Question

Suppose the market demand is QD = 200−P and market supply is QS = 4P−100.

A. Suppose the government imposes a tax of t = 5 on producers. What is the incidence of the tax on consumers? Producers?

B. What is the deadweight loss of the tax?

Answer 1

In pre-tax equilibrium, QD = QS.

200 - P = 4P - 100

5P = 300

P = 60

Q = 200 - 60 = 140

(A)

The tax will shift supply curve leftward by 5 at every output, and new supply curve becomes

QS = 4(P - 5) - 100 = 4P - 20 - 100 = 4P - 120

Equating with QD,

200 - P = 4P - 120

5P = 320

P = 64 (Price paid by buyers)

Price received by sellers = 64 - 5 = 59

Q = 200 - 64 = 136

Tax incidence of consumers = Price paid by buyers after tax - Pre-tax price = 64 - 60 = 4

Tax incidence of producers = Pre-tax price - Price received by sellers = 60 - 59 = 1

(B)

Deadweight loss = (1/2) x Unit tax x Change in quantity = (1/2) x 5 x (140 - 136) = 2.5 x 4 = 10