COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Subject COMMERCE Paper No and

Title

2. MANAGERIAL ECONOMICS Module No and

Title

15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Module Tag COM_P2_M15

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

TABLE OF CONTENTS

1. Learning Outcomes 2. Introduction

3. Isoquants

4. Properties of Isoquants

5. Isoquants and Economic Region of Production 6. Iso-Cost Line

7. Producer’s Equilibrium 8. Summary

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

1. Learning Outcomes

After studying this module, you would be able to

 Know about the properties of isoquants.

 Know about ridge lines and economic region of production.

 Know about iso-cost line.

 Understand producer’s equilibrium.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

2. Introduction

The producers are always faced with the problem of deciding about combination of inputs that should be used for producing a commodity. A given level of output can be produced by employing various combination of inputs. A rational producer will always choose optimum combination of inputs to produce that given level of output. The combination of inputs is optimum if the given quantity of output can be produced with minimum cost or if the maximum quantity of output can be produced with a given cost of production. This decision of the producers is called as “Producer’s Equilibrium”.

International Equities

3. Isoquants

An isoquant represents all possible combinations of labour & capital that can be employed to produce a given level of output. Along an isoquant, the ratio of inputs keeps on changing. It is also known producer’s indifference curve or production indifference curve because the producer is indifferent between these combinations of factors. All combinations lying on the same isoquant produce the same level of output.

Let us suppose a firm producing 20 units of a product using different combination of factors. It is shown below:

Factor

Combination Units of labour Units of Capital Total units of Output

P 2 20 20

Q 4 12 20

R 6 7 20

S 8 5 20

T 10 4 20

The above table shows that 20 units of output can be produced by employing 2 units of labour and 22 units of capital or 4 units of labour and 14 units of capital or any other combination of labour& capital.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig. 1.1

Fig 1.1 shows that all different combinations of factors such P, Q, R, Sand T are capable of producing 20 units of output.

An isoquant is based on the following assumptions:

1. Employment of two factors Labour (L) and Capital (K) 2. Given state of technology

3. Continuous production function

Isoquant Map – A number of isoquants depicting different levels of output are known as isoquant map.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig.1.2

Fig 1.2 shows an isoquant map where isoquant IQ1 depicts the lowest level of output of 20 units while isoquants IQ2 and IQ3 depict higher level of output of 30 units and 40 units respectively. Higher isoquant represents higher level of output than the lower one.4.

4. Properties of Isoquants

The following are the main properties of isoquants:

1. Isoquants are downward sloping from left to right - Isoquant have a negative slope because if a firm wants to employ more units of one factor, than it has to reduce the units of other factor to produce same level of output. It is assumed that marginal product of the factors is positive i.e. increase in the quantity of factor leads to positive increase in the output. Thus if the amount of one factor is increases, the amount of other factor has to be decrease to produce the same level of output.

There are certain inconsistencies follow if the isoquants do not have a negative slope.

If the isoquant are upward sloping (Fig.1.3), this means that the same quantity of output can be produced by employing less units of both capital &labour i.e.

marginal product of at least one factor is negative.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig.1.3

If the isoquant is parallel to Y axis (Fig.1.4) this means that same quantity of output can be produced with the same quantity of labour and any quantity of capital i.e. marginal product of capital is negative. Thus isoquant shown in figure 1.4 is not possible.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig.1.4

If the isoquant is parallel to X axis (Fig.1.5) this means that same quantity of output can be produced with the same quantity of capital and any quantity of labouri.e. marginal product of labour is negative. Thus isoquant shown in figure 1.5 is not possible.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig.1.5

2. Isoquants are convex to the origin - This feature of isoquants is based upon the

‘Principle of Diminishing Marginal Rate of Technical Substitution’. The slope of an isoquant is known as marginal rate of technical substitution. It is defined as the quantity of capital (K) that a firm is willing to sacrifice for an additional quantity of labour (L) to keep the same level of output.

MRTs = ΔK/ ΔL

The MRTs goes on declining as we move down on the isoquant showing that the quantity of capital that is needed to be sacrificed by employing more units of labour, declines so as to maintain the same level of output. Along downward sloping isoquant, marginal productivity of labour decreases with the increase in units of labour and simultaneously marginal productivities of capital increase with the reduction in the units of capital. Thus, lesser amount of capital is required to keep the output constant.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig.1.6

If the isoquants are concave to the origin (Fig.1.7), this means that MRTS is increasing. This shows that firm is willing to sacrifice more & more units of capital for an additional unit of labour. This is against the principle of diminishing marginal rate of technical substitution

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig.1.7

3. Two Isoquants never intersect or touch each other - We prove this property by contradiction.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig.1.8

In fig.1.8, two isoquants IQ1&IQ2 intersect each other at point ‘e’. Point e shows that same combination of capital &labour can produce two different level of output. However, it is not possible that one combination of factor can produce two different level of output. This is illogical and absurd. Thus, isoquants never intersect each other.

4. Higher isoquant represents a higher level of output

Fig.1.9

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig.1.9, shows that combination ‘F’ of factors (OL2 and OK2) on isoquant IQ2

represents higher quantity of output than factor combination ‘E’ (OL1 + OK1) on isoquant IQ1.(OL2 + OK2) produce 200 units of output while (OL1 + OK1) produce 100 units of output. Therefore, isoquant IQ2 shows greater level of output.

5. Exceptions to the normal shape of an isoquant

a) Linear Isoquant- When the two factors are perfect substitutes for each other, then isoquants are straight lines with negative slope (Fig.1.10).

Marginal rate of technical substitution between two perfect substitutes remains constant i.e. for every addition in one factor, equal amount of other factor is sacrificed.

Fig.1.10

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

b) L Shaped Isoquants- Isoquants are L-Shaped or right angled in case two factors are perfect complements. Two factors say labour and capital are perfect complements when they are jointly used in a fixed proportion for producing a good. A producer can increase the output by increasing the amount of both factors proportionately. There will be no change in the level of output if we change the quantity of one factor without changing the quantity of other factor.

Fig.1.11

Fig. 1.11 shows that if labour units are increased from L1 to L2 without increasing the units of capital as shown by point R, then level of output will remains the same. The additional labour is redundant. Thus, both factors must be increased in the same proportion say from point P to Q to increase the level of output.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

5. Isoquants and Economic Region of Production

Fig.1.12

In fig.1.12, isoquants are oval shaped. The oval shape of isoquant means that beyond a point, if firm increases the units of a factor, then it will have to increase the units of the other factor to produce the same output level. Over the convex part of the isoquant, if firm increases the units of a factor then it will have to sacrifice some units of the other factor to maintain the same level of output.

As shown in fig.1.12, A1B1 part of the isoquant IQ1has a negative slope. At point A1,

marginal productivity of capital is zero. This means that output cannot expand, if firm increases the quantity of capital keeping the quantity of labour constant. The addition of capital is redundant. The capital ridge line is formed by joining the points A1,A2,A3 andA4.

At these points, marginal product of capital is zero i.e. MPk= 0.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

points B1,B2,B3 andB4 where marginal productivity of labour is zero i.e. MPL = 0. These points are obtained by drawing a tangent to the isoquant parallel to X axis.

Thus, ridge lines are the locus of points of isoquants on which marginal products of factors is zero. The marginal product of capital is zero at upper ridge line OA and marginal product of labour is zero at lower ridge line OB.

The region inside the two ridge lines formed “Economic Region” or “Technically Efficient” region of production.

Outside the ridge lines, production methods are technically inefficient.

6. Iso-Cost Line

An iso-cost line shows various combination of the two factors (Capital and Labour) that a firm can employ with a given amount of money for a given prices of the factors.

Suppose, a firm has Rs.400 to spend on two factors say labour (L) and Capital (K). The price of labour is Rs.20 per unit and that of capital is Rs.40 per unit. This is explained in fig.1.13.

Fig. 1.13

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

If a firm decides to spend the entire amount of money to

buy labour units, it can purchase only 20 units of labour and no units of capital. The firm will be at point Q. On the other hand, if it spend entire amount to buy capital units, it can purchase 10 units of capital and no units of labour. In this case, the firm will be at point P. If we join point P and Q, we get all the possible combinations of labour and capital which can be buy with Rs.400. This line is called an Iso-cost line as total amount of money spent remains constant whichever combination of factors lying on the line is purchased.

The slope of isocost line is equal to the price ratio of the two factors.

Slope of Iso- cost line = PL / PK

Shifts in the Iso-cost line

Iso cost line depends upon total cost or total money outlay and the prices of the factors of production. If the amount of money that firm spends on the factors increases or prices of both the factors decreases in the same proportion or vice-versa, then iso-cost line shift parallel outwards. The reason is that firm can purchase more quantities of both the factors with the increase in amount of money or proportionate decrease in the prices of the two factors.

Fig.1.14

In the present example, suppose firm increases the money outlay from Rs.400 to Rs.800, keeping the prices of the factors constant. Now, it can purchase 40 units of labour and 20

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

cost line. The new iso-cost line RS is shown in fig.1.14. There will be a parallel shift because the slope of new iso-cost line remains constant.

7. Producer’s Equilibrium

The basic objective of rational producer is to maximize his profits and produces a given quantity of output with that combination of factors that is ‘OPTIMUM’. The optimum combination of resources is that

(1) Which minimize the cost of production for producing a given level of output.

(2) Which produce maximum level of output for a given cost of production.

Thus, there are 2 cases of producer’s equilibrium:

1. Minimization of cost subject to an output constraint.

2. Maximization of output subject to a cost constraint.

Case IMinimization of cost subject to an output constraint

If the level of output is given and producer aims to minimize the total cost of production, then he will be faced with

(a) A single isoquant IQ showing output constraint

(b) A series of iso-cost lines. Higher iso-cost line represents higher money outlay. All iso-cost lines are parallel to one another because slope of all iso-cost line is same as the factor prices remains constant.

The producer will be at equilibrium where the given isoquant is tangent to the lowest possible iso-cost line.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Fig.1.15

In fig.1.15, producer equilibrium is at point ‘e where isoquant IQ touched the iso-cost line RS. Therefore, he will employ OL units of labour and OK units of capital to minimize the total cost.

Point above ‘e’ is not desirable as it implies higher total cost. Point below ‘e’ is not feasible though desirable as given output cannot be produced with these combinations.

Thus, point e is the least cost combination point.

At the point of equilibrium ‘e’, slope of isoquant and slope of iso-cost line is equal. Thus, the conditions of producer’s equilibrium are:

1. Slope of isoquant = Slope of iso-cost line MRTSLK= PL / PK

MPL / MPK = PL / PK

MPL / PL = MPK / PK

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Case II Maximization of output subject to a cost constraint

If the cost of production is given and producer aims to maximize his output, then he will be faced with

1. An iso-cost line PQ showing cost constraint.

2. A series of isoquants. Higher isoquant shows higher level of output.

The producer equilibrium will be at the point where the given iso-cost line is tangent to the highest possible isoquant.

Fig.1.16

In Fig.1.16, point ‘e’ is the equilibrium point, where iso-cost line PQ is tangent to the isoquant IQ2. Therefore, he will employ OL units of labour and OK units of capital to maximize his output given the cost of production.

COMMERCE PAPER No. : 2. MANAGERIAL ECONOMICS MODULE No. : 15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Any point on higher isoquant IQ3 are desirable but not

attainable subject to the cost constraint. Any point on lower isoquant give lesser output.

Thus, point ‘e’ is the equilibrium point.

At the point of tangency, slope of isoquant and slope of iso-cost line is equal. Thus, the conditions of producer’s equilibrium are:

1. Slope of isoquant = Slope of iso-cost line MRTSLK = PL / PK

MPL / MPK = PL / PK

MPL / PL = MPK / PK

3. Isoquants must be convex to the origin.

8. Summary

 An isoquant represents all possible combinations of labour& capital that can be employed to produce a given level of output.

 A number of isoquants depicting different levels of output are known as isoquant map.

 Isoquants are downward sloping, convex to the origin and never intersect each other.

 When the two factors are perfect substitutes for each other, then isoquants are straight lines with negative slope.

 Isoquants are L-Shaped or right angled in case two factors are perfect complements.

 Ridge lines are the locus of points of isoquants on which marginal products of factors is zero.

 An iso-cost line shows various combination of the two factors (Capital and Labour) that a firm can employ with a given amount of money for a given prices of the factors.

 The producer is in equilibrium where the iso-cost line is tangent to an isoquant.

 The conditions of producer’s equilibrium are: MRTSLK = PL / PK and Isoquants must be convex to the origin.