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 find the marginal product of labor (MPL) when \( L = 10 \), we follow these steps:

### Step 1: Find the expression for Marginal Product of Labor (MPL)
The production function is given by:
\[
Q = 2.5L^2
\]
The marginal product of labor (MPL) is the derivative of the production function \( Q \) with respect to labor \( L \):
\[
MPL = \frac{dQ}{dL}
\]
Differentiate the production function with respect to \( L \):
\[
MPL = \frac{d}{dL}(2.5L^2) = 2.5 \cdot 2L = 5L
\]

### Step 2: Calculate MPL when \( L = 10 \)
Substitute \( L = 10 \) into the MPL expression:
\[
MPL = 5 \times 10 = 50
\]

### Answer:
The marginal product of labor (MPL) when \( L = 10 \) is **50** units of output.

Do you want any more details or have any questions?

Here are some related questions to consider:
1. How does the marginal product of labor change as \( L \) increases?
2. What is the significance of the production function being quadratic in \( L \)?
3. How would the MPL change if the coefficient in the production function was different?
4. What is the relationship between MPL and the slope of the total product curve?
5. How does the total revenue change when \( L \) increases?

**Tip:** When dealing with marginal products, always check how they vary with different input levels to understand the efficiency of production at various stages.

Learn how to calculate the marginal product of labor (MPL) using the production function Q = 2.5L². Understand the concept of derivatives in economics and production analysis. Step-by-step solution provided.

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