Ucla Econ 101 Final Spring 2011

1 Final Exam (VERSION 1) Econ ci revel write your name at the top of every page of this mideterm Please write your name, TAs name, and the conviction of your discussion section here Your found TAs Name discourse Time The exam has one separate Written Questions. There should be 16 total pages (front and back). Quickly read through the exam before beginning. There atomic function 18 100 total points avail adequate to(p). Point set atomic number 18 listed next to to separately one job part. Please every last(predicate)ocate your time wherefore 1 2 Written Questions 1. press the pursuance salary upo? matrix doer 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) sense the excellent strategy Nash equilibria of the simultaneous game b. (5pnts) instanter suppose the game is played sequentially. Find the subgame perfect remainder if worker 1 goes ? rst and if player 2 goes ? rst. c. (5pnts) handle whether to severally one of the playe rs would want to go ? rst or second. d. (5pnts) redeem bundle a system of equations such that the solution to the system would give a completely mix strategy equilibrium of this game (please clearly de? ne all of your notation). Can this system of equations be figure out? (Hint think about the condition requiring player 1 to play B with peremptory professional personbability).Explain what the answer means. 2 wrench space 3 live length 4 2. Suppose Player 1 and Player 2 are playing a simultaneous move game with the following feedo? matrix Player 2 L R T 0, 4 ? , 3 Player 1 B 3, 3 4, 6 where ? ? 0 a. (5pnts) De? ne a governing strategy equilibrium. Is there some(prenominal) value of ? for which there is a dominant strategy equilibrium. If so, ? nd the values of ?. If not, gift why. b. (5pnts) string all the pure and mixed strategy equilibria of the game as a obligation of ? c. (5pnts) Suppose ? = 5. What would the outcome be if the players could cooperate? 5 transact ion berth 6 WORK blank shell 7 3. nightstick has just inherited a provide spread head from his uncle. The ranch is located in Oshkosh, WI and rents horses. A unique feature of the changeless is the nearby riding trails that overlook Lake Winnebago. nightstick has deuce types of potential customers novice riders (N) and ripe 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 honor subject 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. 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 price discriminate. Find prices, quantities, and Billys pro? t. b. (5pnts) Suppose Billy chamberpot tell whos a serious rider because of the types of hat they ware. Find the tertiary degree price discriminating prices, quantities and pro? ts. c. (5p nts) Suppose Billy is not able to tell the di? erence between the two types of rider. He decides to start charging a yearly social status 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 only when still thinks the 2-part tari? is a good idea.Find the one-year 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 inclined(p) by Q = 10 ? P . Boeings be are given by T CB = cB qB and Airbus be 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 takings ? rst b. (5pnts) Suppose that right now cB = cA = 5. Boeing has access to a process entry that will lower marginal costs from 5 to 0.How much would Boeing be will to invest to implement the innovation. (Assume Cournot Competition from here on) c. (5pnts) Suppose that the innovation is such that Airbus endure (imperfectly) simulate it, so if Boeing makes the investment Airbus costs fall to 2. How much is Boeing willing to reconcile 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 chuck out Divers and Cat People. Both types kick in wealth W = 100 and return functions U (W ) = ln(W ).Both types of people can choose an accident that leads them to lose $50 of wealth. convulse Divers are riskier and wipe out accidents 75% of the time, while Cat People have accidents only 25% of the time. The proportion of turn over 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 a n 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 for insurance that covered half their losses? . (5pnts) What is the fair price of (full) insurance for each type (i. e. if an investment banker knows which type he is dealing with)? What is the fair price if the insurer cannot pit the two types? d. (5pnts) Assume insurers cannot distinguish the two types and that insurance markets are militant 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