# Production function: Average and Marginal Product of Labor

A firm can manufacture a product according to the production function

Q = F(K, L) = K^(3/4) L^(1/4)

a) Calculate the average product of labor, APL, when the level of capital is fixed at 16 units and the firm uses 16 units of labor. How does the average product of labor change when the firm uses 81 units of labor?

b) Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 16 units. Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor.

c) Suppose capital is fixed at 16 units. If the firm can sell its output at a price of $100 per unit and can hire labor at $25 per unit, how many units of labor should the firm hire in order to maximize profits?

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#### Solution Preview

A firm can manufacture a product according to the production function

Q = F(K, L) = K^(3/4) L^(1/4)

1 a)

Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor.

Find the value of Q by using the production function

where the variables are defined as follows

Q = the level of output produced in the production process

K = quantity of capital

L = quantity of labor

Let the level of capital be K = 81

Let the number of units of labor be L = 16.

Then we ...

#### Solution Summary

The average product of labor and marginal product of labor are found under specific circumstances. Step-by-step computations are provided for each problem. Explanations are given for every formula used.