Question

Suppose that the demand curve and supply functions are qD = 300−5p and qS = 100+20p, respectively.
(a) On the same graph, draw the demand and supply curves with price on the vertical axis.

(b) What is the quantity and price in the equilibrium?

(c) Calculate consumer surplus and producer surplus.

(d) Suppose the government implements a $5 dollar per unit sales tax.
i. Calculate the new quantity and the price paid by the consumer.
ii. Calculate the consumer surplus, producer surplus, tax revenue, and deadweight loss.
iii. What share of the tax is passed on to the consumer and what share of the tax is passed on to the producer? iv. Graph the taxed equilibrium on a new graph.

(e) Recalculate parts a through d but now suppose that quantity supplied is perfectly inelastic. Specifically, suppose that qS = 100.

(f) Recalculate parts a through d but now suppose that quantity demanded is perfectly inelastic. Specifically, suppose that qD = 400

Answer 1

Figure 1

Price 60 40 20 100 200 300 Quantity

Taxed equilibrium

Price -40 -20 100 200 300 Quantity

a) | Figure Figweens ! Equilibrium: ad as . .or, 300-5p = 100+20p 0, 250 200 ::$ = 8 ....9 = 260 c) consumer swepuis: CS 4x (608) * 260-6760 Producers sweplus: PS4* (8+5) * 260 0940 - 4x 5 x 100 = 1440 d) 3 supply aftere tax i qu's = 100'+20(P-5) -20p . Equilibrium a n aś = 90 .. . a 205 = 300-5p 25p - 300 ::p=12, Ps= 7 .::9 = 240. (W) 1190 CS +x (60-12) x 240 = 5760 PS = $x (7+5)*240 -4*5*100= $ TR = 340 x 5 = 12 co DWL = {x.5 * (260-240) = 50 . (m) Burden of tax: on consumer: 12-88x100= 80% on producers: 20°%. e) Figure - 2 pre tox equilibrium: q = 100 P = 40 u " CS 4x(60-40) x 100 = 1000 nu PS = 40*100 = 4000 Post tax equilibrium is same, only now producer receired (40-5) = 35 and burden | n 100% on producer. The cs and PS remain same Tax Yevenue 100X 5 = 500.NO DWIL

Figure 2

Price 60 40 20- 100 200 300 Quantity

f)

Figure 3

Price 60 140 20– 100 200 300 400 Quantity

Pre-tax equilibrium, q=400, p=15

Pre-tax consumer surplus:

CS= oo

Pre-tax producer surplus:

PS = = x (15+5) x 400 x 5 100 = 3750

Post-tax supply is:

9 = 20p

quantity is 400 and price is p=20

The consumer surplus is still and the producer's surplus is still 3750. The full burden goes to the consumer.

CS= oo