Question

What should a firm do if the marginal product obtained from the last dollar spent on capital is smaller than the marginal product derived from the last dollar spent on labor and why?

Answer 1

Considering a typical firm that wants to minimize the total cost of producing a particular level of output. The firm uses two inputs, labor and capital, that can be bought at fixed prices P(L) and P(K). We can find the marginal product of input as the increase in output achieved from employing an extra unit of that input, holding the other one constant. The marginal product per dollar spent on labor is therefore MP(L)/P(L) and for capital it is MP(K)/P(K) . A firm wanting to minimize cost should always seek a mix of inputs, L and K, such the the marginal products per dollar spent on each should be equal.

That is, we want MP(L)/P(L) = MP(K)/P(K).

Suppose not. Let the firm is producing the desired output with MP(L)/P(L) > MP(K)/P(K). Spending one dollar less on capital will reduce output by capital's marginal product per dollar. But because the marginal product per dollar for labor is greater than that for capital, less than a dollar's worth of labor must be bought to achieve the desired output. Costs are reduced by buying more of the input whose marginal product is higher.