Let us suppose that an entrepreneur uses two variable inputs, labour (L) and capital (K), to produce his output. If there is perfect competition in the input markets, the prices of the inputs are given and constant for the firm. Let us suppose that the prices of L and K are given to be w and r, respectively.
Here the condition for the least cost combination of the inputs is:
The left hand side of (16.3) is the marginal cost (MC) of output when an additional unit of labour is used and the right hand side of (16.3) is the MC when an additional unit of capital is used. Condition (16.3) implies that these two MCs should be equal if the firm wants to produce a particular quantity of output at the least possible cost and, by solving (16.3), we would have the least cost combination of the inputs.
We also know that if condition (16.3) is not satisfied, if we have, for example, (w/MPL) > (r/MPK), then the MC of output produced through the use of more of L would be greater than that through the use of more of K.
In this case, the firm cannot be in cost-minimising equilibrium. Here, if the firm uses less of labour and more of capital, then the total cost of producing the given quantity of output would be smaller. So here the firm would be substituting K for L.
Now, as the firm uses more of K and less of L, MPL would be rising and MPK would be falling owing to the law of diminishing marginal product (LDMP), and consequently, w/MPL would be falling and r/MPK would be rising, w and r being given and constant. The firm would go on making this substitution till at some (L, K) combination, w/MPL would become equal to r/MPK and condition (16.3) would be satisfied.
However, if the input markets are monopsonistic, not competitive, then, as the firm uses more (or less) of any input, its price would rise (or fall), i.e., here w and r would no longer be obtained as given and constant.
Therefore, in this case, the marginal expense (ME) for an input would not be the same as its price. Since it is the marginal expense (ME) for an input, not its price, that is more relevant for the cost minimisation of a certain quantity of output, the condition for the least cost combination of the inputs now would be
Here (16.5) implies that MC of output through the use of L is greater than that through the use of K. To minimise the cost of any given quantity of output, or, to obtain the least cost combination of inputs to produce the output, the firm would, therefore, be substituting capital for labour.
As the firm goes on doing this, MPL would be rising and MPK would be falling owing to LDMP, and, on the other hand, MEL would be falling and MEK would be rising owing to the existence of monopsony in the input markets. Consequently, the LHS of (16.5) would be diminishing and the RHS would be increasing, and at some (L, K) combination the two sides would become equal and condition (16.4) would be satisfied.
The (L, K) combination thus obtained would be the required least cost combination of the inputs. It may be noted here that when equality (16.4) prevails, no further change in input composition will be able to reduce the cost of the given output.
Again, equality (16.4) may be rewritten in the form:
From eqns. (16.4) and (16.6), we obtain:
(i) That a monopsonist who uses several variable inputs will adjust the quantities of the inputs until the ratio of the marginal product to marginal expense is the same for all the variable inputs used, and
(ii) that the least cost combination of inputs is obtained when the marginal rate of technical substitution between any two inputs equals the ratio of the marginal expenses for the inputs.
We may also note here that decision-making rule (16.2) is a special case of rule (16.6). The former is obtained from the latter because, under perfect competition, the price of each input is equal to its marginal expense.