Question

Problem 2

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

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?

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?

Answer 1

answer c

Y₁ = AK^0.3L^0.7,      Y₂ = A(1.1K^0.3)L^0.7

Y₂ / Y₁ = (1.1)^0.3 = 1.029

(R/P)₁ = MPK = 0.3AK^-0.7L^0.7,     (R/P)₂ = 0.3A(1.1K^-0.7)L^0.7

(R/P)₂ / (R/P)₁ = 0.935

(W/P)₁ = MPL = 0.7AK^0.3L^-0.3,     (W/P)₂ = 0.7A(1.1K^-0.7)L^-0.7

(W/P)₂ / (W/P)₁ = 1.029

Thus output rises by 2.9%, rental rates fall by 6.5%, and wages rise by 2.9%

answer d

Y₁ = AK^0.3L^0.7,      Y₂ = A(1.1K^0.3)L^0.7

Y₂ / Y₁ = (1.1)^0.3 = 1.10

(R/P)₁ = MPK = 0.3AK^-0.7L^0.7,     (R/P)₂ = 0.3A(1.1K^-0.7)L^0.7   

(R/P)₂ / (R/P)₁ = 1.10

(W/P)₁ = MPL = 0.7AK^0.3L^-0.3,     (W/P)₂ = 0.7A(1.1K^-0.7)L^-0.7   

(W/P)₂ / (W/P)₁ = 1.10

Everything goes up by 10 %