Cost Minimisation Rule

rom this cost combination, we can also derive the principle that any rational entrepreneur, who seeks to maximize his profits by keeping his cost at the minimum level, should satisfy those conditions in which the ratio between the marginal physical product of factors and their prices must be equal. If, the ration of marginal physical product of L (MP_L) and its price PL is more than the ratio of marginal physical product of K (MP_K) and PK, i.e. MP_L /P_L > MP_K /P_K then he must substitute more of labour for capital. This substitution of labour for capital is necessary because each rupee spent on labour yields larger output relative to each rupee spent on capital. Thus by substituting labour for capital cost of output can be further reduced. This process will continue till the cost is minimized, which will happen when

MP_L /P_L = MP_K /P_K

This rule can also be deduced from the equilibrium point of the least cost combination. We have seen that to reach the point of equilibrium E from R, the entrepreneur has substituted labour for capital, but he does not want any further substitution because he has achieved the least cost combination at E where

MRTS_LK = P_L /P_K = MP_L / MP_K.

Now, the rate of substitution between L and K is itself governed by their marginal physical product. A unit of L is substituted for some units of K subject to the condition (as implicit in the term ‘marginal rate of technical substitution’) that the total product remains the same. Thus, the gain in physical product of L is just offset by the loss in physical product of K at the margin.

Thus, in equilibrium position

MRTS_LK = MP_L / MP_K
And also,MRTS_LK = P_L /P_K
: .  MP_L / MP_K = P_L /P_K Or, MP_L / P_L = MP_K / P_K

Hence, the least cost combination is one where the rations of marginal physical product and prices of factor L and K are equal.