Given the table below showing the marginal product of labor (MPL), marginal product of capital (MPK), wage rate (w), and rental rate of capital (r) for a firm producing computer mainframes, which condition must be satisfied for the firm to be minimizing its costs?MPL = 20 units, MPK = 40 units, w = \$10, r = \$20Choose the correct condition for cost minimization.

• A. MPL × w = MPK × r
• B. MPL / MPK = w / r
• C. MPL = MPK
• D. MPL / w = MPK / r

Answer: (D)

Verified step by step guidance

1. Understand that cost minimization for a firm using labor and capital occurs when the firm allocates resources such that the marginal product per dollar spent is equalized across inputs.
2. Recall the condition for cost minimization: the ratio of the marginal product of labor to the wage rate should equal the ratio of the marginal product of capital to the rental rate of capital, expressed as \(\frac{MPL}{w} = \frac{MPK}{r}\).
3. Interpret this condition as meaning the firm gets the same additional output per dollar spent on labor as it does per dollar spent on capital, ensuring no reallocation of spending can reduce costs further.
4. Check the given values by setting up the ratios: calculate \(\frac{MPL}{w}\) and \(\frac{MPK}{r}\) separately using the provided numbers (MPL = 20, w = 10, MPK = 40, r = 20).
5. Confirm that the firm is minimizing costs if and only if these two ratios are equal, which aligns with the condition \(\frac{MPL}{w} = \frac{MPK}{r}\).