Managerial EconomicsM. D University

Paper no. 3.12 July - 2003MBA – 1st Semester

Q No.1 What is the basic objectives of a firm? Explain the role and responsibility on Managerial Economics?

Ans. Conventional theory of firm assumes profit maximization is the sole objective of business firms. But recent researches on this issue reveal that the objectives the firms pursue are more than one. Some important objectives, other than profit maximization are:(a) Maximization of the sales revenue(b) Maximization of firm’s growth rate(c) Maximization of Managers utility function (d) Making satisfactory rate of Profit(e) Long run Survival of the firm(f) Entry-prevention and risk-avoidance

Profit Business Objectives: Profit means different things to different people. To an accountant “Profit” means the excess of revenue over all paid out costs including both manufacturing and overhead expenses. For all practical purpose, profit or business income means profit in accounting sense plus non-allowable expenses.

Economist’s concept of profit is of “Pure Profit” called ‘economic profit’ or “Just profit”. Pure profit is a return over and above opportunity cost, i. e. the income that a businessman might expect from the second best alternatives use of his resources.

Sales Revenue Maximisation: The reason behind sales revenue maximisation objectives is the Dichotomy between ownership & management in large business corporations. This Dichotomy gives managers an opportunity to set their goal other than profits maximisation goal, which most-owner businessman pursue. Given the opportunity, managers choose to maximize their own utility function. The most plausible factor in manager’s utility functions is maximisation of the sales revenue.

The factors, which explain the pursuance of this goal by the managers are following:.First: Salary and others earnings of managers are more closely related to sales revenue than to profits Second: Banks and financial corporations look at sales revenue while financing the corporation.

Third: Trend in sales revenue is a readily available indicator of the performance of the firm.

Maximisation of Firms Growth rate: Managers maximize firm’s balance growth rate subject to managerial & financial constrains balance growth rate defined as:G = GD – GC

Where GD = Growth rate of demand of firm’s product & GC = growth rate of capital supply of capital to the firm.

In simple words, A firm growth rate is balanced when demand for its product & supply of capital to the firm increase at the same time.

Maximisation of Managerial Utility function: The manager seek to maximize their own utility function subject to the minimum level of profit. Managers utility function is express as:U= f(S, M, ID)Where S = additional expenditure of the staff M= Managerial emoluments ID = Discretionary Investments

The utility functions which manager seek to maximize include both quantifiable variables like salary and slack earnings; non- quantifiable variables such as prestige, power, status, Job security professional excellence etc.

Long run survival & market share: according to some economist, the primary goal of the firm is long run survival. Some other economists have suggested that attainment & retention of constant market share is an additional objective of the firm’s. the firm may seek to maximize their profit in the long run through it is not certain.Entry-prevention and risk-avoidance, yet another alternative objectives of the firms suggested by some economists is to prevent entry-prevention can be:

a) Profit maximisation in the long run b) Securing a constant market share c) Avoidance of risk caused by the un-predictable behavior of the new firms

Micro economist has a vital role to play in running of any business. Micro economists are concern with all the operational problems, which arise with in the business organization and fall in with in the preview and control of the management. Some basic internal issues with which micro-economist are concerns:

(i) Choice of business and nature of product i.e. what to produce(ii) Choice of size of the firm i. e how much to produce (iii) Choice of technology i.e. choosing the factor-combination(iv) Choose of price i.e. how to price the commodity (v) How to promote sales(vi) How to face price competition

(vii) How to decide on new investments(viii) How to manage profit and capital (ix) How to manage inventory i.e. stock to both finished & raw

materialThese problems may also figure in forward planning. Micro economist deals with these questions and like confronted by managers of the enterprises.

Q. No 2 Explain the following with examples.a) Short run versus Long runb) Nature of marginal analysis

Ans a). Short Run & Long Run: The concept of short run and long run is used in economic theories like production theory, cost theory etc.

In production, theory short run refers to a period of time in which supply of certain inputs such as plant, building, machinery etc is fixed or is inelastic. In the short run therefore, increasing the use of only one variable input as labour and raw material can increase production of a commodity.

The long run refers to a period of time in which the supply of all the inputs is elastic, but not enough to permit a change in technology. That is, in the long run, all the inputs are variable. Therefore, in the end, production of or commodity can be increased by employing more of both variable and fixed inputs.

Short run costs are the costs that vary with the variation in input, the size of the firm remaining the same. In the other words, short run costs are the same as variable costs. Long run costs, on the other hand are the costs, which are incurred on the fixed assets like plant, building, machinery etc.

Ans.(b) Nature Marginal analysis: The concept of marginal value is widely used in economic analysis, for example marginal utility, marginal cost and marginal revenue. Marginality concept assumes special significance where maximisation or maximization problem is involved e.g. maximization of consumer’s utility, maximisation of firm’s profit, minimization of cost etc. The terun “marginal” refers to the change (increase or decrease) in the total of any quantity due to one unit change in its determinant e.g. the total cost of production of a commodity depends on the number of units produced. In this case “marginal cost” or (MC) can be defined as the change in total cost as result of producing one unit less of a commodity thus,Marginal Cost (MC) = TCn – TCn – 1

Where TCn = total cost of producing n unitsTCn-1 = total cost of producing n – 1 units.

UNIT – II

Q. No. 3 What is elasticity of demand? How can it be measured?

Ans. The degree of responsiveness of demand to the change in its determinants is called elasticity of demand. The concept of demand elasticity is used in business decisions are (1) Price elasticity; (2) Cross – elasticity (3) Income elasticity (4) Elasticity of price expectation.

1) Price elasticity of demand is generally defined as the responsiveness or sensitivity of demand for a commodity to change in its price. More precisely, elasticity of demand is the percentage change in demand because of one percent change in the price of the commodity. The price elasticity of demand (ep) is given as

Ep = Percentage change in quantity demanded Percentage change in price

Ep = Q P = Q P Q Q Q P Q P P P

Q = Changes in quantity Q = Original quantity

P = Change in price P = Original Price

2) Cross Elasticity is the measure of responsiveness of demand for a commodity to the changes in the price of its Substitutes and complementary goods .for example, cross elasticity of demand of tea is the percentage change in its quantity demanded with respect to the changes in the price of its substitutes coffee. The formula for tea and same for coffee is given by

Ep = Percentage change in demanded for tea Qt Percentage change in price of coffee

Ep = Pc . Qt Qt Pc

3) Income Elasticity of demand is responsiveness of demand to the changes in income.

Income elasticity of demand for product X may be defined as

X Y = Y X X Y X Y

Where X = Quantity of X demanded Y = Disposable Income X = Change in quantity demanded Y = Changes in Income

4) Advertisement Elasticity of sales is defined as responsiveness of demand / sales to the changes in advertisement expenditure

Percentage change in demanded for tea Qt Percentage change in Advt expenditure S / S = S . A A/A A S

Where S = Sales, S = increase in sales A = initial advertisement expenditure A = additional expenditure on advertisement

5) Elasticity of Price Expectations refers to the expected range in future price as a result of change in current prices of a product. The elasticity of price expectation is defined as measured by the formula

Ex = Pf / Pf = Pf . Pc Pc/ Pc Pc Pf

Where Pc and Pf are current and future prices respectively.

The co – efficient ex gives the measure of expected percentage change in future price as a result of 1% change in present price, if ex >1, it indicates that future change in price will be greater than the present change in price, and vice versa.

Question 4 – What are the main techniques of demand estimation? What is their reliability?

Answer: Demand estimation is predicting future demand form a product. The information regarding future demand is essential for planning and scheduling production, purchase of raw materials, acquision of finance and advertising.

The various techniques of demand estimation: -

1) Survey Method2) Statistical Method

Survey Method

Survey method is generally used where the purpose is to make short run forecast of demand. Under this method, customer surveys are conducted to collect information about their intentions and future purchase plan. This method includes

(a) Consumer survey method(b) Opinion Poll method

Consumer survey method May be in form of

a) Consumer enumeration: - In this method, almost all the potential users of the product are contacted and are asked about the future plan of purchasing the product in question. The quantities indicated by the consumers are added together to obtain the probable demand for the product.

b) Sample survey method: - Under this method only a few potential consumers selected from relevant market through a sampling method are surveyed, on the basis of the information obtained, the probable demand may be estimated through the following formula.

D = HR (H.AD) HsWhere D = probable demand forecast

H = Census number of households from the relevant market. Hs = number of households reporting demand for the product. HR = number of households reporting demand for the product. AD = average expected consumption by the reporting households.

c) End User Method: - The end user method of demand forecasting is used for estimating demand for inputs. Making forecast by this method requires building up a schedule of probable aggregate future demand for inputs by consuming industries and various other sectors.

Opinion poll Method

The opinion poll methods aim at collecting opinion of those who are supposed to possess knowledge of the market e.g. sales representative, professional marketing experts and consultants. The opinion poll method include

a) Expert opinion method: - Firms having a good network of sales representative can put them to work of assessing the demand for the product in the areas that they represent. Sales representative, beings in close touch with the consumers are supposed to know the future purchase plans of their customer, their reaction to the market changes, their response to the introduction of new products and the demand for competing products. They are, therefore, in a position to provide an estimate of likely demand for their firm’s product in the area. The estimates of demand thus obtained from different regions are added up to get the overall probable demand for a product.

b) Delphi Method: - Delphi method is used to consolidate the divergent expert opinions and arrived at a compromise estimate of future demand.

Under Delphi method the expert are provided information on estimates of forecast of other experts along with the underlying assumptions. The experts may revise their own estimates in the light of forecast made by other experts. The consensus of experts about the forecasts constitutes the final forecast.

Although this method is simple and inexpensive, it has its own limitations. First estimates provided by sales representations and professional experts are reliable only to extend depending upon their skill to analysis the market and their experience. Second, demand estimates way involve the subjective judgement of the which may lead to over or under estimation, finally, the assessment of market demand is usually based on inadequate information’s, such as changes in GNP, available of credit, future prospects of the industry etc, fall outside their purview.

c) Market studies and Experiments:- It is a method of collecting necessary information regarding demand is to carry out market studies and experiments on consumer’s behavior under actual through controlled market conditions. This method is known in common parlance market conditions. This methods is known in common parlance as market experiment method under this method, firms first select some areas of the representative markets – three or four cities having similar features viz. Population, income levels, cultural and social background, occupational distribution, choices and preferences of consumers. Then, they carry out market experiments by changing prices, advt. Expenditure and other controllable variable in the demand function under the assumption that other thing remains same. The controlled variable

may by changed over time either simultaneously in all the markets or in all the markets or in the selected markets. After such changes are introduced in the market, the consequent changes in the demand over a period of time (a week, a fortnight or month) are recorded. On the basis of data collected elasticity coefficient are computed. These coefficients are then used along with the variables of the demand function to assess the demand for product

The market experiments methods have certain serious limitations. First, this method is very expensive and hence cannot be afforded by small forms. Second, being a costly affair, experiments are usually carried out on a scale too small to permit generalization with a high degree of reliability.

Third experimental methods are based on short – term and controlled conditions that may exist in an uncontrolled market. Hence, the results may not be applicable to the uncontrolled long-term conditions of the market.

Statistical Method

Statistical method of demand projection include the following techniques

1) Trends Projection Method2) Barometric Method and3) Economic Method

Trends Projection Method

Trend projection method is a classical method of business forecasting. This method is essentially concerned with the study of movement of variable through time. The use of this method requires a long and reliable time series data. The trend projection method is used under the assumption that the factors responsible for the past trends in variables to be projected (e.g. sales and demand) will continue to play their part in future in the same manner and to the same extend as they did in the past in determining the magnitude and direction of the variable.

There are three (3) techniques of trend projection based on time – series data.

(a) Graphical Method: - under this method, annual sales data is plotted on a graph paper and a line is drawn through the plotted points. Then a free hand line is so drawn that the total distance between the line and the point is minimum.

Sale

YearsTrend Projection

Although this method is very simple and least expensive, the projections made through this method are not very reliable. The reason is that the extension of the trend line involves subjectivity and personal bias of the analysis.

(b) Fitting Trend Equation: Least square method: - Fitting trend equation is a formal technique of projecting the trend in demand. Under this method, a trend line (or curve) is fitted to the time – series data with the aid of statistical techniques. The form of the trend equation that can be fitted to the time series data is determined either by plotting the sales data or by trying different forms of trend equations for the best fit.When plotted, a time series date may show various trends. The most common types of trend equation are 1) liner and 2) exponential trends

Linear Trend: - When a time series data reveals a rising trend in sales than a straight-line trend equation of the following form is fitted

S = A + BTWhere S = annual sales

T = Time (in year) A & B are constant. The parameter b given the measure of annual

increase in sales

Exponential trend:- When sales ( or any dependent variable) have increased over the past years at an increasing rate or at a constant percentage rate, than the appropriate trend equation to be used is an exponential trend equation of any of the following type 1. Y = aebtOr its semi – logarithmic for

Log y = = log a + btThis form of trend equation is used when growth rate is constant.

2. Double log trend equation of equationY = aTB

Or it’s double logarithmic form Log y = log a + b log t

This form of trend equation is used when growth rate is increasing.

LimitationThe first limitations of this method arise out of the assumption that the past rate of change in the dependent variable will persist in the future too. Therefore, the forecast based on this method may be considered to be reliable only for the period during which this assumption holds.Second, this method cannot be used for short-term estimates. Also it cannot be used where trend is cyclical with sharp turning points of trough and perks.

(c) Box – Jenkins Method: - This method of forecasting is used only for short – term predictions. Besides, this method is suitable for forecasting demand with only stationary time series sales data. Stationary time series data is one, which does not reveal long term trend. In other words, Box-Jenkins technique can be used only on those cases in which time-series analysis depicts monthly or seasonal variation recurring with some degree of regularity.

Barometric Method

Many economists use economic indicators as barometer to forecast trends in business activities.The basic approach of barometer technique is to construct an index of relevant economic indicators and to forecast future trends on the basis of movements in the index of economic indicators. The indicators used in this method are classified as (a) Leading indicators: - consists of indicators which move up and down

ahead of some other series e.g. new order of durable goods, new building permits etc.

(b) Coincidental indicators: - are the ones that move up and down simultaneously with the level of economic activity. E.g. number of employees in the non-agricultural sector, rate of unemployment, sales recorded by the manufacturing, trading and the retail sectors etc.

(c) Lagging indicators consists of those indicators, which follow a change after some time lag. E.g. lending rate for short-term loans etc.

Development and allotment of land by Delhi Development Authority to Group Housing Societies (a lead indicator) indicates higher demand prospects for

cement, steel and other construction material (coincidental indicators) and increase in housing loan distribution (lagging indicators).

Econometric method

The econometric methods combine statistical tools with economic theories to estimate economic variables and to forecast the intended economic variables. An econometric model may be single equation regression model or it may consist of a system of simultaneous equations.

Regression methodRegression analysis is the most popular method of demand estimation. This method combines economic theory and statistical techniques of estimation. Economic theory is employed to specify the determinants of demand and to determine the nature of the relationship between the demand for a product and its determinants. Economics theory thus helps in determining the general form of demand function. Statistical techniques are employed to estimate the values of parameters in the estimation equation.

Simultaneous Equation Method It involves estimating several behavioral equations. These equations are generally behavioral equations, Mathematical equations and Market – clearing equations. The first step in this technician is to develop a complete model and specify the behavioral assumption regarding the variables included in the model. The variables that are included in the model are 1) Endogenous variables2) Exogenous variables

Endogenous variables – the variables that are determined within the model are called endogenous variables. Endogenous variables are included in the model as depended variables that are the variables that are to be explained by the model. These are also called controlled variables. The number of equations included in the model must be equal to number of endogenous variables.

Exogenous variables – are those that are determined outside the model. Exogenous variables are inputs of the model whether a variable is treated endogenous variables or exogenous variables depend on the purpose of the model. The examples of exogenous variables are “ Money Supply”, tax rates, govt. spending etc. The exogenous variables are also known as uncontrolled variables.

Unit – III

Question 5: Explain the inter–relationship between the various short run cost curve of a firm. Why is average cost curve U – shaped?

Answer:The basic analytical cost concepts used in the analysis of cost behavior are total, average and Marginal costs. The total cost (TC) is defined as the actual cost that must be incurred to produce a given quantity of output. The short – run total cost is composed of two major elements

I. Total fixed cost (TFC)II. Total variable cost (TVC)

TC = TFC + TVC

For a given quantity of output (q), the average total cost (TAC), average fixed cost (AFC) and average variable cost (AVC) can be defined as

TAC = TC/ Q = TFC + TVC/Q

AFC = TFC/Q; AVC = TVC / Q

TAC = AFC + AVC

Marginal cost (MC) is defined as the change in the total cost divided by change in total output.

i.e. ▲TC / ▲Q

As the first derivative of cost function i.e. DTC / DQ

The total fixed cost (TFC) remains fixed for whole range of output, and hence, takes the form of a horizontal line – TFC. The total variable cost (TVC) curve

TC

TVC

TFC

OutputO

Cost

shows that the total variable cost first increases at decreasing rate and then at increasing rate with the increases in the output. The pattern of change in TVC stems directly from the law of increasing and diminishing returns to the variable inputs, as the output increases, larger quantity of variable inputs are required to produce the same quantity of output due to diminishing returns. This causes a subsequent increase in the variable cost for producing the same output. The total vertical addition to TFC and TVC; and as the TFC is constant; the TC and TVC curve will be parallel.

COST

OOutput

The AFC curve will fall steeply in the beginning and will tend to touch the horizontal axis, but will never become zero. The AVC curve slopes downwards and then rises. As AFC and AVC curves are falling in the initial stages, the AC curve registers a deep fall in the beginning. Its minimum point comes after the AVC curve has reached its minimum. The reason for this is that the AFC curve continues to decline. In the rising phase, both the AC and AVC curve tends to approach each other but never exactly merge into each other, for the AFC curve is above the zero axes. Generally, the average cost curve lies above the AVC – curve at a distance equal to the corresponding height of AFC curve.

The marginal curve represents the change in both TVC and TC curves due to change in output. It downward trend in MC shows increasing marginal productivity of the variable input mainly due to internal economy resulting from increase in production. Similarly, an upward trend in the MC shows increase in

TVC, on the one hand, and decreasing marginal productivity of the variable input on the other.

Question 6: Discuss the equilibrium of a firm under monopoly. What are the conditions of equilibrium?

Answer: Monopoly refers to a market situation on where there is only one seller who has complete control over the supply of a commodity, which has no close substitutes. The monopoly firm can adopt any price it likes; it can charge uniform price, or it can charge different prices from different consumers. It is able to prevent others from entering the industry. The firm and industry refer to one and the same thing; a single firm constitutes the entire industry.

Determination of price and output (Equilibrium under Monopoly)

Marginal cost and marginal revenue – Under monopoly, the firm is a price – maker, a firm can therefore fix the price of its products, given the output. The demand curve (AR curve is therefore, downward sloping under monopoly, and so the MR curve is below the AR curve.

MC = MR and MC cure cuts MR curve from below

Short Run

ARMR

AR

MR

Output (Units)

A monopoly can make either normal profits or supernormal profits in the short – run. If monopolists making sub – normal profit in the short – run so long as it AVC is covered. Thus, in the short run under monopoly there are three possibilities.

ACPrice and MC/ Revenue

A1 P1 Normal Profits

E1 AR

MR O Q1 Output (units)

E1 is the point of equilibrium, OQ1 is he equilibrium output and OP1 is the equilibrium price.

AC = A1Q1 AC = AR, the firm makes normal profits

Super normal profits

AC

Price and MC/ Revenue P2

C1 A2

E2

O

Q2 Output (units)

E2 is the point of equilibrium, OQ2 is the equilibrium output, OP2 is equilibrium price,

AC = A2Q2AR = R2Q2

AR>AC, the firm makes super – normal profits equal to the area given by P2R2A2C2

Sub normal Profits covering AVC

E3 is the point of equilibrium, OQ3 is the equilibrium Output, OP3 is the equilibrium price.

AC – A3Q3AR – R3Q3 AVC – R3Q3

AR<AC, the firm makes sub – normal profits equal to C3AS3R3P3. Even though the firm makes losses. It continues to produce in the short run because AVC is recovered.

Long run equilibrium under Monopoly: A firm under monopoly may make normal profits in the long – run; however, it tries to super – normal (abnormal) profits in the long run. LRAC is flatter than the short run average cost curve, but the conditions of equilibrium are the same as in short run.

AR – R0Q0; AC- C0Q0, AR, AC so the firm makes super normal profits equal to P0R0C0P.

Q No. 7 Explain Baumol’s theory of sales revenue maximization what are its assumptions?

Ans. According to Baumol, every business firm aims at maximization it sales revenue (price x quantity0 rather than its profit. Hence his hypothesis has come to be known as sales maximization theory & revenue maximization theory. According to baumol, sales have become an end by themselves and accordingly sales maximization has become the ultimate objective of the firm. Hence, the management of a firm directs its energies in promoting and maximizing its sales revenue instead of profit.

The goal of sales maximization is explained by the management’s desire to maintain the firm’s competitive position, which is dependent to a large extent on its size. Unlike the shareholders who are interested in profit, the management is interested in sales revenue, either because large sales revenue is a matter of prestige or because its remuneration is often related to the size of the firm’s

operations than to its profits. Baumol, however does not ignore the cost of production which has to be covered and also a margin of profit. In fact, he advocates the adoption of a price, which will cover the cost and also will yield a minimum rate of profits. That is, while the firm is maximizing its revenue from sales, it should also “enough or more than enough profits” to keep the shareholders satisfied. According to Baumol the typical digopolists objective can usually be characterized approximately as sales maximization output does not yield adequate profit, the firm will have to choose that output which will yield adequate profit even through it may not achieve sales maximization.

According to sales revenue maximization theory, graphs, cost and revenue curves are given as in conventional theory of pricing, suppose that the total cost (TC) and the total revenue (TR) curves are given, the profit curves (TP) is obtained by plotting the difference between TR and TC curves. Profit are zero where TR = TC. The total sales revenue is maximization where slope of TR curve i.e MR = is equal to zero. Such a point lies at the highest point of the TR curve. The highest point on the TR curve can be obtained easily by drawing a line parallel to the horizontal axis and tangent to the TR curve. The point H on the TR curve represents the total maximum sales revenue. A line drawn from point H to output axis shows sales revenue is maximized at output OQ3 and its price equals HQ3 / DQ3.

Profit Constraint and Revenue maximization :At output OQ3, the firm maximizes the total revenue and makes profit HM = TQ3. If the profit is enough or more than enough to satisfy the shareholders, the firm will produce output OQ3

and charge a price = HQ / OQ3. But if profit at output OQ3 is not enough to satisfy the shareholders, then the firm’s output must be say OQ2 which yields a profit LQ2> TQ3.

Thus, there are two types of probable equilibrium: one is which the profit constraint does not provide as effective barriers to sales maximization, and second in which profit constraint does provide as effective barriers to sales maximization. In the second type of equilibrium, the firm will produce an output which yields a satisfactory ar target profit. It may be an output between OQ1 and OQ2 .e.g if minimum required profit is OP1, than the firm will stick to its sales maximization goal and produce output OQ3 which yields a profit much greater than the required minimum.Since actual profit (TQ3) is much greater than the minimum required, the minimum profit constraint is not operative, But, if required minimum profit level is OP2, OQ3 will not yield sufficient profit to met the profit target. The firm will, therefore, produce an output OQ2 where its profit is just sufficient to meet requirement of minimum profit. This output OQ2 is less than the sales maximization output OQ3. Evidently the profit maximization output OQ1 is less than the sales maximization output OQ2. (with profit constraint)

Q. No. 8 Explain the technique of multi-product pricing. What is the rationale of the technique?

Ans. Almost all the firms have more than one product in their line of production. Even the most specialized firms produce a commodity in multiple models, styles and size, each so much differentiated from the other that each moder or size of the product may be considered a different products e.g. the various models of television, refrigerators etc produced by the same company may be treated as different product for at least pricing purpose. The various models are so differentiated that consumers view them as different products. Hence each model or product has different average revenue (AR) and Marginal Revenue curves and that one product of the firm concepts against the other product. The pricing under this condition is known as multi-product pricing or product line pricing. In multi-product pricing, each product has a separate demand curve. But, since all of them are produced under one organization by interchangeable production facilities, they have only one inseparable marginal cost curve. That is, while

revenue curves, AR and MR, are separate for each product, cost curves AC and MC are inseparable.

A B C D MC

D1 D2 D3 D4

costand

P1 P2 P3 P4

RevenueEMR

MR1 MR2 MR3 MR4

Q Q1 Q2 Q3 Q4

Quantities demanded per time unitSuppose a firm has four different products A, B, C and D in its line of production. The marginal cost of all the products can be taken together as curve MC, which is the factory marginal cost curve. When the MRs. For the individual products are summed up, the aggregate MR passes through point C on MC curve. If a line parallel to the X – axies, is drawn from point C to the Y- axis through the MRs, the intersecting point will show the points where MC and MRs are equal for each product, represented by the line EMR and MRs determine the output level and price for each product, the output of the four product are given as OQ1 of product A; QQ2 of B; Q2Q3 of C; and Q3Q4 of D. The respective prices for the four products are P1Q1 for product A; P2 Q2 for B; P3Q3 for C; and P4q4 for D, These price and output combinations maximize the profit from each product and hence the overall profit of the firm.