Question

1. The market demand for labour is given by w = 28 – 0.05L, where w is the wage rate ($/week) and L is the number of workers the firm want to employ. The market supply of labour is given by w = 2 + 0.05L, where w is the wage rate ($/hr) and L is the number of workers who want to work.

1. What is the equilibrium wage rate?

2. If the government introduces the minimum wage rate of $15.75/hr, what would be the unemployment rate?

Answer 1

a.

This could be found through the equality of demand and supply.

Demand = Supply

28 – 0.05L = 2 + 0.05L

28 – 2 = 0.05L + 0.05L

26 = 0.1L

26 / 0.1 = L

L = 260

This should be placed in either demand function or supply function to get the equilibrium rate; suppose in the demand function,

w = 28 – 0.05L

    = 28 – 0.05 × 260

    = 28 – 13

    = 15

Answer: the wage rate is $15.

b.

Labor demand and labor supply at the rate, $15.75, should be calculated first.

Labor demand:

w = 28 – 0.05L

15.75 = 28 – 0.05L

15.75 – 28 = - 0.05L

12.25 = 0.05L

12.25 / 0.05 = L

Ld = 245

Labor supply:

w = 2 + 0.05L

15.75 = 2 + 0.05L

15.75 – 2 = 0.05L

13.75 = 0.05L

13.75 / 0.05 = L

Ls = 275

Labor supply is the total labor force.

Unemployment rate = [(Ls – Ld) / Ls] × 100

                                    = [(275 – 245) / 275] × 100

                                    = [30 / 275] × 100

                                    = 3,000 / 275

                                    = 10.91%