Question

Suppose an economy's production is defined by the following neoclassical production function: Y=3K ^1/3L ^2/3. Suppose further that the economy wide supply of capital and labor are given as 125,000 and 1,000 respectively. If congress imposes a minimum wage of 11 units of output in this economy, what will be the likely result of this action?

a. An unemployment rate of 25%

b. An unemployment rate of 10%

c. Full employment, but lower output

d. An unemployment rate of 50%

Answer 1

Production function is given by :

Q = 3K^1/3L^2/3 = 3*125000^1/3L^2/3 = 150L^2/3

In order to maximize profit amount of workers are hired such that Marginal product of Labor = Real wage.

Here Real wage = 11(Note we are measuring every thing in real terms and that's why we are using real wage)

Marginal product of Labor(MPL) = dQ/dL = (2/3)*150L^-1/3

Thus MPL = wage rate => (2/3)*150L^-1/3 = 11 => L = 750(approx)

So amount lf workers which are unemployed = 1000 - 750 = 250

Unemployment rate = ((number of unemployed)/Labor Force)*100 = (250/1000)*100 = 25%

Hence, Unemployment rate = 25%

Hence, the correct answer is (a) An unemployment rate of 25%.