# Determining the production parameters

Throughout this problem, assume labor (L), capital (K), and quantity produced (Q) can be infinitely divided - that is, it is fine to hire 3.3 workers, rent 4.7 machines, and/or produce 134.2 units.

Answer the following questions, assuming the production function for The Corp. is Q=L^1/3K^1/2, where Q is the quantity of tires produced, L is the number of workers employed, and K is the number of machines rented.

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

b. What are the average product of labor (L) and the average product of machines (K) when the input mix is the one given above? Clearly and concisely, please explain how you would interpret these numbers.

c. Continue to assume the input mix given above: What is the marginal product of labor (L), if the number of workers is increased by 1 unit? What is the marginal product of capital (K), if the number of machines is increased by 1 unit, instead? Clearly and concisely, please explain how you would interpret these numbers.

d. Does The Corp's production function display increasing, decreasing, or constant returns to scale? Explain.

e. Does The Corp's production function display increasing, decreasing, or constant returns to labor? Explain.

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#### Solution Preview

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

Q=L^1/3K^1/2

Put L=64

K=36

Q=(64)^(1/3)*(36)^(1/2)=24

b. What are the average product of labor (L) and the average product of machines (K) when the input mix is the one given above? Clearly and concisely, please explain how you would interpret these numbers.

Q=L^1/3K^1/2

Average Product of labor=APL=Q/L=(L^1/3K^1/2)/L=L^(-2/3)K^(1/2)

Put L=64, K=36 we get

APL=64^(-2/3)*36^(1/2)= 0.375

It means that 0.375 tires are produced per unit of labor at current level of inputs.

Average Product of ...

#### Solution Summary

Solution describes the steps to calculate average product and marginal product in the given case. It also determines whether given production function exhibits increasing/decreasing/constant returns to scale.