ECON 2210 Chapter Notes - Chapter 1: Deadweight Loss, Economic Equilibrium, Economic Surplus
155) 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? What portion of
the tax would be borne by buyers and sellers respectively? c.
Calculate the deadweight loss from the tax. Could the tax be justified despite the
deadweight loss? What tax revenue will be generated? Answer: a.
Equate QD and QS to determine equilibrium price and quantity. 140,000 - 25000P = 20,000 + 75,000P
120,000 = 100,000P P = 1.20 Substitute to find Q QS = 20,000 + 75000(1.2) QS = 110,000
b. Four conditions must hold QD = 140,000 - 25,000 PB QS = 20,000 + 75,000 PS QD = QS PB - PS = 0.40
or PB = PS + 0.40 Equilibrium requires: 140,000 - 25,000PB = 20,000 + 75,000 PS Substituting for PB
140,000 - 25,000(PS + 0.40) = 20,000 + 75,000PS 140,000 - 25,000PS - 10,000 = 20,000 + 75,000PS
110,000 = 100,000PS PS = 1.10 PB = PS + 0.40 PB = $1.50
Tax is paid $0.30 by buyer and $0.10 by seller. (Buyersʹ price goes from $1.20 to $1.50,
sellersʹ price from $1.20 to $1.10).
c. Find Q by substituting PB into QD or PS into QS QD = 140,000 - 25,000(1.5) QD = 102,500
QS = 20,000 + 75,000(1.10) QS = 102,500
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Deadweight loss consists of two portions; Aʹ ʹ a loss in C.S. and Bʹ ʹ a loss in producer surplus.
Calculating A: Area A = [(1.50 + 1.20) ÷ 2] × 7500 - (1.20 × 7500) Area A = 10,125 - 9000 = 1,125
Calculating Area B: Area B = (1.20 × 7500) - [(1.10 + 1.20) ÷ 2] × 7500 Area B = 9000 - 8625 = 375
Deadweight Loss = A + B = $1500.
Arguments favoring the policy are the usual externality arguments regarding shared
health costs, lost worker productivity, and the dangers of second-hand smoke. The tax
may approximate costs that have not been reflected in the free market supply curve.
Tax revenue = tax * quantity Tax revenue = (0.40)(102,500)
Tax revenue = 41,000 per day or $14,965,000 per year.
The market demand and supply functions for Easton Redline slow-pitch softball bats are:
QD = 12 - 0.04P and QS = 0.01P + 2. Calculate the equilibrium quantity and price and point
elasticity of demand in equilibrium. Next, calculate consumer surplus. Suppose the Easton
bats are taxed $25 per unit. Calculate the revenues generated by the tax. Calculate the loss in
consumer surplus. What percentage of the burden of the tax is paid for by consumers? Answer:
First we must determine the market equilibrium quantity and price. To do this, we set
quantity demanded equal to quantity supplied and solve for equilibrium price.
QD = 12 - 0.04 P = QS = 0.01P + 2 ⇒ P = 200. At a price of $200, the quantity exchanged
will be 4. The point elasticity of demand is Ed = ΔQD ΔP P Q = -0.04 200 4 = -2. The choke
price (lowest price such that no units are transacted) is $300. The consumer surplus is CS = 1 2
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Document Summary
A country which does not tax cigarettes is considering the introduction of a sh. 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: what are the equilibrium values in the current environment with no tax? b. What portion of the tax would be borne by buyers and sellers respectively? c. Equate qd and qs to determine equilibrium price and quantity. Qs = 20,000 + 75,000(1. 10) qs = 102,500. A loss in c. s. and b a loss in producer surplus. Calculating a: area a = [(1. 50 + 1. 20) 2] 7500 - (1. 20 7500) area a = 10,125 - 9000 = 1,125.
