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 ______.

To maximize profits, the firm should hire labor and capital to the point where the marginal product per dollar spent is equal for both inputs. In other words, we want the marginal product of labor divided by the wage to equal the marginal product of capital divided by the cost of capital.

Let's apply this rule using the given information:

Marginal Product of Labor (MPL) = 16 Wage Rate = $4 Marginal Product of Capital (MPK) = 6 Cost of Capital = $2

Now, calculate the marginal product per dollar spent for both labor and capital:

MPL / Wage = 16 / 4 = 4 MPK / Cost of Capital = 6 / 2 = 3

Here, the marginal product per dollar spent on labor is higher than the marginal product per dollar spent on capital (4 > 3). Thus, to maximize profits, the firm should hire more labor until the marginal product per dollar spent on labor equals the marginal product per dollar spent on capital.