A firm hires labor, capital, and land to produce grapefruits. Currently the marginal product of the last unit of labor input is 40, the marginal product of the last unit of capital input is 60, and the marginal product of the last unit of land input is 200. The market wage is $20 and the market price for capital is $30. If the firm is using the optimal combination of inputs, then the price of land is
A) $4.
B) $40.
C) $100.
D) indeterminate from the given information.

Question

Quizplus · Accepted Answer

For a firm to be using an optimal combination of inputs, the ratio of the marginal product of each input to its price must be equal across all inputs. This condition is derived from the principle of cost minimization or profit maximization, where a firm adjusts its input combination such that the last dollar spent on each input yields the same marginal product. Mathematically, this is represented as MP_L / P_L = MP_K / P_K = MP_T / P_T, where MP represents marginal product and P represents price for Labor (L), Capital (K), and Land (T).Given:- MP_L = 40, P_L = $20- MP_K = 60, P_K = $30- MP_T = 200, P_T = ?Using the formula, we find the price of land (P_T) that equalizes the ratio across all inputs. For labor, the ratio is 40/20 = 2. For capital, the ratio is 60/30 = 2. To find the price of land that makes its ratio equal to 2, we set 200/P_T = 2, solving for P_T gives us P_T = 200/2 = $100.

A Firm Hires Labor, Capital, and Land to Produce Grapefruits