Question

Market for unskilled labor is perfectly competitive: there are lots of potential workers and lots of employers needing such work. Suppose supply of unskilled labor is given by Q^s = 10W and demand for labor is given by Q^d = 240−20W, where W is the hourly wage and Q is the number of hours (in thousands). Keep in mind that workers represent supply of labor, while firms are on the demand side here.

(a) Find the equilibrium wage and number of hours.

(b) Suppose the minimum wage rate of $9 is instituted by the government. What is the new

quantity of labor employed? How much unemployment is there?

(c) What is the deadweight loss from the minimum wage?

(d) Are workers better off as a group? How much worse off are firms/employers? (Hint: How

much does producer surplus change? What about consumer surplus?)

Answer 1

a) At equilibrium

Qd = Qs

240 – 20W = 10W

W = 240/30 = $8

Q = 10*8 = 80 (‘000) hours.

b) At W = 9, Qd = 240 – 20*9 = 60 (‘000) hours and Qs = 10*9 = 90 (‘000) hours.

Hence, new quantity of labor employed is 60 (‘000) hours and there are 30 (‘000) hours of unemployment

c) DWL = 0.5*(9 – 6)*(80000 – 60000) = $30,000

d) Loss in consumer surplus = New – Old

= 0.5*(12 – 9)*60 – 0.5*(12 – 8)*80 = -70,000 (employers are worse-off)

Gain in producer surplus = New – old

= 0.5*(9 – 0 + 9 – 6)*60 – 0.5*(8 – 0)*80 = 40,000 (workers are better off)