Question

Consider an economy with the Cobb–Douglas production function:

Y=4K^0.2 * L^0.8

K = 120000; L=7000

Round answers to two places after the decimal when necessary.

b. The economy has 120000 units of capital and a labor force of 7000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage, total output, and the total amount earned by workers.

Real wages = $ XXX

Total output = XXX units

Total amount earned by workers = $ XXX

c. Now suppose that Congress, concerned about the welfare of the working class, passes a law setting a minimum wage that is 10 percent above the current equilibrium wage. Assuming that Congress cannot dictate how many workers are hired at the mandated wage, calculate what happens to the real wage, employment, output, and the total amount earned by workers.

Real wages = $ XXXX

Employment = XXX workers

Total output = XXX units

Total earned by workers = $ XXX

Answer 1

We are given production function as -

with K = 120,000 and L = 7,000

b. Real wages in equilibrium are equal to marginal product of labour, or w = MPL. MPL is nothing but the rate of change of Y with respect to L. So,

This when calculated comes out approximately equal to 5.64.

Output or Y given all the values can be calculated easily as -

49,428.186

Total amount earned by workers = w * Y = 5.64 * 49,428.186 = 278,774.969

c. Now, new wage rate w' = 1.1w = 1.1(5.64) = 6.204

Equilibrium will only be maintained when w' = MPL.

For given K and given w', we can find out L by equating w' with MPL.

We can acquire the value of L by solving this equation.