Econ 302 Homework #5

1. (20 points) Suppose a public referendum is being held on whether or not to levy a tax on cigarettes.
Currently, the supply of cigarettes is given by Qs = -120 + 28P. You estimate the demand for cigarettes
to be Qd = 200 - 4P.
You are asked to evaluate the likely effects of a tax on cigarettes equal to $2 per pack of cigarettes.
Specifically, you are to file a report which predicts by how much this will reduce the amount of cigarettes
sold. You are also asked to estimate the proportion of the tax that will be paid by the cigarette companies
(sellers), and the proportion of the tax that will be paid by the smokers (consumers) of cigarettes.
To do this, you will first need to calculate the current price and quantity of cigarettes sold.
a) (2 points) What is the equilibrium price and quantity of cigarettes?

Next you know from your economics class that you will need to know the price elasticity of demand and
the price elasticity of supply of cigarettes. (Note: for parts b-e, please leave your answers in the form
of a fraction.)
b) (4 points) What is the price elasticity of demand for cigarettes at the equilibrium price?

c) (4 points) What is the price elasticity of supply of cigarettes at the equilibrium price?

Using your answers to b) and c), you are now able to determine what proportion of the tax will be paid by
buyers, and what proportion of the tax will be paid by sellers.
d) (4 points) What proportion of the tax will be paid by sellers?

e) (2 points) What price will buyers pay after the tax is imposed?

f) (2 points) What quantity of cigarettes will be sold after the tax?

g) (2 points) What is the deadweight loss from the tax?

2. (18 total points) ) Suppose there are two types of consumers. The demand for each type of consumer is
given by:



Type A: Q = 70 2P
Type B: Q = 60 3P

Suppose a monopolist has constant marginal cost = 6. Also, for parts a-b, assume that the monopolist is
unable to distinguish between the two types of consumers.
a) (4 points) What price should the monopolist charge?

b) (2 points) How much profit will this monopolist make?

Now suppose the monopolist is able to distinguish between the two types of consumers and can
effectively price discriminate between them.
c) (4 points) What price should the monopolist charge to each type of consumer?
Price to type A consumers:

Price to type B consumers:

d) (4 points)How much total profit does the price discriminating monopolist make?

e) (2 points) Calculate the price elasticity of demand for Type A consumers at the monopolists profit
maximizing price.

f) ) (2 points) Calculate the price elasticity of demand for Type B consumers at the monopolists profit
maximizing price.

3. (12 points) For Each of the following observations, check to see if the choices satisfy the Weak Axiom
of Revealed Preference (WARP). If it does satisfy WARP, give as much information about the
consumers ranking of the bundles as possible. If it violates WARP, simply write It violates WARP.
a)
Observation
1
2
3

PX
3
1
3

PY
1
4
2

X
2
4
2

Y
4
1
3

PX
1
3
2

PY
5
2
4

X
3
2
1

Y
2
1
4

b)
Observation
1
2
3