Ucla Econ 101 Final Spring 2011

1 Final Exam (VERSION 1) Econ 101 disport write your name at the top of every page of this mideterm transport write your name, TAs name, and the time of your discussion section here(predicate) Your Name TAs Name Discussion Time The trial run has one parts Written Questions. There should be 16 substance pages (front and back). Quickly read through the exam before beginning. There argon 100 total points available. Point values argon listed next to severally problem part. Please allocate your time accordingly 1 2 Written Questions 1. Consider the following comprisemento? ground substance 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) escort the pure strategy Nash equilibria of the simultaneous impale b. (5pnts) Now suppose the game is played sequentially. Find the subgame perfect equilibrium if instrumentalist 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) print down a system of equations such that the solution to the system would crumble a completely mixed strategy equilibrium of this game (please distinctly de? ne all of your notation). Can this system of equations be resolved? (Hint infer about the condition requiring player 1 to play B with positive(p) probability).Explain what the answer means. 2 run pose 3 WORK station 4 2. intend Player 1 and Player 2 argon 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 in that location any value of ? for which there is a dominant strategy equilibrium. If so, ? nd the values of ?. If not, show why. b. (5pnts) tell all the pure and mixed strategy equilibria of the game as a role of ? c. (5pnts) recollect ? = 5. What would the outcome be if the players could cooperate? 5 WORK SPACE 6 WORK SPACE 7 3.truncheon has just transmitted a horse ranch fro m 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. wand has devil types of potential customers novice passengers (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 argon 75 riders of each type in the town. Billys 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 expenditure discriminate. Find prices, quantities, and Billys pro? t. b. (5pnts) Suppose Billy crapper tell whos 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 twain types of rider. He decides to start charging a yearly membership fee, T , as well as an hourly 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 save 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 grow commercial aircraft. The demand for airplanes is given by Q = 10 ? P . Boeings 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 vicissitude that will lower marginal costs from 5 to 0.How a great deal would Boeing be willing to invest to implement the debut. (Assume Cournot Competition from here on) c. (5pnts ) Suppose that the innovation is such that Airbus can (imperfectly) duplicate it, so if Boeing makes the investment Airbus costs take up 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 throng in the world Sky Divers and Cat People. Both types withstand 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 precisely 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 redress 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 for insurance that covered half their losses? . (5pnts) What is the honorable 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. sop up 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 usage 14 WORK SPACE 15 WORK SPACE 16