Question

Assuming that the production function is homogeneous of degree one and Euler’s equation holds, if MPL (marginal product of labour) is greater than APL (average product of labour), then

• A. MPL will be negative
• B. MPL will be zero
• C. MPK will be negative
• D. MPL and MPK will both be negative

Hint:

When a production function is homogeneous of degree one, and Euler’s equation holds, the marginal products of both labor and capital can eventually become negative if diminishing returns set in.

Answer 1

The Correct Option is D

Euler's equation applies to homogeneous functions of degree one, and it states that the sum of the marginal products of each factor of production, weighted by the respective inputs, equals the total output. For a production function f(K, L), we have: f(K, L) = MPL · L + MPK · K where MPL is the marginal product of labor and MPK is the marginal product of capital. We are given that MPL > APL, which means that the marginal product of labor is greater than the average product of labor. This indicates that the production function is still in the increasing phase, but it suggests that the function may soon experience diminishing returns. - (A) MPL will be negative: This is incorrect. The marginal product of labor cannot be negative in the increasing phase of production.
- (B) MPL will be zero: This is incorrect. Since MPL > APL, we are still in the phase where labor is positively contributing to output.
- (C) MPK will be negative: This is not necessarily true. MPK is not directly affected by the relationship between MPL and APL.
- (D) MPL and MPK will both be negative: This is the correct answer. If the production function is homogeneous of degree one, and Euler's equation holds, the diminishing returns imply that both the marginal products of labor and capital can eventually become negative when the inputs are overused.
Final Answer: (D) MPL and MPK will both be negative.