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practice_ak - Practice Final Exam Answer Key Econ 11 Summer...

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Practice Final Exam Answer Key Econ 11 °Summer Session C 2008 University of California, Los Angeles The exam will be worth 100 points, 20 points per question. Handheld calculators are permitted. 1. Suppose the demand for student basketball tickets for UCLA games is given by Q = 8000 ° 40 P . (a) If the price UCLA charges for a student ticket is 10 dollars, what is the price elasticity of demand for tickets? ANSWER: The price elasticity of demand is e P Q = dQ dP P Q = ° 40 P 8000 ° 40 P and at P = 10 , this is e P Q = ° 40 10 8000 ° 400 = ° 1 19 (b) Suppose there is a secondary market on Craig±s List, which resells tickets according to the function Q = 40 P ° 80 . Calculate the market equilibrium price and the quantity of tickets sold. ANSWER: A secondary market will clear where demand equals sup- ply, so where 8000 ° 40 P = 40 P ° 80 8080 = 80 P P = 101 At this price, the market will demand Q (101) = 8000 ° 40 (101) = 3960 (c) What is the total consumer surplus at this price? What is the total producer surplus? ANSWER: We calculate the inverse demand in order to ²nd the price intercept: P = ° 1 40 Q + 200 . Inverse supply is P = 1 40 Q + 2 . Total consumer and producer surplus at this price is CS = 1 2 (200 ° 101) (3960) = 196 ; 020 PS = 1 2 (101 ° 2) (3960) = 196 ; 020 1
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(d) Suggest a method for the college to gain some of this surplus. Sketch your solution in a graph of the market. ANSWER: The college could charge a tax for those tickets that are used by students who were not the purchasers. Then the college would collect revenues 2. Consider two individuals A and B with the following utility functions for goods x and y . U A ( x; y ) = x 2 y U B ( x; y ) = xy (a) True or false: if both individuals have identical endowments, there would be no bene²t to trade. ANSWER: False. These individuals have di/erent marginal rates of substitution, which means that they are willing to trade consumption of these two goods at di/erent rates. Pareto optimal allocations would have 2 y A x A = y B x B which could not happen when x A = x B and y A = y B . (b) Now suppose A has an initial endowment of 20 units of good x and 10 units of good y , while B has an initial endowment of 10 units of good x and 20 units of good y . Calculate the demand functions for each individual assuming p x is the price of x and p y
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