第6章_课后习题答案1006

Unit 1第一题：选词填空1、The roads are clogged with holiday traffic. (be clogged with)2、This study purports to show an increase in the incidence of the disease.(purport to)3、After a hard climb, we were rewarded by a vista of rolling hills under a deep blue summer sky.4、The children bombarded her with questions.(bombard with)5、They exulted over their victory. (exult over)6、The baby’s just scribbled all over my new dictionary!(scribble all over)7、I didn’t find the prospect of a house with no electricity very alluring.(find sth. alluring)8、She’s trying to make a comeback with her first album in nearly twenty years.9、You can use the search facility to call up all the occurrences of a particular word in a document.10、He glanced at the letter and then tossed it into the bin.(toss into)11、He was eliminated in the third round of the competition.(be eliminated)12、I managed to compress ten pages of notes into four paragraphs.(compress into)第二题：用适合形式填空1、The company specializes in customized (custom)computer systems.2、The whole experience left him traumatized(traumatize).3、The writer recently went on a promotional(promotion) tour of his homeland.4、It seems paradoxical(paradox) to me, but if you drink a cup of hot tea it seems to cool you down.5、You shouldn’t treat such a serious subject with frivolity(frivolous).6、Cable television companies have launched major campaigns to increase their number of subscribers(subscribe).7、This range of computers is very fast, but their successors(success)will be even faster.8、His speech was full of inanities(inane)that were meant to be funny.9、What was once an informal event has now become institutionalized(institution).10、The school received a substantial government subsidy(subsidize).1.这项计划为智力迟钝者提供长期的照顾。

Chapter 6 Economies of Scale, Imperfect Competition, a n d I n t e r n a t i o n a l T r a d eMultiple Choice Questions1. External economies of scale arise when the cost per unit(a) rises as the industry grows larger.(b) falls as the industry grows larger rises as the average firm grows larger.(c) falls as the average firm grows larger.(d) remains constant.(e) None of the above.Answer: B2. Internal economies of scale arise when the cost per unit(a) rises as the industry grows larger.(b) falls as the industry grows larger.(c) rises as the average firm grows larger.(d) falls as the average firm grows larger.(e) None of the above.Answer: D3. External economies of scale(a) may be associated with a perfectly competitive industry.(b) cannot be associated with a perfectly competitive industry.(c) tends to result in one huge monopoly.(d) tends to result in large profits for each firm.(e) None of the above.Answer: A4. Internal economies of scale(a) may be associated with a perfectly competitive industry.(b) cannot be associated with a perfectly competitive industry.(c) are associated only with sophisticated products such as aircraft.(d) cannot form the basis for international trade.(e) None of the above.Answer: B5. A monopolistic firm(a) can sell as much as it wants for any price it determines in the market.(b) cannot determine the price, which is determined by consumer demand.(c) will never sell a product whose demand is inelastic at the quantity sold.(d) cannot sell additional quantity unless it raises the price on each unit.(e) None of the above.Answer: C6. Monopolistic competition is associated with(a) cut-throat price competition.(b) product differentiation.(c) explicit consideration at firm level of the feedback effects of other firms’ p ricing decisions.(d) high profit margins.(e) None of the above.Answer: B7. The most common market structure is(a) perfect competition.(b) monopolistic competition.(c) small-group oligopoly.(d) perfectly vertical integration.(e) None of the above.Answer: C8. Modeling trade in monopolistic industries is problematic because(a) there is no one generally accepted model of oligopoly behavior.(b) there are no models of oligopoly behavior.(c) it is difficult to find an oligopoly in the real world.(d) collusion among oligopolists makes usable data rare.(e) None of the above.Answer: A9. Where there are economies of scale, the scale of production possible in a country is constrainedby(a) the size of the country.(b) the size of the trading partner’s country.(c) the size of the domestic market.(d) the size of the domestic plus the foreign market.(e) None of the above.Answer: D10. Where there are economies of scale, an increase in the size of the market will(a) increase the number of firms and raise the price per unit.(b) decrease the number of firms and raise the price per unit.(c) increase the number of firms and lower the price per unit.(d) decrease the number of firms and lower the price per unit.(e) None of the above.Answer: C11. The simultaneous export and import of widgets by the United States is an example of(a) increasing returns to scale.(b) imperfect competition.(c) intra-industry trade.(d) inter-industry trade.(e) None of the above.Answer: C12. If output more than doubles when all inputs are doubled, production is said to occur underconditions of(a) increasing returns to scale.(b) imperfect competition.(c) intra-industry trade.(d) inter-industry trade.(e) None of the above.Answer: A13. Intra-industry trade can be explained in part by(a) transportation costs within and between countries.(b) problems of data aggregation and categorization.(c) increasing returns to scale.(d) All of the above.(e) None of the above.Answer: D14. If some industries exhibit internal (firm specific) increasing returns to scale in each country, weshould not expect to see(a) intra-industry trade between countries.(b) perfect competition in these industries.(c) inter-industry trade between countries.(d) high levels of specialization in both countries.(e) None of the above.Answer: B15. Intra-industry trade is most common in the trade patterns of(a) developing countries of Asia and Africa.(b) industrial countries of Western Europe.(c) all countries.(d) North-South trade.(e) None of the above.Answer: B16. International trade based on scale economies is likely to be associated with(a) Ricardian comparative advantage.(b) comparative advantage associated with Heckscher-Ohlin factor-proportions.(c) comparative advantage based on quality and service.(d) comparative advantage based on diminishing returns.(e) None of the above.Answer: E17. International trade based on external scale economies in both countries is likely to be carried outby a(a) relatively large number of price competing firms.(b) relatively small number of price competing firms.(c) relatively small number of competing oligopolists.(d) monopoly firms in each country/industry.(e) None of the above.Answer: A18. International trade based solely on internal scale economies in both countries is likely to becarried out by a(a) relatively large number of price competing firms.(b) relatively small number of price competing firms.(c) relatively small number of competing oligopolists.(d) monopoly firms in each country/industry.(e) None of the above.Answer: D19. A monopoly firm engaged in international trade will(a) equate average to local costs.(b) equate marginal costs with foreign marginal revenues.(c) equate marginal costs with the highest price the market will bear.(d) equate marginal costs with marginal revenues in both domestic and in foreign markets.(e) None of the above.Answer: D20. A monopoly firm will maximize profits by(a) charging the same price in domestic and in foreign markets.(b) producing where the marginal revenue is higher in foreign markets.(c) producing where the marginal revenue is higher in the domestic market.(d) equating the marginal revenues in domestic and foreign markets.(e) None of the above.Answer: D21. A firm in monopolistic competition(a) earns positive monopoly profits because each sells a differentiated product.(b) earns positive oligopoly profits because each firm sells a differentiated product.(c) earns zero economic profits because it is in perfectly or pure competition.(d) earns zero economic profits because of free entry.(e) None of the above.Answer: D22. The larger the number of firms in a monopolistic competition situation,(a) the larger are that country’s exports.(b) the higher is the price charged.(c) the fewer varieties are sold.(d) the lower is the price charged.(e) None of the above.Answer: D23. The monopolistic competition model is one in which there is/are(a) a monopoly.(b) perfect competition.(c) economies of scale.(d) government intervention in the market.(e) None of the above.Answer: C24. In industries in which there are scale economies, the variety of goods that a country can produceis constrained by(a) the size of the labor force.(b) anti-trust legislation.(c) the size of the market.(d) the fixed cost.(e) None of the above.Answer: C25. An industry is characterized by scale economies, and exists in two countries. Should these twocountries engage in trade such that the combined market is supplied by one country’s industry, then(a) consumers in both countries would suffer higher prices and fewer varieties.(b) consumers in the importing country would suffer higher prices and fewer varieties.(c) consumers in the exporting country would suffer higher prices and fewer varieties.(d) consumers in both countries would enjoy fewer varieties available but lower prices.(e) None of the above.Answer: E26. An industry is characterized by scale economies and exists in two countries. In order forconsumers of its products to enjoy both lower prices and more variety of choice,(a) each country’s marginal cost must equal that of the other country.(b) the marginal cost of this industry must equal marginal revenue in the other.(c) the monopoly must lower prices in order to sell more.(d) the two countries must engage in international trade one with the other.(e) None of the above.Answer: D27. A product is produced in a monopolistically competitive industry with scale economies. If thisindustry exists in two countries, and these two countries engage in trade one with the other, then we would expect(a) the country in which the price of the product is lower will export the product.(b) the country with a relative abundance of the factor of production in which production of theproduct is intensive will export this product.(c) each of the countries will export different varieties of the product to the other.(d) neither country will export this product since there is no comparative advantage.(e) None of the above.Answer: C28. The reason why one country may export a product which is produced with positive scaleeconomies is(a) its labor productivity will tend to be higher.(b) it enjoys a relative abundance of the factor intensely used in the product’s production.(c) its demand is biased in favor of the product.(d) its demand is biased against the product.(e) None of the above.Answer: E29. Two countries engaged in trade in products with no scale economies, produced under conditionsof perfect competition, are likely to be engaged in(a) monopolistic competition.(b) inter-industry trade.(c) intra-industry trade.(d) Heckscher-Ohlin trade.(e) None of the above.Answer: B30. Two countries engaged in trade in products with scale economies, produced under conditions ofmonopolistic competition, are likely to be engaged in(a) price competition.(b) inter-industry trade.(c) intra-industry trade.(d) Heckscher-Ohlinean trade.(e) None of the above.Answer: C31. History and accident determine the details of trade involving(a) Ricardian and Classical comparative advantage.(b) Heckscher-Ohlin model consideration.(c) taste reversals.(d) scale economies.(e) None of the above.Answer: D32. We often observe intra-industry North-South trade in “computers and related devices.” This isdue to(a) classification and aggregation ambiguities.(b) monopolistic competition.(c) specific factors issues.(d) scale economies.(e) None of the above.Answer: A33. We often observe “pseudo-intra-industry trade” between the United States and Mexico. Actually,such trade is consistent with(a) oligopolistic markets.(b) comparative advantage associated with Heckscher-Ohlin model.(c) optimal tariff issues.(d) huge sucking sound.(e) None of the above.Answer: B34. Intra-industry trade will tend to dominate trade flows when which of the following exists(a) Large differences between relative country factor availabilities(b) Small differences between relative country factor availabilities(c) Homogeneous products that cannot be differentiated(d) Constant cost industries(e) None of the above.Answer: B35. The most common form of price discrimination in international trade is(a) non-tariff barriers.(b) V oluntary Export Restraints.(c) dumping.(d) preferential trade arrangements.(e) None of the above.Answer: CEssay Questions1. Why is it that if an industry were operating under conditions of domestic internal scale economies(applies to firm in the country)—then the resultant equilibrium cannot be consistent with the pure competition modelAnswer: Because once one firm became bigger than another, or if one firm began the industry, then no other firm would be able to match its per unit cost, so that they would be drivenout of the industry.2. Is it possible that if positive scale economies characterize an industry, that its equilibrium may beconsistent with purely competitive conditions Explain how this could happen.Answer: Yes. If the scale economies were external to the firm, then there is no reason why the firms may not be in perfect competition.3. If a scale economy is the dominant technological factor defining or establishing comparativeadvantage, then the underlying facts explaining why a particular country dominates world markets in some product may be pure chance, or historical accident. Explain, and compare this with the answer you would give for the Heckscher-Ohlin model of comparative advantage.Answer: This statement is true, since the reason the seller is a monopolist may be that it happened to have been the first to produce this product in this country. It may have noconnection to any supply or demand related factors; nor to any natural or man-madeavailability. This is all exactly the opposite of the Heckscher-Ohlin Neo-Classicalmodel’s explanation of the determin ants of comparative advantage.4. It is possible that trade based on external scale economies may leave a country worse off than itwould have been without trade. Explain how this could happen.Answer: One answer is that the terms of trade effects may dominate any other factors.5. If scale economies were not only external to firms, but were also external to individual countries.That is, the larger the worldwide industry (regardless of where firms or plants are located), the cheaper would be the per-unit cost of production. Describe what world trade would look like in this case.Answer: Presumably each country would specialize in some component of the final product.This would result in much observed intra-industry trade.6. Why are increasing returns to scale and fixed costs important in models of international trade andmonopolistic competitionAnswer: There are many answers. Three of these are(a) Increasing returns to scale, and high fixed costs may be inconsistent with perfectcompetition. In such a case, the initial autarkic state may be a suboptimalequilibrium. For example, relative prices may not equal marginal rates oftransformation. It follows from this that a change in output compositions associatedwith trade may result in a national welfare for one or both trading countries that isinferior to that associated with the initial autarkic conditions. Hence no “gains fromtrade.”(b) In a case of increasing scale economies at the firm or plant level, the determinationof which product will be exported by which country is ex-ante indeterminate.Therefore, deriving clear implications concerning the effects of trade on incomedistributions such as may be derived from the Samuelson-Stolper Theorem is nolonger generally possible.(c) Market structures containing positive scale economies and imperfect competitionmay allow for “two-way trade,” or intra-industry trade. As in b. above, the varioustheorems derivable from the Heckscher-Ohlin model concerning directions of tradeand income distributions are no longer generally applicable.7. Explain why it may be argued that the relative importance of the intra-industry component ofworld trade is likely to lessen economic strife or confrontation (a la Stolper-Samuelson) associated with commercial policy within countries in which overall trade is expandingAnswer: In the case of the Neo-Classical H-O model, the expansion of trade will tend to increase the incomes of those factors in which the exports are relatively intense. This may createsituations in which un skilled labor’s already relatively low relative incomes wouldworsen in a country such as the U.S., hence heating up “class warfare.” In the case ofintra-industry trade, the expanding exports will tend to be in relatively fragmentedsubsets of products (“brands”). Such export expansion will have no determinant orsystematic tendency to affect relative factor returns in any deterministic manner.8. Explain why positive economies of scale in one (of two) sectors may establish a comparativeadvantage for the large (as compared to the small) country in the production of the commodity which exhibits positive scale economies.Answer: In the case of the H-O model, the actual size of the country is irrelevant in the determination of the direction of trade (though it may affect the equilibrium terms oftrade). When positive scale economies apply to the production of one product, thecountry that can devote more resources (in absolute terms) will be able to sell thatproduct cheaper, and therefore will be more likely to gain a “revealed” comparativeadvantage in that product. This will be the country with more factors (both labor andcapital)—the larger country.Quantitative/Graphing Problems1. The figure above represents the demand and cost functions facing a Brazilian Steel producingmonopolist. If it were unable to export, and was constrained by its domestic market, what quantity would it sell at what priceAnswer: It would sell 5 (million tons) at a price of $8/ton.2. Now the monopolist discovers that it can export as much as it likes of its steel at the world priceof $5/ton. It will therefore expand for-export production up to the point where its marginal cost equals $5. How much steel will the monopolist sell, and at what priceAnswer: It would sell 10 million tons at $5/ton.3. Given the opportunity to sell at world prices, the marginal (opportunity) cost of selling a tondomestically is whatAnswer: $5/ton.4. While selling exports it would also maximize its domestic sales by equating its marginal(opportunity) cost to its marginal revenue of $5. How much steel would the firm sell domestically, and at what priceAnswer: 4 million tons at $10/ton.5. The Brazilian firm is charging its foreign (U.S.) customers one half the price it is charging itsdomestic customers. Is this good or bad for the real income or economic welfare of theUnited States Is the Brazilian firm engaged in dumping Is this predatory behavior on the partof the Brazilian steel companyAnswer: Good. Yes, if you define dumping as selling abroad at a price lower than domestically.No, if by dumping you mean selling below marginal cost. No—this is not being done inorder to capture market shares, but rather is “mere” static profit maximization behavior,as is expected of any self-respecting monopolist.6. The following Table describes the labor-input coefficients needed to produce one Widget inEngland and Portugal. Both countries are identical in size, tastes, technology. This technology is described in the table below:To ProduceThis Many Widgets, Or This Many Apples Labor-Hour Requirements1 32 53 64 75 86 97 10Let us assume that each country has 10 labor-hours available. Further, consumers always consume an equal amount of apples and widgets.(a) How of each product will be produced in England under autarky 2 widgets and 2 apples.(b) Judging from autarky conditions, which country has a comparative advantage in widgets(c) If England (completely) specialized in widgets, how many widgets would be produced, andhow many apples(d) If the world terms of trade were established at 3.5 widgets 3.5 Apples, which country wouldenjoy gains from trade (as compared to The autarky solution)(e) If Portugal were to completely specialize in widgets, how would the answers to c and dchange(f) What would the production possibility curve look like in each countryAnswers: (a) 2 widgets and 2 apples(b) None(c) 7 widgets in England and 7 apples in Portugal(d) both would gain from trade. Instead of consuming 2 widgets and 2 apples, theywould each consume 3.5 widgets and 3.5 apples.(e) Same numbers as c, except that the countries will each be assigned a differentproduct. Exactly the same answer for d.(f) convex to the origin.。

Section AvocabularyIII.1. Substantial2. concerning3. negotiation4.exaggerate5. withdrawn6. commissions7. financed8. secure9. impose 10.donationIV1. by2. in3. of4. to5. up6. on/upon7. with8. in9. in 10. betweenV1.O2.E3.G4.15.J6.B7.K8.N9.M 10.DCollocation<br />VI.1. approaches2. reward3. protection4. honor5.advice6. access7. advantages8. help9. sympathy 10.understandingWord BuildingVII.1. foresight2. forewarned3. foreground4. postgraduate5. post-race6. foresaw7. post-Christmas8.post-electionVIII.1. e-shopper2. e-merchant3. e-journal4.e-classroom5. e-commerce6. e-mail7. e-dictionaries8.e-cashsentence structureIX.1. It's pointless to go there next Monday-there's a public holiday.2. It is easy to talk about having high moral standards, but, inpractice, what would one really do insuch a situation?3. It is interesting to see different cultures and ways of life.4. It is really astonishing that she refuses to talk to you.5. It is important that she come straight to me when she arrives.1. Suppose you object to carrying out a particular management order and you are afraid of themanager, what would you do?2. Suppose you have just got married and you are about to work abroad for three years, how wouldyou explain it to your newly-married wife?3. Suppose someone couldn't understand why you didn't arrest Harry, would you explain to removethe doubts?4. Suppose your tenant fails to pay the rent in time, would you throwhim out?5. Suppose you are a very heavy smoker and are anxious to break the habit, where could you get help?TranslationXI.1. Suppose you found out that your colleague takes bribes, would you just ignore it?2. We've given up on him because he is so stubborn. It is pointless to argue with him.3. He hit upon a good method to speed up the progress of theexperiment, but opinions differed amongmembers of the group on it.4. Today I'm able to square my profession with my interest, which Iwasn't able to do before.5. The ability to visually distinguish between red and green isessential to becoming a driver.6. The team consisted of seven people who met on are gular basis to share their information with eachother.1.假设有人向你行贿，要换取一种承诺，你会怎么做？是接受呢，还是坚持自己的原则？2.现在人们不会忍受那些糟糕的境况，可是在那些日子里却只能接受那样的现实。

第二章需求、供给和均衡价格1. 解答：(1)将需求函数Q d＝50－5P和供给函数Q s＝－10＋5P代入均衡条件Q d＝Q s，有50－5P ＝－10＋5P得P e＝6将均衡价格P e＝6代入需求函数Q d＝50－5P，得Q e＝50－5×6＝20或者，将均衡价格P e＝6代入供给函数Q s＝－10＋5P，得Q e＝－10＋5×6＝20所以，均衡价格和均衡数量分别为P e＝6，Q e＝20。

如图2—1所示。

图2—1(2)将由于消费者收入水平提高而产生的需求函数Q d＝60－5P和原供给函数Q s＝－10＋5P代入均衡条件Q d＝Q s，有60－5P＝－10＋5P得P e＝7将均衡价格P e＝7代入Q d＝60－5P，得Q e＝60－5×7＝25…或者，将均衡价格P e＝7代入Q s＝－10＋5P，得Q e＝－10＋5×7＝25所以，均衡价格和均衡数量分别为P e＝7，Q e＝25。

如图2—2所示。

图2—2(3)将原需求函数Q d＝50－5P和由于技术水平提高而产生的供给函数Q s＝－5＋5P代入均衡条件Q d＝Q s，有50－5P＝－5＋5P得P e＝将均衡价格P e＝代入Q d＝50－5P，得Q e＝50－5×＝或者，将均衡价格P e＝代入Q s＝－5＋5P，得Q e＝－5＋5×＝所以，均衡价格和均衡数量分别为P e＝，Q e＝。

如图2—3所示。

图2—3~(4)所谓静态分析是考察在既定条件下某一经济事物在经济变量的相互作用下所实现的均衡状态及其特征。

也可以说，静态分析是在一个经济模型中根据给定的外生变量来求内生变量的一种分析方法。

以(1)为例，在图2—1中，均衡点E就是一个体现了静态分析特征的点。

它是在给定的供求力量的相互作用下达到的一个均衡点。

在此，给定的供求力量分别用给定的供给函数Q s＝－10＋5P和需求函数Q d＝50－5P表示，均衡点E具有的特征是：均衡价格P e＝6，且当P e＝6时，有Q d＝Q s＝Q e＝20；同时，均衡数量Q e＝20，且当Q e＝20时，有P d＝P s＝P e＝6。

Chapter 6Foreign Currency TranslationDiscussion Questions Solutions1.Foreign currency translation is the process of restating aforeign account balance from onecurrency to another. Foreign currency conversion is the process of physically exchanging onecurrency for another.2.In the foreign exchange spot market, currencies bought and sold must be delivered immediately,normally within 2 business days. Thus a Singaporean tourist buying U.S. dollars at the airportbefore boarding a plane for New York would hand over Singapore dollars and immediatelyreceive the equivalent amount in U.S. dollars. The forward market handles agreements toexchange a fixed amount of one currency for another on an agreed date in the future. Forexample, a French manufacturer exporting goods invoiced in euros to a Japanese importer on 60- day credit terms would buy a forward contract to sell yen for euros 2 months in the future.Transactions in the swap market involve the simultaneous purchase (or sale) of one currency in the spot market and the sale (or purchase) of the same currency in the forward market. Thus, a Canadian investor wishing to take advantage of higher interest rates on 6-month Treasury bills in the United States would buy U.S. dollars with Canadian dollars in the spot market and invest in the United States. To guard against a fall in the value of the U.S. dollar before maturity (when the U.S. dollar proceeds are converted back to Canadian dollars), the Canadian investor would simultaneously enter into a forward contract to sell U.S. dollars for Canadian dollars 6 months in the future at today s forward exchange rate.3.The question refers to alternative exchange rates that are usedto translate foreign financialstatements. The current rate is the exchange rate at the financial statement date. It issometimes called the year-end or closing rate. The historical rate is the exchange rate at the time of the underlying transaction. The average rate is the average of various exchange rates during a fiscal period. Since the average rate normally is used to translate income statement items, it isoften weighted to reflect any seasonal changes in the volume of transactions during the period.Translation gains and losses do not occur if exchange rates do not change. However, if exchange rates change, the use of current and average rates causes translation gains and losses.These do not occur when the historical rate is used because the same (constant) rate is used each period.4. In this example, the Mexican Affiliate s Canadian dollar loan is denominated in Canadian dollars.However, because the Mexican affiliate’s functional currency is U.S. dollars, the peso equivalent of the Canadian dollar borrowing would be remeasured in U.S. dollars prior to consolidation. If the Mexican affiliate’s functional currency were the peso, the Canadian dollar loan would beremeasured in pesos before being translated to U.S. dollars.5. A transaction gain or loss occurs when a foreign currency transaction, e.g., a foreign currencyborrowing, is settled at a different exchange rate than that which prevailed when the transaction was originally incurred. In this case there is an exchange of one currency for another. Atranslation gain or loss, on the other hand, is simply the resultof a restatement process. There is1no physical exchange of currencies involved.6. It is not possible to combine, add, or subtract accounting measurements expressed in differentcurrencies; thus, it is necessary to translate those accounts that are measured or denominated in a foreign currency into a singlereporting currency. Foreign currency translation can involverestatement or remeasurement. In restatement, the local (functional) currency is kept as the unit of measure; that is, the translationprocess multiplies the financial results and relationships in the local currency accounts by a constant, the current rate. In contrast, remeasurement translateslocal currency results as if the underlying transactions had taken place in the reporting(functional) currency of the parent company; for example, it changes the unit of measure of aforeign subsidiary from its local (foreign) currency to the U.S. dollar.7. Major advantages and limitations of each of the majortranslation methods follow.Current Rate MethodAdvantages:a. Retains the initial relationships in the foreign currency statements.b. Simple to apply.Limitations:a. Violates the basic purpose of consolidation, which is to present the results of a parent and its subsidiaries as if they were a single entity.b. Inconsistent with historical cost.c. Presumes that all local assets and liabilities are subject to exchange risk.d. While stockholders equity adjustments shield an MNC s bottomline from translation gains and losses, such adjustments could distort certain financial ratios and be confusing.Current-noncurrent MethodAdvantages:a. Distortions in translated gross margins are reduced as inventories and translated at the current rate.b. Reported earnings are shielded from the distorting effects of currency fluctuations as excess translation gains are deferred and used to offset future translation losses.Limitations:a. Uses balance sheet classification as basis for translation.b. Assumes all current assets are exposed to exchange risk regardless of their form.c. Assumes long-term debt is sheltered from exchange rate risk.Monetary-nonmonetary MethodAdvantages:a. Reflects changes in domestic currency equivalent of long-term debt on a timely basis. Limitations:a. Assumes that only monetary assets and liabilities are subject to exchange rate risk.b. Exchange rate changes distort profit margins as sales transacted at current prices are matched against cost of sales measured at historical prices.c. Uses balance sheet classification as basis for translation.d. Nonmonetary items stated at current market values are translated at historical rates.Temporal MethodAdvantages:a. Theoretically valid: compatible with any accounting measurement method.b. Has the effect of translating foreign subsidiaries operations as if they were originally transacted in the home currency, which is desirable for foreign operations that are extensions of the pare nt’s activities. Limitation:a. A company increases its earnings volatility by recognizing translation gains and losses currently.In arguing for one translation method over another, your students should eventually realize that, in the present state of the art, there is probably no one translation method that is appropriate for all circumstances in which translations occur and for all purposes thattranslation serves. It is probably more fruitful to have students identify circumstances in which they think one translation method is more appropriate than another.8.The current rate method is appropriate when the foreign entity being consolidated is largelyindependent of the parent company. Conditions which would justify this methodology is when the foreign affiliate tends to generate and expend cash flows in the local currency, sells a product locally so that its selling price is largely insulated from exchange rate changes, incurs expenses locally, finances its self locally and does not have very many transactions with the parentcompany. In contrast, the temporal method seems appropriate in those instances when theforeign affiliate’s operations are integrally related to the parent company. Conditions whichwould justify use of the temporal method are when the foreign affiliate transacts business in the parent currency and remits such cash flows to the parent company, sells a product largely in the parent country and whose selling price is sensitive to exchange rate changes, sources its factorinputs from the parent company, receives most of its financing from the parent and has a largetwo way flow of transactions with it.9.The history of foreign currency translation in the United States suggests that the development ofaccounting principles does not depend on theoretical considerations so much as on political, institutional, and economic influences that affect accounting standard setting. It may be morerealistic to recognize that theoretically sound solutions are impossible as long as policyprescriptions are evaluated on practical grounds. Without specific choice criteria derived from investor decision models, it is fruitless to argue the conceptual merits of competing accounting treatments. It isfar more productive to admit that foreign currency translation choices are simply arbitrary.Readers of consolidated financial statements should know that the foreign currency translation method used is one of several alternatives, and this should be disclosed. This approach is more open and reduces the chance that readers will draw misleading inferences.10.Foreign inflation, in particular, the differential rate of inflation between the country in which asubsidiary is located and the country of its parent determines foreign exchange rates. Theserates, in turn, are used to translate foreign currency balances to parent currency.11.In the United Kingdom, financial statements of affiliates domiciled in hyperinflationaryenvironments must first be adjusted to current price levels and then translated using the current rate; in the United States, the temporal method would be employed. The second part of thisquestion is designed to get students from abroad to find out what companies in their homecountries are doing and thereby be in a position to share their new found knowledge with theirclassmates. They need simply get on the internet and read the footnotes of a major multinational company in their home country.12.Under FAS No. 52, the parent currency is designated as the functional currency for an affiliate,whose operations are considered to be an integral part of the parent company’s operations.Accordingly, anything that affects consolidated earnings, including foreign currency translation gains and losses, is relevant to parent company shareholders and is included in reported earnings.In contrast, when a foreign affiliate s operations are independent of the parent s, the localcurrency is designated as its functional currency. Since the focus is on the affiliate s localperformance, translation gains and losses that arise solely from consolidation are irrelevant and, therefore, are not included in consolidated income.Exercises Solutions1.￥250,000,000 X .008557 = $2,139,250.￥250,000,000 ÷ ￥116.86 = $2, 139,312The difference is due to rounding.2.Since ￡1 = US$1.9590 and €1 = US$1.3256, ￡1 =US$1.9590/US$1.3256 = €1.4778.Alternatively, €1 = US$1.3256/US$1.9590 = ￡.6767.3.Single Transaction Perspective:4/1 Purchases (￥32,500,000/￥116.91) $277,992Cash $27,800A/P(￥32,500,000 - ￥3,250,000)/￥116.91 250,192(Credit purchase)7/1 Purchases[(￥29,250,000/￥116.91) – (￥29,250,000/￥115.47) 3,120A/P 3,120(To record increase in purchases due to yen appreciation)7/1 Interest expense(￥29,250,000 X .08 X 3/12)/￥115.47 5,066A/P(￥29,250,000/￥115.47) 253,312Cash 258,378(To record settlement)Two Transactions Pers pective:4/1 Purchases $277,992Cash $27,800A/P 250,1927/1 Transaction loss 3,120A/P 3,1207/1 Interest expense 5,066A/P 253,312Cash 258,3784. a. MXN 1,750,000/MXN10.3 = C$169,903.b. The Canadian dollar equivalent of the Mexican inventory account would not change if the functional currencywas the Canadian dollar as the temporal method translates inventory, a nonmonetary asset, at the exchange rate that preserves its original measurement basis. Since inventory is being carried at its netrealizable value, it would be translated at the current rate. Had inventory been carried at historical cosuld have been translated at the historical rate or MXN3,750,000/MXN9.3 = C$403,226.5. Baht is the functional currency:B 2,500,000/20 years = B 125,000B 125,000/B37 = 3,378B 5,000,000/20 years = B 250,000B 250,000/B37 = 6,757U.S. dollar is the functional currency:B 2,500,000/20 years = B 125,000B 125,000/B40 = 3,125B 5,000,000/20 years = B 250,000B 250,000/B38 = 6,579Total depreciation $ 9,7046. If the euro is the German subsidiary’s functional currency, its accounts would be t ranslated into Australian dollarsusing the current rate method. In this case the translation gain of AUD4,545,455 would appear in consolidated equity.Thus the only item affecting current income would be thetransaction loss(loss on an unsettled transac tion) ofAUD1,514,515 on the euro borrowing.If the Australian dollar is deemed to be the functional currency, then the transaction loss andtranslation gain would both appear in reported earnings as follows:AUD(1,514,515) transaction lossAUD4,545,455 translation gainAUD3,030,940 net foreign exchange gain7.U.S. Dollar U.S. Dollar U.S. DollarBefore CNY After CNY After CNYAppreciation Appreciation DepreciationCNY Balance Sheet ($.12=CNY1) ($.15 = C NY1) ($0.09 = CNY1) Assets Amount Current Monetary Current MonetaryNoncurrent Nonmonetary Noncurrent NonmonetaryCash NT5,000 $600 $ 750 $ 750 $ 450 $ 450Accts. R eceivable 14,000 1,680 2,100 2,100 1,260 1,260 Inventories(cost=24,000) 22,000 2,640 3,300 2,640 1,980 2,640Fixed assets, net 39,000 4,680 4,680 4,680 4,680 4,680Total CNY 80,000 $9,600 $10,830 $10,170 $8,370 $9,030 Liabilities & Owners EquityAccts. Payable CNY21,000 $2,520 $ 3,150 $ 3,150 $1,890 $1,890Long-term debt 27,000 3,240 3,240 4,050 3,240 2,430 Stockholders equity 32,000 3,840 4,440 2,970 3,240 4,710 Total CNY 80,000 $9,600 $10,830 $10,170 $8,370 $9,030 Accou nting exposure CNY20,000 (29,000) 20,000 (29,000) Translation gain (loss) US$ 600 (870) (600) 8708.U.S. Dollar U.S. Dollar U.S. DollarBefore CNY After CNY After CNYAppreciation Appreciation DepreciationCNY Balance Sheet ($.12=CNY1) ($.15 = C NY1) ($.09 = C NY1) Assets Amou nt Temporal Current Temporal CurrentCash CNY5,000 $ 600 $ 750 $ 750 $ 450 $ 450Accts. R eceivable 14,000 1,680 2,100 2,100 1,260 1,260 Inventories(cost=24,000) 22,000 2,640 3,300 3,300 1,980 1,980Fixed assets, net 39,000 3,600 3,600 5,850 3,600 3,510 Total CNY 80,000 $8,520 $9,750 $12,000 $11,700 $7,200Liabilities & Owners EquityAccts. Payable CNY21,000 $2,520 $3,150 $3,150 $1,890 $1,890Long-term debt 27,000 3,240 4,050 4,050 2,430 2,430Stockholders equity 32,000 2,760 2,550 4,800 7,380 2,880Total NT$ 80,000 $8,520 $9,750 $12,000 $11,700 $7,200Accou nting exposure NT$ (7,000) 32,000 (7,000) 32,000Translation gain (loss) US$ (210) 960 210 (960)c. Students will quickly discover that each translation method has its advantages and disadvantages. After some discussion, the question of translation objectives will arise. Currency translation objectives are based on how foreign operations are viewed. If foreign operations are considered extensions of the parent, a case can be made for a historical rate method: current-noncurrent, monetary-nonmonetary, or temporal. If foreign operations are viewed from a local company perspective, a case can be made for the current rate method. Given the complexity of multinational business activities, one could argue that a single translation method will not serve all purposes for which translations are done. As long as the objectives of foreign currency translation differ among specific reporting entities, a practical solution is to insist onfull disclosure of the translation procedures used so that users have a basis for reconciling any differences that exist.9.Company A (Country A)(Reporting Currency = Apeso)Beginning of Year End of YearAssets: Exchange Rate Translated Exchange Rate TranslatedApeso 100 Apeso 100 Apeso 100Bol 100 Apeso 1 = Bol 1.25 Apeso 80 Apeso 1 = Bol 2 Apeso 50Apeso 180 Apeso 150Translation loss = A$ 30Company B (Country B)(Reporting Currency = Bol)Beginning of Year End of YearAssets: Exchange Rate Translated Exchange Rate TranslatedApeso 100 Apeso 1 = Bol 1.25 Bol 125 Apeso 1 = Bol 2 Bol 200Bol 100 Bol 100 Bol 100Bol 225 Bol 300Translation gain = Bol 75b. This exercise demonstrates the effect of the reporting currency on foreign currency translation results when the current rate method is used. Both companies are in seemingly identical situations, yet one reports a translation loss while the other reports a translation gain. One company reports shrinking assets while the other reports increasing assets. Nothing has actually happened but an exchange rate change. Also, despite a stronger Apeso, Company A reports a loss. Conversely, the Bol weakened, yet Company B reports a gain. It appears that a strengthening currency is not always good news, nor is a weakening currency always bad news.If the intention is to repatriate the funds invested in the foreign country (Country B from Company A’s perspective, Country A from Company B’s perspective), the scenario makes sense. After all, CompanyA will be repatriating fewer Apesos than originally invested and CompanyB will be repatriating moreB ol’s than originally invested. Fluctuating exchange rates have changed each company s command over a foreign currency. Assuming the company intends to repatriate the currency, it makes sense to include the respective gain or loss in income for the current year. On the other hand it can be argued that the gain or loss should be excluded fromincome if the company intends to keep the foreign assets invested permanently..10.Translation RateLocal Currency is Dollar isFunctional Currency Functional CurrencyCash Current CurrentMarketable securities (cost)Current Historical aAccounts receivable Current CurrentInventory (market) Current CurrentEquipment Current HistoricalAccumulated depreciation Current HistoricalPrepaid expenses Current HistoricalGoodwill Current HistoricalAccounts payable Current CurrentDue to parent (denominated in dollars) Current CurrentBonds payable Current CurrentIncome taxes payable Current CurrentDeferred income taxes Current CurrentCommon stock Historical HistoricalPremium on common stock Historical HistoricalRetained Earnings Balancing Residual Balancing ResidualSales Average AveragePurchases Average AverageCost of Sales Average HistoricalGeneral and administrative expenses Average AverageSelling expenses Average HistoricalDepreciation Average HistoricalAmortization of goodwill Average HistoricalIncome tax expense Average AverageInter-company interest expense Average Average___________________________________________________________________ _______________________________________________________a Fixed income securities intended to be held to maturity.11. a. Before riyal depreciation:Cash SAR 60,000,000 ÷ SA R3.75 = $ 16,000,000Inventory 120,000,000 ÷ SA R3.75 = 32,000,000Fixed Assets 750,000,000 ÷ SA R3.75 = 200,000,000Total $248,000,000After riyal depreciation:Cash SAR 60,000,000 ÷ SA R4.125 = $ 14,545,455Inventory 120,000,000 ÷ SA R3.75 = 32,000,000Fixed Assets 750,000,000 ÷ SA R3.75 = 200,000,000Total $246,545,455Translation loss $(1,454,455)b.The translation loss has no effect on MSC’s cash flows as it is the result of a restatement process.c.equity. However, in addition inventory and fixed assets would be translated at the current rate, as opposed to thehistorical rate, and the resulting translation loss would also be taken to consolidated equity. This would result in a different earnings number as well as asset measures.Before riyal depreciation:Cash SAR 60,000,000 ÷ SA R3.75 = $ 16,000,000Inventory 120,000,000 ÷ SA R3.75 = 32,000,000Fixed Assets 750,000,000 ÷ SA R3.75 = 200,000,000Total $248,000,000After riyal depreciation:Cash SAR 60,000,000 ÷ SA R4.125 = $ 14,545,455Inventory 120,000,000 ÷ SA R4.125 = 29,090,909Fixed Assets 750,000,000 ÷ SA R4.125 = 181,818,182Total $225,454,546Translation adjustnment reflected in equity$(22,545,454)Students could also be probed and asked how the adjusted numbers would impact certain ratios such as ROA or ROE, Debt to Equity, and asset turnover.12. a. The currency effects in the first and third paragraphs have an impact on Alcan’s cash flows. IN the firstparagraph, echange rate changes affect Alcan’s future revenues and costs and directly affect cash receipts andpayments. The third paragraph involves settling foreign currency transactions at a different echange rate than when the transaction were entered into.b.Alcan appears to be employing the monetary-nonmonetary method.c. Many analysts back out translation gains and losses from reported earnings as these are largely non-cash itemsthat simply result from a restatement process. This wouldespecially be the case if Alcan were being compared to a company employing the current rate method. Disregarding translation gains and losses would have the following effect on reported earnings:20X5 20X4 20X3With translation G/L $129m $258m $64mTranslation G/L (86) (153) (326)Without Translation G/L $215m $411m $390mThe impact on the pattern of earnings would change significantly. The year to year changes in earnings both before and after abstracting from currency translation effects are:20X5/20X3 20X5/20X4 20X4/20X3With translation G/L 102% -50% 303%Without Translation G/L 45% -48% 5%Case 6-1 Regents CorporationThe nature of Regents’s operation is such that choice of an appropriate functional currency is ultimately a judgement call. Students can argue for either currency and should be evaluated on the strength of their analysis. A major lesson of this case is that the functional currency choice is important since the currency designation dictateswhich translation method, (current or temporal) is ultimately used. The financial statement effects can be very different. Thus it is importantfor a reader of financial statements to understand how the differing measurement options affect the balance sheet and income statement and be prepared to adjust from one framework to the other, even if only crudely.TEMPORAL METHOD(U.S. DOLLAR IS THE FUNCTIONAL CURRENCY)Balance Sheet Accounts, 12/31/X7 Foreign Currency Exchange RateDollar EquivalentCash ￡ 1,060 1.80 $ 1,908Accounts receivable 2,890 1.90 5,491Inventory 3,040 1.78 5,411Fixed assets 4,400 1.70 7,480 Accumulated depreciation (420) 1.70 (714)Patent ----- -----Total ￡10,970 $19,576 Accounts payable ￡ 1,610 1.80 $ 2,898Due to parent 1,800 1.80 3,240Long-term debt 4,500 1.80 8,100 Deferred taxes 80 1.80 144 Common stock 1,500 1.70 2,550 Retained earnings 1,480 residual 2,644￡10,970 $19,576 Income Statement, 12/31/X8 Foreign Currency Exchange Rate Dollar Equivalent Sales ￡ 16,700 1.86 $ 31,062Cost of sales a (11,300) (20,706) General and administrative (1,600) 1.86 (2,976) Depreciation (280) 1.70 (476)(20) 1.82 (36) Interest (480) 1.86 (893) Transaction gain 125 1.86 233 Aggregate translation adjustment b (368) Taxes:Current (670) 1.86 (1,246)Deferred (40) 1.86 (74)Net income ￡ 2,435 $ 4,520 Retained earnings, 12/31X7 1,480 2,644 Dividends (300) 1.86 (558) Retained earnings, 12/31X8 ￡ 3,615 $ 6,606a Beginning inventory ￡ 3,040 1.78 $ 5,411 Purchases 11,690 1.86 21,743Ending inventory 3,430 1.88 6,448 Cost of Sales 11,300 $20,706b Aggregate translation adjustment:1. Monetary assets, 12/31/X7 ￡ 3,950Monetary liabilities, 12/31/X7 7,990(￡ 4,040) x (1.90 - 1.80) = ($404) 2. Change in negative exposure: 12/31/X7 (￡ 4,040)12/31/X8 (2,565 )￡ 1,475Composition of decrease:Sources of monetary items:Net income ￡2,435Depreciation 300 ￡2,735Uses of monetary items:Inventory increase ￡(390)Addition to fixed assets (500)Purchase of patent (70)Dividends (300 ) (1,260 )￡1,475￡2,345 x (1.90 - 1.86) = $94300 x (1.90 – 1.86) = 12 $1094. Uses of monetary items x difference in year-end rate and rate used to translate those items =￡(390) x (1.90 – 1.86) = $(15)(300) x (1.90 - 1.86) = (12)(500) x (1.90 - 1.82) = (40)(70) x (1.90 - 1.82) = (6 ) (73)Aggregate translation adjustment = ($404)109(73 )($368)Balance Sheet, 12/31/X8 Foreign Currency Exchange Rate Dollar EquivalentCash ￡ 1,150 1.90 $2,185 Accounts receivable 3,100 1.90 5,890 Inventory 3,430 1.88 6,448Fixed assets a 4,900 8,390 Accumulated depreciation b (720) (1,226)Patent 70 1.82 127Total ￡11,930 $21,814 Accounts payable ￡ 1,385 1.90 $ 2,632Due to parent 1,310 1.90 2,489Long-term debt 4,000 1.90 7,600 Deferred taxes 120 1.90 228 Common stock 1,500 1.70 2,550 Retained earnings 3,615 6,309Total ￡11,930 $21,814a Original assets ￡ 4,400 1.70 $ 7,480New assets 500 1.82 910$ 8,390b Original assets ￡ 700 1.70New assets 20 1.82 36$ 1,226CURRENT RATE METHOD(LOCAL CURRENCY IS THE FUNCTIONAL CURRENCY)Balance Sheet Accounts, 12/31/X7 Foreign Currency Exchange Rate Dollar Equivalent Cash ￡ 1,060 1.80 $ 1,908 Accounts receivable 2,890 1.80 5,202 Inventory 3,040 1.80 5,472Fixed assets 4,400 1.80 7,920 Accumulated depreciation (420) 1.80 (756)Patent --- ---Total ￡10,970 $19,746Accounts payable ￡ 1,610 1.80 $ 2,898Due to parent 1,800 1.80 3,240Long-term debt 4,500 1.80 8,100Deferred taxes 80 1.80 144Common stock 1,500 1.70 2,550Retained earnings 1,480 2,355Cumulative translation adjustment --- 459(given)Total ￡ 10,970 $19,746Income Statement, 12/31/X8 Foreign Currency Exchange Rate Dollar Equivalent Sales ￡16,700 1.86 $31,062Cost of sales (11,300) 1.86 (21,018)General and administrative (1,600) 1.86 (2,976) Depreciation (300) 1.86 (558)Interest (480) 1.86 (893) Transaction gain 125 1.86 232Taxes:Current (670) 1.86 (1,246)Deferred (40) 1.86 (74)Net income ￡ 2,435 $ 4,529Retained earnings, 12/31X7 1,480 2,355Dividends (300) 1.86 (558)Retained earnings, 12/31X8 ￡ 3,615 $ 6,326Balance Sheet, 12/31/X8 Foreign Currency Exchange Rate Dollar EquivalentCash ￡ 1,150 1.90 $ 2,185Accounts receivable 3,100 1.90 5,890Inventory 3,430 1.90 6,517Fixed assets 4,900 1.90 9,310Accumulated depreciation (720) 1.90 (1,368)Patent 70 1.90 133Total ￡ 11,930 $22,667Accounts payable ￡ 1,385 1.90 $ 2,632Due to parent 1,310 1.90 2,489Long-term debt 4,000 1.90 7,600Deferred taxes 120 1.90 228Common stock 1,500 1.70 2,550Retained earnings 3,615 6,326Cumulative translation adj. ----- 842aTotal ￡11,930 $22,667a Cumulative translation adjustment:1. Net exposed assets, 12/31/X7, x change in current rate = ￡2.980 x (1.90 - 1.80) = $2982. Change in net assets x difference between year-end and average rate = ￡2.135 x (1.90 - 1.86) = 853. Cumulative translation adjustment 12/31/X7 4594. Cumulative translation adjustment, 12/31/X8 $842Selected policy issues raised by the Regents Corporation case:1. Are the FASB s criteria for selecting a functional currency designation adequate? Are there criteria that are more definitive than those identified in this chapter?2. W ill statement readers understand the nature of the aggregate exchange adjustment appearing in the consolidated income statement under the temporal method of translation that includes both transaction and translation gains and losses?。

Problems and Applications1. If the price ceiling of $40 per ticket is below the equilibrium price, then quantitydemanded exceeds quantity supplied, so there’s a shortage of tickets. The policydecreases the number of people who attend classical music concerts, since supply islower because of the lower price.2. a. The imposition of a binding price floor in the cheese market is shown in Figure6-3. In the absence of the price floor, the price would be P1 and the quantitywould be Q1. With the floor set at P f, which is greater than P1, the quantitydemanded is Q2, while quantity supplied is Q3, so there is a surplus of cheese inthe amount Q3 - Q2.b. The farmers’ complaint that their total revenue has declined is correct ifdemand is elastic. With elastic demand, the percentage decline in quantitywould exceed the percentage rise in price, so total revenue would decline.c. If the government purchases all the surplus cheese at the price floor,producers benefit and taxpayers lose. Producers would produce quantity Q3of cheese, and their total revenue would increase substantially. Butconsumers would buy only quantity Q2 of cheese, so they are in the sameposition as before. Taxpayers lose because they would be financing thepurchase of the surplus cheese through higher taxes.Figure 6-33. a. The equilibrium price of frisbees is $8 and the equilibrium quantity is 6 millionfrisbees.b. With a price floor of $10, the new market price is $10 since the price floor isbinding. At that price, o nly 2 million frisbees are sold, since that’s thequantity demanded.c. If there’s a price ceiling of $9, it has no effect, since the market equilibriumprice is $8, below the ceiling. So the equilibrium price is $8 and theequilibrium quantity is 6 million frisbees.4. a. Figure 6-4 shows the market for beer without the tax. The equilibrium priceis P1 and the equilibrium quantity is Q1. The price paid by consumers is thesame as the price received by producers.Figure 6-4Figure 6-5b. When the tax is imposed, it drives a wedge of $2 between supply and demand,as shown in Figure 6-5. The price paid by consumers is P2, while the pricereceived by producers is P2 - $2. The quantity of beer sold declines to Q2.5. Reducing the payroll tax paid by firms and using part of the extra revenue to reducethe payroll tax paid by workers would not make workers better off because the division of the burden of a tax depends on supply and demand, not who must pay the tax.Since the tax wedge would be larg er, it’s likely that both firms and workers, who share the burden of any tax, would be worse off.6. If the government imposes a $500 tax on luxury cars, the price paid by consumers willrise less than $500, in general. The burden of any tax is shared by both producersand consumers−the price paid by consumers rises and the price received by producers falls, with the difference between the two equal to the amount of the tax. The onlyexceptions would be if the supply curve were perfectly elastic or the demand curvewere perfectly inelastic, in which case consumers would bear the full burden of the tax and the price paid by consumers would rise by exactly $500.7. a. It doesn’t matter whether the tax is imposed on producers or consumers−theeffect will be the same. With no tax, as shown in Figure 6-6, the demandcurve is D1 and the supply curve is S1. If the tax is imposed on producers, thesupply curve shifts up by the amount of the tax (50 cents) to S2. Then theequilibrium quantity is Q2, the price paid by consumers is P2, and the pricereceived (after taxes are paid) by producers is P2 - 50 cents. If the tax isinstead imposed on consumers, the demand curve shifts down by the amountof the tax (50 cents) to D2. The downward shift in the demand curve (whenthe tax is imposed on consumers) is exactly the same magnitude as theupward shift in the supply curve when the tax is imposed on producers. Soagain, the equilibrium quantity is Q2, the price paid by consumers is P2(including the tax paid to the government), and the price received byproducers is P2 - 50 cents.Figure 6-6Figure 6-7b. The more elastic is the demand curve, the more effective this tax will be inreducing the quantity of gasoline consumed. Greater elasticity of demandmeans that quantity falls more in response to the rise in the price of gasoline.Figure 6-7 illustrates this result. Demand curve D1 represents an elasticdemand curve, while demand curve D2 is more inelastic. To get the same tax wedge between demand and supply requires a greater reduction in quantitywith demand curve D1 than for demand curve D2.c. The consumers of gasoline are hurt by the tax because they get less gasolineat a higher price.d. Workers in the oil industry are hurt by the tax as well. With a lower quantityof gasoline being produced, some workers may lose their jobs. With a lowerprice received by producers, wages of workers might decline.8. a. Figure 6-8 shows the effects of the minimum wage. In the absence of theminimum wage, the market wage would be w1 and Q1 workers would beemployed. With the minimum wage (w m) imposed above w1, the marketwage is w m, the number of employed workers is Q2, and the number ofworkers who are unemployed is Q3 - Q2. Total wage payments to workers areshown as the area of rectangle ABCD, which equals w m times Q2.b. An increase in the minimum wage would decrease employment. The size ofthe effect on employment depends only on the elasticity of demand. Theelasticity of supply doesn’t matter, because there’s a surplus of labor.c. The increase in the minimum wage would increase unemployment. The sizeof the rise in unemployment depends on both the elasticities of supply anddemand. The elasticity of demand determines the quantity of labordemanded, the elasticity of supply determines the quantity of labor supplied,and the difference between the quantity supplied and demanded of labor is theamount of unemployment.d. If the demand for unskilled labor were inelastic, the rise in the minimum wagewould increase total wage payments to unskilled labor. With inelasticdemand, the percentage decline in employment would be less than thepercentage increase in the wage, so total wage payments increase. However,if the demand for unskilled labor were elastic, total wage payments woulddecline, since then the percentage decline in employment would exceed thepercentage increase in the wage.Figure 6-8Figure 6-99. a. Figure 6-9 shows the effect of a tax on gun buyers. The tax reduces thedemand for guns from D1 to D2. The result is a rise in the price buyers pay forguns from P1 to P2, and a decline in the quantity of guns from Q1 to Q2.Figure 6-10b. Figure 6-10 shows the effect of a tax on gun sellers. The tax reduces thesupply of guns from S1 to S2. The result is a rise in the price buyers pay forguns from P1 to P2, and a decline in the quantity of guns from Q1 to Q2.c. Figure 6-11 shows the effect of a binding price floor on guns. The increase inprice from P1 to P f leads to a decline in the quantity of guns from Q1 to Q2.There is excess supply in the market for guns, since the quantity supplied (Q3) exceeds the quantity demanded (Q2) at the price P f.Figure 6-11Figure 6-12d. Figure 6-12 shows the effect of a tax on ammunition. The tax on ammunitionreduces the demand for guns from D1 to D2, because ammunition and guns arecomplements. The result is a decline in the price of guns from P1 to P2, and adecline in the quantity of guns from Q1 to Q2.10. a. Programs aimed at making the public aware of the dangers of smoking reducethe demand for cigarettes, shown in Figure 6-13 as a shift from demand curveD1 to D2. The price support program increases the price of tobacco, which isthe main ingredient in cigarettes. As a result, the supply of cigarettes shifts tothe left, from S1 to S2. The effect of both programs is to reduce the quantityof cigarette consumption from Q1 to Q2.Figure 6-13b. The combined effect of the two programs on the price of cigarettes isambiguous. The education campaign reduces demand for cigarettes, whichtends to reduce the price. The tobacco price supports raise the cost ofproduction of cigarettes, which tends to increase the price.c. The taxation of cigarettes further reduces cigarette consumption, since itincreases the price to consumers. As shown in the figure, the quantity falls toQ3.11. a. The effect of a 50 cent per cone subsidy is to shift the demand curve up by 50cents at each quantity, since at each quantity a consumer’s willingness to payis 50 cents higher. The effects of such a subsidy are shown in Figure 6-14.Before the subsidy, the price is P1. After the subsidy, the price received bysellers is P S and the effective price paid by consumers is P D, which equals P Sminus 50 cents. Before the subsidy, the quantity of cones sold is Q1; after thesubsidy the quantity increases to Q2.Figure 6-14b. Because of the subsidy, consumers are better off, since they consume more ata lower price. Producers are also better off, since they sell more at a higherprice. The government loses, since it has to pay for the subsidy.。

§6.4 数列求和1．求数列的前n 项和的方法 (1)公式法①等差数列的前n 项和公式 S n ＝n (a 1＋a n )2＝na 1＋n (n －1)2d .②等比数列的前n 项和公式 (Ⅰ)当q ＝1时，S n ＝na 1；(Ⅱ)当q ≠1时，S n ＝a 1(1－q n )1－q ＝a 1－a n q1－q .(2)分组转化法把数列的每一项分成两项或几项，使其转化为几个等差、等比数列，再求解． (3)裂项相消法把数列的通项拆成两项之差求和，正负相消剩下首尾若干项． (4)倒序相加法把数列分别正着写和倒着写再相加，即等差数列求和公式的推导过程的推广． (5)错位相减法主要用于一个等差数列与一个等比数列对应项相乘所得的数列的求和，即等比数列求和公式的推导过程的推广． (6)并项求和法一个数列的前n 项和中，可两两结合求解，则称之为并项求和．形如a n ＝(－1)n f (n )类型，可采用两项合并求解．例如，S n ＝1002－992＋982－972＋…＋22－12＝(100＋99)＋(98＋97)＋…＋(2＋1)＝5 050. 2．常见的裂项公式 (1)1n (n ＋1)＝1n －1n ＋1； (2)1(2n －1)(2n ＋1)＝12⎝⎛⎭⎫12n －1－12n ＋1；(3)1n ＋n ＋1＝n ＋1－n .【思考辨析】判断下面结论是否正确(请在括号中打“√”或“×”)(1)如果数列{a n }为等比数列，且公比不等于1，则其前n 项和S n ＝a 1－a n ＋11－q .( √ )(2)当n ≥2时，1n 2－1＝12(1n －1－1n ＋1)．( √ )(3)求S n ＝a ＋2a 2＋3a 3＋…＋na n 之和时只要把上式等号两边同时乘以a 即可根据错位相减法求得．( × )(4)数列{12n ＋2n －1}的前n 项和为n 2＋12n .( × )(5)若数列a 1，a 2－a 1，…，a n －a n －1是首项为1，公比为3的等比数列，则数列{a n }的通项公式是a n ＝3n －12.( √ )(6)推导等差数列求和公式的方法叫做倒序求和法，利用此法可求得sin 21°＋sin 22°＋sin 23°＋…＋sin 288°＋sin 289°＝44.5.( √ )1．已知等差数列{a n }的前n 项和为S n ，a 5＝5，S 5＝15，则数列⎩⎨⎧⎭⎬⎫1a n a n ＋1的前100项和为( )A.100101B.99101C.99100D.101100 答案 A解析 利用裂项相消法求和． 设等差数列{a n }的首项为a 1，公差为d . ∵a 5＝5，S 5＝15，∴⎩⎪⎨⎪⎧a 1＋4d ＝5，5a 1＋5×(5－1)2d ＝15，∴⎩⎪⎨⎪⎧a 1＝1，d ＝1， ∴a n ＝a 1＋(n －1)d ＝n . ∴1a n a n ＋1＝1n (n ＋1)＝1n －1n ＋1， ∴数列⎩⎨⎧⎭⎬⎫1a n a n ＋1的前100项和为1－12＋12－13＋…＋1100－1101＝1－1101＝100101.2．数列{a n }的通项公式为a n ＝(－1)n －1·(4n －3)，则它的前100项之和S 100等于( ) A ．200 B ．－200 C ．400 D ．－400 答案 B解析 S 100＝(4×1－3)－(4×2－3)＋(4×3－3)－…－(4×100－3)＝4×[(1－2)＋(3－4)＋…＋(99－100)]＝4×(－50)＝－200.3．(2014·广东)若等比数列{a n }的各项均为正数，且a 10a 11＋a 9a 12＝2e 5，则ln a 1＋ln a 2＋…＋ln a 20＝________ 答案 50解析 因为a 10a 11＋a 9a 12＝2a 10a 11＝2e 5， 所以a 10a 11＝e 5.所以ln a 1＋ln a 2＋…＋ln a 20＝ln(a 1a 2…a 20)＝ln [(a 1a 20)·(a 2a 19)·…·(a 10a 11)]＝ln(a 10a 11)10＝10ln(a 10a 11)＝10ln e 5＝50ln e ＝50. 4．3·2－1＋4·2－2＋5·2－3＋…＋(n ＋2)·2－n ＝________. 答案 4－n ＋42n解析 设S ＝3×12＋4×122＋5×123＋…＋(n ＋2)×12n ，则12S ＝3×122＋4×123＋5×124＋…＋(n ＋2)×12n ＋1. 两式相减得12S ＝3×12＋(122＋123＋…＋12n )－n ＋22n ＋1.∴S ＝3＋(12＋122＋…＋12n －1)－n ＋22n＝3＋12[1－(12)n －1]1－12－n ＋22n ＝4－n ＋42n .题型一 分组转化法求和例1 已知数列{a n }的通项公式是a n ＝2·3n －1＋(－1)n (ln 2－ln 3)＋(－1)n n ln 3，求其前n 项和S n .解 S n ＝2(1＋3＋…＋3n －1)＋[－1＋1－1＋…＋(－1)n ]·(ln 2－ln 3)＋[－1＋2－3＋…＋(－1)n n ]ln 3，所以当n 为偶数时，S n ＝2×1－3n 1－3＋n 2ln 3＝3n ＋n2ln 3－1；当n 为奇数时，S n ＝2×1－3n 1－3－(ln 2－ln 3)＋(n －12－n )ln 3＝3n －n －12ln 3－ln 2－1.综上所述，S n＝⎩⎨⎧3n＋n2ln 3－1，n 为偶数，3n－n －12ln 3－ln 2－1，n 为奇数.思维升华 某些数列的求和是将数列分解转化为若干个可求和的新数列的和或差，从而求得原数列的和，这就要通过对数列通项结构特点进行分析研究，将数列的通项合理分解转化．特别注意在含有字母的数列中对字母的讨论．(1)数列{a n }中，a n ＋1＋(－1)n a n ＝2n －1，则数列{a n }前12项和等于( )A ．76B ．78C ．80D ．82(2)已知数列{a n }的前n 项是3＋2－1,6＋4－1,9＋8－1,12＋16－1，…，则数列{a n }的通项公式a n ＝________，其前n 项和S n ＝________. 答案 (1)B (2)3n －1＋2n12n (3n ＋1)＋2n ＋1－2 解析 (1)由已知a n ＋1＋(－1)n a n ＝2n －1，① 得a n ＋2＋(－1)n ＋1a n ＋1＝2n ＋1，②由①②得a n ＋2＋a n ＝(－1)n ·(2n －1)＋(2n ＋1)， 取n ＝1,5,9及n ＝2,6,10， 结果相加可得S 12＝a 1＋a 2＋a 3＋a 4＋…＋a 11＋a 12＝78. (2)由已知得数列{a n }的通项公式为 a n ＝3n ＋2n －1＝3n －1＋2n ， ∴S n ＝a 1＋a 2＋…＋a n＝(2＋5＋…＋3n －1)＋(2＋22＋…＋2n ) ＝n (2＋3n －1)2＋2(1－2n )1－2＝12n (3n ＋1)＋2n ＋1－2. 题型二 错位相减法求和例2 已知等差数列{a n }的前3项和为6，前8项和为－4. (1)求数列{a n }的通项公式；(2)设b n ＝(4－a n )q n －1(q ≠0，n ∈N *)，求数列{b n }的前n 项和S n . 思维点拨 (1)列方程组求{a n }的首项、公差，然后写出通项a n . (2)q ＝1时，b n 为等差数列，直接求和；q ≠1时，用错位相减法求和． 解 (1)设等差数列{a n }的公差为d .由已知得⎩⎪⎨⎪⎧ 3a 1＋3d ＝6，8a 1＋28d ＝－4，解得⎩⎪⎨⎪⎧a 1＝3，d ＝－1.故a n ＝3＋(n －1)·(－1)＝4－n . (2)由(1)得，b n ＝n ·q n －1，于是 S n ＝1·q 0＋2·q 1＋3·q 2＋…＋n ·q n －1. 若q ≠1，将上式两边同乘以q 有 qS n ＝1·q 1＋2·q 2＋…＋(n －1)·q n －1＋n ·q n .两式相减得到(q －1)S n ＝nq n －1－q 1－q 2－…－q n －1 ＝nq n－q n －1q －1＝nq n ＋1－(n ＋1)q n ＋1q －1.于是，S n ＝nq n ＋1－(n ＋1)q n ＋1(q －1)2.若q ＝1，则S n ＝1＋2＋3＋…＋n ＝n (n ＋1)2.所以S n＝⎩⎪⎨⎪⎧n (n ＋1)2，q ＝1，nq n ＋1－(n ＋1)q n ＋1(q －1)2，q ≠1.思维升华 (1)错位相减法是求解由等差数列{b n }和等比数列{c n }对应项之积组成的数列{a n }，即a n ＝b n ×c n 的前n 项和的方法．这种方法运算量较大，要重视解题过程的训练． (2)注意错位相减法中等比数列求和公式的应用范围．已知首项为12的等比数列{a n }是递减数列，其前n 项和为S n ，且S 1＋a 1，S 2＋a 2，S 3＋a 3成等差数列． (1)求数列{a n }的通项公式；(2)若b n ＝a n ·log 2a n ，数列{b n }的前n 项和为T n ，求满足不等式T n ＋2n ＋2≥116的最大n 值．解 (1)设等比数列{a n }的公比为q ，由题意知a 1＝12，又∵S 1＋a 1，S 2＋a 2，S 3＋a 3成等差数列， ∴2(S 2＋a 2)＝S 1＋a 1＋S 3＋a 3， 变形得S 2－S 1＋2a 2＝a 1＋S 3－S 2＋a 3， 即得3a 2＝a 1＋2a 3，∴32q ＝12＋q 2，解得q ＝1或q ＝12， 又由{a n }为递减数列，于是q ＝12，∴a n ＝a 1q n －1＝(12)n .(2)由于b n ＝a n log 2a n ＝－n ·(12)n ，∴T n ＝－[1·12＋2·(12)2＋…＋(n －1)·(12)n －1＋n ·(12)n ]，于是12T n ＝－[1·(12)2＋…＋(n －1)·(12)n ＋n ·(12)n ＋1]，两式相减得：12T n ＝－[12＋(12)2＋…＋(12)n －n ·(12)n ＋1]＝－12·[1－(12)n ]1－12＋n ·(12)n ＋1，∴T n ＝(n ＋2)·(12)n －2.∴T n ＋2n ＋2＝(12)n ≥116，解得n ≤4， ∴n 的最大值为4. 题型三 裂项相消法求和例3 (2014·山东)已知等差数列{a n }的公差为2，前n 项和为S n ，且S 1，S 2，S 4成等比数列． (1)求数列{a n }的通项公式； (2)令b n ＝(－1)n－14na n a n ＋1，求数列{b n }的前n 项和T n . 解 (1)因为S 1＝a 1，S 2＝2a 1＋2×12×2＝2a 1＋2，S 4＝4a 1＋4×32×2＝4a 1＋12，由题意得(2a 1＋2)2＝a 1(4a 1＋12)，解得a 1＝1， 所以a n ＝2n －1. (2)b n ＝(－1)n－14n a n a n ＋1＝(－1)n －14n (2n －1)(2n ＋1)＝(－1)n －1(12n －1＋12n ＋1)． 当n 为偶数时，T n ＝(1＋13)－(13＋15)＋…＋(12n －3＋12n －1)－(12n －1＋12n ＋1)＝1－12n ＋1＝2n2n ＋1.当n 为奇数时，T n ＝(1＋13)－(13＋15)＋…－(12n －3＋12n －1)＋(12n －1＋12n ＋1)＝1＋12n ＋1＝2n ＋22n ＋1.所以T n＝⎩⎪⎨⎪⎧2n ＋22n ＋1，n 为奇数，2n2n ＋1，n 为偶数.(或T n ＝2n ＋1＋(－1)n －12n ＋1)思维升华 利用裂项相消法求和时，应注意抵消后并不一定只剩下第一项和最后一项，也有可能前面剩两项，后面也剩两项，再就是将通项公式裂项后，有时候需要调整前面的系数，使裂开的两项之差和系数之积与原通项公式相等．在数列{a n }中，a 1＝1，当n ≥2时，其前n 项和S n 满足S 2n ＝a n⎝⎛⎭⎫S n －12. (1)求S n 的表达式；(2)设b n ＝S n2n ＋1，求{b n }的前n 项和T n .解 (1)∵S 2n ＝a n ⎝⎛⎭⎫S n －12， a n ＝S n －S n －1 (n ≥2)， ∴S 2n ＝(S n －S n －1)⎝⎛⎭⎫S n －12， 即2S n －1S n ＝S n －1－S n ，① 由题意得S n －1·S n ≠0，①式两边同除以S n －1·S n ，得1S n －1S n －1＝2，∴数列⎩⎨⎧⎭⎬⎫1S n 是首项为1S 1＝1a 1＝1，公差为2的等差数列．∴1S n ＝1＋2(n －1)＝2n －1，∴S n ＝12n －1. (2)∵b n ＝S n 2n ＋1＝1(2n －1)(2n ＋1)＝12⎝⎛⎭⎫12n －1－12n ＋1， ∴T n ＝b 1＋b 2＋…＋b n ＝12[(1－13)＋(13－15)＋…＋(12n －1－12n ＋1)]＝12⎝⎛⎭⎫1－12n ＋1＝n2n ＋1.四审结构定方案典例：(12分)已知数列{a n }的前n 项和S n ＝－12n 2＋kn (其中k ∈N *)，且S n 的最大值为8.(1)确定常数k ，并求a n ；(2)求数列⎩⎨⎧⎭⎬⎫9－2a n 2n 的前n 项和T n .审题路线图S n ＝－12n 2＋kn 及S n 最大值为8S n 是n 的函数n ＝k 时(S n )max ＝S k ＝8(根据S n 的结构特征确定k 值)k ＝4，S n ＝－12n 2＋4n利用a n 、S n 的关系a n ＝92－n化简数列{}9－2a n 2n9－2a n 2n ＝n2n －1根据数列的结构特征，确定求和方法：错位相减法T n ＝1＋22＋322＋…＋n －12n －2＋n 2n －1①①式两边同乘以22T n ＝2＋2＋32＋…＋n －12n －3＋n2n －2②错位相减T n ＝2＋1＋12＋…＋12n －2－n2n －1＝4－n ＋22n －1.规范解答解 (1)当n ＝k ∈N *时，S n ＝－12n 2＋kn 取得最大值，即8＝S k ＝－12k 2＋k 2＝12k 2，故k 2＝16，k ＝4.当n ＝1时，a 1＝S 1＝－12＋4＝72，[3分]当n ≥2时，a n ＝S n －S n －1＝92－n .[6分]当n ＝1时，上式也成立，综上，a n ＝92－n .(2)因为9－2a n 2n ＝n2n －1，所以T n ＝1＋22＋322＋…＋n －12n －2＋n2n －1，① [7分]所以2T n ＝2＋2＋32＋…＋n －12n －3＋n2n －2 ②②－①得：2T n －T n ＝2＋1＋12＋…＋12n －2－n2n －1＝4－12n －2－n2n －1＝4－n ＋22n －1.[11分]故T n ＝4－n ＋22n －1.[12分]温馨提醒 (1)根据数列前n 项和的结构特征和最值确定k 和S n ，求出a n 后再根据{9－2a n2n }的结构特征确定利用错位相减法求T n .在审题时，要审题目中数式的结构特征判定解题方案； (2)利用S n 求a n 时不要忽视n ＝1的情况；错位相减时不要漏项或算错项数． (3)可以通过n ＝1,2时的特殊情况对结论进行验证.方法与技巧非等差、等比数列的一般数列求和，主要有两种思想：(1)转化的思想，即将一般数列设法转化为等差或等比数列，这一思想方法往往通过通项分解或错位相消来完成；(2)不能转化为等差或等比的特殊数列，往往通过裂项相消法、错位相减法、倒序相加法等来求和． 失误与防范1．直接应用公式求和时，要注意公式的应用范围，如当等比数列公比为参数(字母)时，应对其公比是否为1进行讨论．2．在应用错位相减法时，注意观察未合并项的正负号；结论中形如a n ，a n ＋1的式子应进行合并．3．在应用裂项相消法时，要注意消项的规律具有对称性，即前剩多少项则后剩多少项.A 组 专项基础训练 (时间：45分钟)1．数列112，314，518，7116，…，(2n －1)＋12n ，…的前n 项和S n 的值等于( )A ．n 2＋1－12nB ．2n 2－n ＋1－12nC ．n 2＋1－12n －1D ．n 2－n ＋1－12n答案 A解析 该数列的通项公式为a n ＝(2n －1)＋12n ，则S n ＝[1＋3＋5＋…＋(2n －1)]＋(12＋122＋…＋12n )＝n 2＋1－12n .2．已知函数f (n )＝n 2cos n π，且a n ＝f (n )＋f (n ＋1)，则a 1＋a 2＋a 3＋…＋a 100等于( ) A ．0 B ．－100 C ．100 D ．10 200 答案 B解析 f (n )＝n 2cos n π＝⎩⎪⎨⎪⎧－n 2(n 为奇数)n 2(n 为偶数)＝(－1)n ·n 2， 由a n ＝f (n )＋f (n ＋1) ＝(－1)n ·n 2＋(－1)n ＋1·(n ＋1)2 ＝(－1)n [n 2－(n ＋1)2] ＝(－1)n ＋1·(2n ＋1)， 得a 1＋a 2＋a 3＋…＋a 100＝3＋(－5)＋7＋(－9)＋…＋199＋(－201) ＝50×(－2)＝－100.3．数列a 1＋2，…，a k ＋2k ，…，a 10＋20共有十项，且其和为240，则a 1＋…＋a k ＋…＋a 10的值为( )A ．31B ．120C ．130D ．185 答案 C解析 a 1＋…＋a k ＋…＋a 10 ＝240－(2＋…＋2k ＋…＋20) ＝240－(2＋20)×102＝240－110＝130.4．已知数列{a n }的前n 项和S n ＝n 2－6n ，则{|a n |}的前n 项和T n 等于( ) A ．6n －n 2B ．n 2－6n ＋18C.⎩⎪⎨⎪⎧6n －n 2(1≤n ≤3)，n 2－6n ＋18(n >3) D.⎩⎪⎨⎪⎧6n －n 2(1≤n ≤3)，n 2－6n (n >3) 答案 C解析 ∵由S n ＝n 2－6n 得{a n }是等差数列，且首项为－5，公差为2.∴a n ＝－5＋(n －1)×2＝2n －7，∴n ≤3时，a n <0，n >3时，a n >0，∴T n ＝⎩⎪⎨⎪⎧6n －n 2(1≤n ≤3)，n 2－6n ＋18(n >3). 5．数列a n ＝1n (n ＋1)，其前n 项之和为910，则在平面直角坐标系中，直线(n ＋1)x ＋y ＋n ＝0在y 轴上的截距为( )A ．－10B ．－9C ．10D ．9答案 B解析 数列的前n 项和为11×2＋12×3＋…＋1n (n ＋1)＝1－1n ＋1＝n n ＋1＝910， ∴n ＝9，∴直线方程为10x ＋y ＋9＝0.令x ＝0，得y ＝－9，∴在y 轴上的截距为－9.6．数列{a n }满足a n ＋a n ＋1＝12(n ∈N *)，且a 1＝1，S n 是数列{a n }的前n 项和，则S 21＝________. 答案 6解析 由a n ＋a n ＋1＝12＝a n ＋1＋a n ＋2， ∴a n ＋2＝a n ，则a 1＝a 3＝a 5＝…＝a 21，a 2＝a 4＝a 6＝…＝a 20，∴S 21＝a 1＋(a 2＋a 3)＋(a 4＋a 5)＋…＋(a 20＋a 21)＝1＋10×12＝6. 7．已知数列{a n }满足a n ＋a n ＋1＝(－1)n ＋12(n ∈N *)，a 1＝－12，S n是数列{a n }的前n 项和，则S 2 013＝________.答案 －1 0072解析 由题意知，a 1＝－12，a 2＝1，a 3＝－32，a 4＝2，a 5＝－52，a 6＝3，…， 所以数列{a n }的奇数项构成了首项为－12， 公差为－1的等差数列，偶数项构成了首项为1，公差为1的等差数列，通过分组求和可得S 2 013＝[(－12)×1 007＋1 007×1 0062×(－1)]＋(1×1 006＋1 006×1 0052×1)＝－1 0072. 8．设f (x )＝4x 4x ＋2，若S ＝f (12 015)＋f (22 015)＋…＋f (2 0142 015)，则S ＝________. 答案 1 007解析 ∵f (x )＝4x 4x ＋2，∴f (1－x )＝41－x 41－x ＋2＝22＋4x， ∴f (x )＋f (1－x )＝4x 4x ＋2＋22＋4x＝1. S ＝f (12 015)＋f (22 015)＋…＋f (2 0142 015)，① S ＝f (2 0142 015)＋f (2 0132 015)＋…＋f (12 015)，② ①＋②得，2S ＝[f (12 015)＋f (2 0142 015)]＋[f (22 015)＋f (2 0132 015)]＋…＋[f (2 0142 015)＋f (12 015)]＝2 014， ∴S ＝2 0142＝1 007. 9．已知数列{a n }是首项为a 1＝14，公比为q ＝14的等比数列，设b n ＋2＝143log n a (n ∈N *)，数列{c n }满足c n ＝a n ·b n .(1)求数列{b n }的通项公式；(2)求数列{c n }的前n 项和S n .解 (1)由题意，知a n ＝(14)n (n ∈N *)， 又b n ＝143log 2n a ，故b n ＝3n －2(n ∈N *)．(2)由(1)，知a n ＝(14)n ，b n ＝3n －2(n ∈N *)， 所以c n ＝(3n －2)×(14)n (n ∈N *)． 所以S n ＝1×14＋4×(14)2＋7×(14)3＋…＋(3n －5)×(14)n －1＋(3n －2)×(14)n ， 于是14S n ＝1×(14)2＋4×(14)3＋7×(14)4＋…＋(3n －5)×(14)n ＋(3n －2)×(14)n ＋1. 两式相减，得34S n ＝14＋3[(14)2＋(14)3＋…＋(14)n ]－(3n －2)×(14)n ＋1＝12－(3n ＋2)×(14)n ＋1. 所以S n ＝23－3n ＋23×(14)n (n ∈N *)． 10．(2013·江西)正项数列{a n }的前n 项和S n 满足：S 2n －(n 2＋n －1)S n－(n 2＋n )＝0. (1)求数列{a n }的通项公式a n ；(2)令b n ＝n ＋1(n ＋2)2a 2n，数列{b n }的前n 项和为T n ，证明：对于任意的n ∈N *，都有T n <564. (1)解 由S 2n －(n 2＋n －1)S n －(n 2＋n )＝0，得[S n －(n 2＋n )](S n ＋1)＝0，由于{a n }是正项数列，所以S n ＋1>0.所以S n ＝n 2＋n (n ∈N *)．n ≥2时，a n ＝S n －S n －1＝2n ，n ＝1时，a 1＝S 1＝2适合上式．∴a n ＝2n (n ∈N *)．(2)证明 由a n ＝2n (n ∈N *)得b n ＝n ＋1(n ＋2)2a 2n ＝n ＋14n 2(n ＋2)2 ＝116⎣⎡⎦⎤1n 2－1(n ＋2)2 T n ＝116⎣⎡⎝⎛⎭⎫1－132＋⎝⎛⎭⎫122－142＋⎝⎛⎭⎫132－152＋… ⎦⎤＋⎝⎛⎭⎫1(n －1)2－1(n ＋1)2＋⎝⎛⎭⎫1n 2－1(n ＋2)2 ＝116⎣⎡⎦⎤1＋122－1(n ＋1)2－1(n ＋2)2<116⎝⎛⎭⎫1＋122＝564(n ∈N *)． 即对于任意的n ∈N *，都有T n <564. B 组 专项能力提升(时间：30分钟)11．已知数列2 008,2 009,1，－2 008，－2 009，…，这个数列的特点是从第二项起，每一项都等于它的前后两项之和，则这个数列的前2 014项之和S 2 014等于( )A ．2 008B ．2 010C ．1D ．0答案 B解析 由已知得a n ＝a n －1＋a n ＋1(n ≥2)，∴a n ＋1＝a n －a n －1.故数列的前8项依次为2 008,2 009,1，－2 008，－2 009，－1,2 008,2 009.由此可知数列为周期数列，周期为6，且S 6＝0.∵2 014＝6×335＋4，∴S 2 014＝S 4＝2 008＋2 009＋1＋(－2 008)＝2 010.12．1－4＋9－16＋…＋(－1)n ＋1n 2等于( )A.n (n ＋1)2 B ．－n (n ＋1)2C ．(－1)n＋1n (n ＋1)2 D ．以上答案均不对答案 C 解析 当n 为偶数时，1－4＋9－16＋…＋(－1)n ＋1n 2＝－3－7－…－(2n －1)＝－n 2(3＋2n －1)2＝－n (n ＋1)2； 当n 为奇数时，1－4＋9－16＋…＋(－1)n ＋1n 2＝－3－7－…－[2(n －1)－1]＋n 2＝－n －12[3＋2(n －1)－1]2＋n 2 ＝n (n ＋1)2， 综上可得，原式＝(－1)n ＋1n (n ＋1)2. 13．(2013·湖南)设S n 为数列{a n }的前n 项和，S n ＝(－1)n a n －12n ，n ∈N *，则： (1)a 3＝________；(2)S 1＋S 2＋…＋S 100＝________.答案 (1)－116 (2)13⎝⎛⎭⎫12100－1 解析 ∵a n ＝S n －S n －1＝(－1)n a n －12n －(－1)n －1a n －1＋12n －1(n ≥2)， ∴a n ＝(－1)n a n －(－1)n －1a n －1＋12n (n ≥2)． 当n 为偶数时，a n －1＝－12n ， 当n 为奇数时，2a n ＋a n －1＝12n ， ∴当n ＝4时，a 3＝－124＝－116. 根据以上{a n }的关系式及递推式可求．a 1＝－122，a 3＝－124，a 5＝－126，a 7＝－128， a 2＝122，a 4＝124，a 6＝126，a 8＝128. ∴a 2－a 1＝12，a 4－a 3＝123，a 6－a 5＝125，…，∴S 1＋S 2＋…＋S 100＝(a 2－a 1)＋(a 4－a 3)＋…＋(a 100－a 99)－⎝⎛⎭⎫12＋122＋123＋…＋12100 ＝⎝⎛⎭⎫12＋123＋…＋1299－⎝⎛⎭⎫12＋122＋…＋12100 ＝13⎝⎛⎭⎫12100－1. 14．已知数列{a n }的前n 项和S n ，满足：S n ＝2a n －2n (n ∈N *)．(1)求数列{a n }的通项a n ；(2)若数列{b n }满足b n ＝log 2(a n ＋2)，T n 为数列{b n a n ＋2}的前n 项和，求证：T n ≥12. (1)解 当n ∈N *时，S n ＝2a n －2n ，则当n ≥2时，S n －1＝2a n －1－2(n －1)，两式相减得a n ＝2a n －2a n －1－2，即a n ＝2a n －1＋2，∴a n ＋2＝2(a n －1＋2)，∴a n ＋2a n －1＋2＝2， 当n ＝1时，S 1＝2a 1－2，则a 1＝2，∴{a n ＋2}是以a 1＋2＝4为首项，2为公比的等比数列，∴a n ＋2＝4·2n －1，∴a n ＝2n ＋1－2；(2)证明 b n ＝log 2(a n ＋2)＝log 22n ＋1＝n ＋1，∴b n a n ＋2＝n ＋12n ＋1，则T n ＝222＋323＋…＋n ＋12n ＋1， 12T n ＝223＋324＋…＋n 2n ＋1＋n ＋12n ＋2， 两式相减得12T n ＝222＋123＋124＋…＋12n ＋1－n ＋12n ＋2 ＝14＋14(1－12n )1－12－n ＋12n ＋2 ＝14＋12－12n ＋1－n ＋12n ＋2＝34－n ＋32n ＋2， ∴T n ＝32－n ＋32n ＋1， 当n ≥2时，T n －T n －1＝－n ＋32n ＋1＋n ＋22n ＝n ＋12n ＋1>0， ∴{T n }为递增数列，∴T n ≥T 1＝12. 15．直线l n ：y ＝x －2n 与圆C n ：x 2＋y 2＝2a n ＋n 交于不同的两点A n ，B n ，n ∈N *.数列{a n }满足：a 1＝1，a n ＋1＝14|A n B n |2.(1)求数列{a n }的通项公式；(2)若b n ＝⎩⎪⎨⎪⎧2n －1(n 为奇数)，a n (n 为偶数)，求数列{b n }的前n 项和T n . 解 (1)由题意，知圆C n 的圆心到直线l n 的距离d n ＝n ， 半径r n ＝2a n ＋n ，所以a n ＋1＝(12|A n B n |)2＝r 2n －d 2n ＝(2a n ＋n )－n ＝2a n . 又a 1＝1，所以a n ＝2n －1.(2)当n 为偶数时，T n ＝(b 1＋b 3＋…＋b n －1)＋(b 2＋b 4＋…＋b n ) ＝[1＋5＋…＋(2n －3)]＋(2＋23＋…＋2n －1) ＝n (n －1)2＋2(1－2n )1－4＝n 2－n 2＋23(2n －1)． 当n 为奇数时，n ＋1为偶数，T n ＋1＝(n ＋1)2－(n ＋1)2＋23(2n ＋1－1) ＝n 2＋n 2＋23(2n ＋1－1)． 而T n ＋1＝T n ＋b n ＋1＝T n ＋2n ，所以T n ＝n 2＋n 2＋13(2n －2)． 所以T n ＝⎩⎨⎧n 2－n 2＋23(2n －1)(n 为偶数)，n 2＋n 2＋13(2n －2)(n 为奇数).。

Unitl1.Virtue is …self-centered.By right action, we mean it must help promote personal interest. 2•…(Poverty) was a product of their excessive fecundity...The poverty of the poor was caused by their having too many children.3....the rich were not responsible for either its creation or its amelioration.The rich were not to blame for the existence of poverty so they should not be asked to undertake the task of solving the problem.4.It is merely the working out of a law of nature and a law of God.It is only the result or effect of the law of the survival of the fittest applied to nature of to human society.5.It declined in popularity, and references to its acquired a condemnatory tone・People began to reject Social Darwinism because it seemed to glorify brutal force and oppose treasured values of sympathy, love and friendship. Therefore, when it was mentioned, it was usually the target of criticism.6....the search for a way of getting the poor off our conscience was not at an end; it was only suspended・The desire to find a way to justify the unconcern for the poor had not been abandoned; it had only been put off.7....only rarely given to overpaying for monkey wrenches, flashlights, coffee makers, and toilet seats.Government officials, on the whole, are good; it is very rare that some would pay high prices for office equipment to get kickbacks.8.This is perhaps our most highly influential piece of fiction.It is a very popular story and has been accepted by many but it is not true.9.Belief can be the servant of truth…but even more of convenience.Belief can be useful in the search for truth, but more often than not it is accepted because it is convenient and self-serving.10.George Gilder... Who tells to much applause that the poor must have the cruel spur of their own suffering to ensure effort...George Gilder advances the view that only when the poor suffer from great misery will they be stimulated to make great efforts to change the situation, in other words, suffering is necessary to force the poor to work hard.Unit 21.But these marks of wild country called to may father like the legendary siren song. Though the place was not pleasant or disagreeable, my father was deeply attracted to it precisely because of its unexplored, uncultivated natural state, and the challenge.2.H rm afraid the day f s going to catch us/1 I explained, wondering what great disaster might befall us if it did.As a little girl, I believed my father's words, and was genuinely afraid of the possible disaster—if we didn't hurry up, the day would catch us and terrible things might happen.3....from time to time he was halfheartedly sought for trial, though few crimes seemed to lead directly to his door.In this place, though the police wound make some effort without real earnest to investigate Watson and bring him to court, there seemed to be little concrete evidence to prove that he was responsible for certain illegal activities.4.The stranglehold Watson had over this section of Florida was not dissimilar to the unscrupulous activities of certain lawmen, other legal crooks, and even governors that our state was to suffer through its history.The control Watson had over this part of Florida was much similar to the dishonest or illegal activities of the law-enforcing officials and governors which Florida witnessed in the 20th century.5.There was the little shack, not the most gracious of living quarters, and there was a murderer for our nearest and only neighbor, about thirty miles away.Before the family built their own house, they lived in a shabby cabin at Gopher Key, close to the merciless Watson.6.King Richard in his gluttony never sat at a table more sumptuous than ours was three times a day…We had abundant food on the island, and even the meals enjoyed by King Richard, who was famous for his love of food, couldn^t possibly compare with ours.7.Despite the unrelenting heat, we were happy to be let off from our hours of school indoors, sessions which our mother kept every day, rain or shine.Although it was very hot outside in the sun, we were happy to be dismissed from my mothers sessions indoors, we would have to read and write with her every day no matter what the weather was like.Unit3l....even droughts, floods, and heat waves may become unwitting acts of man.What people do may unintentionally cause droughts, floods, and heat waves.2.But this image, now repeatedly thrust before us in photographs, posters, and advertisements, is misleading.The Earth we see in photos, posters, and ads, which appears so beautiful, is not the true reflection of the world we live in, such image lulls us into complacency.3.The technosphere has become sufficiently large and intense to alter the natural processes that govern the ecosphere.Human activities have taken place over such large areas and with such intensity that they have already caused disastrous effects on ecology.4....which could establish itself only because it fitted properly into the preexisting system.The fish could play its role because it became a necessary link with the processes preceding it and the processes following it in the ecological system.5.Defined so narrowly, it is no surprise that cars have properties that are hostile to their environment.When cars are produced to serve such narrow purposes, it is not surprising that some of their characteristic qualities are harmful to the environment.6.Yields rose, but not in proportion to the rate of fertilizer application...The farmer applied more and more fertilizer, and the production did rise but did notincrease at the same rate of the fertilize匚7...their waste is flushed into the sewer system altered in composition but not in amount at treatment plant…People eat plants and animals, and their waste is flushed into the sewer system. After being processed, the waste is still waste, the residue will go into rivers, oceans, and will have harmful effect on the aquatic ecosystem.8.Left to their own devices, ecosystems are conservative...If the ecosystems are not upset by outside intrusion, they will remain the same with very little change9.In contrast to the ecosphere, the technosphere is composed of objects and materials that reflect a rapid and relentless process of change and variation.The characteristics of the objects and materials in the technosphere are rapid change and great variety.10.But this is done only at the cost of understanding.If we take side in the war of the two words, we are doing so at the risk of failing to have a clear understanding of the nature and cause of the war, thus, we lose the chance to really solve the grave environmental crisis.Unit 4 Nettles1.How all my own territory would be altered, ad if a landslide had gone through it and skimmed off all meaning except loss of Mike.The impact of Mike's leaving on my life was beyond my imagination. I didn't expect that Mike's leaving would have such a tremendous power that it would change the meaning of my existence completely. All my thoughts were about loss of Mike.2.During that time of life that is supposed to be a reproductive daze, with the woman's mind all swamped by maternal juices, we were still compelled to discuss Simone de Beauvoir and Arthur Koestler and "The Cocktail Party11.At that time, we were young mothers, and we were supposed to lead a terribly busy life full of confusion and bewilderment caused by giving birth to and raising babies, and our minds were supposed to be fully occupied by how to feed the babies and things like that. However, in the midst of all this we still felt the need to discuss some of the important thinkers of our time like Simone de Beauvoir and Arthur Koestler and T. S. Eliots sophisticated work "The Cocktail Party n.3•…I would be frightened, not of any hostility but of a kind of nonexistence.I would be frightened, and my fear was not caused by my neighbor's visibly hostile and violent way of life, but by a kind of formless and hidden emptiness and meaninglessness of human existence. What happened around me was totally irrelevant to me, and I felt very isolated and alienated・4.She did not ask me—was it delicacy or disapproval? -一about my new life.She did not ask me about my new life, either out of subtle consideration for my feeling about this sensitive subject or out of disapproval for my new life style.5.It would be a sleazy thing to do, in the house of his friends.It would be a morally low thing, an indecent thing to commit infidelity in the house of a friend.6.1 knew now that he was a person who had hit rock bottom.I knew that he was a person who had experienced the worst in life, the hardest experience a person might have to endure.7.He and wife knew that together and it bound them, as something like that would either break you apart or bind you, for life.They experienced the worst together and they knew what it was like and understood the meaning of that experience. Such an experience posed the gravest test to people. If they stood the test, their friendship or marriage would be strengthened, and a sacred bondage would be formed between them. But if they failed the test, their relationship would be broken and they would be driven apart.8.Not risking a thing yet staying alive as a sweet trickle, an underground resource. With the weight of this now stillness on it, this seal.If they acted on love, they would take risks, they wouldn't do that or go further in their relationship, but they would rather let their love remain as a sweet trickle, which would flow on gently and permanently, and as an underground resource, which would never be fully tapped but would never go dry.Unit 51 ….the national rejection of dogmatic preconceptions about the nature of the social and economic orderThere are such prejudices in an arrogant manner about the characteristic of the social order and economic order and they take it for granted. The country just rejected such prejudice.2. Nor can one suggest that Americans have been consistently vulnerability to secular ideology ever afterNo one can say that Americans have never been tempted by the approach of understanding, preserving or transforming the world according to rigid dogmas.3- ..and any intellect so shaped was ...ever afterA mind influenced by Calvinist theology would surely find it somewhat difficult to resist other ideological temptations to ideological thinking.4.Pragmatism is no more wholly devoid...experiencePragmatism is not completely free from abstract ideas just as ideology is not completely free from experience, that is to say, abstract ideas have a place in pragmatism just as experience has a role in ideology.5.As an ideologist, however, Jefferson.•••historical curiosityAs a man following a fixed set of beliefs, Jefferson is only an interesting historical figure. His beliefs are out of date and are irrelevant to present-day reality.6- ...whose central dogma is confided to the custody of an infallible priesthoodTheir central beliefs are imprisoned by the whole body of priests who are always effective.7....where free men may find partial truths, but where ...on Absolute TruthIn this universe a person whose mind is unconstrained may be able to discover relation truths but no man on earth can claim that he has already grasped the one and only truth.8.But ideology is a drug; no matter how ...it still persists.Ideology has the characteristic of a narcotic. In spite of the fact that it has been provedwrong many times by experience, people still long to commit themselves to ideology.9....the only certainty in an absolute system is the certainty of absolute abuse.The only thing that is sure of a despotic system is the unrestricted exercise of powe r. 10・ The distinctive human triumph..」ies in the capacity to understand the frailty of human striving ...nonethelessThe most outstanding achievement of humanity is they know that no matter how hard they try, they cannot achieve Absolute truth, yet they continue to make great efforts and refuse to give up.Unit71.For man holds in his mortal hands the power to abolish all forms of human life.As a result of technological development, human belongs now have the power to put an end to poverty and human, misery, but at the same time they also possess the power to destroy the whole world, rendering it uninhabitable and lifeless.2....unwilling to witness or permit the slow undoing of those human rights...We do not want to see or to allow the slow destruction of those human rights.3.To those peoples in the huts and villages of half.....of mass misery, we pledge our best efforts to help them help themselves...To the people of the underdeveloped countries living in poverty in rural areas, we are committed to helping them to rid themselves of mass poverty by their own efforts.4.But this peaceful revolution of hope cannot become the prey of hostile powers.But we should not let any communist power take advantage of this alliance for progress to expand its influence.5.And let every other power know that this....of its own house.We want to make clear to the communist powers that Americas are the Americas of the Americans. Do not attempt to penetrate into this area.6....before the dark powers of destruction••…or accidental self-destruction.Before the world is destroyed by a nuclear war launched in a preemptive attack or caused by accident.7....yet both racing to alter the uncertain...of mankinds final war.Yet both sides attempt to get an edge in the nuclear arms race so as to break the mutual deterrence which has so far prevented the outbreak of a nuclear wa匚8....civility is not a sign of weakness, and sincerity is always subject to proof.To be ready to negotiate and establish friendly relations does not mean that we are weak or afraid. Declarations of sincere intention have to be tested by actions.9.Let both sides seek to invoke the wonders of science instead of its terrors.Let the two sides use the fruits of science for the benefit of humanity rather than using high-tech weapons to kill and destroy.10・...each generation of Americans has been summoned to give testimony to its national loyalty.There have been occasions for each generations of Americans to be called upon to fight and die for their country.。