give the production Q=2.5L² where Q and L are quantity of labour and the given total revenue function R= 120Q=0.2Q² find marginal product of labour(L) when L =10

To solve this problem, we need to find the Marginal Product of Labor (MPL) when \( L = 10 \). The production function is given as \( Q = 2.5L^2 \) and the revenue function is given as \( R = 120Q - 0.2Q^2 \).

### Step 1: Calculate the Marginal Product of Labor (MPL)

The Marginal Product of Labor (MPL) is the derivative of the production function \( Q(L) \) with respect to \( L \):

\[
\text{MPL} = \frac{dQ}{dL}
\]

Given \( Q = 2.5L^2 \), differentiate \( Q \) with respect to \( L \):

\[
\text{MPL} = \frac{d}{dL}(2.5L^2) = 2.5 \cdot 2L = 5L
\]

So, \( \text{MPL} = 5L \).

### Step 2: Calculate MPL when \( L = 10 \)

Substitute \( L = 10 \) into the MPL equation:

\[
\text{MPL} = 5 \times 10 = 50
\]

Thus, the Marginal Product of Labor when \( L = 10 \) is 50.

### Conclusion

The Marginal Product of Labor (MPL) when \( L = 10 \) is 50.

Would you like further details on any of the steps or additional insights?

Here are 5 related questions that you might find useful:
1. How does the Marginal Product of Labor change as \( L \) increases?
2. What is the significance of the Marginal Product of Labor in production theory?
3. How does the revenue function impact the total revenue when labor changes?
4. What happens to the production function \( Q(L) \) when you increase labor beyond 10?
5. How can you calculate the total revenue at \( L = 10 \) using the given revenue function?

**Tip:** When dealing with production functions, always check how changes in input (like labor) directly affect the output to understand the efficiency of production.

Learn how to calculate the Marginal Product of Labor (MPL) using the production function Q = 2.5L² and revenue function R = 120Q - 0.2Q². Detailed step-by-step solution provided with calculations for MPL when L = 10. Suitable for advanced learners and professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation