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10 Jun 2018

Give a function Y = AK^0.4 L^0.6

A. if K increase by 10% what is the percentage change in Y, MPK, and MPL?

B. if L increase by 10% what is the percentage change in Y, MPK, and MPL?

c. Is there evidence of diminishing marginal productivity?

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Trinidad Tremblay
Trinidad TremblayLv2
13 Jun 2018

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Related questions

For a production function Q=K0.5L0.5 where K is capital. The marginal products are MPk=0.5K-0.5L0.5 and MPL=0.5K0.5L-0.5. The price of K is $8 and L is $2.

a) What is the average product of capital?

b) Does capital obey the law of diminishing returns? Explain.

c) If Q=144, how much K and L should be employed to minimize costs?

d) If K=16, how much L should be employed to minimize costs?

You are an efficiency expert hired by a manufacturing firm that uses K and L as inputs. The firm produces and sells a given output. If w = $40, r = $100, MPL = 4, and MPK = 40 the firm:

A.) Is cost-minimizing.

B.) Should use less L and more K to cost minimize.

C.) Should use more K and less L to cost minimize.

D.) Is profit-maximizing but not cost-minimizing.

Consider the following production function using capital (K) and labor (L) as inputs. Y = 10.K0.5L0.5. The marginal product of labor is (MPL=) 5.K0.5/L0.5, and the marginal product of capital (MPK) = 5.L0.5/K0.5.

a. If K = 100 and L=100 what is the level of output Y?

b. If labor increases to 110 while K=100, what is the level of output?

c. If labor increases to 110 while K=100, what is the marginal product of labor?

d. If labor increases to 120 while K=100, what is the marginal product of labor?

e. What happens to the marginal product of labor when labor increases while capital remains unchanged?

f. Estimate Marginal Products of Capital in the above cases of (c) and (d) using the equation given in the question.

g. When labor increases from 100 to 110 and then to 120 while the level of capital does not change, what happens to the Marginal Product of Capital?

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