Sloan School of Management 15.010/15.011 Massachusetts Institute of Technology Economic Analysis for Business Decisions SAMPLE FINAL EXAMINATION (Similar to exam given Tuesday, December 17, 2002, 9:00 a.m. to noon) Answer all of the following nine questions (total of 540 points). On numerical questions, please place a box around your final answer. Please write your name and Sloan section on each book, and number your books. Leave the bottom of the front page blank, for the recording of grades. (Note: all prices are in dollars unless otherwise noted.) 1. True, False, Uncertain (63 points, 21 minutes). Decide whether each of the following three statements is true, false or uncertain. Most of the credit will be given for the explanation. (1a) Your company makes chairs in Western Massachusetts, and you have just obtained a large new order. Chairs produced in your Pittsfield plant cost $4.00 each on average, and those made in your North Adams plant cost $ 5.00 each on average. Transportation costs to your warehouse are the same from each plant. Therefore, you should order production increased in Pittsfield to cover the new order. (1b) Consider the following productivity matrix (expressed in dishes per minute). (It means that Richard, if he only washes dishes, can wash 8 dishes per minute.) The organization of tasks that maximizes the number of dishes that get washed and dried in one hour is that Richard washes dishes all the time and Gabriel dries dishes all the time. Wash dishes Dry dishes Richard 8 10 Gabriel 7 8 (1c) A local mattress store has the following ad: “5% LOW PRICE GUARANTEE – We promise to BEAT by 5% any advertised price that undercuts our price on comparable products.” Low price guarantees can sustain high prices.15.010/15.011 Final Exam (2002) p. 2 2. (45 points, 15 minutes) Consider the following game payoff matrix. B Left Middle Right Up 10, 1 3, -10 0, 3 A Middle 6, 10 4, 12 -4, 11 Down -5, 0 8, 5 1, 8 (2a) Define (in one sentence) a dominant strategy. (Start with ‘A dominant strategy is a strategy that ...’). Does A have a dominant strategy? If so, what? Does B have a dominant strategy? If so, what? (2b) Define (in one sentence) a Nash equilibrium. (Start with ‘A Nash equilibrium is a set of strategies, one for each player, such that ...’) Give all Nash equilibria of this game. (2c) If A could commit to an action, what action would it commit to? Suppose B could let A go first in choosing actions (i.e. make itself the second-mover). Would B do so? 3. (45 points, 15 minutes) Old McAdams had a farm. … And on this farm, he grows some corn. … To grow corn, he needs a tractor. A new tractor costs $120,000. There is a very liquid resale market for tractors; a tractor that is one year old sells for $85,000 and a tractor that is two years old sells for $45,000. For simplicity, assume that all tractors three or more years old cannot be used to grow corn and sell for $0. These prices are expected to stay the same in the future. The variable cost of producing corn is the same regardless of whether you are using a tractor that is new, one year old or two years old. (3a) Old McAdams faces an interest rate of 10%. What is the user cost of capital associated with using a new tractor for one year? What is the user cost of capital associated with using a one-year-old tractor for one year? What is the user cost of capital associated with using a two-year-old tractor for one year? (3b) Old McAdams is formulating a plan for growing corn for the next three years. What is the optimal arrangement for the necessary tractor input over the three years? (For instance, should he buy a new tractor and use it for three years, or something else?) (3c) Suppose instead that the interest rate is 0 % (and that present value over the three years involves no discounting). Now suppose that Old McAdams can resell a one-year-old or two-year-old tractor as above, but must pay a broker fee of $ 10,000 for each sale. Three-year-old tractors are junked, which does not require paying a broker fee. Now, what is the optimal arrangement for the necessary tractor input over the three years? Explain your answer. (Assume that at the end of the three year period, a tractor must either be sold or junked.)15.010/15.011 Final Exam (2002) p. 3 4. (60 points, 20 minutes) There are more amusement parks in Orlando, Florida than anywhere in the country. 10,000 visitors arrive daily and buy tickets for rides on the roller coasters. Each ride requires one ticket. Each person’s demand for rides is given by P = 10 – 2Q, and the average cost of providing rides on roller coasters is constant at $2 each. (4a) Given the large number of amusement parks, assume that the market for rides is perfectly competitive. What is the equilibrium ticket price; the quantity of tickets sold; consumer surplus; producer surplus? (4b) Suppose that all parks are owned by one firm, Big D. Big D decides to charge an admission fee for each park, as well as a ticket price per ride. What is the optimal admission fee and ticket price? What are total profits to Big D? How does the total surplus compare to the solution in (4a)? (4c) There are actually 2 groups of people who go to the parks, 2000 local Floridians and 8000 tourists who travel great distances to get there. The demand for each tourist is still P = 10 – 2Q, but each local’s demand is P = 10 – 4Q. Local’s can be identified because they have Florida ID cards. Now, what is the optimal admission fee and ticket price for locals? What is the optimal admission fee and ticket price for tourists? What are total profits now? (4d) Given your answers to (4c), what would a tourist be willing to pay for a fake Florida ID card? 5. (45 points; 15 minutes) The rock band U2 is coming to Boston to perform at Gillette Stadium, and you are in charge of pricing and selling the tickets (assume all seats are the same and you only need to set a single price). Independent of the number of seats sold, you must pay the administration of Gillette Stadium a fixed amount of $ 500,000 (to cover security and cleaning costs), which represents the only cost. There are 50,000 seats in Gillette Stadium. (5a) One month prior to the concert, U2’s newest album is released, with rave reviews about how the band is much better than they have ever