Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![**Example Multiple Choice Question:**
**24. If Q = K^(1/3)L^(2) the MPL is**
a. constant
b. diminishing
c. increasing
d. not enough information to determine
**Explanation:**
This question presents a production function Q = K^(1/3)L^(2). The task is to determine the marginal product of labor (MPL) given this function.
To solve for MPL, one needs to understand the marginal productivity theory which involves taking the partial derivative of the production function with respect to labor (L).
In detail:
\[ Q = K^{\frac{1}{3}} \cdot L^{2} \]
\[ \text{MP}_L = \frac{\partial Q}{\partial L} = K^{\frac{1}{3}} \cdot \frac{\partial (L^2)}{\partial L} = K^{\frac{1}{3}} \cdot 2L \]
Thus, the MPL is \( 2K^{\frac{1}{3}} \cdot L \). The MPL is not constant because it is directly proportional to L, so as L increases, MPL increases. Therefore, the correct answer is:
c. increasing](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6eda1510-d1df-409a-bd42-272e220e24bb%2F3d954575-5264-4565-8b16-d2ad56771fa5%2F8mjnmos_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Multiple Choice Question:**
**24. If Q = K^(1/3)L^(2) the MPL is**
a. constant
b. diminishing
c. increasing
d. not enough information to determine
**Explanation:**
This question presents a production function Q = K^(1/3)L^(2). The task is to determine the marginal product of labor (MPL) given this function.
To solve for MPL, one needs to understand the marginal productivity theory which involves taking the partial derivative of the production function with respect to labor (L).
In detail:
\[ Q = K^{\frac{1}{3}} \cdot L^{2} \]
\[ \text{MP}_L = \frac{\partial Q}{\partial L} = K^{\frac{1}{3}} \cdot \frac{\partial (L^2)}{\partial L} = K^{\frac{1}{3}} \cdot 2L \]
Thus, the MPL is \( 2K^{\frac{1}{3}} \cdot L \). The MPL is not constant because it is directly proportional to L, so as L increases, MPL increases. Therefore, the correct answer is:
c. increasing
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