15. PRODUCER'S EQUILIBRIUM WITH ISOQUANTS Subject ...

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PAPER No. : 2. MANAGERIAL ECONOMICS

MODULE No. : 15. PRODUCER’S EQUILIBRIUM

WITH ISOQUANTS

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Paper No and

Title

2. MANAGERIAL ECONOMICS

Module No and

Title

15. PRODUCER’S EQUILIBRIUM WITH ISOQUANTS

Module Tag COM_P2_M15

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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Fig.1.7

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

by contradiction.

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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

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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

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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.

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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.

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Similarly, the labour ridge line is formed by joining the

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

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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

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units of capital or any combination lying on the new iso-

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.

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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

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2. Isoquants must be convex to the origin.

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.

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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.

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