Question

Imagine a labor market where Ld = 128-9w, while Ls= 7w-32, where w is the hourly wage rate.

(a)What is the equilibrium level of employment and wage?

(b) If the present minimum wage is $7.15/hr. and the government raises it $8.50/hr, how many workers will lose their jobs? What is the unemployment rate?

(c) If instead the government voted to raise the minimum wage to $12/hr, how many workers will lose their jobs? What is the unemployment rate?

(d) Assume now that the workers who lost their jobs in (c) are able to move to another sector that is not covered by the minimum wage (and are willing to work for any positive wage). Before the unemployed workers arrive, aggregate labor demand and labor supply in the uncovered sector are given by Ld = 140-20w and Ls = 15+5w, respectively. What is equilibrium wage in the uncovered sector before and after the minimum wage is raised to $12/hr.?

Answer 1

1. What is the equilibrium level of employment and wage?
Answers:
= = 20 +10ω = 125 − 5ω s d L L
15ω = 105
ω = $7
= 125 − 5ω = 125 − 5(7) = 90

2.  Equilibrium wage (ω = $7 ) is higher than the minimum wage of $5.85/hr. It is also higher
than the new minimum wage of $6.50/hr. When the minimum wage is below the market
equilibrium wage, the minimum wage is a non-binding price floor. The market will pay
ω = $7 and there will be no unemployment.

3.

If the minimum wage is raised to $8/hr (above the equilibrium wage (ω = $7 )), the

minimum wage is a binding price floor.

With a minimum wage of $8/hr, the quantity of labor supplied is 100.

L

In problem (a), 90 workers were working in the labor market. Because of the minimum

wage of $8/hr, the quantity of labor demanded is 85 so 5 workers lose their jobs.

= 125 − 5ω = 125 − 5(8) = 85 d L

The difference between the quantity of labor supplied and the quantity of labor demanded

with the new minimum wage is 15. This means that 15 workers who are willing and able to

work cannot find jobs or are unemployed. There are 100 total workers at a wage of $8/hr

who are willing and able to work or are in the labor force.

− = 100 − 85 = 15 s d L L

Unemployment rate = total unemployed / labor force = 15 / 100 = 15%

4. Before worker migration, the equilibrium wage rate in the uncovered sector is $7/hr.

= = 15 + 5ω = 190 − 20ω s d L L

25ω = 175

ω = $7

= 15 + 5ω = 15 + (5)(7) = 50 s L

After worker migration, the equilibrium wage rate in the uncovered sector is $6.25.

The labor supply migrating from the covered market ( = 15 sm L ) is added to the labor supply

in the uncovered sector ( = 50 s L ) for a total labor supply of 60.

+ = 50 +15 = 65 s sm L L

= = 65 = 190 − 20ω s d L L

20ω = 125

ω = $6.25