Consider a production function is given by Q= 10*L^0.5, where Q represents the output and L represents labor input. Calculate the limit as L approaches infinity of the Marginal Production of Labor Function 

The marginal product of labor (MPL) is obtained by taking the derivative of the production function \( Q = 10L^{0.5} \) with respect to \( L \). 

1. **Find the derivative of the production function:**

   \[
   Q = 10L^{0.5}
   \]

   The derivative of \( Q \) with respect to \( L \) is given by:

   \[
   \text{MPL} = \frac{dQ}{dL} = 10 \cdot \frac{1}{2}L^{-0.5} = 5L^{-0.5}
   \]

   This can also be written as:

   \[
   \text{MPL} = \frac{5}{\sqrt{L}}
   \]

2. **Calculate the limit as \( L \) approaches infinity:**

   \[
   \lim_{L \to \infty} \frac{5}{\sqrt{L}} = 0
   \]

As \( L \) approaches infinity, the marginal product of labor approaches zero. This implies that, at very high levels of labor input, each additional unit of labor contributes less and less to the output.

Would you like a detailed explanation or have any questions? 

Here are some related questions:
1. What is the interpretation of a diminishing marginal product in economics?
2. How does the marginal product relate to the law of diminishing returns?
3. What happens to the average product of labor as L increases indefinitely?
4. Can a production function have increasing marginal returns? If so, under what conditions?
5. How would changing the exponent in the production function affect the marginal product?

**Tip:** In economic models, diminishing marginal returns often reflect real-world constraints, such as limited machinery or resources that restrict additional productivity.

Consider a production function is given by Q= 10*L^0.5, where Q represents the output and L represents labor input. Calculate the limit as L approaches infinity of the Marginal Production of Labor Function

Explore the concept of marginal productivity with the production function Q = 10L^0.5. Learn how to calculate the marginal product of labor and find its limit as labor approaches infinity, illustrating the law of diminishing returns. Ideal for advanced high school or undergraduate economics and calculus students.

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