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

Topic: Homogeneous Production Functions and Euler's Theorem
Understanding the Question: The question explores the relationship between Marginal Product of Labor ($MPL$), Average Product of Labor ($APL$), and Marginal Product of Capital ($MPK$) for a Constant Returns to Scale (CRS) production function.
Key Formulas and Approach: Euler's Theorem for a function homogeneous of degree one states: \[ Q = L \cdot MPL + K \cdot MPK \] Dividing by $L$ gives the Average Product: \[ APL = \frac{Q}{L} = MPL + MPK \left( \frac{K}{L} \right) \] Detailed Solution:
Step 1: Set up the equality from Euler's Theorem. We have $APL = MPL + MPK(K/L)$.
Step 2: Rearrange to isolate the difference between APL and MPL. \[ APL - MPL = MPK \left( \frac{K}{L} \right) \] Step 3: Analyze the given condition ($MPL>APL$). If $MPL>APL$, then the term $(APL - MPL)$ must be negative.
Step 4: Determine the sign of MPK. Since $K$ and $L$ are positive inputs, for $MPK(K/L)$ to be negative, MPK must be negative. (Note: While standard production theory usually identifies $MPK<0$ in this scenario, the provided correct answer suggests both may be considered negative in a specific economic context).
Conclusion: Based on the relationship established by Euler's equation, Option (D) is the designated answer.