late 1990s.

Dueling EconomistsSome of the most important testimony on bothsides of the Microsoft case came from econo-mists.1 The government’s primary economic wit-ness, MIT professor Franklin Fisher (who was onthe other side when he led the defence team ofIBM against the U.S. government in the 1970s)argued that control of the Windows operatingsystem gave Microsoft significant power overmost PC applications and that the firm had usedthat power specifically to make it difficult for usersto install other firms’ software—notably NetscapeNavigator. Fisher expressed some caution in evalu-ating the harm that such actions caused to currentconsumers. After all, Microsoft was giving awayits browser free of charge. Instead, he argued, thereal danger was that permitting Microsoft to gaindomination of the browser market would allowthe firm to eliminate any potential competition inoperating systems.

Microsoft countered with an expert witness ofits own, Richard Schmalensee (also a professor atMIT and once a student of Fisher’s). He arguedthat fears of Microsoft’s ability to deter the devel-opment of new operating systems in the futurewere purely hypothetical and that the companydid not in fact currently operate as a monopoly.

He cited estimates that Microsoft, if it had truemonopoly power, could probably have chargedmore than $1,000 for its Windows operatingsystem though, in fact, the system routinely soldfor much less than $100.

The Law Works SlowlyAs in most large antitrust cases, legal proceedingsin the Microsoft case have moved slowly. Initially,Microsoft was found guilty of violating Section II ofthe Sherman Act, but a major portion of thatfinding was sent back for further review by anappeals court. In an attempt to hasten matters, theU.S. Department of Justice reached a proposedsettlement with Microsoft that, it was claimed,would encourage competition in “middleware”(such as Internet browsers). But several states (whohad also sued Microsoft) declined to go along withthis settlement on the basis that it was not toughenough. Whether the legal system can everfashion a remedy for Microsoft’s allegedly monop-olistic conduct in the rapidly changing computerindustry remains an open question.

To Think About1. How can two economists come to such dif-

ferent opinions on this case? Are they usingdifferent methods of analysis? Or are theyfocusing on different issues?

2. If you had to craft a plan for limiting the pos-sible monopoly power of Microsoft, howwould you do it?

1 All of the documents in the Microsoft case are available from the U.S. Justice Department website:www.usdoj.gov/atr/cases/ms_index.htm. The Spring 2001 issue of The Journal of Economic Perspectives featured asymposium on the Microsoft case.

THE BASIC SUPPLY–DEMAND MODEL

As the saying goes, “Even your pet parrot can learn economics—just teach it tosay ‘supply and demand’ in answer to every question.” Of course, there is oftenmore to the story. But economists tend to insist that market behaviour can usu-ally be explained by the relationship between preferences for a good (demand)

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and the costs involved in producing that good (supply). The basicsupply–demand model of price determination is a staple of all courses in introduc-tory economics—in fact, this model may be the first thing you studied in yourintroductory course. Here we provide a quick review of the model, adding a bit ofhistorical perspective.

Adam Smith and the Invisible HandThe Scottish moral philosopher Adam Smith (1723–1790) is generally creditedwith being the first true economist. In The Wealth of Nations (published in1776), Smith examined a large number of the pressing economic issues of his dayand tried to develop economic tools for understanding them. Smith’s most impor-tant insight was his recognition that the system of market-determined prices thathe observed was not as chaotic and undisciplined as most other writers hadassumed. Rather, Smith saw prices as providing a powerful “invisible hand” thatdirected resources into activities where they would be most valuable. Prices playthe crucial role of telling both consumers and firms what resources are “worth”and thereby prompt these economic actors to make efficient choices about howto use them. To Smith, it was this ability to use resources efficiently that providedthe ultimate explanation for a nation’s “wealth.”

Because Adam Smith placed great importance on the role of prices indirecting how a nation’s resources are used, he needed to develop some theoriesabout how those prices are determined. He offered a very simple and only partlycorrect explanation. Since, in Smith’s day (and, to some extent, even today), theprimary costs of producing goods were costs associated with the labour that wentinto a good, it was only a short step for him to embrace a labour-based theory ofprices. For example, to paraphrase an illustration from The Wealth of Nations,if it takes twice as long for a hunter to catch a deer as to catch a beaver, one deershould trade for two beavers. The relative price of a deer is high because of theextra labour costs involved in catching one.

Smith’s explanation for the price of a good is illustrated in Figure 1.2(a). Thehorizontal supply curve at P* shows that any number of deer can be producedwithout affecting the relative cost of doing so. That relative cost sets the price ofdeer (P*), which might be measured in beavers (a deer costs two beavers), in dol-lars (a deer costs $200, whereas a beaver costs $100), or in any other units thatthis society uses to indicate exchange value. This value will change only whenthe technology for producing deer changes. If, for example, this society devel-oped better running shoes (which would aid in catching deer but be of little usein capturing beavers), the relative labour costs associated with hunting deerwould fall. Now a deer would trade for, say, 1.5 beavers, and the supply curveillustrated in the figure would shift downward. In the absence of such technicalchanges, however, the relative price of deer would remain constant, reflectingrelative costs of production.


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Supply–demandmodelA model describinghow a good’s price isdetermined by thebehaviour of theindividuals who buythe good and of thefirms that sell it.

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David Ricardo and Diminishing ReturnsThe early nineteenth century was a period of considerable controversy in eco-nomics, especially in England. The two most pressing issues of the day werewhether international trade was having a negative effect on the economy andwhether industrial growth was harming farmland and other natural resources. Itis testimony to the timelessness of economic questions that these are some of thesame issues that still spark heated debate in Canada. One of the most influentialcontributors to the earlier debates was the British financier, statesman, and par-liamentarian David Ricardo (1772–1823).

Ricardo believed that labour and other costs would tend to rise as the levelof production of a particular good expanded. He drew this insight primarily fromhis consideration of the way in which farmland was expanding in England at thetime. As new and less-fertile land was brought into use, it would naturally takemore labour (say, to pick out the rocks in addition to planting crops) to producean extra bushel of grain. Hence, the relative price of grain would rise. Similarly,as deer hunters exhaust the stock of deer in a given area, they must spend moretime locating their prey, so the relative price of deer would also rise. Ricardobelieved that the phenomenon of increasing costs was quite general, and todaywe refer to his discovery as the law of diminishing returns. This generalization of


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DiminishingreturnsHypothesis that thecost associated withproducing one moreunit of a good risesas more of that goodis produced.

Price

P*

Quantity per week

(a) Smith’s model (b) Ricardo’s model

Price

P2

P1

Quantity per weekQ1 Q2

FIGURE 1.2 Early Views of Price Determination To Adam Smith, the relative price of a good was determined by relativelabour costs. As shown in the left-hand panel, relative price would be P* unless something altered such costs. Ricardo addedthe concept of diminishing returns to this explanation. In the right-hand panel, relative price rises as quantity produced risesfrom Q1 to Q2.

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Smith’s notion of supply is reflected in Figure 1.2(b), in which the supply curveslopes upward as quantity produced expands.

The problem with Ricardo’s explanation was that it really did not explainhow prices are determined. Although the notion of diminishing returns undoubt-edly made Smith’s model more realistic, it did so by showing that relative pricewas not determined by production technology alone. Instead, according toRicardo, the relative price of a good can be practically at any level depending onhow much of it is produced.

To complete his explanation, Ricardo relied on a subsistence argument.If, for example, the current population of a country needs Q1 units of outputto survive, Figure 1.2(b) shows that the relative price would be P1. With agrowing population, these subsistence needs might expand to Q2, and the rel-ative price of this necessity would rise to P2. Ricardo’s suggestion that the rel-ative prices of goods necessary for survival would rise in response todiminishing returns provided the basis for much of the concern about popu-lation growth in England during the 1830s and 1840s. It was largely respon-sible for the application of the term dismal science to the study of economics.

Marginalism and Marshall’s Model of Supply and DemandContrary to the fears of many worriers, relative prices of food and other necessi-ties did not rise significantly during the nineteenth century. Instead, as methodsof production improved, prices tended to fall and levels of material well-beingimproved rather dramatically. As a result, subsistence became a less plausibleexplanation of the amounts of particular goods consumed and economists foundit necessary to develop a more general theory of demand. In the latter half of thenineteenth century, they adapted Ricardo’s law of diminishing returns to thistask. Just as diminishing returns mean that the cost of producing one more unitof a good rises as more is produced, so too, these economists argued, the willing-ness of people to pay for that last unit declines. Only if some individuals areoffered a lower price for a good will they be willing to consume more of it. Byfocusing on the value to buyers of the last, or marginal, unit purchased, theseeconomists had at last developed a comprehensive theory of price determination.

The clearest statement of these ideas was presented by the English economistAlfred Marshall (1842–1924) in his Principles of Economics, published in 1890.Marshall showed how the forces of demand and supply simultaneously deter-mine price. Marshall’s analysis is illustrated by the familiar cross diagram shownin Figure 1.3.

As before, the amount of a good purchased per period (say, each week) isshown on the horizontal axis and the price of the good appears on the vertical axis.The curve labelled “Demand” shows the amount of the good people want to buyat each price. The negative slope of this curve reflects the marginalist principle:Because people are willing to pay less and less for the last unit purchased, they willbuy more only at a lower price. The curve labelled “Supply” shows the increasing


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www.infotrac-college.comKeywords: Microeconomics,Dismal science, Alfred Marshall

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cost of making one more unit ofthe good as the total amount pro-duced increases. In other words,the upward slope of the supplycurve reflects increasing marginalcosts, just as the downward slopeof the demand curve reflectsdecreasing marginal usefulness.

Market EquilibriumIn Figure 1.3, the demand andsupply curves intersect at thepoint (Q*,P*). At that point, P*is the equilibrium price. That is,at this price, the quantity thatpeople want to purchase (Q*) isprecisely equal to the quantitythat suppliers are willing to pro-duce. Because both demandersand suppliers are content withthis outcome, no one has anincentive to alter his or her behaviour. Theequilibrium (Q*,P*) will tend to persistunless something happens to changethings. This illustration is the first of manywe encounter in this book about the wayin which a balancing of forces results in asustainable equilibrium outcome. To con-ceptualize the nature of this balancing offorces, Marshall used the analogy of a pairof scissors: Just as both blades of the scis-sors work together to do the cutting, sotoo the forces of demand and supply worktogether to establish equilibrium prices.

Nonequilibrium OutcomesThe smooth functioning of market forces envisioned by Marshall can, however, bethwarted in many ways. For example, a government decree that requires a price tobe set in excess of P* (perhaps because P* was regarded as being the result of “unfair,ruinous competition”) would prevent the establishment of equilibrium. With a priceset above P*, demanders would wish to buy less than Q*, whereas suppliers wouldproduce more than Q*. This would lead to a surplus of production in the market—a situation that characterizes many agricultural markets. Similarly, a regulation that


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Price Demand

Supply

Equilibrium pointP*

Quantityper week

0 Q*

FIGURE 1.3 The Marshall Supply–Demand Cross Marshall believed thatdemand and supply together determine the equilibrium price (P*) andquantity (Q*) of a good. The positive slope of the supply curve reflectsdiminishing returns (increasing marginal cost), whereas the negative slope of the demand curve reflects diminishing marginal usefulness. P* is anequilibrium price. Any other price results in either a surplus or a shortage.

Another way to describe the equilibrium in Figure 1.3is to say that at (Q*,P*) neither the supplier nor thedemander has any incentive to change behaviour. Usethis notion of equilibrium to explain:

1. Why the fact that (Q*,P*) occurs where the supplyand demand curves intersect implies that both partiesto the transaction are content with this result; and

2. Why no other (Q,P) point on the graph meets thisdefinition of equilibrium.

MicroQuiz 1.2

Equilibrium priceThe price at whichthe quantitydemanded by buyersof a good is equal to the quantity sup-plied by sellers of the good.

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holds a price below P* wouldresult in a shortage. With such aprice, demanders would want tobuy more than Q*, whereas sup-plies would produce less than Q*.In Chapter 9, we look at severalsituations where this occurs.

Change in MarketEquilibriumThe equilibrium pictured inFigure 1.3 can persist as long asnothing happens to alter demandor supply relationships. If one ofthe curves were to shift, however,the equilibrium would change. InFigure 1.4, people’s demand forthe good increases. In this case,the demand curve moves out-ward (from curve D to curve D′).At each price, people now wantto buy more of the good. Theequilibrium price increases (fromP* to P**). This higher priceboth tells firms to supply moregoods and restrains individuals’demand for the good. At the newequilibrium price of P**, supplyand demand again balance—atthis higher price, the quantity ofthis good demanded is exactlyequal to the quantity supplied.

A shift in the supply curvealso affects market equilibrium.In Figure 1.5, the effects of anincrease in supplier costs (forexample, an increase in wagespaid to workers) are illustrated.For any level of output, mar-ginal costs associated with thesupply curve S′ exceed thoseassociated with S. This shift insupply causes the price of this


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Price

DS

P*

P**

Quantityper week

0 Q* Q**

FIGURE 1.4 An Increase in Demand Alters Equilibrium Price and Quality If the demand curve shifts outward to D′ because there is moredesire for the product, (Q*,P*) will no longer be an equilibrium. Instead,equilibrium occurs at (Q**,P**), where D′ and S intersect.

Price

D

S

P*

P**

Quantityper week

0 Q** Q*

FIGURE 1.5 A Shift in Supply Alters Equilibrium Price and Quantity A rise in costs would shift the supply curve upward to S′. This would cause an increase in equilibrium price from P* to P** and a decline in quantity fromQ* to Q**.

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product to rise (from P* to P**), and con-sumers respond to this price rise byreducing quantity demanded (from Q* toQ**) along the demand curve, D. As forthe case of a shift in demand, the ultimateresult of the shift in supply depicted inFigure 1.5 depends on the shape of boththe demand curve and the supply curve.

Marshall’s model of supply anddemand should be quite familiar to yousince it provides the principal focus ofmost courses in introductory economics.Indeed, the concepts of marginal cost,marginal value, and market equilibrium encountered in this model provide thestarting place for most of the economic models you will learn about in this book.Application 1.5: Economics According to Bono shows that even rock stars cansometimes get these concepts right.


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Supply and demand curves show the relationshipbetween the price of a good and the quantity supplied ordemanded when other factors are held constant. Explain:

1. What factors might shift the demand or supplycurve for, say, personal computers.

2. Why a change in the price of PCs would shift nei-ther curve. Indeed, would this price ever change if allof the factors identified previously did not change?

MicroQuiz 1.3

The Spring 2002 trip to Africa by the Irish rock starBono and the U.S. Treasury Secretary at the time,Paul O’Neill, sparked much interesting dialogueabout economics.1 Especially intriguing was Bono’sclaim that recently enacted agricultural subsidies inthe United States were harming struggling farmersin Africa—a charge that O’Neill was forced toattempt to refute. A simple supply–demandanalysis shows that, overall, Bono did indeed havethe better of the arguments, though he neglectedto mention a few fine points.

Graphing African ExportsFigure 1 shows the supply and demand curves fora typical crop that is being produced by an Africancountry. If the world price of this crop (P*)exceeds the domestic price that would prevail inthe absence of trade (PD), this country will be anexporter of this crop. The total quantity of exportsis given by the distance QS – QD. That is, exportsare given by the difference in the quantity of this

APPLICATION 1.5 Economics According to Bono

P

P*

P**

D

S

QD QQD QsQs

PD

FIGURE 1 U.S. Subsidies Reduce African Exports U.S. farmsubsidies reduce the world price of this crop from P* to P**. Exports from this African country fall from QS – QD to Q′S – Q′D.

(continued)

1 One estimate is that grain farmers in Europe receive a subsidy of $6.00 per bushel and those in the United Statesreceive $2.50 per bushel, while the subsidy to Canadian farmers is a small fraction of that received by their foreigncompetitors—a mere $0.40 per bushel.

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HOW ECONOMISTS EVALUATE THEORETICAL MODELS

Not all models are as useful as Marshall’s model of supply and demand. An important purpose of studying economics is to sort out bad models from good ones. Two methods are used to provide such a test of economic models.Testing assumptions looks at the assumptions on which a model is based; testing predictions, on the other hand, uses the model to see if it can correctlypredict real-world events. This book uses both approaches to try to illustratethe validity of the models that are presented. We now look briefly at the dif-ferences between them.

Testing AssumptionsOne approach to testing the assumptions of an economic model might begin withintuition. Do the model’s assumptions seem reasonable? Unfortunately, this ques-tion is fraught with problems, since what appears reasonable to one person may


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crop produced and the quantity that is demandeddomestically. Such exporting is quite common formany African countries because they have largeagrarian populations and generally favourable cli-mates for many types of food production.

Canadian farmers have long expressed con-cern about the high level of subsidies received bytheir American and European counterparts. Theintroduction of much higher subsidies to Americanand European farmers in 2002 had the effect oflowering world crop prices. This would be shownin Figure 1 as a drop in the world price to P**. Thisfall in price would be met by a reduction in quan-tity produced of the crop to Q′S and an increase inthe quantity demanded domestically to Q′D. Cropexports would decline significantly.

So, Bono’s point is essentially correct—American and European agricultural subsidies doharm African farmers, especially those in the exportbusiness. But he might also have pointed out thatAfrican consumers of food do benefit from theprice reduction. They are able to buy more food atlower prices. Effectively, some of the subsidy to for-eign farmers has been transferred to African con-sumers. Hence, even disregarding whether farm

subsidies make any sense for Europeans,Americans, and Canadians, their effects on thewelfare of Africans is somewhat ambiguous.

Other Barriers to African Agricultural TradeAgricultural subsidies by the United States and theEuropean Union amount to nearly $400 billion peryear. Undoubtedly they have a major effect inthwarting African exports. Perhaps even moredevastating are the large number of special meas-ures adopted in various developed countries toprotect favoured domestic industries such aspeanuts in the United States, rice in Japan, andlivestock in the European Union. Becauseexpanded trade is one of the major avenuesthrough which poor African economiesmight grow, these restrictions have become verycontroversial.

To Think About1. Why do agricultural subsidies paid to pro-

ducers in exporting countries reduce worldcrop prices?

2. How would you modify Figure 1 in order todepict the effects of trade restrictions?

TestingassumptionsVerifying economicmodels by examiningthe reasonableness ofthe assumptions onwhich they are based.TestingpredictionsVerifying economicmodels by asking ifthey can accuratelypredict real-worldevents.

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seem preposterous to someone else (try arguing with a noneconomics studentabout whether people usually behave rationally, for example).

Assumptions can also be tested with empirical evidence. For example, econ-omists usually assume that firms are in business to maximize profits—in fact,much of our discussion in this book is based on that assumption. Using the directapproach to test this assumption with real-world data, you might send question-naires to managers asking them how they make decisions and whether they reallydo try to maximize profits. This approach has been used many times, but theresults, like those from many opinion polls, are often difficult to interpret.

Testing PredictionsSome economists, such as Milton Friedman, do not believe that in order to assessthe value of a theory it is necessary to examine the truth or accuracy of its assump-tions. They argue that all theories are based on unrealistic assumptions; the verynature of theorizing requires that we make what may appear to be unrealisticassumptions.2 Such economists believe that the value of a theory should be meas-ured by its ability to explain and predict real-world events. The real test of anyeconomic model is whether it is consistent with events from the economy itself.

Friedman gives a good example of this idea by asking which theory explainsthe shots that an expert pool player will make. He argues that the laws ofvelocity, momentum, and angles from physics make a suitable theoretical model,because the pool player certainly shoots as if he or she followed these laws. If weasked the players whether they could state these physical principles, they wouldundoubtedly answer that they could not. That does not matter, Friedman argues,because the physical laws give very accurate predictions of the shots made andare therefore useful as theoretical models.

Going back to the question of whether firms try to maximize profits, the indi-rect approach would try to predict the firms’ behaviour by assuming that they doact as if they were maximizing profits. If we find that we can predict firms’ behav-iour, then we can believe the profit-maximization hypothesis. Even if the managersof these firms stated on questionnaires that they do not consciously seek to max-imize profits, the theory would still be valid, much as the pool players’ disclaimingknowledge of the laws of physics does not make these laws untrue. The ultimatetest in both cases is the theory’s ability to predict real-world events.

The Positive–Normative DistinctionRelated to the question of how the validity of economic models should betested is the issue of how such models should be used. To some economists, theonly proper analysis is “positive” in nature. As in the physical sciences, they


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2 Milton Friedman, Essays in Positive Economics (Chicago: University of Chicago Press, 1953),Chapter 1. Another view stressing the importance of realistic assumptions can be found in H. A.Simon, “Rational Decision Making in Business Organizations,” American Economic Review(September 1979): 493–513.

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argue, the correct role for theory is to explain the real world as it is. In thisview, developing “normative” theories about how the world should be is anexercise for which economists have no more special skills than anyone else.For other economists, this positive–normative distinction is not so clear-cut.They argue that economic models invariably have normative consequencesthat should be recognized.

Microeconomic theory has increasingly embraced the analytical frameworkand tools of game theory (which are introduced in Chapter 12) to model theinteraction between economic agents. It is generally accepted that game theorydoes not perform well in predicting human behaviour, either in the real world orin controlled laboratory experiments. Economists have been reluctant to rejectgame theory on the grounds that it predicts behaviour poorly. Rather, they haverationalized prediction failures by arguing that game theoretic models weredesigned to indicate how perfectly rational agents ought to behave in their inter-action with other perfectly rational agents. They were not designed to predictreal-world behaviour. Game theoretic models in economics should therefore beregarded as strictly normative.

Robert Aumann makes the following insightful observation about the imped-iments to accurate prediction when such prediction is based on the assumptionthat people behave rationally:

Homo rationalis is the species that always acts both purposefully and logically, has well-defined goals, is motivated solely by the desire to approach these goals as closely as pos-sible, and has the calculating ability required to do so.… [But] Homo rationalis is amythical species, like the unicorn and the mermaid. His real-life cousin, Homo sapiens,is often guided by subconscious psychological drives, or even by conscious ones, thatare totally irrational; herd instincts play a large role in his behaviour; even when his goalsare well-defined, which isn’t often, his motivation to achieve them may be less thancomplete; far from possessing infinite calculating ability, he is often downright stupid;and even when intelligent, he may be tired or hungry or distracted or cross or drunk orstoned, unable to think under pressure, able to think only under pressure, or guidedmore by his emotions than his brains. And this is only a very partial list of departuresfrom the rational paradigm.3

Application 1.6: Do Economists Ever Agree? shows that, contrary tocommon perceptions, there is considerable agreement among economists aboutissues that are suitable for positive scientific analysis. There is far less agreementabout normative questions related to what should be done. In this book, we takeprimarily a positive approach by using economic models to explain real-worldevents. The book’s applications pursue these explanations in greater detail. Youshould feel free to adapt these models to whatever normative goals you believeare worth pursuing.


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Positive–normativedistinctionDistinction betweentheories that seek toexplain the world asit is and theoriesthat postulate theway the worldshould be.

3 Robert J. Aumann, “What Is Game Theory Trying to Accomplish?” Collected Papers, Volume I(Cambridge, MA: MIT Press, 2000): 11–12.

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APPLICATION 1.6 Do Economists Ever Agree?

Proposition United States Switzerland Germany

Tariffs reduce economic welfare 95 87 94Flexible exchange rates are

effective for international transactions 94 91 92

Rent controls reduce the quality of housing 96 79 94

Government should redistributeincome 68 51 55

Government should hire the jobless 51 52 35

Source: B. S. Frey, W. W. Pommerehue, F. Schnieder, and G. Gilbert, Consensus and Dissension among Economists:An Empirical Inquiry,” American Economic Review (December 1984): 986–994. Percentages represent fraction that“Generally Agree” or “Agree with Provisions.”

TABLE 1 Percentage of Economists Agreeing with Various Propositions in Three Nations

To the general public, economists are confusing.In many conversations, economists bear the bruntof pointed jokes. Some of our favourites are the following:

If all economists in the world were laid endto end, they would never reach a decision.

How many economists does it take tochange a light bulb? Two—one to turn thebulb and one to say, “Turn it the other way.”

Positive versus Normative EconomicsThese jokes convey the perception that economistsnever agree on anything. But that perceptionarises primarily from an inability to differentiatebetween the positive and normative argumentsthat economists make. Economists (like everyoneelse) often disagree over political questions. Theymay, therefore, find themselves on opposite sidesof controversial policy questions. Economists mayalso differ on empirical matters. For instance, they

may disagree about whether a particular effect islarge or small. But on basic theoretical questionsthere is far less disagreement. Because most econ-omists use the same tools, they tend to “speak thesame language” and disagreements on positivequestions are far less frequent.

Survey ResultsThis conclusion is supported by surveys of econo-mists, a sample of which is described in Table 1.The table shows a high degree of agreementamong U.S., Swiss, and German economistsabout relatively positive questions such as theeffects of tariffs or of rent controls.1

There is considerably less agreement aboutbroad normative questions, such as whether thegovernment should redistribute income or act asthe employer of last resort. For these types ofquestions, economists’ opinions are as varied asthose of any other group of citizens.

1Surveys also tend to show considerable agreement over the likely size of many economic effects. For a summary, seeVictor R. Fuchs, Alan B. Krueger, and James M. Poterba, “Economists’ Views about Parameters, Values, and Policy,”Journal of Economic Literature (September 1998): 1387–1425.

(continued)

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To Think About1. Economists from the United States,

Switzerland, and Germany may not reflect theviews of economists from lower-income coun-tries. Do you think such economists mightanswer the questions in Table 1 differently?

2. What is the difference between a and an economist? Answer: .

(Lawyers and engineers are often compared toeconomists—and not necessarily favourably. Ifyou have particularly suitable suggestions tofill in the blanks, please e-mail the Canadianauthor, Irwin Lipnowski, at [email protected]. We will consider including yoursuggestions in a future edition of this text.)

SUMMARY

This chapter provides you with some background tobegin your study of microeconomics. Much of thismaterial should be familiar to you from your intro-ductory economics course, but that should come asno surprise. In many respects, the study of economicsrepeatedly investigates the same questions with anincreasingly sophisticated set of tools. This coursegives you some more of these tools. In establishingthe basis for that investigation, this chapter remindsyou of several important ideas:

• Economics is the study of allocating scarceresources among possible uses. Because resourcesare scarce, choices have to be made on how theywill be used. Economists develop theoreticalmodels to explain these choices.

• The production possibility frontier provides asimple illustration of the supply conditions in twomarkets. The curve clearly shows the limitsimposed on any economy because resources are

scarce. Producing more of one good means thatless of something else must be produced. Thisreduction in output elsewhere measures the oppor-tunity cost involved in such additional production.

• The most commonly used model of the allocationof resources is the model of supply and demanddeveloped by Alfred Marshall in the latter part ofthe nineteenth century. The model shows howprices are determined by creating an equilibriumbetween the amount people want to buy and theamount firms are willing to produce. If supply anddemand curves shift, new prices are established torestore equilibrium to the market.

• Proving the validity of economic models is difficultand sometimes controversial. Occasionally thevalidity of a model can be determined by whetherit is based on reasonable assumptions. More often,however, models are judged by how well theyexplain actual economic events.

REVIEW QUESTIONS

1. “To an economist, a resource is ‘scarce’ only ifit has a positive price. Resources with zeroprices are, by definition, not scarce.” Do youagree? Or does the term scarce convey someother meaning?

2. In many economic problems, time is treated as ascarce resource. Describe how problems in usingtime meet our definition of “economics.” Canyou think of something that is different aboutusing time than about using physical resources?

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3. Provide a formal economic analysis of why hon-eybees find it in their interest to leave somenectar in each flower they visit. Can you think of any human activities that produce a similaroutcome?

4. Classical economists struggled with the“Water–Diamond Paradox,” which seeks anexplanation for why water (which is very useful)has a low price, whereas diamonds (which arenot particularly important to life) have a highprice. How would Smith explain the relativeprices of water and diamonds? Would Ricardo’sconcept of diminishing returns pose someproblem for this explanation? Can you resolvematters by using Marshall’s model of supply anddemand? Is water “very useful” to the deman-ders in Marshall’s model?

5. Marshall’s model pictures price and quantity asbeing determined simultaneously by the inter-action of supply and demand. Using thisinsight, explain the fallacies in the followingparagraph:

A rise in the price of oranges reduces thenumber people who want to buy. Thisreduction by itself reduces growers’ costsby allowing them to use only their besttrees. Price, therefore, declines along withcosts, and the initial price rise cannot besustained.

6. “Gasoline sells for $1 per litre this year, and itsold for $0.70 per litre last year. But consumersbought more gasoline this year than they did lastyear. This is clear proof that the economictheory that people buy less when the price risesis incorrect.” Do you agree? Explain.

7. “A shift outward in the demand curve alwaysresults in an increase in total spending (pricestimes quantity) on a good. On the other hand, ashift outward in the supply curve may increaseor decrease total spending.” Explain.

8. A recent news report suggested that the currentquantity of personal computers supplied exceeds

the quantity of those computers demanded. Usea supply and demand graph to see whether youcan make any sense out of this assertion.

9. A key concept in the development of positive eco-nomic theories is the notion of “refutability”—a“theory” is not a “theory” unless there is someevidence that, if true, could prove it wrong. Usethis notion to discuss whether one can conceiveof evidence with which the following theoriesmight be refuted:

• Friedman’s claim that pool players play as ifthey were using the rules of physics

• The theory that firms operate so as to maxi-mize profits

• The theory that demand curves have a nega-tive slope

• The theory that adoption of capitalism makespeople who are poor more miserable

10. The following conversation was heard amongfour economists discussing whether the min-imum wage should be increased:

Economist A. “Increasing the minimum wagewould reduce employment of minorityteenagers.”

Economist B. “Increasing the minimum wagewould represent an unwarranted interferencewith private relations between workers andtheir employers.”

Economist C. “Increasing the minimum wagewould raise the incomes of some unskilledworkers.”

Economist D. “Increasing the minimum wagewould benefit higher-wage workers andwould probably be supported by organizedlabour.”

Which of these economists are using positiveanalysis and which are using normative analysisin arriving at their conclusions? Which of thesepredictions might be tested with empirical data?How might such tests be conducted?

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PROBLEMS

Note: These problems involve mainly the mathemat-ical material from the Appendix to Chapter 1, whichstarts on page 29.

1.1 The following data represent five points on thesupply curve for orange juice:

a. Graph these points with price on the vertical (Y)axis and quantity on the horizontal (X) axis.

b. Do these points seem to lie along a straight line?If so, what is that line?

c. Use the equation calculated in part (b) to state how much will be supplied when P = 0 and when P = 6.

1.2 The following data represent five points on thedemand curve for orange juice:

a. Graph these points with price on the vertical (Y)axis and quantity on the horizontal (X) axis.

b. Do these points seem to lie along a straight line?If so, which line?

c. Use the equation calculated in part (b) to statehow much orange juice will be demanded whenP = 0 and when P = 6.

1.3 Marshall defined an equilibrium price as one atwhich the quantity demanded equals the quantitysupplied.

a. Using the data provided in problems 1.1 and 1.2,show that P = 3 is the equilibrium price in theorange juice market.

b. Using these data, explain why P = 2 and P = 4 arenot equilibrium prices.

c. Graph your results and show that the supply–demand equilibrium resembles that shown inFigure 1.3.

d. Suppose the demand for orange juice were to increase so that people want to buy 300 mil-lion more litres at every price. How would thatchange the data in problem 1.2? How would itshift the demand curve you drew in part (c)?

e. What is the new equilibrium price in the orangejuice market given this increase in demand? Showthis new equilibrium in your supply–demandgraph.

1.4 Suppose that a freeze in Florida reduces orangejuice supply by 300 million litres at every price listedin problem 1.1.

a. How would this shift in supply affect the data inproblem 1.1? How would it affect the algebraicsupply curve calculated in that problem?

b. Given this new supply relationship together withthe demand relationship shown in problem 1.2,what is the equilibrium price in this market?

c. Explain why P = 3 is no longer an equilibrium inthe orange juice market. How would the partici-pants in this market know P = 3 is no longer anequilibrium?

d. Graph your results for this supply shift.

1.5 This problem involves solving demand and supply equations together to determine price andquantity.

a. Consider a demand curve of the form

QD = –2P + 20

Price Quantity($ per litre) (millions of litres)

1 7002 6003 5004 4005 300

Price Quantity($ per litre) (millions of litres)

1 1002 3003 5004 7005 900

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where QD is the quantity demanded of a good andP is the price of the good. Graph this demandcurve. Also draw a graph of the supply curve

QS = 2P – 4

where QS is the quantity supplied. Be sure to putP on the vertical axis and Q on the horizontalaxis. Assume that all the Qs and Ps are nonnega-tive for parts (a), (b), and (c). At what values ofP and Q do these curves intersect—that is, wheredoes QD = QS?

b. Now suppose at each price that individualsdemand four more units of output—that thedemand curve shifts to

QD′ = –2P + 24

Graph this new demand curve. At what values ofP and Q does the new demand curve intersect theold supply curve—that is, where does QD′ = QS?

c. Now, finally, suppose the supply curve shifts to

QS′ = 2P – 8

Graph this new supply curve. At what values of Pand Q does QD′ = QS′? You may wish to refer to thissimple problem when we discuss shifting supplyand demand curves in later sections of this book.

1.6 Taxes in Oz are calculated according to the formula

T = 0.01I2

where T represents thousand of dollars of tax lia-bility and I represents income measured in thousandsof dollars. Using this formula, answer the followingquestions:

a. How much in taxes is paid by individuals withincomes of $10,000, $30,000, and $50,000?What are the average tax rates for these incomelevels? At what income level does tax liabilityequal total income?

b. Graph the tax schedule for Oz. Use your graph toestimate marginal tax rates for the income levelsspecified in part (a). Also show the average taxrates for these income levels on your graph.

c. Marginal tax rates in Oz can be estimated moreprecisely by calculating tax owed if persons with

the incomes in part (a) get one more dollar. Makethis computation for these three income levels.Compare your results to those obtained from thecalculus-based result that, for the Oz tax func-tion, its slope = 0.02I.

1.7 The following data show the production possi-bilities for a hypothetical economy during one year:

a. Plot these points on a graph. Do they appear to liealong a straight line? What is that straight-lineproduction possibility frontier?

b. Explain why output levels of X = 400, Y = 200 orX = 300, Y = 300 are inefficient. Show theseoutput levels on your graph.

c. Explain why output levels of X = 500, Y = 350are unattainable in this economy.

d. What is the opportunity cost of an additional unitof X output in terms of Y output in thiseconomy? Does this opportunity cost depend onthe amounts being produced?

1.8 Suppose an economy has a production possi-bility frontier characterized by the equation

X2 + 4Y2 = 100

a. In order to sketch this equation, first compute itsintercept. What is the value of X if Y = 0? Whatis the value of Y if X = 0?

b. Calculate three additional points along this pro-duction possibility frontier. Graph the frontierand show that it has a general elliptical shape.

c. Is the opportunity cost of X in terms of Y con-stant in this economy or does it depend on thelevels of output being produced? Explain.

d. How would you calculate the opportunity cost ofX in terms of Y in this economy? Give anexample of this computation.

Output of X Output of Y

1000 0800 100600 200400 300200 400

0 500

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1.9 Suppose consumers in the economy described inproblem 1.8 wished to consume X and Y in equalamounts.

a. How much of each good should be produced tomeet this goal? Show this production point on agraph of the production possibility frontier.

b. Assume that this country enters into internationaltrading relationships and decides to produce onlygood X. If it can trade one unit of X for one unitof Y in world markets, what possible combina-tions of X and Y might it consume?

c. Given the consumption possibilities outlined inpart (b), what final choice will the consumers ofthis country make?

d. How would you measure the costs imposed onthis country by international economic sanctionsthat prevented all trade and required the countryto return to the position described in part (a)?

1.10 Consider the function

where X � 0, Z � 0. Draw the contour lines (in thepositive quadrant) for this function for Y = 4, Y = 5,and Y = 10. What do we call the shape of these con-tour lines? Where does the line 20X + 10Z = 200intersect the contour line Y = AB5B0? (Hint: It may beeasier to graph the contour lines for Y2 here.)

Y ZX = ⋅

INTERNET EXERCISES

1. Opportunity costs. Imagine that you have justreceived a B.A. degree. You are wonderingwhether or not to spend an additional 2 years toearn an M.A. degree. What is the estimated returnon this additional investment? Let’s find out (youprobably wish to review Application 1.2 first,however). Go to the website of Human Resourcesand Social Development Canada that presents acomprehensive survey of postsecondary Canadiangraduates. To reach this website, use a searchengine to find “Special Edition on the NationalGraduates Surveys June 2001.” Click on the topic“The pathways to a post-secondary degree” andscroll down to the statement “Five years aftergraduating, full-time Bachelor’s graduates earned$37,000 in 1995 dollars compared to $46,000 forMaster’s and $50,000 for Doctoral graduates.”Supposing that an annual earnings difference of$9,000 persists for a 30-year career and that a stu-dent completing an M.A. degree forgoes $37,000in income for 2 years and incurs the tuition/feecosts given in Application 1.2, how does the costof an M.A. degree (following completion of a B.A.degree) compare with the earnings benefit of

attaining the M.A. degree? At this point, youmight want to ignore discounting and the timevalue of money.

After studying the appendix to Chapter 14,Compound Interest, particularly the section enti-tled The Present Discounted Value Approach toInvestment Decisions, you might want to reex-amine whether the cost of proceeding to an M.A.degree after completing a B.A. degree represents aworthwhile investment when it is considered onlyin monetary terms.

2. Economic jokes. Have you heard any good jokeslately? How about this one? Q: How many econ-omists does it take to screw in a lightbulb? A:None—if it really needed changing, market forceswould have caused it to happen. . . . Believe it ornot, these and other jokes about economics andeconomists can be found at http://netec.wustl.edu/JokEc.html. In fact, many, if not most, of thejokes posted at this website were contributed byeconomists themselves. Now who said econo-mists have no sense of humour? Or does viewingthese jokes only confirm your belief that econo-mists do indeed have no sense of humour?

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29

Mathematics began to be widely used in economics near the end of the nineteenthcentury. For example, Marshall’s Principles of Economics, published in 1890,included a lengthy mathematical appendix that developed his arguments moresystematically than the book itself. Today, mathematics is indispensable for econ-omists. They use it not to hide behind symbols or to make their arguments hardto understand but to move logically from the basic assumptions of a model toderiving the results of those assumptions. Without mathematics, this processwould be both more cumbersome and less accurate.

This appendix reviews some of the basic concepts of algebra. We also discussa few issues that arise in applying those concepts to the study of economics. Thetools introduced here are used throughout the rest of the book.

FUNCTIONS OF ONE VARIABLE

The basic elements of algebra are called variables. These can be labelled X and Yand may be given any numerical value. Sometimes the values of one variable (Y)may be related to those of another variable (X) according to a specific functionalrelationship. This relationship is denoted by the functional notation

Y = f(X) (1A.1)

This is read, “Y is a function of X,” meaning that the value of Y depends onthe value given to X. For example, if we make X calories eaten per day and Ybody weight, then equation 1A.1 shows the relationship between the amount offood intake and an individual’s weight. The form of equation 1A.1 also showscausality. X is an independent variable and may be given any value. On the otherhand, the value of Y is completely determined by X; Y is a dependent variable.This functional notation shows that “X causes Y.”

Mathematics Used in Microeconomics

APPENDIX TO CHAPTER 1

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VariablesThe basic elementsof algebra, usuallycalled X, Y, and soon, that may begiven any numericalvalue in an equation.FunctionalnotationA way of denotingthe fact that thevalue taken on byone variable (Y)depends on thevalue taken on bysome other variable(X) or set ofvariables.IndependentvariableIn an algebraic equa-tion, a variable thatis unaffected by theaction of anothervariable and may beassigned any value.DependentvariableIn algebra, a variablewhose value isdetermined byanother variable orset of variables.

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The exact functional relationship between X and Y may take on a widevariety of forms. Two possibilities are:

1. Y is a linear function of X. In this case

Y = a + bX (1A.2)

where a and b are constants that may be given any numerical value. Forexample, if a = 3 and b = 2, this equation would be written as

Y = 3 + 2X (1A.3)

We could give equation 1A.3 an economic interpretation. For example, if wemake Y the labour costs of a firm and X the number of labour hours hired,then the equation could record the relationship between costs and workershired. In this case there is a fixed cost of $3 (when X = 0, Y = $3), and thewage rate is $2 per hour. A firm that hired 6 labour hours, for example,would incur total labour costs of $15 [= 3 + 2(6) = 3 + 12]. Table 1A.1 illus-trates some other values for this function for various values of X.

2. Y is a nonlinear function of X. This case covers a wide variety of possibilitiesincluding quadratic functions (containing X2), higher-order polynomials (con-taining X3, X4, and so forth), and those based on special functions such aslogarithms. All of these have the property that a given change in X can havedifferent effects on Y depending on the value of X. This contrasts with linearfunctions for which a given change in X always changes Y by the sameamount.

30 Part 1: IntroductionA

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Linear Function Quadratic Function

Y= f(X) Y= f(X)X = 3 + 2X X = –X2 + 15X

–3 –3 –3 –54–2 –1 –2 –34–1 1 –1 –160 3 0 01 5 1 142 7 2 263 9 3 364 11 4 445 13 5 506 15 6 54

TABLE 1A.1 Values of X and Y for Linear and Quadratic Functions

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To see this, consider the quadratic equation

Y = –X2 + 15X (1A.4)

Y values for this equation for values of X between –3 and +6 are shown inTable 1A.1. Notice that as X increases by one unit, the values of Y go up rap-idly at first but then slow down. When X increases from 0 to 1, for example,Y increases from 0 to 14. But when X increases from 5 to 6, Y increases onlyfrom 50 to 54. This looks like Ricardo’s notion of diminishing returns—as Xincreases, its ability to increase Y diminishes.1

GRAPHING FUNCTIONS OF ONE VARIABLE

When we write down the functional relationship between X and Y, we are sum-marizing all there is to know about that relationship. In principle, this book, orany book that uses mathematics, could be written using only these equations.Graphs of some of these functions, however, are very helpful. Graphs not onlymake it easier for us to understand certain arguments, they also can take the placeof a lot of the mathematical notation that must be developed. For these reasons,this book relies heavily on graphs to develop its basic economic models. Here welook at a few simple graphic techniques.

A graph is simply one way to show the relationship between two variables.Usually, the values of the dependent variable (Y) are shown on the vertical axisand the values of the independent variable (X) are shown on the horizontal axis.2

Figure 1A.1 uses this form to graph equation 1A.3. Although we use heavy dotsto show only the points of this function that are listed in Table 1A.1, the graphrepresents the function for every possible value of X. The graph of equation 1A.3is a straight line, which is why this is called a linear function. In Figure 1A.1, Xand Y can take on both positive and negative values. The variables used in eco-nomics generally take on only positive values, and therefore we only have to usethe upper right-hand (positive) quadrant of the axes.

Linear Functions: Intercepts and SlopesTwo important features of the graph in Figure 1A.1 are its slope and its intercepton the Y-axis. The Y-intercept is the value of Y when X is equal to 0. For

1 Of course, for other nonlinear functions, increases in X may result in increasing amounts of Y (con-sider, for example, X2 + 15X).2 In economics, this convention is not always followed. Sometimes a dependent variable is shown onthe horizontal axis as, for example, in the case of demand and supply curves. In that case, the inde-pendent variable (price) is shown on the vertical axis and the dependent variable (quantity) on thehorizontal axis.

Linear functionAn equation that isrepresented by astraight-line graph.

InterceptThe value of Y whenX equals zero.

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3 One can also speak of the X-intercept ofa function, which is defined as that valueof X for which Y = 0. For equation 1A.3it is easy to see that Y = 0 when X = –3/2,which is then the X-intercept. The X-intercept for the general linear functionin equation 1A.2 is given by X = –a/b, asmay be seen by substituting that valueinto the equation.

example, as we can see in Figure 1A.1, when X = 0, Y = 3; this means that 3 isthe Y-intercept.3 In the general linear form of equation 1A.2,

Y = a + bX

the Y-intercept will be Y = a, since this is the value of Y when X = 0.We define the slope of any straight line to be the ratio of the change in Y to

the change in X for a movement along the line. The slope can be defined mathe-matically as

(1A.5)

where the Δ (“delta”) notation simply means “change in.” For the particularfunction shown in Figure 1A.1, the slope is equal to 2. We can clearly see fromthe dashed lines, representing changes in X and Y, that a given change in X ismet by a change of twice that amount in Y. Table 1A.1 shows the same result—

as X increases from 0 to 1, Yincreases from 3 to 5.Consequently

(1A.6)

It should be obvious that thisis true for all the other points inTable 1A.1. Everywhere alongthe straight line, the slope is thesame. Generally, for any linearfunction, the slope is given by bin equation 1A.2. The slope of astraight line may be positive (asit is in Figure 1A.1), or it may benegative, in which case the linewould run from upper left tolower right.

Slope YX

5 31 0

2= = =

Slope Change in YChange in X

YX

= =


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SlopeThe direction of aline on a graph;shows the change inY that results from aunit change in X.

10

5

3

1 5 10

Y-axis

Y-intercept

X-intercept

2

X-axis0

FIGURE 1A.1 Graph of the Linear Function Y = 3 + 2X The Y-intercept is3; when X = 0, Y = 3. The slope of the line is 2; an increase in X by 1 willincrease Y by 2.

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A straight line may also have a slope of 0, which is a horizontal line. In thiscase the value of Y is constant; changes in X will not affect Y. The function wouldbe Y = a + 0X, or Y = a. This equation is represented by a horizontal line (par-allel to the X-axis) through point a on the Y-axis.

Slope and Units of MeasurementThe slope of a function depends on the units in which X and Y are measured. Forexample, a study of a family’s consumption of oranges might reveal that thenumber of oranges (Y) purchased in a week is equal to 3 + 2X, where X is thefamily’s income measured in hundreds of dollars per week. Consequently, ΔY/ΔX= 2; that is, a $100 increase in income one week causes 2 more oranges to be pur-chased. If income (X) is measured in single dollars, the relationship is Y = 3 +0.02X and ΔY/ΔX = 0.02. In this case,although the interpretation of this slope isthe same (a $100 increase in income stillincreases orange purchases by 2 perweek), the numerical value of the slope isvery different. Similarly, if Y were meas-ured in dozens of oranges per week and Xin hundreds of dollars, the relationshipwould be Y = 1⁄4 + 1⁄6 X. An increase infamily income of $100 still increasesorange purchases by 2 (1⁄6 of a dozen), butnow the slope is different again. Clearly,one must be very careful when discussingthe slope of a function to know how thevariables are measured.

Changes in SlopeQuite often in this text we are interested in changing the parameters (that is, a andb) of a linear function. We can do this in two ways: change the Y-intercept, orchange the slope. Figure 1A.2 shows the graph of the function

Y = –X + 10 (1A.7)

This linear function has a slope of –1 and a Y-intercept of Y = 10. Figure 1A.2also shows the function

Y = –2X + 10 (1A.8)

We have doubled the slope of equation 1A.7 from –1 to –2 and kept the Y-intercept at Y = 10. This causes the graph of the function to become steeper andto rotate about the Y-intercept. In general, a change in the slope of a function will

Suppose that the quantity of sockeye salmon caughteach week in British Columbia coastal waters is givenby Q = 100 + 5P (where Q is the quantity of sockeyesalmon measured in thousands of kilograms and P isthe price per kilogram in dollars). Explain:

1. What are the units of the intercept and the slope inthis equation?

2. How would this equation change if the catch weremeasured in kilograms and price measured in cents perkilogram?

MicroQuiz 1A.1

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cause this kind of rotation without changing the value of its Y-intercept. Since alinear function takes on the value of its Y-intercept when X = 0, changing the slopewill not change the value of the function at this point.

Changes in InterceptFigure 1A.3 also shows a graph of the function Y = –X + 10. It shows the effectof changes in the constant term, that is, the Y-intercept only, while the slope staysat –1. Figure 1A.3 shows the graphs of

Y = –X + 12 (1A.9)

and

Y = –X + 5 (1A.10)


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Y

X

10

5

0 5 10

FIGURE 1A.2 Changes in the Slope of a Linear Function When the slope of a linear function ischanged but the Y-intercept remains fixed, the graph of the function rotates about the Y-intercept.

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All three lines are parallel; they havethe same slope. Changing the Y-interceptonly makes the line shift up and down.Its slope does not change. Of course,changes in the Y-intercepts also cause theX-intercepts to change, and you can seethese new intercepts.

In many places in this book we showhow economic changes can be representedby changes in slopes or in intercepts.Although the economic context varies, themathematical form of these changes is of the general type shown in Figure 1A.2and Figure 1A.3. Application 1A.1: Property Tax Assessment uses these linear con-cepts to illustrate one such use that may be depressingly familiar to homeowners.

Y

X

10

12

5

0 5 10 12

FIGURE 1A.3 Changes in the Y-Intercept of a Linear Function When the Y-intercept of afunction is changed, the graph of the function shifts up or down and is parallel to the other graphs.

In Figure 1A.2, the X-intercept changes from 10 to 5 asthe slope of the graph changes from –1 to –2. Explain:

1. What would happen to the X-intercept in Figure 1A.2 if the slope changed to –5⁄6?

2. What do you learn by comparing the graphs inFigure 1A.2 to those in Figure 1A.3?

MicroQuiz 1A.2

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Nonlinear FunctionsGraphing nonlinear functions is also straightforward. Figure 1A.4 shows agraph of

Y = –X2 + 15X (1A.11)

for relatively small, positive values of X. Heavy dots are used to indicate the spe-cific values identified in Table 1A.1, though, again, the function is defined for allvalues of X. The general concave shape of the graph in Figure 1A.4 reflects thenonlinear nature of this function.


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Y

60

50

40

A

B

30

20

10

0 1 2 3 4 5 6X

YX

FIGURE 1A.4 Graph of the Quadratic Function Y = –X2 + 15X The quadratic equation Y = –X2 + 15Xhas a concave graph—the slopes of the tangents to the curve diminish as X increases. This shapereflects the economic principle of diminishing marginal returns. The slope of a ray from the origin to apoint (X’,Y’) on the graph would equal .Y’

X’

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In most Canadian communities, property taxes payfor schools, the local police force, the fire depart-ment, and so forth. Conceptually, figuring what aproperty owner owes in taxes is a simple matter—the municipal assessors multiply the tax rate by themarket value of the property.1 A major problemwith this procedure, however, is that currentmarket values for most properties are not knownbecause properties only rarely change hands. Tocome up with accurate market values, localitiesincreasingly turn to sophisticated computermethods to assess properties.

A Simple Linear MethodLocal property assessors begin by collecting infor-mation on all houses that were recently sold in thearea. With these data, they can estimate a rela-tionship between sale price (Y) and a relevantcharacteristic of the house, say, its square metrage(X). Such a relationship might be stated as

Y = $10,000 + $50X (1)

This equation means that a house with zerosquare metrage (X = 0) should sell for $10,000(because of the value of its land) and each squaremetre of living space adds $50 to the value of thehouse. Using the square metrage of a house, theassessor can predict its current value by usingequation 1. This procedure is shown in Figure 1.According to the figure, a house with 2,000 squaremetres would have a market value of $110,000and one with 3,000 square metres would be worth$160,000.

Valuing Other Features of HomesOf course, assessors must take into account morefeatures of a house than just its area. Supposecurrent sales suggest that a nice view is worth$30,000 in the current housing market. Assumingequation 1 reflects the values of houses withoutviews, the values of houses with views can becomputed by

Y = $30,000 + $10,000 + $50X = $40,000 + $50X (2)

APPLICATION 1A.1 Property Tax Assessment

1 The property tax rate is generally expressed as the “mill rate” and equals the number of dollars owed by the propertyowner per dollar of the property’s assessed market value. For example, with a mill rate of 0.02, a homeowner wouldhave to pay $0.02 per dollar of the market value. On a $200,000 house, the annual property tax would be $4,000.

(continued)

The Slope of a Nonlinear FunctionBecause the graph of a nonlinear function is, by definition, not a straight line, itdoes not have the same slope at every point. Instead, the slope of a nonlinearfunction at a particular point is defined to be the slope of the straight line that istangent to the function at that point. For example, the slope of the functionshown in Figure 1A.4 at point B is the slope of the tangent line illustrated at thatpoint. As is clear from the figure, in this particular case, the slope of this functiongets smaller as X increases. This graphical interpretation of “diminishingreturns” to increasing X is simply a visual illustration of a fact already pointedout in the discussion of Table 1A.1.

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Equation 2 shows that the entire relation-ship between a house’s area and its value shiftsupward by $30,000 if a house has a nice view.This relationship is also shown in Figure 1.

Hedonic PricesUse of this procedure is not limited only toappraisers. Any analyst who wishes toexamine how the features of a property affectits value can apply such hedonic proceduresusing information from sales prices. Thisapproach has been used to study the effectsof air or noise pollution on house values andto examine the effects of safety features onthe values of used cars.

To Think About1. Suppose spectacular views are more valu-

able in large houses than in small ones.How would this effect be representedwith algebra?

2. How would you measure the effect of air-craft noise on housing values?

House value(dollars)

40,000

110,000

160,000House with view

House withoutview

10,000

Floor area(square metres)

0 2,000 3,000

FIGURE 1 Relationship between the Floor Area of a Houseand Its Market Value Using data on recent house sales, realestate appraisers can calculate a relationship between floor area(X, measured in square metres) and market value (Y). The entirerelationship shifts upward by $30,000 if a house has a nice view.


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Marginal and Average EffectsEconomists are often interested in the size of the effect that X has on Y. Thereare two different ways of making this concept precise. The most usual is to lookat the marginal effect—that is, how does a small change in X change Y? For thistype of effect, the focus is on ΔY/ΔX, the slope of the function. For the linearequations illustrated in Figure 1A.1 to Figure 1A.3, this effect is constant—ineconomic terms, the marginal effect of X on Y is constant for all values of X.For the nonlinear equation graphed in Figure 1A.4, this marginal effect dimin-ishes as X gets larger. Diminishing returns and diminishing marginal effectsamount to the same thing.

Sometimes economists speak of the average effect of X on Y. By this, theysimply mean the ratio Y/X. For example, as shown in Chapter 5, the average pro-ductivity of labour in, say, automobile production is measured as the ratio oftotal auto production (say, 2.5 million cars per year) to total labour employed(say, 50,000 workers). Hence, average productivity is 50 (= 2,500,000 ÷ 50,000)cars per year per worker.

Marginal effectThe change in Ybrought about by aone-unit change in Xat a particular valueof X. (Also the slopeof the function.)

Average effectThe ratio of Y to X ata particular value of X. (Also the slopeof the ray from the origin to thefunction.)

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Appendix to Chapter 1: Mathematics Used in Microeconomics 39

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Showing average values on a graph isa bit more complex than showing mar-ginal values (slopes). To do so, we takethe point on the graph that is of interest(say, point A in Figure 1A.4 whose coor-dinates are X = 4, Y = 44) and draw thechord 0A. The slope of 0A is then Y/X =44/4 = 11—the average effect we seek tomeasure. By comparing the slope of 0Ato that of 0B (= 54/6 = 9), it is easy to seethat the average effect of X on Y alsodeclines as X increases in Figure 1A.4.This is another reflection of the dimin-ishing returns in this function. In laterchapters, we show the relationship between marginal and average effects inmany different contexts. Application 1A.2: Can a “Flat” Tax Be Progressive?shows how the concepts arise in disputes about revising personal income taxrates in Canada.

Suppose that the relationship between grapes har-vested per hour (G, measured in kilograms) and thenumber of workers hired (L, measured in worker-hours)is given by G = 100 + 20L.

1. How many additional grapes are harvested by the10th worker? The 20th worker? The 50th worker?

2. What is the average productivity when 10 workers arehired? When 20 workers are hired? When 50 workersare hired?

MicroQuiz 1A.3

We in Canada live under a “progressive” incometax regime, where the average tax rate (ATR), thefraction of income that must be paid in taxes,increases as income increases. The 1966 CarterRoyal Commission on Taxation in Canadareviewed the principles that should guide taxpolicy in Canada and endorsed a progressive taxsystem. The ethical basis for progressive incometax is that the pain from contributing each dollarof tax is felt more acutely by a poor taxpayer thanby a rich taxpayer because of diminishing mar-ginal utility of income.

Figure 1 illustrates how ATR can be deter-mined graphically. Denoting pre-tax income by Yand income tax due by T, the diagram depicts a taxrule in which an individual is exempt from payingtax on the first $10,000 of income and must pay atax of 40 percent of all income exceeding$10,000. Expressing this more concisely, T = 0 for

Y � $10,000 and T = 0.4(Y – $10,000) for Y �

$10,000. For income Y1 = $25,000, T1 = $6,000,so that ATR = T1/Y1 = 24 percent, and this is simplythe slope of a ray from the origin (with angle �) tothe (Y1,T1) point on the T(Y) graph. If income dou-bled to Y2 = $50,000, then T2 = $16,000, so theATR would more than double (with the slope ofthe steeper ray having angle �), becoming T2/Y2 =$16,000/$50,000 = 32 percent. Taking anextremely high level of income, if Y = $1 million, T =$396,000 and the ATR = 39.6 percent. As incomein excess of $10,000 rises, the ATR continues toincrease, approaching (but never quite reaching)an upper limit of 40 percent.

Turning to the tax structure in Canada in 2006,where individuals were exempt from federal tax onthe initial $9,039 of income, the federal marginaltax rate (MTR) was 0 percent for Y � $9,039; 15.25percent for $9,039 � Y � $36,378; 22 percent for

APPLICATION 1A.2 Can a “Flat” Tax Be Progressive?

(continued)

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$16,000 = T2

$6,000 = T1

0 10 20 30 Y2

Incometax due

40Y1

T(Y)

Pre-taxincome($000)

��

FIGURE 1 Flat Tax Schedule Combined with Tax-Exempt Income The slope of a rayfrom the origin to any point on the tax schedule shows the ATR at that point. As incomeincreases beyond $10,000, the slopes of rays from the origin increase, implying anincreasing ATR and a progressive tax structure.

$36,378 � Y � $72,756; 26 percent for $72,756� Y � $118,285; and 29 percent for Y �

$118,285, as shown in Figure 2.Since MTRs vary by province, and since

Manitoba is typically the median province in termsof economic indicators, we will use the 2006 MTRfor Manitoba for illustrative purposes. Manitoba’sMTR was 0 percent for Y � $7,734; 10.9 percentfor $7,734 � Y � $30,544; 13.5 percent for$30,544 � Y � $65,000; and 17.4 percent for Y � $65,000.

Figure 3 combines the federal and ManitobaMTRs to depict the total income tax. The combined

MTRs are 0 percent for Y � $7,734; 10.9 per-cent for $7,634 � Y � $9,039; 26.15 percentfor $9,039 � Y � $30,544; 28.75 percent for$30,544 � Y � $36,378; 35.5 percentfor $36,378 � Y � $65,000; 39.4 percent for$65,000 � Y � $72,756; 43.4 percentfor $72,756 � Y � $118,285; and 46.4 percentfor Y � $118,285, as shown in Figure 3. Theincome tax due at the kinked points in the fed-eral and in the combined federal–provincial(Manitoba) tax schedules appears in Tables 1and 2.

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FIGURE 2 Federal Income Tax in Canada, 2006 When income exceeds the tax-exempt level, the average federalincome tax rate increases as income increases, implying a progressive federal income tax structure.

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140

Annual income ($000)

Tax

du

e ($

000)

0.00

5.00

10.00

15.00

20.00

25.00

30.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00

Annual income ($000)

Tax

du

e ($

000)

35.00

40.00

45.00

50.00

FIGURE 3 Combined (Federal and Provincial) Income Tax in Manitoba, 2006 When income exceeds the tax-exemptlevel, the average tax rate for combined federal–provincial income taxes for Manitoba increases as income increases, implying aprogressive income tax structure. For extremely high pre-tax income levels, the average tax rate approaches (but never exceeds)the maximum marginal tax rate of 46.4 percent.

(continued)

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Annual income Tax due

$ 9,039 $ 0,00036,378 4,16972,756 12,172

118,285 24,010

TABLE 1 Federal Income Tax in Canada, 2006

Annual income Tax due ATR

$ 7,734 $ 0,000 0.0%9,039 0,153 1.7

30,544 5,777 18.936,378 7,454 20.565,000 17,913 27.672,756 20,969 28.8

118,285 40,729 34.4

TABLE 2 Combined (Federal and Provincial)Income Tax in Manitoba, 2006

When the Carter Royal Commission publishedits report in 1966, the highest combined MTR inCanada was 80 percent for Y � $400,000. Thereport noted that “rates as high as this are on thestatute books only because they are readilyavoided by most of the few wealthy people withincomes of this size … through a myriad of taxavoidance techniques … so that the effective mar-ginal rate is much lower.” The report recom-mended a maximum combined MTR in Canada of50 percent, which is slightly above the combinedmaximum MTR currently found in Canada.

A striking observation by the Carter RoyalCommission was that “the effective average rateof tax on all income, including property gains, isnow probably no more for extremely wealthypeople than it is for those with much lowerincomes.” If this claim were true today, Canadianswould have a progressive tax regime in theory anda flat tax regime in practice after the army oflawyers specializing in tax planning and account-ants engaging in aggressive accounting were fin-ished plying their arcane tools of tax avoidance forwealthy clients.

Whereas tax avoidance is perfectly legal, taxevasion is a criminal offence. There is a grey areainvolving measures designed to avoid taxes, theuncertain legality of which will ultimately beresolved by a court of law. A suggestive hybrid of“evasion” and “avoidance” that has yet to makeits appearance in any recognized dictionary, “taxavoision” describes tax-reduction strategies whoselegality has yet to be established by a court of law.

To Think About

1. Suppose that each adult in society is uncondi-tionally granted $4,000 by the government,and for each dollar of earned income, $0.40must be paid to the government—a tax andtransfer arrangement known as a “negativeincome tax” or NIT. How would this alter thegraph in Figure 1? Would this NIT constitute aprogressive income tax structure?

2. At what level of income would an individualbecome a net contributor to the govern-ment’s treasury? In other words, at what levelof income would an individual’s tax liabilitybegin to exceed the $4,000 grant?

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Calculus and MarginalismAlthough your course in microeconomics may not require that you know cal-culus, it should be clear that many of the concepts that we cover were originallydiscovered using that branch of mathematics. Specifically, many economic con-cepts are based on looking at the effect of a small (marginal) change in a variableX on some other variable Y. You should be familiar with some of these concepts(such as marginal cost, marginal revenue, or marginal productivity) from yourintroductory economics course. Calculus provides a way of making the defini-tions for these ideas more precise. For example, in calculus, denoting “the changein” by using the delta symbol, �, mathematicians develop the idea of thederivative of a function, which is simply defined as the limit of the ratio ΔY

ΔX asΔX gets very small. In graphical terms, the derivative of a function and its slopeare the same concept. Both provide a measure of the marginal impact of X on Y.Derivatives provide a convenient shorthand way of studying marginal effects. Allof the major results in this book were discovered by making use of this connec-tion between mathematics and economics. For example, the eminent Frencheconomist Augustin Cournot (about whom we learn more later in the text) dis-covered the concept of marginal revenue in the early nineteenth century when hewas given the very practical problem of setting prices for water in Paris. Hisapplication of calculus to this problem provides the basic approach today to allstudies of monopoly pricing.

FUNCTIONS OF TWO OR MORE VARIABLES

Economists are usually concerned with functions of more than just one variable,since there is almost always more than a single cause of an economic outcome.To see the effects of many causes, economists must work with functions of sev-eral variables. A two-variable function might be written in functional notation as

Y = f(X,Z) (1A.12)

This equation shows that Y’s values depend on the values of two independentvariables, X and Z. For example, an individual’s weight (Y) depends not only oncalories eaten (X) but also on how much the individual exercises (Z). Increases in Xincrease Y, but increases in Z decrease Y. The functional notation in equation 1A.12hints at the possibility that there might be trade-offs between eating and exercise.In Chapter 2, we start to explore such trade-offs because they are central to thechoices that both individuals and firms make.

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A Simple ExampleIn general, we could have Y dependon the values of more than two vari-ables, but a simple two-variable func-tion can be used to explain most ofthe relevant facts about how multiplevariable functions work. Suppose therelationship between Y, X, and Z isgiven by

Y = X ⋅ Z (1A.13)

The form of this particular func-tion is widely used in economics.Later chapters use a closely relatedform to show the utility (Y) that anindividual receives from using twogoods (X and Z) and also to showthe production relationship betweenan output (Y) and two inputs (say,labour X and capital Z). Here, how-ever, we are interested mainly in thisfunction’s mathematical properties.

Some values for the function in equation 1A.13 are recorded in Table 1A.2.Two important facts are shown by this table. First, even if one of the variablesis held constant (say, at X = 2), changes in the other independent variable (Z)will cause the value of the dependent variable (Y) to change. The value of Yincreases from 4 to 6 as Z rises from 2 to 3, even though X is held constant. Ineconomic terms, this illustrates the “marginal” influence of variable Z. Second,several different combinations of X and Z will result in the same value of Y. Forexample, Y = 4 if X = 2, Z = 2 or if X = 1, Z = 4 (or, indeed, for an infinitenumber of other (X,Z) combinations if fractions are used). Using this equalityof values of Y for a number of (X,Z) combinations, functions of two variablescan be graphed rather simply.

GRAPHING FUNCTIONS OF TWO VARIABLES

We would need to use three dimensions to graph a function of two variables com-pletely: one axis for X, one for Z, and one for Y. Drawing three-dimensionalgraphs in a two-dimensional book is quite difficult. Not only must an artist begood enough to be able to show depth in only two dimensions, but the reader


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X Z Y

1 1 11 2 21 3 31 4 42 1 22 2 42 3 62 4 83 1 33 2 63 3 93 4 124 1 44 2 84 3 124 4 16

TABLE 1A.2 Values of X, Z, and Y That Satisfy the Relationship Y = X · Z

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must have enough imagination to read the graph as a three-dimensional model.Since economists are not necessarily good artists, they graph these functionsanother way that is much like the techniques mapmakers use.

Mapmakers are also confined to working with two-dimensional drawings. Theyuse contour lines to show the third dimension. These are lines of equal altitude thatoutline the physical features of the territory being mapped. For example, acontour line labelled “1,000 metres” on a map shows all those points of land thatare 1,000 metres above sea level. By using a number of contour lines, mapmakerscan show the heights and steepness of mountains and the depths of valleys andocean trenches. In this way, they add the third dimension to a two-dimensional map.

Economists also use contour lines—that is, lines of equal “altitude.”Equation 1A.13 can be graphed in two dimensions (one dimension for the valuesof X and another dimension for values of Z), with contour lines to show thevalues of Y, the third dimension. This equation is graphed in Figure 1A.5, withthree contour lines: one each for Y = 1, Y = 4, and Y = 9.

Each of the contour lines in Figure 1A.5 is a rectangular hyperbola. The con-tour line labelled “Y = 1” is a graph of

Y = 1 = X ⋅ Z (1A.14)

“Y = 4” is a graph of

Y = 4 = X ⋅ Z (1A.15)

and the line labelled “Y = 9” is a graph of

Y = 9 = X ⋅ Z (1A.16)

Some of the values along these contour lines are shown in Table 1A.2 on theprevious page. It would be easy to compute other points on the curves. Othercontour lines for the function could also be drawn by making Y equal to thedesired level and graphing the resulting relationship between X and Z. Since wecan give Y any value we want, an infinite number of contour lines can be drawn.In this way, we can show the original function in equation 1A.13 as accurately aswe want without resorting to three dimensions.

SIMULTANEOUS EQUATIONS

Another mathematical concept that is often used in economics is simultaneousequations. When two variables (say, X and Y) are related by two differentequations, it is sometimes, though not always, possible to solve these equations

Contour linesLines in two dimen-sions that show thesets of values of theindependent vari-ables that yield thesame value for thedependent variable.

SimultaneousequationsA set of equationswith more than onevariable that must besolved together for aparticular solution.

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together for a single set of values of X and Y that satisfies both of the equations.For example, it is easy to see that the two equations

X + Y = 3X – Y = 1

(1A.17)

have a unique solution of

X = 2Y = 1

(1A.18)

These equations operate “simultaneously” to determine the solutions for Xand Y. One of the equations alone cannot determine a specific value for eithervariable—the solution depends on both of the equations.


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Z

9

4

3

2

1

0 1 2 3 4 9X

FIGURE 1A.5 Contour Lines for Y = X ⋅ Z Contour lines for the function Y = X ⋅ Z are rectangularhyperbolas. They can be represented by making Y equal to various supplied values (here Y = 1, Y = 4,Y = 9) and then graphing the relationship between the independent variables X and Z.

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Changing Solutions forSimultaneous EquationsIt makes no sense in these equations to askhow a change in, say, X would affect thesolution for Y. There is only one solutionfor X and Y from these two equations. Aslong as both equations must hold, thevalues of neither X nor Y can change. Ofcourse, if the equations themselves arechanged, then their solution will alsochange. For example, the equation system

X + Y = 5X – Y = 1

(1A.19)

is solved as

X = 3Y = 2

(1A.20)

Changing just one of the parameters in equation set 1A.17 gives us an entirelydifferent solution set.

Graphing Simultaneous EquationsThese results are illustrated in Figure 1A.6 (page 48). The two equations in equa-tion set 1A.17 are straight lines that intersect at the point (2,1). This point is thesolution to the two equations since it is the only one that lies on both lines.Changing the constant in the first equation of this system gives us a differentintersection for equation set 1A.19. In that case, the lines intersect at point (3,2),and that is the new solution. Even though only one of the lines shifted, both Xand Y take on new solutions.

The similarity between the algebraic graph in Figure 1A.6 and the supply anddemand graphs in Figure 1.3 and Figure 1.4 is striking. The point of intersectionof two curves is called a “solution” in algebra and an “equilibrium” in eco-nomics, but in both cases we are finding the point that satisfies both relation-ships. The shift of the demand curve in Figure 1.4 clearly resembles the change inthe simultaneous equation set in Figure 1A.6. In both cases, the shift in one of thecurves results in new solutions for both of the variables. Marshall’s analogy of the blades of the supply and demand “scissors” determining market price andquantity can be seen in the algebraic notion of simultaneous systems and their

Figure 1A.5 shows three contour lines for the functionY = X ⋅ Z. How do these lines compare to the followingcontour lines?

1. Contour lines for Y = 3, 2, and 1 for the function Y = �X ⋅ Z

2. Contour lines for Y = 81, 16, and 1 for the functionY = X2 ⋅ Z2.

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solutions. Throughout this book, we usesuch graphs to show how markets arriveat equilibrium outcomes that satisfy bothsupply and demand relationships simul-taneously. Application 1A.3: The IraqWar and World Oil Prices provides a firstglimpse of this sort of analysis.


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Y

5

3

2

1

0 1 2 3 5X

FIGURE 1A.6 Solving Simultaneous Equations The linear equations X + Y = 3 (Y = 3 – X) and (X – Y = 1) can be solved simultaneously to find X = 2, Y = 1. This solution is shown by the point ofintersection of the graphs of the two equations. If the first equation is changed (to Y = 5 – X), thesolution will also change (to X = 3, Y = 2).

Economists use the ceteris paribus assumption to hold“everything else” constant when looking at a partic-ular effect. How is this assumption reflected in simulta-neous equations? Specifically:

1. Explain how the changes illustrated in Figure 1A.6represent a change in “something else”; and

2. Explain how the changes illustrated in Figure 1A.6might occur in a supply–demand context in the real world.

MicroQuiz 1A.5

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APPLICATION 1A.3 The Iraq War and World Oil Prices

In the aftermath of the United States–led invasionof Iraq, continuing acts of terrorism and sabotagehave impaired Iraq’s oil-production capability sig-nificantly. From a normal output level of 2.5 mil-lion barrels per day (bpd) of oil, it was estimatedthat 2006 production had fallen to 1.8 millionbpd. In a worst-case scenario, the extremevolatility of the political and military situation inIraq could bring oil production to a standstill.

What would be the impact onworld oil prices of a complete paral-ysis of Iraq’s petroleum industry? Canthe war in Iraq account for the sharprise in the world oil price to a 13-yearhigh of US$40 per barrel? And whateffect does this dramatic rise in theworld price of oil have on Canada?Without giving definitive answers, asimple supply–demand model can beused to suggest how these issues canbe addressed.

Short-Run ModelSince crude oil is traded in a worldmarket, we begin by presenting amodel of this market prior to the warin Iraq, when Iraq was producing2.5 million bpd. The world demandfor oil might be represented by thefollowing equation, where QD is thequantity of crude oil demanded,expressed in millions of bpd, and P isprice, expressed in dollars per barrel.

QD = 80 – 0.4P (1)

The pre-war world supply of oilmight be represented by

QS = 55 + 0.6P (2)

Market Equilibrium Before the Iraq WarThe pre-war equilibrium values are shown by theintersection of the world demand curve QD andthe world supply curve QS in Figure 1. The equilib-rium price of US$25 per barrel and equilibriumoutput of 70 million bpd were approximately thevalues that prevailed in the world oil market inmid-2002. Market equilibrium in the international

27.5

60

200

25

Q(bpd)

0 52.555

P(US$/barrel)

6970

8088.5

112.5

QD

QS

QD QS

FIGURE 1 The World Market for Oil Possible market equilibria assuming ahypothetical demand curve and several hypothetical supply curves. Theintersection of QS and QD depict equilibrium in 2002, prior to the U.S.-ledinvasion of Iraq.

(continued)

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oil market prior to the war in Iraq could be deter-mined by equating QD and QS:

80 – 0.4P = 55 + 0.6P or P = 25, Q = 70 (3)

The Effect of Shutting Down Iraq’s Oil Flow To examine the potential impact of the war inIraq, consider the effect of a decrease in Iraq’s oilproduction from the pre-war level of 2.5 millionbpd to 0 bpd. This assumes that the situationcontinues to deteriorate and production is even-tually halted. The world oil supply curve wouldthen shift from QS to Q’S, as shown in Figure 1,where Q’S is parallel to QS and is a horizontal dis-tance of 2.5 million bpd to its left. The position ofQ’S reflects the fact that at every price, therewould be 2.5 million fewer barrels supplied eachday. The equation of the new world supply curvewould be

Q’S = (55 – 2.5) + 0.6P = 52.5 + 0.6P (4)

The new equilibrium price would be US$27.50 perbarrel and the equilibrium quantity would be 69million bpd, indicating that other oil-producingcountries would respond to the higher price byincreasing production by 1.5 million bpd, partiallyoffsetting the 2.5 million bpd decrease in Iraqi oilproduction.

How Does This Affect Canada?If this were the only effect of the war in Iraq, itsimpact on Canada would be quite modest, sincethe price would rise only 10 percent. A more

important consideration is that Canada exports(by pipeline to the United States) approximatelythe same amount of crude oil that it imports (bytanker from Venezuela); therefore, the gain inrevenue to oil producers in Alberta would equalthe loss to Canadian consumers due to higheroil prices.

Admittedly, a redistribution of wealth fromconsumers to producers would take place.However, if Canadian society does not considerthe widows and orphans who are shareholders ofthe oil companies in Alberta to be less deservingthan the car owners across the country, the gainto one group would just offset the loss to theother, and the net impact of higher world oilprices on Canada would be neutral.1

Why Did the Price of Oil More Than Double?By mid-2004, the world price of oil reachedUS$40 per barrel for the first time since 1990. AsFigure 1 shows, even without any change in QD, aprice of US$40 per barrel of oil could result froma decision by the Organization of the PetroleumExporting Countries (OPEC) to have its membersexploit the turmoil in the Middle East by deliber-ately restricting supply in order to increase rev-enue. In Figure 1, the combination of Iraq’simpaired production and significantly greaterdemand could result in oil prices as high as US$60per barrel.2

An increase in demand, with QD shifting toQ’D, reflects the highly volatile situations in Iraq

1 Of course, the higher cost of energy would affect the cost of production in virtually every sector in Canada and couldresult in inflationary pressures, but the analysis of these secondary effects requires a more complicated set of toolsthan the supply–demand curves of Figure 1.2 Notice that the point elasticity of demand is very easy to calculate for the linear demand curve in Figure 1. This topicis discussed in Chapter 4 in the section Linear Demand Curves and Price Elasticity, for those of you who might wantto refer to it. At (70 bpd, US$25/barrel), point elasticity of demand is –10/70 = –0.14; at (64 bpd, US$40/barrel), it is–16/64 = –0.25; and at (40 bpd, $100/barrel)—the revenue-maximizing point on QD—point elasticity of demandwould be –1. Thus, if the oil-producing countries behaved like a disciplined cartel while consumers behaved like pricetakers, an oil cartel could impose a price of $100/barrel, selling 40 million bpd and generating revenue of US$4 bil-lion daily. This is more than double the oil producers’ daily revenue of US$1.75 billion in mid-2002 when the equilib-rium was (70 bpd, US$25 million). At the equilibrium price for Q’S and Q’D of $60 per barrel, namely at (88.5 bpd,US$60 per barrel), the point of elasticity of demand is –24/88.5 = –0.27. At this point, if OPEC members restrict supply,the resulting price increase will generate increasing revenue and higher profits for OPEC members.

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EMPIRICAL MICROECONOMICS AND ECONOMETRICS

As we discussed in Chapter 1, economists are not only concerned with devisingmodels of how the economy works. They must also be concerned with estab-lishing the validity of those models, usually by looking at data from the realworld. The tools used for this purpose are studied in the field of econometrics (lit-erally, “economic measuring”). Because many of the applications that appear inthis book are taken from econometric studies, and because econometrics hascome to play an increasingly important role in all of economics, here we brieflydiscuss a few aspects of this subject. Any extended treatment is, of course, betterhandled in a full course on econometrics, but discussion of a few key issues maybe helpful in understanding how economists draw conclusions about theirmodels. Specifically, we look at two topics that are relevant to all of economet-rics: (1) random influences; and (2) the ceteris paribus assumption.

Random InfluencesIf real-world data fit economic models perfectly, econometrics would be a verysimple subject. For example, suppose an economist hypothesized that the demandfor pizza (Q) was a linear function of the price of pizza (P) of the form

Q = a – bP (1A.21)

where the values for a and b were to be determined by the data. Because anystraight line can be established by knowing only two points on it, all the

(on the brink of a civil war), in Iran (as it rushes todevelop nuclear weapons, in defiance of theUnited Nations), and in Nigeria (with rebels sabo-taging the flow of oil), as well as the voraciousappetites of Asia’s emerging industrial giants(China and India). This increase in demand resultsin a new equilibrium price of US$60 per barrel atthe intersection of Q’D and Q’S. Indeed, geopoliticalfactors have propelled energy prices to unprece-dented levels. By mid-2006, geopolitical factors,combined with speculative panic, resulted in theprice of a barrel of oil briefly exceeding US$70 per barrel.

To Think About1. Suppose that Iraq’s oil production fell to 0 bpd

(as shown by Q’S in Figure 1) and that theincreasing appetite for energy by developingcountries such as China and India resulted inan increase in the world demand for oil. InFigure 1, by how much would QD have to shiftto the right (assuming that the higher demandcurve is parallel to QD) in order to bring abouta price of US$40 per barrel?

2. Following such an increase in world demandfor oil, how high would the new equilibriumquantity of oil (expressed in bpd) be?

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researcher would have to do is: (1) find two places or time periods where “every-thing else” was the same (a topic we take up next); (2) record the values of Qand P for these observations; and (3) calculate the line passing through the twopoints. Assuming that the demand equation 1A.21 holds in other times orplaces, all other points on this curve could be determined with perfect accuracy.

Unfortunately, no economic model exhibits such perfect accuracy. Instead, theactual data on Q and P will be scattered around the “true” demand curve becauseof the huge variety of random influences (such as whether people get a yearningfor pizza on a given day) that affect demand. This situation is illustrated in Figure1A.7. The true demand curve for pizza is shown by the black line, D.Unfortunately, researchers do not know this line. They can “see” only the actualpoints shown in colour. The problem the researcher faces then is how to infer whatthe true demand curve is from these scattered points.

Technically, this is a problem instatistical inference. The researcheruses various statistical techniques in anattempt to abstract from all of therandom things that affect the demandfor pizza and to infer what the rela-tionship between Q and P actually is.A discussion of the techniques used forthis purpose is beyond the scope of thisbook, but a glance at Figure 1A.7makes clear that no technique will finda simple line that fits the points per-fectly. Instead, some compromises willhave to be made in order to find ademand curve that is “close” to mostof the data points. Careful considera-tion of the nature of the randominfluences present in a problem canhelp in devising which technique touse.4 A few of the applications in thistext describe how researchers haveadapted techniques to their purposes.

Price (P)

D

Quantity (Q)

FIGURE 1A.7 Inferring the Demand Curve from Real-WorldData Even when the ceteris paribus assumption is in force, actualdata (shown by the points) will not fit the demand curve (D) perfectlybecause of random influences. Statistical procedures must be used to infer the location of D.


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StatisticalinferenceUse of actual dataand statistical tech-niques to determinequantitative eco-nomic relationships.

4 In many problems, the statistical technique of “ordinary least squares” is the best available. Thistechnique proceeds by choosing the line for which the sum of the squared deviations from the line forall of the data points is as small as possible. For a discussion, see R. Ramanathan, IntroductoryEconometrics with Applications, 5th ed. (Mason, OH: South-Western College Publishing, 2001).

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The Ceteris ParibusAssumptionAll economic theories employ theassumption that “other things are heldconstant.” In the real world, of course,many things do change. If the data pointsin Figure 1A.7 come from differentweeks, for example, it is unlikely thatconditions such as the weather or theprices of pizza substitutes (hamburgers?)have remained unchanged over theseperiods. Similarly, if the data points in thefigure come from, say, different towns, itis unlikely that all factors that may affectpizza demand are exactly the same inevery town. Hence, a researcher mightreasonably be concerned that the data inFigure 1A.7 do not reflect a single demand curve. Rather, the points may lie onseveral different demand curves, and attempting to force them into a single curvewould be a mistake.

To address this problem, two things must be done: (1) Data should be col-lected on all of the other factors that affect demand, and (2) appropriate proce-dures must be used to control for these measurable factors in analysis. Althoughthe conceptual framework for doing this is fairly straightforward,5 many prac-tical problems arise. Most important, it may not in fact be possible to measureall of the other factors that affect demand. Consider, for example, the problem ofdeciding how to measure the precise influence of a pizza advertising campaign onpizza demand. Would you measure the number of ads placed, the number of adreaders, or the “quality” of the ads? Ideally, one might like to measure people’sperceptions of the ads—but how would you do that without an elaborate andcostly survey? Ultimately, then, the researcher will often have to make some com-promises in the kinds of data that can be collected, and some uncertainty willremain about whether the ceteris paribus assumption has been imposed faithfully.Many controversies over testing the reliability of economic models arise for pre-cisely this reason.

An economic consulting firm is hired to estimate thedemand for DVD movies among several cities. Explainusing a graph why each of the following “solutions” tothe ceteris paribus problem is in fact no solution at all.Why would the demand curves developed by applyingeach assumption probably be wrong?

Approach 1: Use statistical procedures to control forwhat is easily measured (i.e., average income) andforget about what cannot be easily measured (i.e., thenumber of homes with DVD players).

Approach 2: Control for “everything” that affectsdemand; don’t worry about the possibility that thesupply of DVDs may differ from city to city.

MicroQuiz 1A.6

5 To control for the older measurable factors (X) that affect demand, the demand curve given in equa-tion 1A.21 must be modified to include these other factors as Q = a – bP + cX. Once the parametersa, b, and c have been determined, this allows the researcher to hold X constant (as is required by theceteris paribus assumption) while looking at the relationship between Q and P. Changes in X shift theentire Q–P relationship.

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SUMMARY

This chapter reviews material that should be familiarto you from prior math and economics classes. Thefollowing results will be used throughout the rest ofthis book:

• Linear equations have graphs that are straightlines. These lines are described by their slopes andby their intercepts with the Y-axis.

• Changes in the slope cause the graph of a linearequation to rotate about its Y-intercept. Changesin the Y-intercept cause the graph to shift in a par-allel way.

• Nonlinear equations have graphs that have curvedshapes. Their slopes change as X changes.

• Economists often use functions of two or morevariables because economic outcomes have many

causes. These functions can sometimes be graphedin two dimensions by using contour lines.

• Simultaneous equations determine solutions fortwo (or more) variables that satisfy all of the equa-tions. An important use of such equations is toshow how supply and demand curves determineequilibrium prices. For that reason, such equationsare widely encountered in economics.

• Testing economic models usually requires the useof real-world data together with appropriateeconometric techniques. An important problem inall such applications is to ensure that the ceterisparibus assumption has been imposed correctly.

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