What is Isocost line Discuss the shifting of isocost line?

Answer 1

Isocost Lines

Recall that a universally accepted objective of any firm is to maximise profit.

If the firm maximises profit, it will necessarily minimise cost for producing a

given level of output or maximise output for a given level of cost. Suppose

there are 2 inputs: capital (K) and labour (L) that are variable in the relevant

time period. What combination of (K,L) should the firm choose in order to

maximise output for a given level of cost?

If there are 2 inputs, K,L, then given the price of capital (P

k

) and the price of

labour (P

L

), it is possible to determine the alternative combinations of (K,L) that

can be purchased for a given level of expenditure. Suppose C is total

expenditure, then

C= P

L

* L + P

k

* K

This linear function can be plotted on a graph.

ISOCOST

K

C/P

k

A

B

O

C/P L

L

•

N

•

P

Figure 7.7: Isocost line

If only capital is purchased, then the maximum amount that can be bought is

C/P

k

shown by point A in figure 7.7. If only labour is purchased, then the

maximum amount of labour that can be purchased is C/P

L

shown by point B in

the figure. The 2 points A and B can be joined by a straight line. This straight

line is called the isocost line or equal cost line. It shows the alternative

combinations of (K,L) that can be purchased for the given expenditure level C.

Any point to the right and above the isocost is not attainable as it involves a

level of expenditure greater than C and any point to the left and below the

isocost such as P is attainable, although it implies the firm is spending less than

C. You should verify that the slope of the isocost is

1

-

k

L

k L

P

P

P

C

*

P

C

∆ L

∆ K

EXAMPLE :

Consider the following data:

P

L

= 10, P

k

= 20 Total Expenditure = 200.

Let us first plot the various combinations of K and L that are possible. We

1 The nagative sign is due to the fact that the slope of the isocost is negative.15

consider only the case when the firm spends the entire budget of 200. The

alternative combinations are shown in the figure (7.8).

P r o d u c t i o n F u n c t i o n

K

A

10

9

8

7

6

5

4

3

2

1

O

B

L

C

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

Figure 7.8: Shifting of Isocost

The slope of this isocost is -½. What will happen if labour becomes more

expensive say P

L

increases to 20? Obviously with the same budget the firm

can now purchase lesser units of labour. The isocost still meets the Y-axis at

point A (because the price of capital is unchanged), but shifts inwards in the

direction of the arrow to meet the X-axis at point C. The slope therefore

changes to -1. You should work out the effect on the isocost curve on the

following:

(i) decrease in the price of labour

(ii) increase in the price of capital

(iii) decrease in the price of capital

(iv) increase in the firms budget with no change in the price of labour and capital