Question

The market for unskilled labour is represented by Q = 1,200 – 40w and Q = 160w – 800 where Q is the number of workers per hour and w is the hourly wage rate.

a) What are the equilibrium wage rate and equilibrium quantity in this market? Show your calculations.

b) How much total employment income do workers earn at the market equilibrium? Show your calculations.

c) Suppose the government decides to impose a minimum wage of $14/hour in this market. Is this minimum wage binding on the market and if yes, what is the new total employment income of workers? Show your calculations.

d) Do workers as a group support the government’s minimum wage of $14/hour? Explain.

e) Suppose after imposing a minimum wage of $14/hour, the government decides to increase it to $18/hour. What is the new total employment income of workers? Show your calculations.

f) Is demand in this market elastic or inelastic when the wage rate is between $14/hour and $18/hour? Explain.

g) Do workers as a group support the government’s increase in the minimum wage from $14/hour to $18/hour? Explain.

Answer 1

Labor demand: 1,200 - 40w

Labor supply: 160w - 800

a) At equilibrium, demand of labor = supply of labor

1,200 - 40w = 160w - 800

200w = 2,000

w = 10

At this wage rate, equilibrium labor = 1,200 - 40 * 10 = 800

b) Total earning at equilibrium = Wage rate * Labor hired = 800 * 10 = 8,000

c) Minimum wage = $14

This minimum wage is binding because this is set above the equilibrium wage and government prevents it from falling. At this wage rate, demand of labor = 1,200 - 40 * 14 = 640 while supply of labor 160 * 14 - 800 = 1,440. Surplus / Unemployment of labor becomes 1,440 - 640 = 800

d) Total payment made to labor 640 * 14 = 8,960 which will induce labor as a group to support minimum wage because they are now getting more payment.  

e) If minimum wage rises to $18, labor demand at this wage is 1,200 - 40 * 18 = 480 while supply of labor at this wage is 160 * 18 - 800 = 2,080. There would be surplus of labor = 2,080 - 480 = 1,600

Total employment income now is 480 * 18 = 8,640

f) When wage rises from $14 to $18, demand of labor falls from 640 to 480.

Elasticity of labor demand = %change in labor demanded / %change in wage rate

%change in labor demanded = [(480 - 640) / 640] * 100 = -25%

%change in wage rate = [(18 - 14) / 14] * 100 = 28.57%

Elasticity of labor demand = -25% / 28.57% = -0.875

Elasticity of labor is inelastic between this wage rate.

g) As total payment made falls from 8,960 to 8,640 when wage rate rises from $14 to $18, labor as a group will not support this.