5. Suppose that an economy’s production function is cobb-douglass with CRS(Y=AK^

Question

5. Suppose that an economy’s production function is cobb-douglass with CRS(Y=AK^ * L^1- ) and =.3

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

b. Suppose that labor force increases by 15 percent. How much does output increase or decrease by in percentage terms? The rental price of capital? The real wage?

c. Suppose that the capital stock decreases by 15 percent. How much does output increase or decrease by in percentage terms? The rental price of capital? The real wage?

d. Suppose that a technological advance raises the value of the parameter A by 15 percent. How much does output increase or decrease by in percentage terms? The rental price of capital? The real wage?

Explanation / Answer

Y = AKL1-

= AK0.3L0.7

(a)

Fraction of income received by capital, MPK = dY / dK

= 0.3A (L / K)0.7

Fraction of income received by labor, MPL = dY / dL

= 0.7A (K / L)0.3

(b)

If L increases by 15%,

Y1 = AK0.3 (1.15L)0.7 = Y x 1.103

So, output increases by 10.3%.

An increase in labor force will reduce wage rate, but rental price of capital will remain unchanged.

(c)

If K decreases by 15%,

Y1 = Y x (0.85)0.3 = 0.95Y

So, output decreases by 5%.

A reduction in capital will increase the rental rate of capital but real wage will remain unchanged.

(d)

A 15% increase in A will increase output by 15%. This being a change in exogenous variable, increased A will affect neither rental rate or wage rate.

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