Isoquants

Isoquants depict physical relationship of all combinations of labour and capital input rates that will produce the same level of output. Generally they are smooth and continuous curves, convex to the origin sloping downwards to the right.

The data in Table 5.4 reproduced from Table 5.1 illustrates the two input case. To produce 52 units of cut-put the firm can employ several combinations of capital and labour as shown the table.

By joining combinations of labour and capital an isoquant is graphed as shown in fig. 5.5. Similarly, we can plot isoquants for 64 units (7K<, 2L) (6K, 3L) (3K, 6L) and 73 units (6K, 4L) (4K, 6L) (3K, 8L) of output. A higher isoquant depicts a larger level of output. Note that to produce a greater amount of output, more labour or more capital or both are required. 

The slope of the isoquant depicts the Marginal rate of technical substitution (MRTS) i.e., the rate at which one input can be substituted for the other to maintain the same level of output. In other words, the MRTS is the rate at 'which a marginal unit of labour can substitute a marginal unit of capital. The slope of the isoquant indicates this rate (MRTS = DK/ D/L). Consider combinations A, B and C for 52 units of output. The movement from A to B indicates that the firm gives up 2 units of capital by adding 1 unit of labour. Thus the slope between points A and B is -2K/1L. Between points Band C the slope is -1K/1L and so on.

We also note that the MRTS of labour for capital diminishes as we move from A to E. This is referred as the law of diminishing MRTS. The smooth shape of the isoquant, convex to the origin, implies that the inputs are perfectly substitutable and the rate of substitution declines as one input is substituted for another. The MRTS of labour for capital is also equal to MP_L / MP_K. That is for a movement down a given isoquant, the gain in output resulting from the use of more labour must be equal to the loss in the output resulting from the use of less capital." Therefore the slope of the isoquant is equal to the negative of the ratio of marginal product of the two inputs.

MRTS = ΔK/ΔL = -MP_L/MP_K

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