Suppose that a paving company produces paved parking spaces (q) using a fixed quantity of land (T) and variable quantities of cement (C) and labor (L). The firm is currently paving 1,000 parking spaces. The firm's cost of cement is $4 comma 200.004,200.00 per acre covered (c) and its cost of labor is $12.0012.00 /hour (w). For the quantities of C and L that the firm has chosen, MP Subscript Upper C Baseline equals 70MPC=70 and MP Subscript Upper L Baseline equals 4MPL=4

Cost minimization occurs when Marginal Product of Cement / Price of Cement = Marginal Product of Labor / Price of Labor.

Costs are minimized when the marginal product per dollar spent on all inputs is the same.

a.) Using the equation above, 50 / $4000 = 4 / $12

0.0125 =.333333 which is NOT equal. Therefore, the firm is not minimizing its cost of producing parking spaces. This is because the marginal products per dollar spent on inputs is not the same.

b.) Since the firm is not cost-minimizing, the firm must either choose quantities of C and L that make the marginal products per dollar equal. This can be done several ways, but for a concrete example, the firm can choose a quantity of C that will increase the MPC to $1,333.33. Then MPC / Price of C = 1,333.33 / $4,000 = 0.3333333 which would be equal to MPL / Price of L.

You can also decrease the MPL to meet 0.15. Then MPL / Price of L = 0.15 / $12 = 0.0125 which would be equal to MPC / Price of C.