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Unformatted text preview: Economics 3010
Fall 2008 Professor Daniel Benjamin
Cornell University FINAL EXAM You have 150 minutes for this exam. No calculators are allowed. There are 120 points on the exam, and you should plan to spend approximately as many minutes per question as they are worth in points. This should leave you ten minutes at the beginning to read over the test and twenty minutes at the end to check your answers. Please do all of the questions on this exam. Use a separate blue book for each part of the exam (I, II, III, IV, and V), five in total. On the cover of each blue book, please write your name, your TA’s name, your section time, and the part of the exam answered in that book. Read over the whole test before starting. To keep the test as fair as possible, we will only answer questions during the first ten minutes. Some advice: Complete answers will include definitions of relevant terms and verbal intuition (in addition to graphs or formulas, if those are appropriate). Do not get hung up on calculations when answering a question. If you get the formulas and explanation correct, little credit will be deducted for mistakes in calculation. The questions vary in difficulty, so try to keep moving through the exam; if you are having trouble with something, it is probably a good idea to skip it and come back later. Good luck! I. True / False / Uncertain Your grade on these questions will depend on the generality, completeness, and persuasiveness of your explanation, not simply on whether the “true” or “false” is correct. The objective here is to provide an answer that convinces; not merely an answer that is “not wrong.” At the very least, make sure that you give clear definitions for the relevant economic terms used in the question. Please use a separate blue book for this section. (5 points) 1) If Ann’s (ordinal) utility function is UA(a, b) = a + b and Bob’s utility function is B
U (a, b) = (a + b) , then Ann and Bob have the same preferences. (5 points) 2) If cars become more energy‐efficient, then individuals’ consumption of gasoline will surely decrease. (5 points) 3) If demand for a good is inelastic, then government policies designed to restrict supply of the good will actually increase revenues accruing to suppliers. (5 points) 4) Clean air is a public good. (5 points) 5) Total surplus is always higher when a market is perfectly competitive rather than dominated by a monopolist who can perfectly price‐discriminate. (5 points) 6) If individuals who already have a lot of cavities are more likely to buy dental insurance, that is an example of adverse selection. (5 points) 7) The Net Present Value (NPV) of an investment project (that has immediate costs and generates delayed benefits) will generally fall when the interest rate rises. (5 points) 8) The No‐Arbitrage Condition implies that all risky assets will have the same rate of return. II. Brief Problem #1 (10 points) Imagine that Native Alaskans have been hit hard by the rising costs of heating oil. A state agency is considering two alternative solutions: (i)
Subsidize the Native Alaskans’ purchases of heating oil. (ii)
Take the money that would have been spent on the subsidy program and give it to the Native Alaskans. Assuming administrative costs of each option is zero, which of the two plans would the aid recipient
prefer? Which of the two plans leads to higher use of heating oil by the aid recipient? In answering these questions, you can assume that the aid recipient’s optimum is interior (i.e., not a corner solution). Draw a budget constraint / indifference curve diagram to illustrate your answers. III. Brief Problem #2 (10 points) Bob Vila sells building materials in a competitive industry. He receives $100 for each unit of material sold. The table below presents how output changes as additional units of labor are hired. Bob hires workers from a competitive labor market. Labor Output Units of Labor 1 5 2 9 3 12 4 14 5 15 How many employees should Bob hire if the market‐determined wage per work period is $150? How (if at all) would your answer change if the going wage increased to $250? How (if at all) would your answer change if Bob also has a weekly fixed cost of $400 in addition to his variable cost of labor? What would the opportunity cost of Bob’s own time have to be in order for it to be optimal for him to permanently close his business? Explain the economic intuition for your answers. IV. Multi‐Part Problem #1 Note: This question is designed so that if you skip part of the question, you still have enough information (stated explicitly earlier in the question) to answer later parts of the question. Please answer as many parts as you can. Consider the market for news in a small town. Suppose there are fixed costs, C = 20, associated with running a newspaper (e.g., hiring reporters, establishing distribution routes, contracting with printing companies), but the marginal cost of printing additional copies of the newspaper is zero. However, the number of copies of the newspaper to be printed must be decided in advance because setting up the infrastructure takes time. The town residents care about getting news, but not whom they get it from; regardless of the number of newspaper‐producing firms, all newspapers are perfect substitutes for the consumers. The (inverse) demand function for the total number of newspapers purchased from all firms, y, is given by: p(y) = 24 – 2y. (5 points) (a) Assuming the market were perfectly competitive, draw a supply/demand diagram. Show that the competitive equilibrium price and quantity are p*comp = 0 and y*comp = 12. What would a competitive newspaper‐producing firm’s profit be? Explain why perfect competition cannot persist in this market. (7 points) (b) Suppose that a single firm, the Leader Ledger, emerges as a monopolist in this market. Show that the Ledger’s marginal revenue curve is given by MR(y) = 24 – 4y. Show that monopoly price and quantity are p*monop = 12 and y*monop = 6. On a diagram, illustrate the demand curve, the monopolist’s marginal revenue curve, and the monopolist’s profit. (3 points) (c) Now suppose a new firm, the Follower Journal, makes plans to enter the market. As the incumbent, the Ledger can set its own output level, y1, before the Journal sets its output level, y2. Show that the Journal’s marginal revenue function is given by MR2(y1, y2) = 24 – 2y1 – 4y2. Show that the Journal’s optimal output as a function of the Ledger’s output is y2*(y1) = (12 – y1) / 2. (5 points) (d) Show that the Ledger’s marginal revenue function (taking into account theJournal’s response optimal response from part c, y2*(y1)) is MR1(y1) = 12 – 2y1. Show that the Stackelberg equilibrium price and quantities are p*stac = 6, y1*stac = 6, and y2*stac = 3. Explain why the Ledger will survive in this market, while the Journal will go out of business. (7 points) (e) Instead of going out of business, the Follower Journal is acquired by National News Corporation (NNC). NNC has a strict corporate policy requiring affiliated newspapers to act as aggressive competitors in any market. Hence, the Ledger and the Journal now simultaneously choose their production capacities. Explain why the two firms’ marginal revenue functions (taking into account the other’s response) are MR1(y1, y2) = 24 – 2y2 – 4y1 and MR2(y1, y2) = 24 – 2y1 – 4y2. Show that the Cournot equilibrium price and quantities are p*cour = 8, y1*cour = 4, and y2*cour = 4. What will each firm’s profit be? (3 points) (f) Suddenly, the Internet becomes widely available to consumers. Now that there is no need to distribute print copies of the news, the only decision the firms must make is how much to charge consumers for an on‐line newspaper subscription. Explain why the Bertrand equilibrium prices are p1*bert = p2*bert = 0. Explain why one of the firms will go out of business. V. Multi‐Part Problem #2 Note: This question is designed so that if you skip part of the question, you still have enough information (stated explicitly earlier in the question) to answer later parts of the question. Please answer as many parts as you can. Two firms have agreed to collude. Now each must decide whether to keep prices high (as agreed) or to cheat. If both firms keep prices high, then each will earn profit of $2 billion. If both cheat, then each will earn profit of $0 billion. If one keeps prices high and the other cheats, then the cheater will earn $3 billion, while the other firm earns ‐$3 billion. (5 points) (a) Draw the normal form for this game (assuming that each firm seeks only to maximize profit). Is there a dominant strategy? What is the Nash equilibrium? (4 points) (b) Suppose that the two firms can write a legally‐enforced contract. What does the Coase theorem predict will occur? (5 points) (c) Unfortunately for the firms, a contract promising (illegal) anti‐competitive behavior (as in part b) will not be enforceable in court. However, suppose that the firms’s cheating decision is repeated. In particular, they will face the same decision about whether to cheat every year from now on, forever, and the interest rate is 10%. Explain why the following two observations are true: • Maintaining collusion forever has a present value of $20 billion. • Consider this sequence of events: in the first year, firm 1 cheats, while firm 2 keeps prices high; thereafter, both firms always cheat. The present value of this sequence of events is $3 billion for firm 1 and ‐$3 billion for firm 2. (4 points) (d) In the repeated game described in part c, consider the “punishment strategy”: keep a high price as long as the other firm has always maintained a high price in the past; otherwise cheat. Explain why, if both players follow this punishment strategy, it is optimal for each player to collude in every period. Explain why it follows that it is a Nash equilibrium (of this infinitely‐repeated game) for both firms to follow this punishment strategy. (7 points) (e) Now suppose once again that there is no repetition; the firms must make a once‐
and‐for‐all decision about whether to collude. However, each firm elects a new Chief Executive Officer (CEO), and the two CEOs happen to be friends. In particular, each CEO does not only care about his own success but also cares about his friend’s success, so the players’s Bernoulli utility functions are: u1 = π1 + ½ π2 u2 = π2 + ½ π1. With the payoffs being the players’s Bernoulli utilities, explain why the normal form of the game is now: Keep Cheat Keep (3, 3) (‐1.5, 1.5) Cheat (1.5, ‐1.5) (0, 0) Firm 1 Firm 2 Find the three Nash equilibria. (5 points) (f) One of the CEOs is worried about potential miscoordination, so she takes the initiative and sets her price before her friend does. Draw the extensive form for this sequential‐move game (that has the same Bernoulli utility payoffs as in part e). What is the unique subgame perfect equilibrium? ...
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