A monopsonist has market power in the hiring of its labor, so faces an upward-sloping supply of labor. In symbols, we could write w = w(L) where w is the wage, L is the number of workers hired, and the condition w’(L) > 0 reflects the firm’s monopsony power.

The firm’s labor cost is the wage times the number of workers hired: C(L) = w(L) x L. To find the firm’s marginal resource cost, MRC, we differentiate C(L) with respect to L. Using the product rule, MRC = w(L) + Lw’(L). Since w’(L) > 0, this proves the proposition stated in the text: MRC > w.

Note that the MRC is the sum of two terms, the wage rate and Lw’(L). What is the second term? w’(L) is the increase in the wage rate required to obtain one more worker and L is the number of workers hired. Consequently, we can think of Lw’(L) as the total cost of increasing each current worker’s wage to the level required to bring in the marginal worker.

Of course, this modification in the firm’s market power requires that we revisit the earlier rules for the least-cost and profit-maximizing combinations of labor and capital from the previous chapter. Suppose the firm has monopsony power in its purchase of capital as well, so that r = r(K) and r’(K) > 0. Now the firm’s profit is given by p (L, K) = Pg(L, K) - (w(L)L + r(K)K). P is the market price of the firm’s output, and g(L, K) is the firm’s production relationship. Differentiating with respect to L and K, we obtain the first-order conditions:

= P - (w(L) + Lw’(L)) = PxMP_L - MRC_L = MRP_L - MRC_L = 0

= P - (r(K) + Kr’(K)) = PxMP_K - MRC_K = MRP_K - MRC_K = 0