西财作业英文版附答案.doc

第五章 外部性P1002. In the following figure, the number of parties that Cassanova gives per month is measured on the horizontal axis, and dollars are measured on the vertical. MCp is the marginal cost of providingparties and MBp is Cassanovas marginal benefit schedule from having parties. a. Graphically, show how many parties Cassanovawill host.b. Suppose there is a fixed marginal external benefit, $b, per party to Cassanovas friends.Illustrate this on your graph.c. What is the socially (no pun intended) optimal level of parties? How could the SocialCommittee induce Cassanova to throw this number?d. On your graph, show the optimal subsidy per party and the total amount paid to Cassanova.Who gains and loses under this plan?答案：2.a. The number of parties per month that would be provided privately is P.b. See schedule MSBp.c. P*. Give a per-unit subsidy of $b per party.d. The total subsidy=abcd. “Society” comes out ahead by ghc, assuming the subsidy can be raised without any efficiency costs. (Cassanovas friends gain gchd; Cassanova loses chd but gains abcd, which is a subsidy cost to government.)7. The Finger Lakes region of New York State attracts tourists who wish to sample its superbwines. In recent years, hog-raising farmssome with more than a thousand hogshave takenroot in the region. The smells emanating from the massive amounts of pig manure adverselyaffect the tourism. “Wine and swine, in other words, do not mix” Chen, 2001, p. L1. Imagine that the Little Pigs (LP) hog farm is situated near the Tipsy vineyard. The followingtable shows, for each level of LPs output, the marginal cost of a hog, the marginal benefit toLP, and the marginal damage done to Tipsy: a. How many hogs does LP produce?b. What is the efficient number of hogs?c. The owner of LP gets tired of Tipsys complaints about her hog farm, and she buys outTipsy. After the merger, how many hogs does LP produce?d. How does the merger affect the sum of the profits earned by LP and Tipsy?答案：7.a.When the Little Pigs hog farm produces on its own, it sets marginal benefitequal to marginal cost. This occurs at 4 units.b.The efficient number of hogs sets marginal benefit equal to marginal social cost, which is the sum of MC and MD. At 2 units, MB=MSC=13.c.The merger internalizes the externality. The combined firm worries about the joint profit maximization problem, not the profit maximization problem at either firm alone. Thus, the LP farm produces 2 units, the socially efficient amount.d.Before the merger, the LP farm produced 4 units. By cutting back to 2 units, it loses marginal profit of $3. On the other hand, the Tipsy Vineyards profits increase by $20. Thus, profits increase by $17 altogether.8. The private marginal benefit for commodity X is given by 10 _ X, where X is the number ofunits consumed. The private marginal cost of producing X is constant at $5. For each unit ofX produced, an external cost of $2 is imposed on members of society. In the absence of anygovernment intervention, how much X is produced? What is the efficient level of productionof X? What is the gain to society involved in moving from the inefficient to the efficientlevel of production? Suggest a Pigouvian tax that would lead to the efficient level. Howmuch revenue would the tax raise?答案：8.Private Marginal Benefit = 10 - XPrivate Marginal Cost = $5External Cost = $2Without government intervention, PMB = PMC; X = 5 units.Social efficiency implies PMB = Social Marginal Costs = $5 + $2 = $7; X = 3 units.Gain to society is the area of the triangle whose base is the distance between the efficient and actual output levels, and whose height is the difference between private and social marginal cost. Hence, the efficiency gain is (5 - 3)(7 - 5) = 2.A Pigouvian tax adds to the private marginal cost the amount of the external cost at the socially optimal level of production. Here a simple tax of $2 per unit will lead to efficient production. This tax would raise ($2) (3 units) = $6 in revenue.9. Suppose that two firms emit a certain pollutant. The marginal cost of reducing pollution foreach firm is as follows: MC1 _ 300e1 and MC2 _ 100e2, where e1 and e2 are the amounts (intons) of emissions reduced by the first and second firms, respectively. Assume that in theabsence of government intervention, Firm 1 generates 100 units of emissions and Firm 2generates 80 units of emissions.a. Suppose regulators decide to reduce total pollution by 40 units. In order to be cost effective, how much should each firm cut its pollution?b. What emissions fee should be imposed to achieve the cost-effective outcome? How much would each firm pay in taxes?c. Suppose that instead of an emissions fee, the regulatory agency introduces a tradable permitsystem and issues 140 permits, each of which allows the emission of one ton of pollution. Firm 1 uses it political influence to convince the regulatory agency to issue 100 permits to itself and only 40 permits to Firm 2. How many, if any, permits are traded between the firms? What is the minimum amount of money that must be paid (total) for these permits? By how many tons doeseach firm end up reducing its pollution?答：9.a.The total cost of emissions reduction is minimized only when the marginal costs are equal across all polluters, therefore a cost-effective solution requires that MC1 = MC2 or that 300e1 = 100e2. Substituting 3e1 for e2 in the formula e1 + e2 = 40 (since the policy goal is to reduce emissions by 40 units) yields the solution. It is cost-effective for Firm 1 to reduce emissions by 10 units and for Firm 2 to reduce emissions by 30 units. b.In order to achieve cost-effective emission reductions, the emissions fee should be set equal to $3,000. With this emissions fee, Firm 1 reduces 10 units and Firm 2 reduces 30 units, but Firm 1 has to pay $3,000 for each unit of pollution they continue to produce, which gives them a tax burden of $3,000 x 90 (Firm 1 generated 100 units in the absence of government intervention) or $270,000. Firm 2 has a lower tax burden because it is reducing emissions from 80 units to 50 units. Firm 2 pays $3,000 x 50 = $150,000. As the text concludes, the firm that cuts back pollution less isnt really getting away with anything because it has a larger tax liability than if it were to cut back more.c.From an efficiency standpoint, the initial allocation of permits does not matter. If the two firms could not trade permits, then Firm 2 would have to undertake all of the emissions reduction. Initially, Firm 1s MC is zero, while Firm 2s MC is $4,000, so there is a strong incentive for Firm 2 to purchase permits from Firm 1. Trading should continue until MC1 = MC2, which is the cost-effective solution. This means that the market price for permits will equal $3,000, the same as the emissions fee. At this price, Firm 2 will purchase 10 permits from Firm 2, allowing Firm 2 to reduce emissions by 30 rather than 40 and requiring Firm 1 to reduce emissions by 10. This solution is the same as the solution achieved with the emissions fee. However, Firm 1 is better off because instead of having to pay taxes, it will receive a payment of $30,000 for its permits. Firm 2 must pay $30,000 for the extra permits, but it also avoids the payment of taxes. The government lost $420,000 in tax revenue. The firms must still pay the cost of emissions reduction, plus Firm 2 must pay for the permits purchased from Firm 1.第六章 政治经济学P1289. Assume that the demand curve for milk is given by Q _ 100 _ 10P, where P is the priceper gallon and Q is the quantity demanded per year. The supply curve is horizontal at a priceof 2.a. Assuming that the market is competitive, what is the price per gallon of milk and thenumber of gallons sold?b. With the connivance of some politicians, the dairy farmers are able to form and maintaina cartel. (Such a cartel actually operates in the northeastern United States.) What is the cartel price, and how many gallons of milk are purchased? Hint: The marginal revenue curve (MR) is given by MR _ 10 _ Q/5. Also, remember that the supply curve shows the marginal cost associated with each level of output.c. What are the rents associated with the cartel?d. Suppose that in order to maintain the cartel, the dairy farmers simply give lump-sum campaigncontributions to the relevant politicians. What is the maximum contribution they would be willing to make? What is the deadweight loss of the cartel?e. Suppose that instead of lump-sum contributions to politicians, the dairy farmers hire lobbyists and lawyers to make their case in Congress. How does this change your estimate of the deadweight loss associated with this rent-seeking activity?答案：9.a.With the demand curve of Q=100-10P and a perfectly elastic supply curve at P=2, then the milk is sold at a price of $2, and a quantity of 80 units is sold.b.The marginal revenue curve associated with the inverse demand curve P=10-(1/10)Q is MR=10-(1/5)Q, while the marginal cost curve is MC=2. The cartel would ideally produce a quantity where MR=MC, or 10-(1/5)Q=2, or Q=40. The price associated with a cartel quantity of 40 units is P=10-(1/10)*40, or P=6.c.The rent associated with the cartel is the product of the marginal profit per unit and the number of units produced. The marginal profit per unit of milk is $4 (=$6 price - $2 marginal cost), while 40 units are produced. Thus, the rents equal $160.d.The most the cartel would be willing to contribute to politicians is the full economic rent of $160. The cartel situation, the quantity of milk produced is too low from societys point of view. The deadweight loss triangle is computed using the difference between the cartel output and competitive output as the “base” of the triangle, and the difference between the cartel price and competitive price as the “height.” Thus, the triangle is equal to (1/2)*(80-40)*($6-$2)=$40.e.As Figure 6.5 in the textbook shows, the deadweight loss could now go as high as the sum of the conventional deadweight loss and the rents, or $160 rents + $80 DWL = $240. This is because, as noted in the text, “rent-seeking can use up resources lobbyists spend their time influencing legislators, consultants testify before regulatory panels, and advertisers conduct public relations campaigns. Such resources, which could have been used to produce new goods and services, are instead consumed in a struggle over the distribution of existing goods and services. Hence, the rents do not represent a mere lump-sum transfer; it is a measure of real resources used up to maintain a position of market power.”第八章 成本-效益分析P1664. Suppose that you are planning to take a year vacation to bike across the United States. Someoneis willing to sell you a new bicycle for $500. At the end of the year, you expect to resell the bicycle for $350. The benefit to you of using the bicycle is the equivalent of $170.a. What is the internal rate of return?b. If the discount rate is 5 percent, should you buy the bicycle?答案：4.a.The internal rate of return is the discount rate that would make the projects net present value (NPV) equal zero. To solve for the internal rate of return, r, set the present value of benefits minus the present value of costs equal to zero. If we assume the benefit of using the bicycle is immediate (and worth $170), there is also the benefit of re-selling the bicycle for $350, but it cant be re-sold until next year, so must be discounted. Therefore, NPV is 170 + 350/(1+r) 500 = 0. Solving this expression for r yields r = 6 percent. If we assume that the benefits of the vacation will not be enjoyed for one year, then NPV is (170+350)/(1+r) 500 and setting this expression equal to zero and solving for r yields r = 4 percent.b.If the discount rate is 5 percent, purchasing the bicycle is a good idea if r is 6 percent, but a bad idea if r is 4 percent.5. Bill rides the subway at a cost of 75 cents per trip, but would switch if the price were anyhigher. His only alternative is a bus that takes five minutes longer, but costs only 50 cents. Hemakes 10 trips per year. The city is considering renovations of the subway system that wouldreduce the trip by 10 minutes, but fares would rise by 40 cents per trip to cover the costs. Thefare increase and reduced travel time both take effect in one year and last forever. The interestrate is 25 percent.a. As far as Bill is concerned, what are the present values of the projects benefits and costs?b. The citys population consists of 55,000 middle- class people, all of whom are identical toBill, and 5,000 poor people. Poor people are either unemployed or have jobs close to theirhomes, so they do not use any form of public transportation. What are the total benefitsand costs of the project for the city as a whole? What is the net present value of the project?c. Some members of the city council propose an alternative project that consists of animmediate tax of $1.25 per middle-class person to provide “free” legal services for thepoor in both of the following two years. The legal services are valued by the poor at atotal of $62,500 per year. (Assume this amount is received at the end of each of the two years.) What is the present value of the project?d. If the city must choose between the subway project and the legal services project, whichshould it select?e. What is the “distributional weight” of each dollar received by a poor person that would make the present values of the two projects just equal? That is, how much must each dollar of income to a poor person be weighted relative to that of a middle-class person? Interpret your answer.答案：5.a.Bill is willing to pay 25 cents to save 5 minutes, so he values time at 5 cents per minute. The subway saves him 10 minutes per trip, or 50 cents. The value of 10 trips per year is $5. The cost of each trip is 40 cents, or $4 per year. The annual net benefit to Bill is therefore $1. The present value of the benefits = $5/.25 = $20; the present value of the costs is $4/.25 = $16.b. Total benefits = $20x55,000=$1,100,000.Total costs = $16x55,000 = $880,000.Net benefits = $220,000.c. Costs = $1.25 x 55,000 = $68,750.Benefits =($62,500/1.25) + ($62,500/1.252) = $90,000.Net benefit = $21,250.d. The subway project has a higher present value. If a dollar to the “poor” is valued the same as a dollar to the “middle class,” choose the subway project.e. Let l = distributional weight. set220,000 = -68,750 + l(62,500/1.25) + (62,500/1.252)l = 3.21This distribution weight means that $1 of income to a poor person must be viewed as more important than $3.21 to the middle class for the legal services to be done.第十四章 税收与收入分配P3142. In 2004, Congress adopted a Medicare prescription drug benefit which would, in effect,subsidize the purchase of drugs by the elderly. Opponents of the new subsidy argued that itwould only result in higher prices for prescription drugs, with little benefit to the elderly.Under what conditions is this view likely to be correct? Do you think that these conditions arerealistic? (Note: Although the prescription drug program is very complicated, for purposes ofthis problem, simply model the benefit as an ad valorem subsidy.)答案：2.As shown in the graph, the subsidy acts to increase the demand for prescription drugs, so the price rises. However, consumers pay P2 subsidy, so the elderly benefit by paying less for prescription drugs and consuming more.8. Assume that in a given country, tax revenues, T, depend on income, I, according to the formulaThus, for example, when a household has an income of $50,000, its tax burden is -4,000 +0.250,000, or $6,000. Is this a progressive tax schedule? Hint: Compute average tax ratesat several different levels of income.Now lets generalize the tax schedule in this problem to:where a and t are numbers. (For example, in the tax schedule above, a = -4,000 and t = 0.2.)Write down a formula for the average tax rate as a function of the level of income. Show thatthe tax system is progressive if a is negative, and regressive if a is positive. Hint: The averagetax rate is T/I.答案：8.The equation T=-4000+.2I is somewhat similar to the exercise in Table 14.1. If we follow the text and define progressivity with respect to average tax rates rather than marginal tax rates, then the average tax rate equal ATR=(-4000/I)+.2 for any income level. Clearly this average tax rate converges to ATR=20% as income gets large, and is lower for lower income levels. Replicating Table 14.1 for the tax system given here, we get:IncomeTax LiabilityAverage Tax RateMarginal Tax Rate$2,000$-3,600-1.800.23,000$-3,400-1.130.25,000$-3,000-0.600.210,000$-2,000-0.200.230,000$2,0000.0660.2第十五章 税收与效率P3344. Some countries rely relatively heavily on taxes that distort economic behavior, and others donot. A recent econometric study found that countries in the latter category tend to grow fasterthan countries in the former Kneller et al., 1999. Use the discussion surrounding Figure 15.9 to explain this phe