Question

In: Economics

3. Suppose that the production function is CobbDouglas with parameter α = 0.3. a. What fractions...

3. Suppose that the production function is CobbDouglas with parameter α = 0.3.

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

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

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

please explain it like how to they get digits from suddenly out of no where

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

Solutions

Expert Solution

a) Fraction recieved by Capital

Paid to Capital =

which is simply α which is given as 30%

Fraction recieved by labour is 1-fraction by labour which is 70%

b)

(Increasing labour by 10)

Y2/Y1 = 1.069

(Increasing labour by 10)

Dividing them, we get 1.069

(Increasing labour by 10)

Dividing them, we get 0.972

Thus, we notice a 6.9% rise is output and the rental rate while the wages fall by 2.8%

c) (Increasing capital by 10%)

Y2/Y1 = 1.029

  (Increasing capital by 10%)

(R/P)2/(R/P)1 = 0.935

  (Increasing capital by 10%)

(W/P)2/(W/P)1 = 1.029

Thus we notice there is a rise in output and wage by 2.9 and rental wage fall by 6.5%

d) In such a scenario, everything increases by 10%

Rahul Sunny answered 2 years ago
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