ECO 340
Problem Set 5
Due on Thursday October 29th at the beginning of class
You must show how you arrived at every single answer on the problem set. You will
receive ZERO credit for any answer where you don’t show your work.
1. (30 pts) Suppose you are an aide to a U.S. Senator who is concerned about the
impact of a recently proposed excise tax on the welfare of her constituents. You
explained to the Senator that one way of measuring the impact on her constituents
is to determine how the tax change affects the level of total surplus enjoyed by the
constituents. Based on your arguments, you are given the go-ahead to conduct a
formal analysis, and obtain the following estimates of demand and supply:
.
a. (5 pts) What are the equilibrium quantity and equilibrium price in this market?
b. (5 pts) Graph the market equilibrium and identify the consumer surplus, the
producer surplus and the total surplus in this market.
c. (5 pts) Compute the price elasticities of demand and supply at the market
equilibrium.
d. (5 pts) If a $2 excise tax is levied on the firms that produce this good, what will
happen to the price paid by consumers, the price received by firms, and the
quantity traded in the market?
e. (5 pts) What is the incidence of this tax on consumers and producers? Explain
why the incidence of the tax is split this way?
f. (5 pts) Graph the market equilibrium and identify the new consumer surplus,
the producer surplus, the government revenue, and the dead weight loss. What
is the change in consumer and producer surplus associated with the tax.
2
(20 pts) Suppose that the market for cigarettes is initially in equilibrium and is
perfectly competitive. The demand curve can be expressed as P = 60 − Q d ; the
supply curve can be expressed as P = 0.5Q s . Quantity is expressed in millions of
boxes per month.
a. (10 pts) What are the equilibrium quantity and equilibrium price in this market?
Graph the market equilibrium and identify the consumer surplus, the producer
surplus, and the total surplus in this market
ECON 340
Fall 2005
1
b. (10 pts) Now suppose that the federal government imposes a production quota
on cigarettes of 30 million boxes per month. Graph the new market equilibrium
and identify the new consumer surplus, producer surplus, total surplus. What is
the deadweight loss (per million boxes), the change in consumer surplus (per
million boxes) and the change in producer surplus (per million boxes)
associated with the quota?
3. (20 pts) In a perfectly competitive market, the market demand curve is given by
Qd = 200 − 5Pd, and the market supply curve is given by Qs = 35Ps.
a. (4 pts) Find the equilibrium market price and quantity demanded and
supplied in the absence of price controls.
b. (4 pts) Graph the market equilibrium and identify the consumer surplus,
the producer surplus, and the total surplus in this market
c. (4 pts) Suppose a price ceiling of $2 per unit is imposed. What is the
quantity supplied with a price ceiling of this magnitude? What is the size
of the shortage created by the price ceiling?
d. (4 pts) Assume that rationing of the scarce good is as efficient as possible.
What is the total surplus in this case? Does the price ceiling result in a
deadweight loss? If so, how much is it?
e. (4 pts) Find the consumer surplus and producer surplus under the price
ceiling, assuming that the rationing of the scarce good is as inefficient as
possible. What is the net economic benefit in this case? Does the price
ceiling result in a deadweight loss? If so, how much is it?
4. (30 pts) The domestic demand curve for headphones is given by Qd = 5000 −
100P. The domestic supply curve for headphones is given by Qs = 150P. Suppose
headphones can be obtained in the world market at a price of $10 per headphone.
a. (10 pts) Draw a graph illustrating the free trade equilibrium. Clearly illustrate the
equilibrium price, the amount produced domestically, and the amount imported.
Estimate and clearly identify in your graph the domestic consumer surplus and the
domestic producer surplus.
b. (10 pts) Domestic headphone producers have successfully lobbied Congress to
impose a tariff of $5 per headphone. Draw a graph illustrating the equilibrium
with the tariff. Clearly illustrate the equilibrium price, the amount produced
domestically, and the amount imported. Estimate and clearly identify in your
graph the domestic consumer surplus, the domestic producer surplus, the
government revenue, and the deadweight loss from the tariff.
c. (10 pts) Suppose the government imposed a trade prohibition (quota = 0) Draw
a graph illustrating the equilibrium with the trade prohibition. Clearly illustrate
the equilibrium price, the amount produced domestically, and the amount
imported. Estimate and clearly identify in your graph the domestic consumer
surplus, the domestic producer surplus, and the deadweight loss from the trade
prohibition.