Question

Suppose that the government subsidizes the cost of workers by paying for 25% of the wage...

Suppose that the government subsidizes the cost of workers by paying for 25% of the wage (the rate offered by the U.S. government in the late 1970s under the New Jobs Tax Credit program). What effect will this subsidy have on the firm’s choice of labor and capital to produce a given level of output? What happens if both capital and labor are subsidized at 25%?

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Answer #1

A firm has the marginal rate of technical substitution MRTS= w/r, or MPL/MPK=w/r where MPL = marginal product of labor, MPK is marginal product of capital, w= wage rate and r = cost per unit of capital.

Before the implementation of the subsidy by the government a firm hired L0 workers and employed K0 capital. Then,MP0L/MP0K=w/r.

If the government subsidizes the cost of workers by paying 25% of the wage then the cost of wage to the firm paying a wage w will be 0.75w. Then MP1L/MP1K=0.75*w/r, such that MP1L/MP1K< MP0L/MP0K. Relatively cheaper labor will be substituted for capital, so that L1>L0 and MP1L<MP0L and K1<K0, which will make MP1K>MP0K.The firm will decrease capital and increase labor after the subsidy is imposed.

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