Answer: The firm should minimize cost and always seek a mix of inputs, L and K,
such that the marginal products per dollar spent on each should be equal.
Explanation:
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.
If a firm uses two inputs, labor and capital, that can be bought
at fixed prices P(L) and P(K). We can find (for any amounts of the inputs) the marginal
product of, say, L as the increase in output achieved from employing an extra unit of
labor, holding capital constant. The marginal product per dollar spent on labor is
therefore MP(L)/P(L). This is the increase in output the firm can achieve from spending
another dollar on labor. Similar definitions hold for capital.
