Answer all parts

9. In the 1970's and 1980's, car theft was a major crime in the United States. Much of this illegal activity was part of an organized effort in which cars stolen cars were driven to "Chop Shops" and turned into about valuable components or given false new registration numbers and shipped overseas. Since 1991, however, auto theft has declined every year and is down about a 50% over the last decade. Many credit this decline to the use of Vehicle Recovery Systems (VRS) such as that marketed by LoJack (of Dedham, MA). These systems essentially make use of a homing device planted secretly in the car. As soon as the car is reported stolen, police can use a transmitter to locate the vehicle's location. This has led to the recovery of millions of vehicles. More importantly, the homing device has often led police directly to the "Chop Shop" itself thereby enabling authorities to close the entire operation down. The elimination of these criminal organizations is of course good news for all car owners whether they have a LoJack type system or not. Demand for Vehicle Recovery Systems is estimated to be: P = 4,800-0.30, where P is the price per system and O is the number (in thousands) of systems sold. That is, if equals 10,000 it really means 10 million systems were purchased. The cost of producing and maintaining a VRS is constant at about $600. a. What will be the price of a VRS and how many will be sold if the market is competitive? b. Is the competitive equilibrium described above likely to be efficient? Explain. 10. One thousand people live in Waterford, a small New England town with a water reservoir and pumping station. The total cost of delivering water is: TC= Q". Marginal cost is given by: 20. Average cost is given by: Q. Here, Q is measured in thousands of gallons per week. Weekly water demand is given by: P = 1200 -40 (where ( is again measured in thousands of gallons and P is the price per thousand gallon unit). The Waterford Water Board (which is hard to say) must set the same price for each gallon sold. a. What price should the Water Board set if it wants to maximize economic efficiency? How much water will it sell at this price? Explain. b. What price should the Water Board set if it wants to maximize the profit from selling water? How much water will it sell at this price? Explain c. What price should the Water Board set if it wants to maximize the amount of water consumed while still covering its costs? How much water will it sell at this price? Explain. d. Over time, the Water Board vacillates over each of the three policies described above. Can you explain this outcome? 11. The central input used by Matrix Enterprises in manufacturing its warp drives is the dilithium crystal. The revenue that Matrix earns from these drives is such that it is willing to pay as much as $10,000 per crystal and it will buy at this price or any lower price, exactly 10 crystals. Currently, the only manufacturer of such crystals is Aloca. Aloca can manufacture dilithium crystals at a cost of $5,000 apiece. However, there is a possibility that a new firm, Rexull, will enter into the production and marketing of dilithium crystals next period. Rexull is hard at work right now trying to develop a production process that is cost efficient. The outcome of this process is, as noted, probabilistic. To be specific, Rexull's cost per crystal as the result of its research is uniformly distributed on the interval, 0 to $10,000. In other words, there is a 10% chance that it will develop a process to produce crystals at a cost of less than $1,000; a 100% chance that it will develop a process to produce crystals at a cost between $1,000 and $2,000; and so on. a. Assume that if Rexull does not enter the market, Aloca can extract the entire surplus from Matrix and sell at a price of $10,000 per crystal. Assume as well that Rexull knows Aloca's cost and will only enter if its own cost is below $5,000. In light of the probabilities associated with Rexull's research, and given the Matrix will buy crystals from the firm with the lowest price, what is the actual probability that Rexull will be able to enter the market successfully next period? b. If Rexull does enter, what price will it charge? (Think carefully.) c. Given your answers to 1 la) and 1 1b) above, what price should Matrix expect to pay for each of its 10 dilithium crystals next period? What profit should Aloca expect to earn next period? 12. Return to Problem 11 above. Suppose now that Aloca offers Matrix a "long-term" contract. Specifically, suppose Aloca offers to sell Matrix dilithium crystals next period at a guaranteed price of $7,500 apiece. However, once signed, the contract is binding. Matrix must buy the 10 crystals and if it does not, it must pay a penalty of $5,000 per crystal ($50,000 overall). a. What is now the probability that Rexull will successfully enter the dilithium crystal market next period? What price will it charge Matrix if it does enter' b. Relative to the initial, no-contract scenario, is Matrix worse off, better off, or just as well off if it signs the contract? Relative to the initial scenario, does Aloca do better or worse if Matrix signs the contract?1:57 RM 0 B/s 7 attachment Final Exam 1. (20 points) The weekly demand for beer in Maltown is described by: P = 1000 -20, where O is measured as the number of six-packs consumed each week and P is the price of a six-pack. The marginal cost of producing a six-pack is constant at $8 and beer producers have no fixed costs. a. What is the equilibrium price and output if the Maltown beer market is perfectly competitive? What will the total amount of producer surplus in the competitive equilibrium? What will be the total amount of consumer surplus? b. What is the equilibrium price and output if the Maltown beer market is monopolized and the monopolist charges a single, uniform price to all consumers? What will be the value of producer surplus in this case? What will be the value of consumer surplus? c. What will be the equilibrium output if the Maltown beer market is monopolized but the monopolist can perfectly price discriminate? What will be the value of producer surplus in this case? What will be the value of consumer surplus? 2. (20 points) The Tower of London is a store of great treasure. It has been the seat of British government as well as the site of infamous political intrigue. It has housed notorious traitors, virtuous members of court, lions, bears, and ravens. Most famously perhaps, it has been and continues to be the repository of Britain's Crown Jewels. Almost as well-known as Her Majesty's Tower are the Yeoman Warders often called the Beefeaters who guard the fortress. It is an honor and a great privilege to serve as a Yeoman Warder. Historically, it was also a great opportunity to enrich oneself at the public expense. It seems that a few hundred years ago, when the Tower also served as the store for much of Britain's gold, many of the guards could not resist the temptation to steal the occasional gold coin out of the treasury. Of course, if a guard was caught stealing, the guard was summarily dismissed. It seemed impossible though to watch the Beefeaters constantly and make sure that they never took anything. To do that would require hiring a second layer of guards and that would be expensive. Historians of the Tower have noted that shortly after this problem emerged, the Crown raised the basic pay of a Yeoman Warder to f7 per year, notably higher then the going market wage rate at that time of f5 per year. Historians have also noted that to get a job as a Yeoman Warder it was not enough to apply. One also had to pay a big, up-front fee, i.e., any successful applicant had to make a one-time payment right at the start if they were actually to be hired. Comment on these developments. Why do you think that the British government decided to pay above market wages to its Beefeaters? Why do you think people paid to obtain Beefeater jobs? What other methods do you think the British monarchy might have used to achieve its objectives? 3. (20 points) In nearly each of the last 20 years, the faculty at Sloneybrook University has reviewed the course requirements that all of their students must fulfill to graduate. Such reviews are initiated in the Committee on Academic Policy (CAP), which is comprised of representatives from each of the academic departments. Proposed reforms typically include dropping some classes from the required list and adding in others. Any reform that is proposed by the CAP is then voted on by the entire Sloneybrook faculty. Yet despite this continuing effort, no major reform proposal has been adopted with the result that the set of courses required for the Sloneybrook degree has not changed in over two decades. In chronicling this failure, outsiders have noted the following features of the Sloneybrook decision-making process: a) departmental budgets and/or salaries are related to the number of students enrolled in departmental courses; b) there are a large number of required courses; c) faculty are risk averse; and d) the governance process is very inconsistent-the reform proposal that wins in one committee is later defeated in another committee or in a general faculty vote. Use these observations and what you know about group decision-making to analyze briefly the failure of the Sloneybrook faculty to reform its graduation course requirements. 4. (20 points) Imagine that Dry Gulch has two potential water suppliers. One is Northern Springs whose water is naturally carbonated but also somewhat "hard." The other is Southern Pellegrino whose water is crystal clear but not carbonated. The marketing department of each firm has worked out the following profit matrix depending on the price per 2 gallon container charged by each firm. Northern Spring's profits are shown as the first entry in each cell, e.g., if Northern Springs sets a price of 4 and Southern Pellegrino sets a price of 3, Northern Springs nets $25,000 in profits and Southern Pellegrino nets $30,000. Southern Pelligrino's Price is: 3 6 3 24,24 30,25 36.20 42,12 4 25,30 32,32 41.30 48.24 Northern Springs' Price Is: 5 20.36 30.41 40.40 50.36 12,42 24,48 36.50 48,48 a. Suppose that the two firms set their prices simultaneously. What is the (Nash) equilibrium? b. Suppose that Northern Springs must set its price first, and stick with it, while Southern Pellegrino then reacts as best it can to the choice of Northern Springs. What is the price equilibrium in this case? c. Does going first help or hurt Northern Springs? 5. (20 points) Consider the following data on the relative price-cost markups for selected cars in different European Countries in 1997. Here, the markup is measured as the percentage of the price by which the O