Question

Qd=400-200P and Qs=80P+20

How much will the producer and consumer surplus increase/decrease due to a 70 cents tax?

Answer 1

In pre-tax equilibrium, Qd = Qs.

400 - 200P = 80P + 20

280P = 380

P = 1.36

Q = 400 - (200 x 1.36) = 400 - 272 = 128

The tax (assuming imposed on sellers) will lower supply, shifting supply curve leftward by $0.7. New supply function will be

Qs = 80(P - 0.7) + 20 = 80P - 56 + 20 = 80P - 36

Equating with Qd,

400 - 200P = 80P - 36

280P = 436

P = 1.56 (Price paid by buyers)

Price received by sellers = 1.56 - 0.7 = 0.86

Q = 400 - (200 x 1.56) = 400 - 312 = 88

After the tax,

Decrease in consumer surplus = (1/2) x (1.56 - 1.36) x (128 + 88) = (1/2) x 0.2 x 216 = 21.6

Decrease in producer surplus = (1/2) x (1.36 - 0.86) x (128 + 88) = (1/2) x 0.5 x 216 = 54