Question

Suppose demand for and supply of labour in Australia are
Demand: LD = 2000 – 50W
Supply: LS = 1000 + 50W,
where, Demand and Supply are expressed in total hours worked per week, and W = hourly wage rate (dollars per hour).

a) What would be the equilibrium hourly wage rate and quantity of labour employed in the absence of any government intervention in the market?

b) At the market equilibrium, what are the elasticities of labour demand and supply?
c) Suppose that the Australian government introduces a wage subsidy of $2 per hour for workers. What will be the effect on the market outcome?
d) Draw a graph to illustrate your answers to parts a) and c).

Answer 1

A) Without government intervention, equilibrium occurs where demand equals supply.

LD=LS

2000-50W=1000+50W

1000=100W

Equilibrium wage W*= 10

Equilibrium labor L*=2000-50*10= 1500

B) Elasticity of labor demand= (dLD/dW)(W*/L*)= -50*(10/1500)= -0.33

Elasticity of labor supply= (dLS/dW)(W*/L*)= 50*(10/1500)= 0.33

C) wage subsidy= Wage received by workers- Wage paid by employers= $2.

New labor supply LS'= 1000+50(W+2)= 1000+50W+100=1100+50W

New equilibrium

LS'=LD

1100+50W=2000-50W

100W=900

Wage paid by employers W*= $9

Wage received by workers= $9+$2=$11

Equilibrium Quantity of labor= 2000-50*9= 1550

D)