ECO 3306 Name:
Spring 2005
FINAL EXAMINATION
Answer the following questions in your bluebook. Clearly label your answers.
1. A consumer’s preferences over two goods are represented by the utility function 2121 ),( xxxxu
=
.
a. (2 points) Write down another utility function that represents the same preferences.
b. (8 points) Find the consumer’s generalized demand functions for the two goods,
),,(* 211 mppx and ),,(* 212 mppx .
c. (2 points) What is the equation for the consumer’s income-offer curve (also called the
income expansion path)?
d. (3 points) Suppose that the market for good 2 consists only of 1000 identical consumers
with these preferences, that the price of good 1 is $10, and that each consumer has an
income of $400. What is the market demand function, )( 2
pD ?
2. Another consumer’s preferences over two goods are represented by the utility function
2121 )ln(),( xxxxu += .
a. (6 points) Find the consumer’s generalized demand functions for the two goods,
),,(* 211 mppx and ),,(* 212 mppx .
b. (6 points) Suppose that )100,20,2(),,( 21
=
mpp . If 1
p increases to 4, find the income
and substitution effects of the price change on the consumption of good 1.
3. (3 points each) For a particular good, the demand function is given by
211 ln8.0ln5.1ln6.010ln PMPQ
−
+
−
=,
where 1
Q is the quantity demanded of good 1, 1
P is the price of good 1,
M
is the aggregate
income of all consumers in the market for good 1, and 2
P is the price of good 2.
a. Calculate and interpret the price elasticity of demand for good 1.
b. Calculate and interpret the income elasticity of demand for good 1.
c. Calculate and interpret the cross-price elasticity of demand for good 1.
4. The perfectly competitive market for street-vendor hot dogs is characterized by the demand
function ppD 2500000,15)( −= and the supply function 000,10000,10)( −
=
ppS , where p in
each function represents the price of a hot dog measured in dollars.
a. (4 points) Find the equilibrium price and quantity in this market.
b. (5 points) Suppose that the city imposes a tax of $1 per hot dog. How many hot dogs will
be sold under this taxation scheme? What price will hot dog consumers pay, including
the tax? What price will hot dog sellers actually receive after forwarding the tax to the
government?
