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Production Function and Marginal Product of Labour

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2. Assume the Production Function for Hamburgers is Q = 4L^.50K.^33. where Q is the quantity of hamburgers, L is the number of workers employed and K is number of grills.

a. What is the quantity of hamburgers produced when the company employs 64 workers & 36 machines?

b. Continue to assume the input mix given above—what is the marginal product of labor? Note that K is fixed when we calculate the marginal product of Labor.

c. In one paragraph, interpret these numbers.

d. Does Hamburger production function display increasing, decreasing, or constant returns to scale? Would your answer change if the production function were to be Q = L^.66K^.50? If yes, what would it be (increasing, decreasing, or constant returns to scale)?

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Solution Preview

a) Substituting 64 and 36 for L and K in the Production Function, the Q of hamburgers produced is 104.41

b)
With K held constant, MPL is the derivative of the Production Function with respect ...

Solution Summary

This solution shows how to calculate quantity of production, formula of marginal product of labor and specific input mix, and how to determine if the production function is increasing, decreasing or constant.

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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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