lecture - 10 - isoquant approach

7/27/2019 Lecture - 10 - Isoquant Approach

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Cost of Production: The

Isoquant-Isocost approach/least cost


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WHAT IS ISOQUANT?

ISO- EQUAL/ SAME

QUANT- QUANTITY


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The different combinations oflabor and capital used toproduce a certain quantity of

products are illustrated throughIsoquants.

`ISOQUANTS`


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Isoquant curve a curve that representscombinations of factors of production that results in

equal amounts of output.

A point on the isoquant curve is technically

efficient.

An ISOQUANT CURVE shows differentcombinations of labor and and capital to producecertain output.

The isoquant curve is bowed inward because of the

law of diminishing marginal productivity.


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Labor Machines Pairs of shoes

A 1 4 15

B 2 2 15

C 4 1 15


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1 2 3 4 5

5

4

3

2

1

0

workers

m

a

c

h

i

n

e

s 4 10 13 15 16

10 15 18 20 21

13 18 22 24 25

15 21 24 26 27

`ISPOOSED SHU` PRODUCTION

(Shoes per day)


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Isoquant map a set of isoquant curves that showtechnically efficient combinations of inputs that canproduce different levels of output.


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An Isoquant Map

a

b

c

10 sweaters

15 sweaters

Capital(machin

esperday)

Labor (workers per day)

21 sweaters

51

4

2

0


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PROPERTIES OF ISOQUANTS

some of the main properties of isoquants.

Isoquants further from the origin represent greater

output levels

Isoquants slope down to the right

Isoquants do not intersect

Isoquants are usually convex to the origin/that is,bowed towards the origin.


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An Isoquant that Lies Above and to the Right ofAnother Represents a Higher Output Level:


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An Isoquant Slopes Downward fromLeft to Right:


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Isoquants Cannot Cut Each Other:


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Isoquants are Convex to the Origin:


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The marginal rate of technicalsubstitution

Isoquants are typically convex to the origin reflectingthe fact that the two factors are substitutable foreach other at varying rates.

It measures the reduction in one input per unitincrease in the other input that is just sufficient tomaintain a constant level of production. For example,the marginal rate of substitution of labor for capital

gives the amount of capital that can be replaced byone unit of labor while keeping output unchanged.


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Or Marginal rate of substitution for production therate at which one factor must be added to compensate forthe loss of another factor, to keep output constant

It is the slope of the isoquant curve

The absolute value of the slope at a point on the isoquantcurve equals the ratio of the marginal productivity of labor

to the marginal productivity of machines.

onsubstitutiofrateMarginal

MP

MPSlope

machine

labor


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To move from point A to point B in the diagram, the amount

of capital is reduced from Ka to Kb while the amount of laboris increased only from La to Lb. To move from point C topoint D, the amount of capital is reduced from Kc to Kd whilethe amount of labo ris increased from Lc to Ld.


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The opposite is true when going in the otherdirection (from D to C to B to A). In this case we arelooking at the marginal rate of technical substitution

capital for labour (which is the reciprocal of themarginal rate of technical substitution labour forcapital).

It can also be shown that the marginal rate of

substitution labour for capital, is equal to themarginal physical product of labour divided by themarginal physical product of capital.


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The Marginal Rate of TechnicalSubstitution

13 sweaters

a

b

Capital(machinesperday)

Labor (workers per day)51

1

0

3

MRTS =-1/3

MRTS =- 3

2.5

5

2.5


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Factor

Combinations

Units

ofLabor

Units of

Capital

Units of Output of

Commodity X

MRTS of Labor

for Capital

A 1 15 150 -B 2 11 150 4:1C 3 8 150 3:1D 4 6 150 2:1

E 5 5 150 1:1


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Isocost LinesIsocost line a line that representsalternative combinations of factors ofproduction that have the same costs.

An Isocost line shows all the

combinations of capital(machines)and labor(workers) that can be

bought for a given total cost


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Isocost Line

b

d


Labor (workers per day)40

4Total Cost = $100

c

e

a

PL= $25

PK= $25


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The Isocost Equation

The Isocost line can be described by an equation:

TC = PLL + PKK

To calculate the isocost equation, divide the firms

Total Cost by the price of capital and then subtract(PL/PK)L from both sides of the resulting equation.The isocost equation is:

K = TC/PK (PL/PK) L

This equation tells us how the firm can vary itscapital input as it varies its labor input, holding totalcost constant.


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Isocost Map

1

2

3

4

5

1 2 3 4 5

TC=$75 TC=$100 TC=$125

M

a

c

h

I

n

e

s

workers


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Input Prices and the Isocost Line



40

4

Labor $50

Capital $25

2

2

B Ac

Labor $25

Capital $25

Labor $25

Capital $50

TC = $100


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The Least-Cost Technique ofProduction

a

b

Capital(machines

perday)


51

2

0

4

5

c

15 sweaters

Least-Costtechnique


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Exercise

Q.1.Define Iso-cost line with the help of adiagram.


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Exercise

Draw the Iso-cost curve for theTC=$150,

L = $25 & K = $50L = $50 & K = $25

L = $25 & K = $25

L = $50 & K = $50

lecture - 10 - isoquant approach

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