4. Suppose that an economy's production function is Cobb-Douglas with parameter a=0.3. a. What fractions of...

4. Suppose that an economy's production function is Cobb-Douglas with parameter a=0.3.

a. What fractions of income do capital and labor receive?

b. Suppose that immigration increases the labor force by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?

c. Suppose that a gift of capital from abroad raises the capital of stock by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?

Solutions

Expert Solution

a. What fractions of income do capital and labor receive?
Solution: Fractions of income capital = 0.3 or 30%
Fractions of income labor = 0.7 or 70%

b. Suppose that immigration increases the labor force by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?
Total output grows at the rate of 6.9% or 1.068993
The rental price of capital grows at the rate of 6.89%
The real wage grows at the rate of -2.819%
Working: Enclosed

c. Suppose that a gift of capital from abroad raises the capital of stock by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?
Total output grows at the rate of 2.9% or 1.029006
The rental price of capital grows at the rate of -6.4%
The real wage grows at the rate of 2.9%
Working: Enclosed

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?
Total output grows at the rate of 10%
The rental price of capital grows at the rate of 10%
The real wage grows at the rate of 10%

Rahul Sunny answered 1 year ago

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