Question

3. In 1996, Congress raised the minimum wage from $4.25 per hour to $5.15 per hour, and then raised it again in 2007. Some people suggested that a government subsidy could help employers finance the higher wage. This exercise examines the economics of a minimum wage and wage subsidies. Suppose the supply of low-skilled labor is given by LS = 10w, where LS is the quantity of low-skilled labor, and w is the wage rate. The demand for labor is given by LD = 80 – 10w. a. What will be the free-market wage rate and employment level? Suppose the government sets a minimum wage of $5 per hour. How many people would then be employed? (Assume that workers (i.e. suppliers) correctly anticipate the quantity demanded with the minimum wage). Calculate the DWL associated with minimum wage. b. Suppose that instead of a minimum wage, the government pays a subsidy of $1 per hour for each employee. What will the total level of employment be now? What wage will employees receive? Calculate the DWL.

Answer 1

(a)

(i) In equilibrium, LD = LS.

80 - 10w = 10w

20w = 80

w = 4

L = 10 x 4 = 40

(ii) When w = 5,

LD = 80 - 10 x 5 = 80 - 50 = 30

LS = 10 x 5 = 50

Since workers will be hired only to the extent firms will recruit, market employment = 30.

Unmployment = LS - LD = 50 - 30 = 20

(iii) When LS = 30,

10w = 30

w = 3 (supply wage)

Deadweight loss = (1/2) x (Minimum wage - Supply wage) x Change in L = (1/2) x (5 - 3) x (40 - 30) = (1/2) x 2 x 10 = 10

(b)

The subsidy will increase labor demand, shifting labor demand curve rightward. New labor demand function is:

LD = 80 - 10(w - 1) = 80 - 10w + 10 = 90 - 10w

Equating with LS,

90 - 10w = 10w

20w = 90

w = 4.5 (wage received by workers)

Wage paid by firms = 4.5 - 1 = 3.5

L = 10 x 4.5 = 45

Deadweight loss = (1/2) x Unit subsidy x Change in L = (1/2) x 1 x (45 - 40) = 0.5 x 5 = 2.5