The Isocost Line

Cost of labour and capital should be considered to determine the optimal input combination. The isocost lines provide this information. The isocost line is the locus of alternative combinations of labour and capital that a firm can purchase with a given monetary cost outlay. Since the input prices are assumed constant, they are linear and parallel to each other. Given the per unit prices of capital (r) and labour (w), the total cost (C) on capital (K) and labour (L) used is

C = rK + wL

By solving for K as a function of L we get,

K=(C/r)-(W/r)L

This is an equation of a straight line where C/r is the vertical intercept while­- w/r is the slope. The ratio - w / r is the rate that labour can be exchanged for capital in the market. For example if w = 2 and r = 3, one unit of labour can be traded for 1.5 units of capital. Using the data from the preceding example (w = 2, r = 3 and C = 40) the isocost line becomes

40 = 3K + 2L

Solving for K yields

K = 13.33 - 2/3L 

This information is shown as the Rs 40 isocost line in Fig. 5.7. Note the intercept points on the capital and labour axis. If the firm has Rs 40, then it has three options:

to spend entire finance on labour from which 20 units can be obtained as shown by point B in the figure,

to spend entire finance on capital from which 13.3 units can be obtained as shown by point A in the figure, and

to spend on both labour and capital. In this case the firm has to choose any point on the line AB.

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