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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.
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ECO 3306 Name: Spring 2005
FINAL EXAMINATION
Answer the following questions in your bluebook. Clearly label your answers.
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 )?
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.
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.
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?
( )= 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.
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?
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?