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11 Aug 2019

Assume that the production function for Cambodias economy is given by the following Cobb-Douglas production function:

Y=AK^(2/3)L^(1/3)

Derive the Marginal Product of Capital

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Related questions

Suppose that an economy’s production function is Cobb-Douglas with parameter a=0.36,

and is given by

Y= AK^a L^1-a

(a) Prove that this Cobb-Douglas function has constant returns to scale.

(b) What fraction of income do capital and labor receive?

(c) Suppose that immigration raises the labor force by 20 percent. What happens to total output (in percent)? The rental price of capital? The real wage?

(d) Suppose that a gift of capital from abroad raises the capital stock by 20 percent. What happens to total output (in percent)? The rental price of capital? The real wage?

a) Define A , K , and L

b) What does it mean that Y is proportional to A?


c) What does it mean that the marginal product of capital (MPK) and the marginal product of labor (MPL) are greater than zero? Show that the marginal products are positive in the Cobb-Douglas case.

d) What does it mean that the marginal product of capital (MPK) and the marginal product of la- bor (MPL) are decreasing? Show that the marginal products are decreasing in the Cobb-Douglas case.

e) What does it mean that the marginal product of capital (MPK) is increasing in labor? Show that the marginal product of capital increases as labor increases. Is the same true for capital?

f) Does the Cobb-Douglas production function display “constant returns to scale?” (Doubling both inputs doubles outputs). If this is true, show it, otherwise, show it is false.

Consider a Cobb-Douglas production function with three inputs. K is capital, L is unskilled labor, and H is skilled labor:

Y = K1/3L1/3H1/3

Find:

1. The marginal product of unskilled labor

2. The marginal product of skilled labor

3. The marginal product of capital

4. The wage of unskilled labor

5. The wage of skilled labor

6. The ratio of skilled wage to unskilled wage

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