Question

1. The market demand for labour is given by w = 20 – 0.05L, where w is the wage rate ($/week) and L is the number of workers the firm want to employ. The market supply of labour is given by w = 10 + 0.05L, where w is the wage rate ($/week) and L is the number of workers who want to work.

a. What is the equilibrium wage rate?

b. If the government introduces the minimum wage rate of $15.25/hr, what would be the unemployment rate?

Answer 1

Question 1

(a)

Demand for labor is as follows -

w = 20 - 0.05L

Supply of labor is as follows -

w = 10 + 0.05L

At equilibrium,

Demand = Supply

20 - 0.05L = 10 + 0.05L

- 0.05L - 0.05L = 10 - 20

0.1L = 10

L = 10/0.1 = 100

Putting value of L in demand equation,

w = 20 - 0.05L = 20 - (0.05 * 100) = 20 - 5 = 15

Thus,

The equilibrium wage rate is $15 per hour.

(b)

Now, government introduces the minimum wage rate of $15.25/hr.

labor demanded at $15.25/hr,

w = 20 - 0.05L

15.25 = 20 - 0.05L

0.05L = 4.75

L = 4.75/0.05 = 95

The labor demanded at $15.25/hr is 95 workers.

labor supplied at $15.25/hr,

w = 10 + 0.05L

15.25 = 10 + 0.05L

0.05L = 5.25

L = 5.25/0.05 = 105

The labor supplied at $15.25/hr is 105 workers.

Calculate number of unemployed -

Number of unemployed = Labor supplied - Labor demanded = 105 workers - 95 workers = 10 workers

Calculate the unemployment rate -

Unemployment rate = (Number of unemployed/Labor supplied) * 100

Unemployment rate = (10/105) * 100 = 9.52%

The unemployment rate would be 9.52%.