Question

A firm's labor demand and labor supply equations are shown below.

Labor demand equation: Ld =60−3w
Labor supply equation: Ls =−20+5w,
where w is the wage per hour worked, Ld is the number of workers demanded by firms, and Ls is the number of people willing to work.
Instructions: Round your answers to the nearest whole number.
a. The equilibrium wage is $___ and the equilibrium quantity of labor employed is __ people.
b. The workers, thinking that their wages are too low, decide to strike. After tense negotiations, the firm decides to raise the wage by 50 percent.
After the wage increase, __ people are unemployed.

Answer 1

a. The equilibrium wage is $10 and the equilibrium quantity of labor employed is 30 people.

b. After the wage increase, 15 people are unemployed.

Step-by-step explanation:

a. The equilibrium wage can be found by setting the labor demand equal to the labor supply and solving for w. In this case, we have:

Ld = Ls

60 - 3w = -20 + 5w

8w = 80

w = 10

Therefore, the equilibrium wage is $10 per hour.

b. To find the equilibrium quantity of labor employed, we can substitute the equilibrium wage into either the labor demand or labor supply equation. Let's use the labor demand equation:

Ld = 60 - 3(10)

Ld = 60 - 30

Ld = 30

Therefore, the equilibrium quantity of labor employed is 30 people.

After the wage increase of 50 percent, the new wage would be $15 per hour. To find the number of people unemployed, we compare the labor demand at the new wage to the labor supply.

Ld = 60 - 3(15)

Ld = 60 - 45

Ld = 15

Ls = -20 + 5(15)

Ls = -20 + 75

Ls = 55

Therefore, after the wage increase, 15 people are unemployed.