Assume that a perfectly competitive firm faces a fixed wage rate of $4 and a constant per-unit cost of capital of $2. If the marginal product of labor and capital are 16 and 6, respectively, then to maximize profits the firm should

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To maximize profits, a firm should use more of the input that has a higher marginal product per dollar spent (i.e., higher marginal productivity) and less of the input that has a lower marginal product per dollar spent.

In this case, the marginal product of capital per dollar spent ($3) is lower than the marginal product of labor per dollar spent ($4). Therefore, the firm should use relatively less capital and relatively more labor to maximize profits. This means the firm should choose a labor-capital ratio where the marginal productivity of labor per dollar spent is equal to the marginal productivity of capital per dollar spent. In this case, that ratio would be 2.67 (16/4 = 6/2), which means the firm should use 2.67 units of labor for every unit of capital.

Assume That a Perfectly Competitive Firm Faces a Fixed Wage