Question

Question 2. This question looks at the minimum wage. Suppose that the demand and supply of labor are summarized by the following equations where W is the wage rate.

Qd = 200 – 10W
Qs = 10W

a.   What is the Wage rate in this market?

Suppose now the government introduces a minimum wage rate of $15.

b.   What is employment after the minimum wage is introduced?
c.   What is unemployment after the minimum wage? In other words, how many workers are there who would like to work at the minimum wage but who do not receive a job?
d.   What is the loss in consumer surplus by the demanders of labor (employers) from the minimum wage?

Answer 1

a) A market is in equilibrium when demand and supply become equal.

The given demand function is

Qd = 200-10W

The given supply function is

Qs = 10 W

When Qd= Qs

200-10W = 10W

200 = 10W+10W

200 = 20W

W = 200/20 = 10

The wage rate in the market is 10

b) Quantity demand for labour when minimum wage is 15

Qd = 200-10*15

200-150 =50

The employment of labour = 50

C) The quantity supplied of labour when minimum wage is 15

Qs = 10*15 =150

When minimum wage is 15, quantity supplied of labour is 150 and demand for labour is 50.

Unemployment after minimum wage = 150-50 = 100

d) Consumer surplus for labour demanders is the difference between the maximum wage they are willing to oay and the actual wage they pay. The consumer surplus for labour demanders will be the area below the demand curve

The given demand function is

Qd =200-10W

The maximum wage the demanders willing to pay is the wage at quantity demand 0 (Y axis intercept of demand curve)

0 = 200-10W

-200 = -10W

W = -200/-10 =20

The maximum price the demanders willing to pay = 20

The difference between maximum price willing to pay 20 and actual price 10

= 20 -10 =10

When wage = 10, the total deamand is 100, then the demanders total surplus = (1/2) *100*10 =500.

When minimum wage is 15, the difference between maximum price and actual price = 20-15 = 5

When wage is 15, the demand is 50. Then the demanders surplus = (1/2)*5*50 =125

The loss from minimum wage = 500-125 = 375