Question

The supply curve of work requiring a high school degree or less is Q_S = - 13,000 + 2000P and the demand for such work is Q_D = 11,000 - 1000P. Assume this is a competitive market.

1. What quantity is hired if a minimum wage of $10 is imposed? What is the deadweight loss (DWL) of this policy?

2. Instead of a minimum wage, policymakers introduce a $1.5 wage subsidy (think EITC). What is the quantity of work supplied under this policy? What is the DWL of this policy?

3. What percentage of the subsidy is captured by the employers? (Hint: the buyer's burden is represented by

Answer 1

1.

The equilibrium condition is

- 13,000 + 2000P = 11,000 - 1000P

or 3000P = 24000

or P = 8

Equilibrium quantity is -13000 + 2000 * 8 = -13000 + 16000 = 3000

With a minimum wage of $10, the total quantity demanded will be 11000 - 1000*10 = 1000

Price at which supply will be 1000 is 1000 = -13000 + 2000P or P = 7

Deadweight Loss = 1/2 * (10 - 7) * (3000 - 1000) = 1/2 * 3 * 2000 = 3000

2.

With a wage subsidy of 1.5, the new supply curve is

Q = -13000 + 2000 (P + 1.5)

or Q = -13000 + 2000P + 3000

or Q = -10000 + 2000P

or P = (Q + 10000)/2000

Demand CUrve is Q = 11000 - 1000P

or P = (11000 - Q)/1000

So at equilibrium

(Q + 10000)/2000 = (11000 - Q)/1000

or Q + 10000 = 22000 - 2Q

or 3Q = 12000

or Q = 4000

So the quantity supplied will be 4000

P = (11000 - Q)/1000 = (11000 - 4000) / 1000 = 7

Deadweight Loss = 1/2 * (8.5 - 7) * (4000 - 3000) = 1/2 * 1.5 * 1000 = 750

3. Initially the employers had to pay $8. Now they have to pay $7. So their profit is $1.

Total subsidy given is $1.5

Price received by employees = 7 + 1.5 = $8.5

So Employers get 1/1.5 or 66.67% of the subsidy while employees who used to get $8 are now getting $8.5. SO they get 0.5/1.5 or 33.33% of the subsidy.

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