Ucla Econ 101 Final Spring 2011

1 Final Exam (VERSION 1): Econ 101 †¢ Please write your name at the top of every page of this mideterm †¢ Please write your name, TA’s name, and the time of your discussion section here Your Name: TA’s Name: Discussion Time: †¢ The exam has one parts: Written Questions. †¢ There should be 16 total pages (front and back). Quickly read through the exam before beginning. †¢ There are 100 total points available. Point values are listed next to each problem part. Please allocate your time accordingly 1 2 Written Questions 1. Consider the following payo? matrix Player L M T 2, 0 3, 1 Player 1 C 3, 4 1, 2 B 1, 3 0, 2 2 R 4,2 2,3 3,0 . (5pnts) Find the pure strategy Nash equilibria of the simultaneous game b. (5pnts) Now suppose the game is played sequentially. Find the subgame perfect equilibrium if player 1 goes ? rst and if player 2 goes ? rst. c. (5pnts) Discuss whether each of the players would want to go ? rst or second. d. (5pnts) Write down a sy stem of equations such that the solution to the system would give a completely mixed strategy equilibrium of this game (please clearly de? ne all of your notation). Can this system of equations be solved? (Hint: think about the condition requiring player 1 to play B with positive probability).Explain what the answer means. 2 WORK SPACE 3 WORK SPACE 4 2. Suppose Player 1 and Player 2 are playing a simultaneous move game with the following payo? matrix: Player 2 L R T 0, 4 ? , 3 Player 1 B 3, 3 4, 6 where ? ? 0 a. (5pnts) De? ne a dominant strategy equilibrium. Is there any value of ? for which there is a dominant strategy equilibrium. If so, ? nd the values of ?. If not, show why. b. (5pnts) Describe all the pure and mixed strategy equilibria of the game as a function of ? c. (5pnts) Suppose ? = 5. What would the outcome be if the players could cooperate? 5 WORK SPACE 6 WORK SPACE 7 3.Billy has just inherited a horse ranch from his uncle. The ranch is located in Oshkosh, WI and rents horses. A unique feature of the stable is the nearby riding trails that overlook Lake Winnebago. Billy has two types of potential customers: novice riders (N) and serious riders (S). The (per customer) demand for horse rides on the ranch is qS = 75 ? 1. 25PS , where qS is the number of hourlong rides a serious rider makes per year. The demand for novice riders is qN = 57 ? 1. 25PN . Assume there are 75 riders of each type in the town. Billy’s cost function is T C = 12q, where q is the total number of hours the horses are ridden per year. . (5pnts) Suppose Billy does not price discriminate. Find prices, quantities, and Billy’s pro? t. b. (5pnts) Suppose Billy can tell who’s a serious rider because of the types of hat they ware. Find the 3rd degree price discriminating prices, quantities and pro? ts. c. (5pnts) Suppose Billy is not able to tell the di? erence between the two types of rider. He decides to start charging a yearly membership fee, T , as well as an h ourly price, p. Find the optimal choices of T and p d. (5pnts) Suppose Billy IS able to tell the di? erence between the two types of but still thinks the 2-part tari? is a good idea.Find the annual fee and per hour price that Billy would charge to each group 8 WORK SPACE 9 WORK SPACE 10 4. (16pnts) Boeing and Airbus are the 2 ? rms that produce commercial aircraft. The demand for airplanes is given by: Q = 10 ? P . Boeing’s costs are given by T CB = cB qB and Airbus’ costs are given by: T CA = cA qA where cA , cB are constants. a. (5pnts) Find the Cournot quantities, prices and pro? ts. Find Stackelberg quantities, prices, and pro? ts assuming Boeing chooses output ? rst b. (5pnts) Suppose that right now cB = cA = 5. Boeing has access to a process innovation that will lower marginal costs from 5 to 0.How much would Boeing be willing to invest to implement the innovation. (Assume Cournot Competition from here on) c. (5pnts) Suppose that the innovation is such that Airbu s can (imperfectly) copy it, so if Boeing makes the investment Airbus’ costs fall to 2. How much is Boeing willing to pay now? d. (5pnts) If Airbus can perfectly copy the innovation, how much would Boeing be willing to pay? Why is Boeing willing to pay a positive amount? 11 WORK SPACE 12 WORK SPACE 13 5. There are two types of people in the world Sky Divers and Cat People. Both types have wealth W = 100 and utility functions U (W ) = ln(W ).Both types of people can have an accident that leads them to lose $50 of wealth. Sky Divers are riskier and have accidents 75% of the time, while Cat People have accidents only 25% of the time. The proportion of Sky Divers in the economy is pS and the proportion of Cat People is pC = 1 ? pS a. (5pnts) How much would each type be willing to pay for an insurance policy that fully reimbursed them in the event of an accident? b. (5pnts) Write down the equations that, if you solved them, would give the amount each type would be willing to pay f or insurance that covered half their losses? . (5pnts) What is the fair price of (full) insurance for each type (i. e. if an insurer knows which type he is dealing with)? What is the fair price if the insurer cannot distinguish the two types? d. (5pnts) Assume insurers cannot distinguish the two types and that insurance markets are competitive so prices are the fair prices. Describe prices and who is insured in equilibrium as a function of pS e. (5pnts) Discuss the meaning of adverse selection in the context of this example 14 WORK SPACE 15 WORK SPACE 16