According to the chief engineer at the Zodiac Company, Q = AL? K? , where Q is t

Question

According to the chief engineer at the Zodiac Company, Q = AL? K? , 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 ? = 0.8 and ? = 0.3. The firm's owner claims the plant has increasing returns to scale.
a. Is the owner correct? Yes
b. If ? were 0.2 rather than 0.3, would she be correct? No
c. Does output per unit of labor depend only on ? and ?? Why or why not? no because it doesnot output per unit of labor depend only on a and

Explanation / Answer

a)Yes. Note that in the equation for Q, and represent output elasticities. Specifically, = 0.8 implies that a 1 percent increase in labor will increase output by 0.8 percent, whereas = 0.3 implies that a 1 percent increase in capital will increase output by 0.3 percent. Therefore, increasing both L and K by 1 percent will cause output to go up by more than 1 percent.

b)No. In this case, there would be constant, not increasing returns to scale. If = 0.8 and = 0.2, this means that increasing both L and K by 1 percent will cause output to go up by 1 percent.

c)Output per unit of labor also depends on A, K, and L. The average product of labor is a function of L because the marginal product of L is not constant .The average product depends on K because as

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