Question

A country which does not tax cigarettes is considering the introduction of a $0.40 per pack tax. The economic advisors to the country estimate the supply and demand curves for cigarettes as: QD = 140,000 - 25,000P QS = 20,000 + 75,000P, where Q = daily sales in packs of cigarettes, and P = price per pack. The country has hired you to provide the following information regarding the cigarette market and the proposed tax. a. What are the equilibrium values in the current environment with no tax? b. What price and quantity would prevail after the imposition of the tax? How much do buyers now pay? How much do produces recieve? c. How much revenue is raised by the tax? d. Calculate the deadweight loss from the tax. e. Based on your answer in (b), is supply or demand more elastic? Explain.

Answer 1

Qd = 140,000 - 25,000P

Qs = 20,000 + 75,000P

At equilibrium, demand = supply

140,000 - 25,000P = 20,000 + 75,000P

120,000 = 100,000P

P = 1.2

At P = 1.2, Q = 110,000

a) Equilibrium price is 1.2 and equilibrium quantity is 110,000

b) Benefit of tax falls on buyers and sellers in the ratio of (point at which demand curve touch price axis - equilibrium price) to (equilibrium price - supply curve touching price axis) = (5.6 - 1.2) / (1.2 + 0.266) = 4.4 / 1.466

Burden of tax on consumer is [4.4 / (4.4 + 1.466)] = 75% which is 0.4 * 0.75 = 0.3 while burden of tax on producer is [1.466 / (4.4 + 1.466) ] = 25% which is 0.25 * 0.4 = 0.1

Price consumer pay will rise to 1.5 and price producer receive falls to 1.1. Quantity traded at this price is 102,500

c) Revenue raised by the tax is area of portion A + B in the above diagram whose area is (102,500 - 0) * (0.4) = 41,000

d) Deadweight loss is area of portion C + D in above diagram whose sum is (1/2) * (110,000 - 102,500) * 0.4 = 1,500

e) Demand is more elastic as burden of tax falls more heavily on inelastic side of the market.