Question

Assuming that the production function is homogeneous of degree one and Euler's equation holds, if \( MP_L \) (marginal product of labour) is greater than \( AP_L \) (average product of labour), then:

• A. \( MP_L \) will be negative.
• B. \( MP_L \) will be zero.
• C. \( MP_K \) will be negative.
• D. \( MP_L \) and \( MP_K \) will both be negative.

Hint:

When marginal product exceeds average product, it indicates diminishing returns, and eventually both marginal products may turn negative.

Answer 1

The Correct Option is D

Step 1: Understanding the production function.
A production function that is homogeneous of degree one satisfies Euler's equation: \[ F(K, L) = K \cdot \frac{\partial F}{\partial K} + L \cdot \frac{\partial F}{\partial L} \] where \( F(K, L) \) is the output, \( K \) is capital, and \( L \) is labor. If \( MP_L > AP_L \), this suggests diminishing returns to labor.

Step 2: Analysis of options.
- (A) \( MP_L \) will be negative: This is incorrect. Marginal product of labor cannot be negative if the production function is still in the positive range.
- (B) \( MP_L \) will be zero: This is incorrect. \( MP_L \) is greater than \( AP_L \), so it cannot be zero.
- (C) \( MP_K \) will be negative: This is incorrect. We don't have enough information about capital to assert that \( MP_K \) is negative.
- (D) \( MP_L \) and \( MP_K \) will both be negative: This is correct because when marginal products are decreasing, both labor and capital may experience negative marginal returns at certain levels of output.

Step 3: Conclusion.
The correct answer is (D). When marginal product of labor exceeds the average product, both \( MP_L \) and \( MP_K \) may be negative.