Question

Consider an economy with the following Cobb–Douglas production function: Y = 4K1/4L3/4. Now suppose that Congress, concerned about the welfare of the working class, passes a law setting a minimum wage that is 5 percent above the equilibrium wage you derived in part (b). Assuming that Congress cannot dictate how many workers are hired at the mandated wage, what are the effects of this law? Specifically, calculate what happens to the real wage, employment, output, and the total amount earned by workers. Real Wage (rounded to one decimal place)= Employment (rounded to the nearest whole number)= Total Output (rounded to the nearest whole number) = Total Amount Earned by Workers (rounded to the nearest whole number) = Does Congress succeed in its goals of helping the working class? A. Yes, Congress does succeed in its goal of helping the working class. B. No, Congress does not succeed in its goal of helping the working class. Does this analysis provide a good way of thinking about a minimum wage law? A. Yes, this analysis does provide a good way of thinking about a minimum wage law. B. No, this analysis does not provide a good way of thinking about a minimum wage law.

Answer 1

(1)

At this higher minimum wage, demand for labor will fall and unemployment will rise. Employment falls, output falls.

Revised wage = $10 x 1.1 = $11

3 x 10 x 1.1 = 10 x (K / L)^1/3

3.3 = (K / L)^1/3

(K / L) = 35.937

L = K / 35.937 = 27,000 / 35.937 = 751.31 (employment decreases)

Y = 5 x (27,000)^1/3 x (751.31)^2/3 = 5 x 30 x 82.64 = 12,396.69 (Y falls)

Total amount earned by workers = w x L = 11 x 751.31 = 8,264.41 (Decreases)

(2)- (b). No, congress does not succeed in its goal of helping the working class.

(3)- (b). Yes, this analysis does provide a good way of thinking about a minimum-wage law.