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Analyzing Returns to Scale of the Production Function

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Consider the production function Q=100L^.5K^.4. Suppose L=1 and K=1 so that Q=100

a. If L is increased by 1 percent, that is to L=1.01 with capital unchanged, what is the resulting percentage increase in output?

b. Describe the nature of returns to scale for this production function.

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a. If L is increased by 1 percent, that is to L=1.01 with capital unchanged, what is the resulting percentage increase in output?

Output level for L=1 and K=1 is
Q=100*1^0.5*1^0.4=100 units

Output level for L=1.01 and K=1 ...

Solution Summary

Solution discusses the nature of returns to scale for the given production functions along with step-by-step calculations.

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Production Theory

According to the chief engineer at the Zodiac Company, Q=AL a K b, where Q is the output rate, L is the rate of labor input, and K is the rate of capital input. Statistical analysis indicates that a=0.8 and b=0.3. The firm's owner claims the plant has increasing returns to scale.
a. Is the owner correct?
b. If B were 0.2 rather than 0.3, would she be correct?
c. Does output per unit of labor depend only on a and b? Why or why not?

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