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ECO 3306 Spring 2005 Final Exam: Microeconomics Questions, Exams of Microeconomics

The final exam questions for a microeconomics course, eco 3306, offered in spring 2005. The exam covers various topics such as consumer preferences, demand functions, income elasticity, price elasticity, cross-price elasticity, market equilibrium, monopolies, and game theory. Students are required to answer questions related to utility functions, generalized demand functions, income expansion paths, market demand functions, price elasticity, income elasticity, cross-price elasticity, equilibrium price and quantity, taxation, long run equilibrium, monopoly quantity and price, profit, deadweight loss, and perfect price discrimination.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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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?
pf3

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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 u ( x 1 , x 2 )= x 1 x 2.

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, x 1 (^) * ( p 1 , p 2 , m )and x 2 (^) * ( p 1 , p 2 , m ). 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, D ( p 2 )?

  1. Another consumer’s preferences over two goods are represented by the utility function u ( x 1 , x 2 )= ln( x 1 )+ x 2.

a. (6 points) Find the consumer’s generalized demand functions for the two goods, x 1 (^) * ( p 1 , p 2 , m )and x 2 (^) * ( p 1 , p 2 , m ). b. (6 points) Suppose that ( p 1 (^) , p 2 , m )=( 2 , 20 , 100 ). If p 1 increases to 4, find the income and substitution effects of the price change on the consumption of good 1.

  1. (3 points each) For a particular good, the demand function is given by

ln Q 1 (^) = 10 − 0. 6 ln P 1 + 1. 5 ln M − 0. 8 ln P 2 ,

where Q 1 is the quantity demanded of good 1, P 1 is the price of good 1, M is the aggregate income of all consumers in the market for good 1, and P 2 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.

  1. The perfectly competitive market for street-vendor hot dogs is characterized by the demand function D ( p )= 15 , 000 − 2500 p and the supply function S ( p )= 10 , 000 p − 10 , 000 , 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?

  1. (15 points) The market for lawn service in a large city is perfectly competitive. Monthly demand in the market is given by the function Q (^) D = 5 , 250 , 000 − 26 , 250 P , where Q (^) D is quantity demanded measured in number of lawn service visits per month, and P is the price of one lawn service visit. Each lawn service firm utilizes a technology represented by the long run cost function c Q Q Q 100 Q 5

( )= 3 −^2 + , where Q is the number of lawn service visits provided

per month by the firm. For the market’s long run equilibrium, find (a) the number of lawn service visits for each firm (b) the equilibrium price of lawn service visits, (c) the total number of lawn service visits per month in the whole market, and (d) the number of firms that will be in the market.

  1. Dora the Explorer is the delightful star of a series of children’s videos. Inverse demand for Dora

videos is given by PD Q 100 , 000

= 50 − , where PD is the price charged for Dora videos in

dollars, and Q is the quantity of Dora videos demanded. Because of the nature of video production, Dora videos have a high fixed cost but a low, constant marginal cost. This technology is represented by the cost function c ( Q )= 30 , 000 , 000 + 5 Q , where Q is the quantity of videos produced, and c ( Q ) is measured in dollars. Because Dora videos are protected by copyright laws, the copyright owner has a monopoly on the production and sale of Dora videos.

a. (8 points) Find the monopoly quantity and price for Dora videos. b. (2 points) How much profit will the owner of Dora videos earn? c. (2 points) Calculate the deadweight loss of the monopoly. d. (3 points) Suppose that the owner Dora videos could engage in perfect (“first-degree”) price discrimination. What would its profit be? What would be the deadweight loss?

  1. (5 points each) Jerry’s Java and Connie’s Coffee Haus are the only two espresso shops in a small

college town. Daily inverse demand for espressos is PD Y Y 90

( )= 11 − , where PD is the price of

one espresso in dollars, Y = yJ + yC , y (^) J is the quantity of espressos sold by Jerry’s Java, and y (^) C is the quantity of espressos sold by Connie’s Coffee Haus. Both shops produce espresso at a constant marginal cost of 50 cents and no fixed costs.

a. Find the Cournot-Nash equilibrium price and quantity in this market. How much profit will each firm make in a Cournot-Nash equilibrium? b. Find the Bertrand-Nash equilibrium price and quantity in this market. How much profit will each firm make in a Bertrand-Nash equilibrium?