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In: Economics

Let the production function be Q=K^(1/3)L^(1/5). Is the Marginal Product of Labor increasing decreasing or constant?...

Let the production function be Q=K^(1/3)L^(1/5). Is the Marginal Product of Labor increasing decreasing or constant? Show your work.

Expert Solution

Answer: The Marginal Product of Labor is decreasing.

Given:

Production function:

The marginal product of labor is the additional output produced by additional labor.

It is the derivative of the total output with respect to the quantity of labor.

We can see that as L (i.e. labor units) is inversely related to the marginal product of labor. It means that as we increase the labor units, the marginal product decreases. That is, with an increase in the units of labor employed, the marginal product of labor decreases. Each additional labor adds less than the last one. Therefore The Marginal Product of Labor is decreasing.

For example:

Let's fix K = 27, and now the marginal product of labor for the 1st labor is:

now, as we employ the second labor:

K = 27 and L = 2

Therefore the Marginal product of labor decreases from 0.6 to 0.34 when we increase the labor employed from 1 to 2. It means that the first labor added more to the production than the second labor. The additional output produces decreases as more and more labor are employed.

Rahul Sunny answered 1 year ago

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