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Final Exam Outline of Answers Principles of Microeconomics Prof. A. Waldkirch EC 133, Sections C and D Fall 2006 December 13, 2006 Final Exam Outline of Answers 1. A recent newspaper report states that “Hawaiian Tropic Zone is just the latest in a series of outsized restaurants that have moved into Manhattan, where space is at a true premium but where entrepreneurs who are able to rent huge and sell theater along with food to make it work financially have caught on big time. In the Meatpacking District alone, cavernous, hyper-styled Morimoto and Buddakan are doing numbers that might even make Applebee's envious — 900 on an average Saturday night for the latter. Nearby, Tom Colicchio's Craftsteak seats 120 in a space so huge the waiter will walk you to the restroom rather than expecting you to leave a trail of crumbs.” Assuming that owners of restaurants are profit-maximizers and that overall demand for restaurant meals has not changed, can you think of an explanation why restaurants are increasing in size? (4 points) The restaurant industry must be characterized by increasing returns to scale. Thus, greater scale will reduce average cost. A hint that this is indeed the explanation can be found in the newspaper report when it states that in Manhattan, “space is at a true premium”, i.e. the fixed cost of a restaurant in the form of rent must be very high, which gives rise to increasing returns to scale. 2. You won a free ticket to see a Jay-Z concert (which you cannot re-sell). LL Cool J is performing on the same night and is your next-best alternative activity. Tickets to see LL Cool J cost $95. On any given day, you would be willing to pay up to $200 to see LL Cool J. Assume that there are no other costs of seeing either performer. (8 points) a) Based on this information, what is the opportunity cost of seeing Jay-Z? The opportunity cost of seeing Jay-Z is missing out on the LL Cool J concert. Your net benefit of that concert would have been $200 - $95 = $105. 1 b) Based on this information, which concert will you attend? You cannot tell without more information, since the question does not say how much you value Jay-Z. If you valued Jay-Z by more than $105, you would go see him, else you would go see LL Cool J. 3. Consider the oligopolistic game consoles industry. Suppose that there are only two firms, Sunny and Cher. Suppose that each company advertises to differentiate its product from the other company’s. The following matrix shows the payoffs for the two firms (in millions of dollars). (20 points) Cher Advertise Not advertise Sunny Advertise 11 \ 11 16 \ 9 Not advertise 9 \ 16 14 \ 14 a) What is the non-cooperative Nash equilibrium, if any, if this is a one-shot game, i.e. the firms interact only one time? Both firms would advertise since irregardless of the action of the other firm, advertising provides a higher payoff/profit. b) If it is legal to write a binding contract, what is the cooperative solution to this game that the firms would outline in their contract? The would commit to not advertising since the profit for each firm would then be higher. c) If it is not legal to write a binding contract, how could the two firms achieve the cooperative solution nonetheless if they interact repeatedly? Yes. They could play tit-for-tat. They both commit to not advertising, but when one firm deviates and advertises nonetheless, they would obtain the higher payoff once; in subsequent periods, however, the other firm would retaliate and advertise also, leading to losses relative to the cooperative outcome. If this is a credible strategy and the firms interact a sufficient number of times, the cooperative outcome could still be achieved. 2 d) Suppose that Cher (only) now has a third option, advertising less. As a result, its payoff would increase by $1 million relative to advertising heavily. Sunny’s payoffs would be $11 million if it advertised as before, and $13 million if it did not. What is the non-cooperative Nash equilibrium, if any, now? Since advertising (heavily) was the dominant strategy before, advertising less must now be the dominant strategy for Cher since payoffs would be higher, irregardless of what Sunny is doing. Since Sunny’s payoff is higher if it does not advertise, the new Nash equilibrium is for Cher to advertise less and for Sunny to not advertise at all. Sunny’s payoff then is $13 million, whereas Cher’s payoff is $12. 4. Congress has decided to overhaul the current federal income tax system. The table below illustrates several different tax plans that are under consideration. (26 points) Plan A Plan B Plan C Plan D Marginal Marginal Marginal Marginal Income tax rate tax rate tax rate tax rate $0-$10,000 10% 0% 0% 0% up to $30,000 10% 5% 10% 25% up to $50,000 10% 10% 20% 25% up to $100,000 10% 15% 20% 60% up to $150,000 10% 20% 10% 80% over $150,000 10% 30% 0% 100% a) For each plan, explain whether it would be a proportional, regressive or progressive tax system. Since the marginal tax rate is constant for all income levels, Plan A would result in a proportional tax system. This can be seen in the diagram in part b) as the tax schedule is linear. Increasing marginal tax rates in Plans B and D indicate that both plans would result in a progressive tax system. This can be seen in the diagram in part c) for plan D (at least up to $150,000). Plan C’s marginal tax rates are first increasing, then decreasing, implying that the plan would be progressive at first, but become regressive for incomes above $100,000. This can be seen in the diagram since the slope of the tax schedule is first increasing, then decreasing. 3 b) In the following diagram, plot the tax schedule for Plans A and C (up to an income of $200,000). Tax (thousands of $) Plan A 16 Plan C 10 4 10 30 50 100 150 Income (thousands of $) c) In the following diagram, plot the tax schedule for Plan D (up to an income of $180,000). Tax (thousands of $) 80 50 20 10 30 50 100 150 Income (thousands of $) A subtlety here is that since a tax rate of 100% gives no incentive to work, no one would want to earn more than $150,000 and thus tax revenue would not increase further. d) If the government wanted to implement a tax schedule that causes no inefficiencies whatsoever, which of these plans, if any, would it implement? Would such a plan be fair? All of these plans cause inefficiencies. The only tax plan that would not cause any inefficiencies is a lump-sum or poll tax, a fixed dollar amount for everyone, regardless of income. Such a plan would be unfair since it would violate the ability-to-pay principle. 4 5. True or False? Explanation determines grade! (6 points each) a) For goods that are rival in consumption, but non-excludable (such as fish), the government must restrict their use by requiring a license, and must limit the amount of licenses. In order to sustain such a common resource, it is indeed necessary to limit access to the resource, i.e. make it excludable to some extent. Licenses (either auctioned off or given away via a lottery) are a viable way of achieving this objective. However, in certain instances it might also be feasible to achieve excludability by assigning property rights. E.g., if someone is assigned property rights to a lake, (s)he has an interest in preserving the resource. b) Whenever long run average total cost is decreasing, the decrease in average fixed cost is dominating the increase in average variable cost. False. In the long run, there is no fixed factor of production, hence no fixed cost. c) The long run equilibrium in a perfectly competitive market is both efficient and fair. True. It is efficient because production occurs at minimum average cost, thus using the least of our scarce resources. It is fair in the sense that everyone earns the same return on their investment (horizontal equity) and everyone has the same chance of earning that return (equality of opportunity). 6. The following diagram depicts the marginal benefit (MB) (Demand) and marginal cost (MC) for Claus, Inc., for their holiday wreaths. (20 points) Marginal Cost / Marginal Benefit MSC 10 B MPC 5 A MSB E MPB Quantity 5 10 of wreaths 5 a) In the absence of any other costs and benefits, what is the optimal amount of wreaths? This would be at the intersection of private marginal benefit (now indicated as MPB) and private marginal cost (now indicated as MPC), point E in the diagram. The optimal quantity of wreaths is 6. b) Suppose that in order to make wreaths it is necessary to cut down trees. The social cost of disappearing forests is estimated to be $4 per wreath. What is the optimal amount of wreaths now? In the diagram above, shift the appropriate curve and mark the new equilibrium as point A. This would shift the marginal cost curve up by $4 and result in the marginal social cost (MSC) curve. The intersection of this curve with private marginal benefit gives the new socially optimal quantity of wreaths, which is 2.
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