曼昆 宏观经济经济学第九版 英文原版答案9
国际经济学第九版英文课后答案
CHAPTER 1*(Core Chapter)INTRODUCTIONOUTLINE1.1 Importance of International EconomicsCase Study 1-1: The Dell and Other PCs Sold in the United States Are All ButAmericanCase Study 1-2: What Is an "American" Car?1.2 International Trade and The Nation's Standard of LivingCase Study 1-3: Rising Importance of International Trade to the United States 1.3 The Major U.S. Trade Partners: The Gravity Model1.4 The Subject Matter of International Economics1.5 Purpose of International Economic Theories and Policies1.6 Current International Economic Challenges1.7 The Globalization Challenge1.8 Organization and Methodology of the BookAppendix: A1.1 Basic International Trade DataA1.2 Sources of Additional International Data and InformationKey TermsInterdependence Adjustment in the balance of payments Gravity model MicroeconomicsInternational trade theory MacroeconomicsInternational trade policy Open economy macroeconomicsNew protectionism International financeForeign exchange markets GlobalizationBalance of payments Anti-globalization movementLecture Guide1. As the first chapter of the book, the general aim here is simply to define the fieldof study of international economics and its importance in today's interdependent world.The material in this chapter can be covered in two classes. I would utilize oneclass to cover Sections 1 to 4 and the second class to cover Sections 5 to 8. Iwould spend most of the second class on Section 6 on the major currentinternational economic challenges facing the United States and the world todayand to show how international economics can suggest ways to solve them. Thisshould greatly enhance students' motivation.Answer to Problems1. a) International economic problems reported in our daily newspapers are likely toinclude:•trade controversies between the United States, Europe, Japan, and China;•great volatility of exchange rates;•Increasing international competition from China and fear of job losses in the United States and other advanced countries.•structural unemployment and slow growth in Europe, and stagnation in Japan;•financial crises in emerging market economies;•restructuring problems of transition economies;•deep poverty in many developing nations in the world.b) Can result in trade restrictions or even a trade war, which reduce the volumeand the gains from trade;•discourage foreign trade and investments, and thus reduce the benefits from trade;•Can result in trade restrictions or even a trade war, which reduce the volume and the gains from trade;•reduces European and Japanese imports and the volume and the benefits from trade;•financial crises in emerging market economies could spread to the United States;•can lead to political instability, which will adversely affect the United States;•can lead to political instability in these countries - which also adversely affect the United States.c) Can result in your paying higher prices for imported products;•lead to great fluctuations in the price of imported products and cost of foreign travel;•Can lead higher prices for imported products and increases the chances that you will have to change jobs;•can lead you to support demands for trade protection in the United States;•can reduce the value of your investments (such as a stocks) in the United States;•can lead to your paying higher taxes for the United States to respond to these threats;•can result in your paying higher taxes to help these nations.2. a) Five industrial nations not mentioned are: Italy, France, Canada, Austria, andIreland.b) See Table 1A.c) Smaller nations, such as Ireland and Austria, are more interdependent than thelarger ones. Note that interdependence was measured by the percentage of thevalue of imports and exports (line 98c and 90c, respectively in IFS) to GDP (line99b).Table 1AEconomic Interdependence asMeasured by Imports and Exports*Source: International Financial Statistics(Washington, D.C., IMF, March 2006).3. a) Five developing nations not mentioned in the text are: Brazil, Pakistan,Colombia, Nepal, and Tunisia.b) See Table 1B.c) In general, the smaller the nation, the greater is its economic interdependence.Note that interdependence was measured by the percentage of the value ofimports and exports (line 98c and 90c, respectively in IFS) to GDP (line 99b).Table 1BEconomic Interdependence asMeasured by Imports and Exports*Source: International Financial Statistics(Washington, D.C., IMF, March 2006).4. Trade between the United States and Brazil is much larger than trade between theUnited States and Argentina. Since Brazil is larger and closer than Argentina, this trade does follow the predictions of the gravity model.5. a) Mankiw’s Economics (4th., 2007) includes the following microeconomicstopics:•The market forces of demand and supply;•elasticity and its application;•the theory of consumer choice;•consumers, producers, and the efficiency of markets;•the costs of production;•firms in competitive markets;•monopoly;•oligopoly;•monopolistic competition;•markets for the factors of production;•the demand for resources;b) Just as the microeconomics parts of your principles text deal with individualconsumers and firms, and with the price of individual commodities and factors of production, so do Parts One and Two of this text deal with production andconsumption of individual nations with nations with and without trade, and withthe relative price of individual commodities and factors of production.c) Mankiw’s Economi cs (4th., 2007) includes the following microeconomics topics:measuring a nation’s income and the cost of living;•production and growth;•savings investment and the financial system;•unemployment and its natural rate;•the monetary system, growth and inflation;•money growth and inflation;•open-economy macroeconomics: basic concepts;• a macroeconomic theory of the open economy;•aggregate demand and aggregate supply;•the influence of monetary and fiscal policy on aggregate demand;•the short-run trade off between inflation and unemployment•five debates over macroeconomic policy.d) Just as the macroeconomics parts of your principles text deal with the aggregatelevel of savings, consumption, investment, and national income, the general price level, and monetary and fiscal policies, so do Parts Three and Four of this textdeal with the aggregate amount of imports, exports, the total international flow of resources, and the policies to affect these broad aggregates.6. a) Consumer demand theory predicts than when the price of a commodity rises(cet. par.), the quantity demanded of the commodity declines.When the price of imports rises to domestic consumers, the quantity demanded of exports can be expected to decline (if everything else remains constant).7. a) A government can reduce a budget deficit by reducing governmentexpenditures and/or increasing taxes.b) A nation can reduce or eliminate a balance of payments deficit by taxingimports and/or subsidizing exports, by borrowing more abroad or lending less toother nations, as well as by reducing the level of its national income.8. a) Nations usually impose restrictions on the free international flow of goods,services, and factors. Differences in language, customs, and laws also hamperthese international flows. In addition, international flows may involve receipts and payments in different currencies, which may change in value in relation to oneanother through time. This is to be contrasted with the interregional flow ofgoods, services, and factors, which face no such restrictions as tariffs and areconducted in terms of the same currency, usually in the same language, and under basically the same set of customs and laws.b) Both international and interregional economic relations involve the overcomingof space or distance. Indeed, they both arise from the problems created bydistance. This distinguishes them from the rest of economics, which abstractsfrom space and treats the economy as a single point in space, in which production, exchange, and consumption take place.9. We can deduce that nations benefit from voluntarily engaging in internationaltrade because if they did not gain or if they lost they could avoid those losses bysimply refusing to trade. Disagreement usually arises regarding the relativedistribution of the gains from specialization in production and trade, but this does not mean that each nation does not gain from trade.10. International trade results in lower prices for consumers but harms domesticproducers of products, which compete with imports. Often those domesticproducers that stand to lose a great deal from imports band together to pressurethe government to restrict imports. Since consumers are many and unorganizedand each individually stands to lose only very little from the import restrictions,governments often give in to the demands of producers and impose some importrestrictions. These topics are discussed in detail in Chapter 9.11. A nation can subsidize exports of the commodity to other nations until it drivesthe competing nation's industry out of business, after which it can raise its priceand benefit from its newly acquired monopoly power.Some economists and politicians in the United States have accused Japan of doing just that (i.e., of engaging in strategic trade and industrial policy at the expense of U.S. industries), but this is a very complex and controversial aspect of tradepolicy and will be examined in detail in Chapter 9.12. a) When the value of the U.S. dollar falls in relation to the currencies of othernations, imports become more expensive for Americans and so they wouldpurchase a smaller quantity of imports.b) When the value of the U.S. dollar falls in relation to the currencies of othernations, U.S. exports become chapter for foreigners and so they would purchase a greater quantity of U.S. exports.Multiple-Choice Questions1. Which of the following products are not produced at all in the United States?*a. Coffee, tea, cocoab. steel, copper, aluminumc. petroleum, coal, natural gasd. typewriters, computers, airplanes2. International trade is most important to the standard of living of:a. the United States*b. Switzerlandc. Germanyd. England3. Over time, the economic interdependence of nations has:*a. grownb. diminishedc. remained unchangedd. cannot say4. A rough measure of the degree of economic interdependence of a nation is given by:a. the size of the nations' populationb. the percentage of its population to its GDP*c. the percentage of a nation's imports and exports to its GDPd. all of the above5. Economic interdependence is greater for:*a. small nationsb. large nationsc. developed nationsd. developing nations6. The gravity model of international trade predicts that trade between two nations is largera. the larger the two nationsb. the closer the nationsc. the more open are the two nations*d. all of the above7. International economics deals with:a. the flow of goods, services, and payments among nationsb. policies directed at regulating the flow of goods, services, and paymentsc. the effects of policies on the welfare of the nation*d. all of the above8. International trade theory refers to:*a. the microeconomic aspects of international tradeb. the macroeconomic aspects of international tradec. open economy macroeconomics or international financed. all of the above9. Which of the following is not the subject matter of international finance?a. foreign exchange marketsb. the balance of payments*c. the basis and the gains from traded. policies to adjust balance of payments disequilibria10. Economic theory:a. seeks to explain economic eventsb. seeks to predict economic eventsc. abstracts from the many detail that surrounds an economic event*d. all of the above11. Which of the following is not an assumption generally made in the study of international economics?a. two nationsb. two commodities*c. perfect international mobility of factorsd. two factors of production12. In the study of international economics:a. international trade policies are examined before the bases for tradeb. adjustment policies are discussed before the balance of paymentsc. the case of many nations is discussed before the two-nations case*d. none of the above13. International trade is similar to interregional trade in that both must overcome: *a. distance and spaceb. trade restrictionsc. differences in currenciesd. differences in monetary systems14. The opening or expansion of international trade usually affects all members of society:a. positivelyb. negatively*c. most positively but some negativelyd. most negatively but some positively15. An increase in the dollar price of a foreign currency usually:a. benefit U.S. importers*b. benefits U.S. exportersc. benefit both U.S. importers and U.S. exportersd. harms both U.S. importers and U.S. exporters16. Which of the following statements with regard to international economics is true?a. It is a relatively new field*b. it is a relatively old fieldc. most of its contributors were not economistsd. none of the above。
曼昆《宏观经济学》第9版章节习题精编详解(失业)【圣才出品】
曼昆《宏观经济学》（第9版）章节习题精编详解第2篇古典理论：长期中的经济第7章失业一、概念题1．自然失业率（natural rate of unemployment）答：自然失业率又称“有保证的失业率”、“正常失业率”、“充分就业失业率”等，它是经济围绕其波动的平均失业率，是经济在长期中趋近的失业率，是充分就业时仍然保持的失业水平。
自然失业率是在没有货币因素干扰的情况下，让劳动市场和商品市场自发供求力量起作用时，总供给和总需求处于均衡状态时的失业率。
“没有货币因素干扰”是指失业率的高低与通货膨胀率的高低之间不存在替代关系。
自然失业率决定于经济中的结构性和摩擦性的因素，取决于劳动市场的组织状况、人口组成、失业者寻找工作的能力愿望、现有工作的类型、经济结构的变动、新加入劳动者队伍的人数等众多因素。
任何把失业降低到自然失业率以下的企图都将造成加速的通货膨胀。
任何时候都存在着与实际工资率结构相适应的自然失业率。
自然失业率是弗里德曼对菲利普斯曲线发展的一种观点，他将长期的均衡失业率称为“自然失业率”，它可以和任何通货膨胀水平相对应，且不受其影响。
2．摩擦性失业（frictional unemployment）答：摩擦性失业指劳动力市场运行机制不完善或者因为经济变动过程中的工作转换而产生的失业。
摩擦性失业是劳动力在正常流动过程中所产生的失业。
在一个动态经济中，各行业、各部门和各地区之间劳动需求的变动是经常发生的。
即使在充分就业状态下，由于人们从学校毕业或搬到新城市而要寻找工作，总是会有一些人的周转。
摩擦性失业量的大小取决于劳动力流动性的大小和寻找工作所需要的时间。
由于在动态经济中，劳动力的流动是正常的，所以摩擦性失业的存在也是正常的。
3．部门转移（sectoral shift）答：部门转移是指劳动力在不同部门和行业的重新配置。
由于许多原因，企业和家庭需要的产品类型一直在变动。
随着产品需求的变动，对生产这些产品的劳动力的需求也在改变，因此就出现劳动力在部门之间的转移。
曼昆宏观经济经济学第九版英文原版答案
A n s w e r s t o T e x t b o o k Q u e s t i o n s a n d P r o b l e m s CHAPTER 7?Unemployment and the Labor MarketQuestions for Review1. The rates of job separation and job finding determine the natural rate of unemployment. The rate of jobseparation is the fraction of people who lose their job each month. The higher the rate of job separation, the higher the natural rate of unemployment. The rate of job finding is the fraction of unemployed people who find a job each month. The higher the rate of job finding, the lower the natural rate ofunemployment.2. Frictional unemployment is the unemployment caused by the time it takes to match workers and jobs.Finding an appropriate job takes time because the flow of information about job candidates and job vacancies is not instantaneous. Because different jobs require different skills and pay different wages, unemployed workers may not accept the first job offer they receive.In contrast, structural unemployment is the unemployment resulting from wage rigidity and job rationing. These workers are unemployed not because they are actively searching for a job that best suits their skills (as in the case of frictional unemployment), but because at the prevailing real wage the quantity of labor supplied exceeds the quantity of labor demanded. If the wage does not adjust to clear the labor market, then these workers must wait for jobs to become available. Structural unemployment thus arises because firms fail to reduce wages despite an excess supply of labor.3. The real wage may remain above the level that equilibrates labor supply and labor demand because ofminimum wage laws, the monopoly power of unions, and efficiency wages.Minimum-wage laws cause wage rigidity when they prevent wages from falling to equilibrium levels. Although most workers are paid a wage above the minimum level, for some workers, especially the unskilled and inexperienced, the minimum wage raises their wage above the equilibrium level. It therefore reduces the quantity of their labor that firms demand, and creates an excess supply ofworkers, which increases unemployment.The monopoly power of unions causes wage rigidity because the wages of unionized workers are determined not by the equilibrium of supply and demand but by collective bargaining between union leaders and firm management. The wage agreement often raises the wage above the equilibrium level and allows the firm to decide how many workers to employ. These high wages cause firms to hire fewer workers than at the market-clearing wage, so structural unemployment increases.Efficiency-wage theories suggest that high wages make workers more productive. The influence of wages on worker efficiency may explain why firms do not cut wages despite an excess supply of labor. Even though a wage reduction decreases th e firm’s wage bill, it may also lower workerproductivity and therefore the firm’s profits.4. Depending on how one looks at the data, most unemployment can appear to be either short term orlong term. Most spells of unemployment are short; that is, most of those who became unemployed find jobs quickly. On the other hand, most weeks of unemployment are attributable to the small number of long-term unemployed. By definition, the long-term unemployed do not find jobs quickly, so they appear on unemployment rolls for many weeks or months.5. Europeans work fewer hours than Americans. One explanation is that the higher income tax rates inEurope reduce the incentive to work. A second explanation is a larger underground economy in Europe as a result of more people attempting to evade the high tax rates. A third explanation is the greater importance of unions in Europe and their ability to bargain for reduced work hours. A final explanation is based on preferences, whereby Europeans value leisure more than Americans do, and therefore elect to work fewer hours.Problems and Applications1. a. In the example that follows, we assume that during the school year you look for a part-time job,and that, on average, it takes 2 weeks to find one. We also assume that the typical job lasts 1semester, or 12 weeks.b. If it takes 2 weeks to find a job, then the rate of job finding in weeks isf = (1 job/2 weeks) = 0.5 jobs/week.If the job lasts for 12 weeks, then the rate of job separation in weeks iss = (1 job/12 weeks) = 0.083 jobs/week.c. From the text, we know that the formula for the natural rate of unemployment is(U/L) = [s/(s + f )],where U is the number of people unemployed, and L is the number of people in the labor force.Plugging in the values for f and s that were calculated in part (b), we find(U/L) = [0.083/(0.083 + 0.5)] = 0.14.Thus, if on average it takes 2 weeks to find a job that lasts 12 weeks, the natural rate ofunemployment for this population of college students seeking part-time employment is 14 percent.2. Call the number of residents of the dorm who are involved I, the number who are uninvolved U, and thetotal number of students T = I + U. In steady state the total number of involved students is constant.For this to happen we need the number of newly uninvolved students, (0.10)I, to be equal to thenumber of students who just became involved, (0.05)U. Following a few substitutions:(0.05)U = (0.10)I= (0.10)(T – U),soWe find that two-thirds of the students are uninvolved.3. To show that the unemployment rate evolves over time to the steady-state rate, let’s begin by defininghow the number of people unemployed changes over time. The change in the number of unemployed equals the number of people losing jobs (sE) minus the number finding jobs (fU). In equation form, we can express this as:U t + 1–U t= ΔU t + 1 = sE t–fU t.Recall from the text that L = E t + U t, or E t = L –U t, where L is the total labor force (we will assume that L is constant). Substituting for E t in the above equation, we findΔU t + 1 = s(L –U t) –fU t.Dividing by L, we get an expression for the change in the unemployment rate from t to t + 1:ΔU t + 1/L = (U t + 1/L) – (U t/L) = Δ[U/L]t + 1 = s(1 –U t/L) –fU t/L.Rearranging terms on the right side of the equation above, we end up with line 1 below. Now take line1 below, multiply the right side by (s + f)/(s + f) and rearrange terms to end up with line2 below:Δ[U/L]t + 1= s – (s + f)U t/L= (s + f)[s/(s + f) – U t/L].The first point to note about this equation is that in steady state, when the unemployment rate equals its natural rate, the left-hand side of this expression equals zero. This tells us that, as we found in the text, the natural rate of unemployment (U/L)n equals s/(s + f). We can now rewrite the above expression, substituting (U/L)n for s/(s + f), to get an equation that is easier to interpret:Δ[U/L]t + 1 = (s + f)[(U/L)n–U t/L].This expression shows the following:? If U t/L > (U/L)n (that is, the unemployment rate is above its natural rate), then Δ[U/L]t + 1 is negative: the unemployment rate falls.? If U t/L < (U/L)n (that is, the unemployment rate is below its natural rate), then Δ[U/L]t + 1 is positive: the unemployment rate rises.This process continues until the unemployment rate U/L reaches the steady-state rate (U/L)n.4. Consider the formula for the natural rate of unemployment,If the new law lowers the chance of separation s, but has no effect on the rate of job finding f, then the natural rate of unemployment falls.For several reasons, however, the new law might tend to reduce f. First, raising the cost of firing might make firms more careful about hiring workers, since firms have a harder time firing workers who turn out to be a poor match. Second, if job searchers think that the new legislation will lead them to spend a longer period of time on a particular job, then they might weigh more carefully whether or not to take that job. If the reduction in f is large enough, then the new policy may even increase the natural rate of unemployment.5. a. The demand for labor is determined by the amount of labor that a profit-maximizing firm wants tohire at a given real wage. The profit-maximizing condition is that the firm hire labor until themarginal product of labor equals the real wage,The marginal product of labor is found by differentiating the production function with respect tolabor (see Chapter 3 for more discussion),In order to solve for labor demand, we set the MPL equal to the real wage and solve for L:Notice that this expression has the intuitively desirable feature that increases in the real wagereduce the demand for labor.b. We assume that the 27,000 units of capital and the 1,000 units of labor are supplied inelastically (i.e., they will work at any price). In this case we know that all 1,000 units of labor and 27,000 units of capital will be used in equilibrium, so we can substitute these values into the above labor demand function and solve for W P .In equilibrium, employment will be 1,000, and multiplying this by 10 we find that the workers earn 10,000 units of output. The total output is given by the production function: Y =5K 13L 23Y =5(27,00013)(1,00023)Y =15,000.Notice that workers get two-thirds of output, which is consistent with what we know about theCobb –Douglas production function from Chapter 3.c. The real wage is now equal to 11 (10% above the equilibrium level of 10).Firms will use their labor demand function to decide how many workers to hire at the given realwage of 11 and capital stock of 27,000:So 751 workers will be hired for a total compensation of 8,261 units of output. To find the newlevel of output, plug the new value for labor and the value for capital into the production function and you will find Y = 12,393.d. The policy redistributes output from the 249 workers who become involuntarily unemployed tothe 751 workers who get paid more than before. The lucky workers benefit less than the losers lose as the total compensation to the working class falls from 10,000 to 8,261 units of output.e. This problem does focus on the analysis of two effects of the minimum-wage laws: they raise thewage for some workers while downward-sloping labor demand reduces the total number of jobs. Note, however, that if labor demand is less elastic than in this example, then the loss ofemployment may be smaller, and the change in worker income might be positive.6. a. The labor demand curve is given by the marginal product of labor schedule faced by firms. If acountry experiences a reduction in productivity, then the labor demand curve shifts to the left as in Figure 7-1. If labor becomes less productive, then at any given real wage, firms demand less labor. b. If the labor market is always in equilibrium, then, assuming a fixed labor supply, an adverseproductivity shock causes a decrease in the real wage but has no effect on employment orunemployment, as in Figure 7-2.c. If unions constrain real wages to remain unaltered, then as illustrated in Figure 7-3, employment falls to L 1 and unemployment equals L – L 1.This example shows that the effect of a productivity shock on an economy depends on the role ofunions and the response of collective bargaining to such a change.7. a. If workers are free to move between sectors, then the wage in each sector will be equal. If the wages were not equal then workers would have an incentive to move to the sector with the higher wage and this would cause the higher wage to fall, and the lower wage to rise until they were equal.b. Since there are 100 workers in total, L S = 100 – L M . We can substitute this expression into thelabor demand for services equation, and call the wage w since it is the same in both sectors:L S = 100 – L M = 100 – 4wL M = 4w.Now set this equal to the labor demand for manufacturing equation and solve for w:4w = 200 – 6ww = $20.Substitute the wage into the two labor demand equations to find L M is 80 and L S is 20.c. If the wage in manufacturing is equal to $25 then L M is equal to 50.d. There are now 50 workers employed in the service sector and the wage w S is equal to $12.50.e. The wage in manufacturing will remain at $25 and employment will remain at 50. If thereservation wage for the service sector is $15 then employment in the service sector will be 40. Therefore, 10 people are unemployed and the unemployment rate is 10 percent.8. Real wages have risen over time in both the United States and Europe, increasing the reward forworking (the substitution effect) but also making people richer, so they want to “buy” more leisure (the income effect). If the income effect dominates, then people want to work less as real wages go up. This could explain the European experience, in which hours worked per employed person have fallen over time. If the income and substitution effects approximately cancel, then this could explain the U.S.experience, in which hours worked per person have stayed about constant. Economists do not have good theories for why tastes might differ, so they disagree on whether it is reasonable to think that Europeans have a larger income effect than do Americans.9. The vacant office space problem is similar to the unemployment problem; we can apply the sameconcepts we used in analyzing unemployed labor to analyze why vacant office space exists. There is a rate of office separation: firms that occupy offices leave, either to move to different offices or because they go out of business. There is a rate of office finding: firms that need office space (either to start up or expand) find empty offices. It takes time to match firms with available space. Different types of firms require spaces with different attributes depending on what their specific needs are. Also, because demand for different goods fluctuates, there are “sectoral shifts”—changes in the composition ofdemand among industries and regions that affect the profitability and office needs of different firms.。
曼昆宏观经济经济学第九版英文原版答案
曼昆宏观经济经济学第九版英文原版答案3(总13页)--本页仅作为文档封面，使用时请直接删除即可----内页可以根据需求调整合适字体及大小--Answers to Textbook Questions and ProblemsCHAPTER3?National Income: Where It Comes From and Where It Goes Questions for Review1. The factors of production and the production technology determine theamount of output an economy can produce. The factors of production are the inputs used to produce goods and services: the most important factors are capital and labor. The production technology determines how much output can be produced from any given amounts of theseinputs. An increase in one of the factors of production or animprovement in technology leads to an increase in the economy’soutput.2. When a firm decides how much of a factor of production to hire ordemand, it considers how this decision affects profits. For example, hiring an extra unit of labor increases output and thereforeincreases revenue; the firm compares this additional revenue to the additional cost from the higher wage bill. The additional revenue the firm receives depends on the marginal product of labor (MPL) and the price of the good produced (P). An additional unit of labor produces MPL units of additional output, which sells for P dollars per unit.Therefore, the additional revenue to the firm is P ? MPL. The cost of hiring the additional unit of labor is the wage W. Thus, this hiring decision has the following effect on profits:ΔProfit= ΔRevenue –ΔCost= (P ? MPL) –W.If the additional revenue, P ? MPL, exceeds the cost (W) of hiring the additional unit of labor, then profit increases. The firm will hire labor until it is no longer profitable to do so—that is, until the MPL falls to the point where the change in profit is zero. In the equation abov e, the firm hires labor until ΔP rofit = 0, which is when (P ? MPL) = W.This condition can be rewritten as:MPL = W/P.Therefore, a competitive profit-maximizing firm hires labor until the marginal product of labor equals the real wage. The same logicapplies to the firm’s decision regarding how much capital to hire:the firm will hire capital until the marginal product of capitalequals the real rental price.3. A production function has constant returns to scale if an equalpercentage increase in all factors of production causes an increase in output of the same percentage. For example, if a firm increases its use of capital and labor by 50 percent, and output increases by50 percent, then the production function has constant returns toscale.If the production function has constant returns to scale, then total income (or equivalently, total output) in an economy ofcompetitive profit-maximizing firms is divided between the return to labor, MPL ? L, and the return to capital, MPK ? K. That is, under constant returns to scale, economic profit is zero.4. A Cobb–Douglas production function has the form F(K,L) = AKαL1–α.The text showed that the parameter αgives capital’s share ofincome. So if capital earns one-fourth of total income, then ? = .Hence, F(K,L) = Consumption depends positively on disposable income—. the amount of income after all taxes have been paid. Higher disposable income means higher consumption.The quantity of investment goods demanded depends negatively on the real interest rate. For an investment to be profitable, itsreturn must be greater than its cost. Because the real interest rate measures the cost of funds, a higher real interest rate makes it more costly to invest, so the demand for investment goods falls.6. Government purchases are a measure of the value of goods and servicespurchased directly by the government. For example, the government buys missiles and tanks, builds roads, and provides services such as air traffic control. All of these activities are part of GDP.Transfer payments are government payments to individuals that are not in exchange for goods or services. They are the opposite of taxes: taxes reduce household disposable income, whereas transfer payments increase it. Examples of transfer payments include Social Security payments to the elderly, unemployment insurance, and veterans’benefits.7. Consumption, investment, and government purchases determine demandfor the economy’s output, whereas the factors of production and the production function determine the supply of output. The real interest rate adjusts to ensure that the deman d for the economy’s goodsequals the supply. At the equilibrium interest rate, the demand for goods and services equals the supply.8. When the government increases taxes, disposable income falls, andtherefore consumption falls as well. The decrease in consumptionequals the amount that taxes increase multiplied by the marginalpropensity to consume (MPC). The higher the MPC is, the greater is the negative effect of the tax increase on consumption. Becauseoutput is fixed by the factors of production and the productiontechnology, and government purchases have not changed, the decrease in consumption must be offset by an increase in investment. Forinvestment to rise, the real interest rate must fall. Therefore, a tax increase leads to a decrease in consumption, an increase ininvestment, and a fall in the real interest rate.Problems and Applications1. a. According to the neoclassical theory of distribution, the realwage equals the marginal product of labor. Because of diminishing returns to labor, an increase in the labor force causes themarginal product of labor to fall. Hence, the real wage falls.Given a Cobb–Douglas production function, the increase in the labor force will increase the marginal product of capital and will increase the real rental price of capital. With more workers, the capital will be used more intensively and will be more productive.b. The real rental price equals the marginal product of capital. Ifan earthquake destroys some of the capital stock (yet miraculously does not kill anyone and lower the labor force), the marginalproduct of capital rises and, hence, the real rental price rises.Given a Cobb–Douglas production function, the decrease in the capital stock will decrease the marginal product of labor and will decrease the real wage. With less capital, each worker becomesless productive.c. If a technological advance improves the production function, thisis likely to increase the marginal products of both capital andlabor. Hence, the real wage and the real rental price bothincrease.d. High inflation that doubles the nominal wage and the price levelwill have no impact on the real wage. Similarly, high inflationthat doubles the nominal rental price of capital and the pricelevel will have no impact on the real rental price of capital.2. a. To find the amount of output produced, substitute the given valuesfor labor and land into the production function:Y = = 100.b. According to the text, the formulas for the marginal product oflabor and the marginal product of capital (land) are:MPL = (1 –α)AKαL–α.MPK = αAKα–1L1–α.In this problem, α is and A is 1. Substitute in the given values for labor and land to find the marginal product of labor is andmarginal product of capital (land) is . We know that the real wage equals the marginal product of labor and the real rental price of land equals the marginal product of capital (land).c. Labor’s share of the output is given by the marginal product oflabor times the quantity of labor, or 50.d. The new level of output is .e. The new wage is . The new rental price of land is .f. Labor now receives .3. A production function has decreasing returns to scale if an equalpercentage increase in all factors of production leads to a smaller percentage increase in output. For example, if we double the amounts of capital and labor output increases by less than double, then the production function has decreasing returns to scale. This may happen if there is a fixed factor such as land in the production function, and this fixed factor becomes scarce as the economy grows larger.A production function has increasing returns to scale if an equalpercentage increase in all factors of production leads to a larger percentage increase in output. For example, if doubling the amount of capital and labor increases the output by more than double, then the production function has increasing returns to scale. This may happen if specialization of labor becomes greater as the population grows.For example, if only one worker builds a car, then it takes him a long time because he has to learn many different skills, and he must constantly change tasks and tools. But if many workers build a car, then each one can specialize in a particular task and become more productive.4. a. A Cobb–Douglas production function has the form Y = AKαL1–α. Thetext showed that the marginal products for the Cobb–Douglasproduction function are:MPL = (1 –α)Y/L.MPK = αY/K.Competitive profit-maximizing firms hire labor until its marginal product equals the real wage, and hire capital until its marginal product equals the real rental rate. Using these factsand the above marginal products for the Cobb–Douglas productionfunction, we find:W/P = MPL = (1 –α)Y/L.R/P = MPK = αY/K.Rewriting this:(W/P)L = MPL ? L = (1 –α)Y.(R/P)K = MPK ? K = αY.Note that the terms (W/P)L and (R/P)K are the wage bill and total return to capital, respectively. Given that the value of α = ,then the above formulas indicate that labor receives 70 percent of total output (or income) and capital receives 30 percent of total output (or income).b. To determine what happens to total output when the labor forceincreases by 10 percent, consider the formula for the Cobb–Douglas production function:Y = AKαL1–α.Let Y1 equal the initial value of output and Y2 equal final output.We know that α = . We also know that labor L increases by 10percent:Y 1 = Y 2 = .Note that we multiplied L by to reflect the 10-percent increase in the labor force.To calculate the percentage change in output, divide Y 2 by Y 1:Y 2Y 1=AK 0.31.1L ()0.7AK 0.3L 0.7=1.1()0.7=1.069.That is, output increases by percent. To determine how the increase in the labor force affects therental price of capital, consider the formula for the real rental price of capital R/P :R/P = MPK = αAK α–1L 1–α.We know that α = . We also know that labor (L ) increases by 10percent. Let (R/P )1 equal the initial value of the rental price ofcapital, and let (R/P )2 equal the final rental price of capitalafter the labor force increases by 10 percent. To find (R/P )2,multiply L by to reflect the 10-percent increase in the laborforce:(R/P )1 = – (R/P )2 = –.The rental price increases by the ratioR /P ()2R /P ()1=0.3AK -0.71.1L ()0.70.3AK -0.7L 0.7=1.1()0.7=1.069So the rental price increases by percent. To determine how the increase in the labor forceaffects the real wage, consider the formula for the real wage W/P :W/P = MPL = (1 – α)AK αL –α.We know that α = . We also know that labor (L ) increases by 10percent. Let (W/P )1 equal the initial value of the real wage, andlet (W/P )2 equal the final value of the real wage. To find (W/P )2, multiply L by to reflect the 10-percent increase in the laborforce:(W/P )1 = (1 – –. (W/P )2 = (1 – –.To calculate the percentage change in the real wage, divide (W/P )2 by (W/P )1:W /P ()2W /P ()1=1-0.3()AK 0.31.1L ()-0.31-0.3()AK 0.3L -0.3=1.1()-0.3=0.972That is, the real wage falls by percent.c. We can use the same logic as in part (b) to setY 1 = Y 2 = A Therefore, we have:Y 2Y 1=A 1.1K ()0.3L 0.7AK 0.3L 0.7=1.1()0.3=1.029This equation shows that output increases by about 3 percent. Notice that α < means that proportional increases to capital will increase output by less than the same proportional increase to labor.Again using the same logic as in part (b) for the change in the real rental price of capital:R /P ()2R /P ()1=0.3A 1.1K ()-0.7L 0.70.3AK -0.7L 0.7=1.1()-0.7=0.935The real rental price of capital falls by percent because there are diminishing returns to capital; that is, when capital increases, its marginal product falls.Finally, the change in the real wage is:W /P ()2W /P ()1=0.7A 1.1K ()0.3L -0.30.7AK 0.3L -0.3=1.1()0.3=1.029Hence, real wages increase by percent because the added capitalincreases the marginal productivity of the existing workers.(Notice that the wage and output have both increased by the same amount, leaving the labor share unchanged —a feature of Cobb –Douglas technologies.)d. Using the same formula, we find that the change in output is:Y 2Y 1= 1.1A ()K 0.3L 0.7AK 0.3L 0.7=1.1This equation shows that output increases by 10 percent. Similarly,the rental price of capital and the real wage also increase by 10 percent:R /P ()2R /P ()1=0.31.1A ()K -0.7L 0.70.3AK -0.7L 0.7=1.1W /P ()2W /P ()1=0.71.1A ()K 0.3L -0.30.7AK 0.3L -0.3=1.15. Labor income is defined asW P ´L =WL PLabor’s share of income is defined asWL P æèççöø÷÷/Y =WL PYFor example, if this ratio is about constant at a value of , then the value of W/P = *Y/L. This means that the real wage is roughlyproportional to labor productivity. Hence, any trend in laborproductivity must be matched by an equal trend in real wages.O therwise, labor’s share would deviate from . T hus, the first fact(a constant labor share) implies the second fact (the trend in realwages closely tracks the trend in labor productivity).6. a. Nominal wages are measured as dollars per hour worked. Prices aremeasured as dollars per unit produced (either a haircut or a unit of farm output). Marginal productivity is measured as units ofoutput produced per hour worked.b. According to the neoclassical theory, technical progress thatincreases the marginal product of farmers causes their real wageto rise. The real wage for farmers is measured as units of farmoutput per hour worked. The real wage is W/P F, and this is equalto ($/hour worked)/($/unit of farm output).c. If the marginal productivity of barbers is unchanged, then theirreal wage is unchanged. The real wage for barbers is measured ashaircuts per hour worked. The real wage is W/P B, and this is equal to ($/hour worked)/($/haircut).d.If workers can move freely between being farmers and being barbers,then they must be paid the same wage W in each sector.e. If the nominal wage W is the same in both sectors, but the realwage in terms of farm goods is greater than the real wage in terms of haircuts, then the price of haircuts must have risen relativeto the price of farm goods. We know that W/P = MPL so that W = P ?MPL. This means that PF MPLF= P H MPL B, given that the nominal wagesare the same. Since the marginal product of labor for barbers has not changed and the marginal product of labor for farmers hasrisen, the price of a haircut must have risen relative to theprice of the farm output. If we express this in growth rate terms, then the growth of the farm price + the growth of the marginalproduct of the farm labor = the growth of the haircut price.f. The farmers and the barbers are equally well off after the technological progress in farming, giventhe assumption that labor is freely mobile between the two sectorsand both types of people consume the same basket of goods. Given that the nominal wage ends up equal for each type of worker andthat they pay the same prices for final goods, they are equallywell off in terms of what they can buy with their nominal income.The real wage is a measure of how many units of output areproduced per worker. Technological progress in farming increased the units of farm output produced per hour worked. Movement oflabor between sectors then equalized the nominal wage.7. a. The marginal product of labor (MPL)is found by differentiatingthe production function with respect to labor:MPL=dY dL=13K1/3H1/3L-2/3An increase in human capital will increase the marginal product of labor because more human capital makes all the existing labor more productive.b. The marginal product of human capital (MPH)is found bydifferentiating the production function with respect to humancapital:MPH=dY dH=13K1/3L1/3H-2/3An increase in human capital will decrease the marginal product of human capital because there are diminishing returns.c. The labor share of output is the proportion of output that goes tolabor. The total amount of output that goes to labor is the real wage (which, under perfect competition, equals the marginalproduct of labor) times the quantity of labor. This quantity is divided by the total amount of output to compute the labor share:Labor Share=(13K1/3H1/3L-2/3)LK1/3H1/3L1/3=1 3We can use the same logic to find the human capital share:Human Capital Share=(13K1/3L1/3H-2/3)HK1/3H1/3L1/3=1 3so labor gets one-third of the output, and human capital gets one-third of the output. Since workers own their human capital (we hope!), it will appear that labor gets two-thirds of output.d. The ratio of the skilled wage to the unskilled wage is:Wskilled Wunskilled =MPL+MPHMPL=13K1/3L-2/3H1/3+13K1/3L1/3H-2/313K1/3L-2/3H1/3=1+LHNotice that the ratio is always greater than 1 because skilledworkers get paid more than unskilled workers. Also, when Hincreases this ratio falls because the diminishing returns tohuman capital lower its return, while at the same time increasing the marginal product of unskilled workers.e. If more colleges provide scholarships, it will increase H, and itdoes lead to a more egalitarian society. The policy lowers thereturns to education, decreasing the gap between the wages of more and less educated workers. More importantly, the policy evenraises the absolute wage of unskilled workers because theirmarginal product rises when the number of skilled workers rises.8. The effect of a government tax increase of $100 billion on (a) publicsaving, (b) private saving, and (c) national saving can be analyzed by using the following relationships:National Saving = [Private Saving] + [Public Saving]= [Y –T –C(Y –T)] + [T –G]= Y –C(Y –T) –G.a. Public Saving—The tax increase causes a 1-for-1 increase inpublic saving. T increases by $100 billion and, therefore, publicsaving increases by $100 billion.b.Private Saving—The increase in taxes decreases disposable income,Y –T, by $100 billion. Since the marginal propensity to consume (MPC) is , consumption falls by ? $100 billion, or $60 billion.Hence,ΔPrivate Saving = –$100b – (–$100b) = –$40b.Private saving falls $40 billion.c. National Saving—Because national saving is the sum of privateand public saving, we can conclude that the $100 billion taxincrease leads to a $60 billion increase in national saving.Another way to see this is by using the third equation for national saving expressed above, that national saving equals Y –C(Y –T) –G. The $100 billion tax increase reduces disposable income and causes consumption to fall by $60 billion. Sinceneither G nor Y changes, national saving thus rises by $60 billion.d. Investment—To determine the effect of the tax increase oninvestment, recall the national accounts identity:Y = C(Y –T) + I(r) + G.Rearranging, we findY –C(Y –T) –G = I(r).The left side of this equation is national saving, so the equation just says that national saving equals investment. Since national saving increases by $60 billion, investment must also increase by $60 billion.How does this increase in investment take place We know that investment depends on the real interest rate. For investment to rise, the real interest rate must fall. Figure 3-1 illustrates saving and investment as a function of the real interest rate.The tax increase causes national saving to rise, so the supply curve for loanable funds shifts to the right. The equilibrium real interest rate falls, and investment rises.9. If consumers increase the amount that they consume today, thenprivate saving and, therefore, national saving will fall. We know this from the definition of national saving:National Saving = [Private Saving] + [Public Saving]= [Y –T –C(Y –T)] + [T –G].An increase in consumption decreases private saving, so national saving falls.Figure 3-2 illustrates saving and investment as a function of the real interest rate. If national saving decreases, the supply curve for loanable funds shifts to the left, thereby raising the realinterest rate and reducing investment.10. a. Private saving is the amount of disposable income, Y – T,that is not consumed:S private= Y – T – C= 8,000 – 2,000 – [1,000 + (2/3)(8,000 –2,000)]= 1,000.Public saving is the amount of taxes the government has left over after it makes its purchases:S public= T – G= 2,000 – 2,500= –500.National saving is the sum of private saving and public saving:S national= S private+ S public= 1,000 + (500)= 500.b. The equilibrium interest rate is the value of r that clears themarket for loanable funds. We already know that national saving is 500, so we just need to set it equal to investment:S national= I500 = 1,200 – 100rSolving this equation for r, we find:r = or 7%.c. When the government increases its spending, private saving remainsthe same as before (notice that G does not appear in the S privateequation above) while government saving decreases. Putting the newG into the equations above:S private= 1,000S public= T – G= 2,000 – 2,000= 0.Thus,S national= S private+ S public= 1,000 + (0)= 1,000.d. Once again the equilibrium interest rate clears the market for loanable funds:S national= I1,000 = 1,200 – 100rSolving this equation for r, we find:r = or 2%.11. To determine the effect on investment of an equal increase in bothtaxes and government spending, consider the national income accounts identity for national saving:National Saving = [Private Saving] + [Public Saving]= [Y –T –C(Y –T)] + [T –G].We know that Y is fixed by the factors of production. We also know that the change in consumption equals the marginal propensity toconsume (MPC) times the change in disposable income. This tells us thatΔNational Saving = {–ΔT – [MPC ? (–ΔT)]} + [ΔT –ΔG]= [–ΔT + (MPC ? ΔT)] + 0= (MPC –1) ΔT.The above expression tells us that the impact on national saving of an equal increase in T and G depends on the size of the marginal propensity to consume. The closer the MPC is to 1, the smaller is the fall in saving. For example, if the MPC equals 1, then the fall in consumption equals the rise in government purchases, so nationalsaving [Y –C(Y –T) –G] is unchanged. The closer the MPC is to 0 (and therefore the larger is the amount saved rather than spent for a one-dollar change in disposable income), the greater is the impact on saving. Because we assume that the MPC is less than 1, we expect that national saving falls in response to an equal increase in taxes and government spending.The reduction in saving means that the supply of loanable funds curve will shift to the left in Figure 3-3. The real interest rate rises, and investment falls.12. a. The demand curve for business investment shifts out to theright because the subsidy increases the number of profitableinvestment opportunities for any given interest rate. The demandcurve for residential investment remains unchanged.b. The total demand curve for investment in the economy shifts out tothe right since it represents the sum of business investment,which shifts out to the right, and residential investment, whichis unchanged. As a result the real interest rate rises as inFigure 3-4.c. The total quantity of investment does not change because it isconstrained by the inelastic supply of savings. The investment tax credit leads to a rise in business investment, but an offsettingfall in residential investment. That is, the higher interest rate means that residential investment falls (a movement along thecurve), whereas the rightward shift of the business investmentcurve leads business investment to rise by an equal amount. Figure3-5 shows this change. Note thatI 1B +I 1R +I 2B +I 2R =S .13. In this chapter, we concluded that an increase in governmentexpenditures reduces national saving and raises the interest rate. The increase in government expenditure therefore crowds outinvestment by the full amount of the increase. Similarly, a tax cut increases disposable income and hence consumption. This increase in consumption translates into a fall in national saving, and theincrease in consumption crowds out investment by the full amount of the increase.If consumption depends on the interest rate, then saving will also depend on it. The higher the interest rate, the greater the return to saving. Hence, it seems reasonable to think that an increase in the interest rate might increase saving and reduce consumption. Figure 3-6 shows saving as an increasing function of the interest rate.Consider what happens when government purchases increase. At anygiven level of the interest rate, national saving falls by the change in government purchases, as shown in Figure 3-7. The figure shows that if the saving function slopes upward, investment falls by less than the amount that government purchases rises by. This happens because consumption falls and saving increases in response to the higher interest rate. Hence, the more responsive consumption is tothe interest rate, the less investment is crowded out by government purchases.14. a. Figure 3-8 shows the case where the demand for loanablefunds is stable but the supply of funds (the saving schedule)fluctuates perhaps reflecting temporary shocks to income, changes in government spending, or changes in consumer confidence. In this case, when interest rates fall, investment rises; when interestrates rise, investment falls. We would expect a negativecorrelation between investment and interest rates.b. Figure 3-9 shows the case where the supply of loanable funds(saving) is stable, whereas the demand for loanable fundsfluctuates, perhaps reflecting changes in firms’ expectationsabout the marginal product of capital. We would now find apositive correlation between investment and the interest rate—when demand for funds rises, it pushes up the interest rate, so we observe that investment and the real interest rate increase at the same time.c. If both curves shift, we might generate a scatter plot as inFigure 3-10, where the economy fluctuates among points A, B, C, and D. Depending on how often the economy is at each of thesepoints, we might find little clear relationship between investment and interest rates.d. Situation (c) seems fairly reasonable—as both the supply of anddemand for loanable funds fluctuate over time in response tochanges in the economy.。
曼昆_宏观经济经济学第九版_英文原版答案9
Answers to Textbook Questions and ProblemsCHAPTER 9 Economic Growth II: Technology, Empirics, and PolicyQuestions for Review1. In the Solow model, we find that only technological progress can affect the steady-staterate of growth in income per worker. Growth in the capital stock (through high saving) has no effect on the steady-state growth rate of income per worker; neither doespopulation growth. But technological progress can lead to sustained growth.2. In the steady state, output per person in the Solow model grows at the rate oftechnological progress g. Capital per person also grows at rate g. Note that this implies that output and capital per effective worker are constant in steady state. In the U.S. data, output and capital per worker have both grown at about 2 percent per year for the past half-century.3. To decide whether an economy has more or less capital than the Golden Rule, we needto compare the marginal product of capital net of depreciation (MPK –δ) with the growth rate of total output (n + g). The growth rate of GDP is readily available. Estimating the net marginal product of capital requires a little more work but, as shown in the text, can be backed out of available data on the capital stock relative to GDP, the total amount of depreciation relative to GDP, and capital’s share in GDP.4. Economic policy can influence the saving rate by either increasing public saving orproviding incentives to stimulate private saving. Public saving is the difference between government revenue and government spending. If spending exceeds revenue, thegovernment runs a budget deficit, which is negative saving. Policies that decrease the deficit (such as reductions in government purchases or increases in taxes) increase public saving, whereas policies that increase the deficit decrease saving. A variety of government policies affect private saving. The decision by a household to save may depend on the rate of return; the greater the return to saving, the more attractive saving becomes. Tax incentives such as tax-exempt retirement accounts for individuals and investment tax credits for corporations increase the rate of return and encourage private saving.5. The legal system is an example of an institutional difference between countries that mightexplain differences in income per person. Countries that have adopted the English style common law system tend to have better developed capital markets, and this leads to more rapid growth because it is easier for businesses to obtain financing. The quality of government is also important. Countries with more government corruption tend to have lower levels of income per person.6. Endogenous growth theories attempt to explain the rate of technological progress byexplaining the decisions that determine the creation of knowledge through research and development. By contrast, the Solow model simply took this rate as exogenous. In the Solow model, the saving rate affects growth temporarily, but diminishing returns tocapital eventually force the economy to approach a steady state in which growth depends only on exogenous technological progress. By contrast, many endogenous growth models in essence assume that there are constant (rather than diminishing) returns to capital, interpreted to include knowledge. Hence, changes in the saving rate can lead topersistent growth.Problems and Applications1. a. In the Solow model with technological progress, y is defined as output per effectiveworker, and k is defined as capital per effective worker. The number of effectiveworkers is defined as L E (or LE), where L is the number of workers, and E measures the efficiency of each worker. To find output per effective worker y, divide totaloutput by the number of effective workers:Y LE =K12(LE)12LEY LE =K12L12E12LEY LE =K1 L12E12Y LE =KLE æèççöø÷÷12y=k12b. To solve for the steady-state value of y as a function of s, n, g, and δ, we begin withthe equation for the change in the capital stock in the steady state:Δk = sf(k) –(δ + n + g)k = 0.The production function y can also be rewritten as y2 = k. Plugging thisproduction function into the equation for the change in the capital stock, we find that in the steady state:sy –(δ + n + g)y2 = 0.Solving this, we find the steady-state value of y:y* = s/(δ + n + g).c. The question provides us with the following information about each country:Atlantis: s = 0.28 Xanadu: s = 0.10n = 0.01 n = 0.04g = 0.02 g = 0.02δ = 0.04δ = 0.04Using the equation for y* that we derived in part (a), we can calculate the steady-state values of y for each country.Developed country: y* = 0.28/(0.04 + 0.01 + 0.02) = 4Less-developed country: y* = 0.10/(0.04 + 0.04 + 0.02) = 12. a. In the steady state, capital per effective worker is constant, and this leads to a constantlevel of output per effective worker. Given that the growth rate of output per effective worker is zero, this means the growth rate of output is equal to the growth rate ofeffective workers (LE). We know labor grows at the rate of population growth n and the efficiency of labor (E) grows at rate g. Therefore, output grows at rate n+g. Givenoutput grows at rate n+g and labor grows at rate n, output per worker must grow at rate g. This follows from the rule that the growth rate of Y/L is equal to the growth rate of Y minus the growth rate of L.b. First find the output per effective worker production function by dividing both sides ofthe production function by the number of effective workers LE:Y LE =K13(LE)23LEY LE =K13L23E23LEY LE =K13 L13E13Y LE =KLE æèçöø÷13y=k13To solve for capital per effective worker, we start with the steady state condition:Δk = sf(k) –(δ + n + g)k = 0.Now substitute in the given parameter values and solve for capital per effective worker (k):Substitute the value for k back into the per effective worker production function tofind output per effective worker is equal to 2. The marginal product of capital is given bySubstitute the value for capital per effective worker to find the marginal product ofcapital is equal to 1/12.c. According to the Golden Rule, the marginal product of capital is equal to (δ + n + g) or0.06. In the current steady state, the marginal product of capital is equal to 1/12 or0.083. Therefore, we have less capital per effective worker in comparison to the GoldenRule. As the level of capital per effective worker rises, the marginal product of capital will fall until it is equal to 0.06. To increase capital per effective worker, there must be an increase in the saving rate.d. During the transition to the Golden Rule steady state, the growth rate of output perworker will increase. In the steady state, output per worker grows at rate g. The increase in the saving rate will increase output per effective worker, and this will increase output per effective worker. In the new steady state, output per effective worker is constant ata new higher level, and output per worker is growing at rate g. During the transition,the growth rate of output per worker jumps up, and then transitions back down to rateg.3. To solve this problem, it is useful to establish what we know about the U.S. economy:• A Cobb–Douglas production function has the form y = kα, where α is capital’s share of income. The question tells us that α = 0.3, so we know that the productionfunction is y = k0.3.•In the steady state, we know that the growth rate of output equals 3 percent, so we know that (n + g) = 0.03.•The deprec iation rate δ = 0.04.•The capital–output ratio K/Y = 2.5. Because k/y = [K/(LE)]/[Y/(LE)] = K/Y, we also know that k/y = 2.5. (That is, the capital–output ratio is the same in terms of effectiveworkers as it is in levels.)a. Begin with the steady-state condition, sy = (δ + n + g)k. Rewriting this equation leadsto a formula for saving in the steady state:s = (δ + n + g)(k/y).Plugging in the values established above:s = (0.04 + 0.03)(2.5) = 0.175.The initial saving rate is 17.5 percent.b. We know from Chapter 3 that with a Cobb–Douglas production function, capital’sshare of income α = MPK(K/Y). Rewriting, we haveMPK = α/(K/Y).Plugging in the values established above, we findMPK = 0.3/2.5 = 0.12.c. We know that at the Golden Rule steady state:MPK = (n + g + δ).Plugging in the values established above:MPK = (0.03 + 0.04) = 0.07.At the Golden Rule steady state, the marginal product of capital is 7 percent, whereas it is 12 percent in the initial steady state. Hence, from the initial steady state we need to increase k to achieve the Golden Rule steady state.d. We know from Chapter 3 that for a Cobb–Douglas production function, MPK = α(Y/K). Solving this for the capital–output ratio, we findK/Y = α/MPK.We can solve for the Golden Rule capital–output ratio using this equation. If we plug in the value 0.07 for the Golden Rule steady-state marginal product of capital, and the value 0.3 for α, we findK/Y = 0.3/0.07 = 4.29.In the Golden Rule steady state, the capital–output ratio equals 4.29, compared to the current capital–output ratio of 2.5.e. We know from part (a) that in the steady states = (δ + n + g)(k/y),where k/y is the steady-state capital–output ratio. In the introduction to this answer, we showed that k/y = K/Y, and in part (d) we found that the Golden Rule K/Y = 4.29.Plugging in this value and those established above:s = (0.04 + 0.03)(4.29) = 0.30.To reach the Golden Rule steady state, the saving rate must rise from 17.5 to 30percent. This result implies that if we set the saving rate equal to the share going tocapital (30 percent), we will achieve the Golden Rule steady state.4. a. In the steady state, we know that sy = (δ + n + g)k. This implies thatk/y = s/(δ + n + g).Since s, δ, n, and g are constant, this means that the ratio k/y is also constant. Sincek/y = [K/(LE)]/[Y/(LE)] = K/Y, we can conclude that in the steady state, the capital–output ratio is constant.b. We know that capital’s share of income = MPK ⨯ (K/Y). In the steady state, we knowfrom part (a) that the capital–output ratio K/Y is constant. We also know from the hint that the MPK is a function of k, which is constant in the steady state; therefore theMPK itself must be constant. Thus, capital’s share of income is constant. Labor’s share of income is 1 – [C apital’s S hare]. Hence, if capital’s share is constant, we see thatlabor’s share of income is also constant.c. We know that in the steady state, total income grows at n + g, defined as the rate ofpopulation growth plus the rate of technological change. In part (b) we showed thatlabor’s and capital’s share of income is constant. If the shares are constant, and totalincome grows at the rate n + g, then labor income and capital income must alsogrow at the rate n + g.d. Define the real rental price of capital R asR = Total Capital Income/Capital Stock= (MPK ⨯K)/K= MPK.We know that in the steady state, the MPK is constant because capital per effectiveworker k is constant. Therefore, we can conclude that the real rental price of capital is constant in the steady state.To show that the real wage w grows at the rate of technological progress g, defineTLI = Total Labor IncomeL= Labor ForceUsing the hint that the real wage equals total labor income divided by the laborforce:w = TLI/L.Equivalently,wL = TLI.In terms of percentage changes, we can write this asΔw/w + ΔL/L = ΔTLI/TLI.This equation says that the growth rate of the real wage plus the growth rate of the labor force equals the growth rate of total labor income. We know that the labor force grows at rate n , and, from part (c), we know that total labor income grows at rate n + g . We, therefore, conclude that the real wage grows at rate g .5. a. The per worker production function isF (K, L )/L = AK α L 1–α/L = A (K/L )α = Ak αb. In the steady state, Δk = sf (k ) – (δ + n + g )k = 0. Hence, sAk α = (δ + n + g )k , or,after rearranging:k *=sA d +n +g éëêêùûúúa 1-a æèççöø÷÷.Plugging into the per-worker production function from part (a) givesy *=A a 1-a æèççöø÷÷s d +n +g éëêêùûúúa 1-a æèççöø÷÷.Thus, the ratio of steady-state income per worker in Richland to Poorland isy *Richland/y *Poorland ()=s Richland d +n Richland +g /s Poorland d +n Poorland +g éëêêùûúúa1-=0.320.05+0.01+0.02/0.100.05+0.03+0.02éëêêùûúúa1-ac. If α equals 1/3, then Richland should be 41/2, or two times, richer than Poorland.d. If 4a 1-a æèççöø÷÷= 16, then it must be the case thata 1-a æèççöø÷÷, which in turn requires that αequals 2/3. Hence, if the Cobb –Douglas production function puts 2/3 of the weighton capital and only 1/3 on labor, then we can explain a 16-fold difference in levels of income per worker. One way to justify this might be to think about capital more broadly to include human capital —which must also be accumulated through investment, much in the way one accumulates physical capital.6. How do differences in education across countries affect the Solow model? Education isone factor affecting the efficiency of labor , which we denoted by E . (Other factors affecting the efficiency of labor include levels of health, skill, and knowledge.) Since country 1 has a more highly educated labor force than country 2, each worker in country 1 is more efficient. That is, E 1 > E 2. We will assume that both countries are in steady state.a. In the Solow growth model, the rate of growth of total income is equal to n + g ,which is independent of the work force’s level of education. The two countries will, thus, have the same rate of growth of total income because they have the same rate of population growth and the same rate of technological progress.b. Because both countries have the same saving rate, the same population growth rate,and the same rate of technological progress, we know that the two countries will converge to the same steady-state level of capital per effective worker k *. This is shown in Figure 9-1.Hence, output per effective worker in the steady state, which is y* = f(k*), is the same in both countries. But y* = Y/(L E) or Y/L = y*E. We know that y* will be the same in both countries, but that E1 > E2. Therefore, y*E1 > y*E2. This implies that (Y/L)1 > (Y/L)2.Thus, the level of income per worker will be higher in the country with the moreeducated labor force.c. We know that the real rental price of capital R equals the marginal product of capital(MPK). But the MPK depends on the capital stock per efficiency unit of labor. In the steady state, both countries have k*1= k*2= k* because both countries have the same saving rate, the same population growth rate, and the same rate of technological progress. Therefore, it must be true that R1 = R2 = MPK. Thus, the real rental price of capital is identical in both countries.d. Output is divided between capital income and labor income. Therefore, the wage pereffective worker can be expressed asw = f(k) –MPK • k.As discussed in parts (b) and (c), both countries have the same steady-state capital stock k and the same MPK. Therefore, the wage per effective worker in the twocountries is equal.Workers, however, care about the wage per unit of labor, not the wage per effective worker. Also, we can observe the wage per unit of labor but not the wage per effective worker. The wage per unit of labor is related to the wage per effective worker by the equationWage per Unit of L = wE.Thus, the wage per unit of labor is higher in the country with the more educated labor force.7. a. In the two-sector endogenous growth model in the text, the production function formanufactured goods isY = F [K,(1 –u) EL].We assumed in this model that this function has constant returns to scale. As inSection 3-1, constant returns means that for any positive number z, zY = F(zK, z(1 –u) EL). Setting z = 1/EL, we obtainY EL =FKEL,(1-u)æèççöø÷÷.Using our standard definitions of y as output per effective worker and k as capital per effective worker, we can write this asy = F[k,(1 –u)]b. To begin, note that from the production function in research universities, the growthrate of labor efficiency, ΔE/E, equals g(u). We can now follow the logic of Section 9-1, substituting the function g(u) for the constant growth rate g. In order to keep capital per effective worker (K/EL) constant, break-even investment includes three terms: δk is needed to replace depreciating capital, nk is needed to provide capital for newworkers, and g(u) is needed to provide capital for the greater stock of knowledge E created by research universities. That is, break-even investment is [δ +n + g(u)]k.c. Again following the logic of Section 9-1, the growth of capital per effective worker isthe difference between saving per effective worker and break-even investment per effective worker. We now substitute the per-effective-worker production function from part (a) and the function g(u) for the constant growth rate g, to obtainΔk = sF [k,(1 –u)] – [δ + n + g(u)]kIn the steady state, Δk = 0, so we can rewrite the equation above assF [k,(1 –u)] = [δ + n + g(u)]k.As in our analysis of the Solow model, for a given value of u, we can plot the left and right sides of this equationThe steady state is given by the intersection of the two curves.d. The steady state has constant capital per effective worker k as given by Figure 9-2above. We also assume that in the steady state, there is a constant share of time spent in research universities, so u is constant. (After all, if u were not constant, it wouldn’t be a “steady” state!). Hence, output per e ffective worker y is also constant.Output per worker equals yE, and E grows at rate g(u). Therefore, output per worker grows at rate g(u). The saving rate does not affect this growth rate. However, the amount of time spent in research universities does affect this rate: as more time is spent in research universities, the steady-state growth rate rises.e. An increase in u shifts both lines in our figure. Output per effective worker falls forany given level of capital per effective worker, since less of each worker’s time isspent producing manufactured goods. This is the immediate effect of the change, since at the time u rises, the capital stock K and the efficiency of each worker E are constant. Since output per effective worker falls, the curve showing saving pereffective worker shifts down.At the same time, the increase in time spent in research universities increases the growth rate of labor efficiency g(u). Hence, break-even investment [which we foundabove in part (b)] rises at any given level of k, so the line showing breakeveninvestment also shifts up.Figure 9-3 shows these shifts.In the new steady state, capital per effective worker falls from k1 to k2. Output per effective worker also falls.f. In the short run, the increase in u unambiguously decreases consumption. After all,we argued in part (e) that the immediate effect is to decrease output, since workers spend less time producing manufacturing goods and more time in researchuniversities expanding the stock of knowledge. For a given saving rate, the decrease in output implies a decrease in consumption.The long-run steady-state effect is more subtle. We found in part (e) that output per effective worker falls in the steady state. But welfare depends on output (and consumption) per worker, not per effective worker. The increase in time spent inresearch universities implies that E grows faster. That is, output per worker equals yE.Although steady-state y falls, in the long run the faster growth rate of E necessarily dominates. That is, in the long run, consumption unambiguously rises.Nevertheless, because of the initial decline in consumption, the increase in u is not unambiguously a good thing. That is, a policymaker who cares more aboutcurrent generations than about future generations may decide not to pursue a policy of increasing u. (This is analogous to the question considered in Chapter 8 of whethera policymaker should try to reach the Golden Rule level of capital per effective workerif k is currently below the Golden Rule level.)8. On the World Bank Web site (), click on the data tab and then theindicators tab. This brings up a large list of data indicators that allows you to compare the level of growth and development across countries. To explain differences in income per person across countries, you might look at gross saving as a percentage of GDP, gross capital formation as a percentage of GDP, literacy rate, life expectancy, andpopulation growth rate. From the Solow model, we learned that (all else the same) a higher rate of saving will lead to higher income per person, a lower population growth rate will lead to higher income per person, a higher level of capital per worker will lead toa higher level of income per person, and more efficient or productive labor will lead tohigher income per person. The selected data indicators offer explanations as to why one country might have a higher level of income per person. However, although we might speculate about which factor is most responsible for the difference in income per person across countries, it is not possible to say for certain given the large number of othervariables that also affect income per person. For example, some countries may have more developed capital markets, less government corruption, and better access to foreigndirect investment. The Solow model allows us to understand some of the reasons why income per person differs across countries, but given it is a simplified model, it cannot explain all of the reasons why income per person may differ.More Problems and Applications to Chapter 91. a. The growth in total output (Y) depends on the growth rates of labor (L), capital (K),and total factor productivity (A), as summarized by the equationΔY/Y = αΔK/K + (1 –α)ΔL/L + ΔA/A,where α is capital’s share of output. We can look at the effect on output of a 5-percent increase in labor by setting ΔK/K = ΔA/A = 0. Since α = 2/3, this gives usΔY/Y = (1/3)(5%)= 1.67%.A 5-percent increase in labor input increases output by 1.67 percent.Labor productivity is Y/L. We can write the growth rate in labor productivity asD Y Y =D(Y/L)Y/L-D LL.Substituting for the growth in output and the growth in labor, we findΔ(Y/L)/(Y/L) = 1.67% – 5.0%= –3.34%.Labor productivity falls by 3.34 percent.To find the change in total factor productivity, we use the equationΔA/A = ΔY/Y –αΔK/K – (1 –α)ΔL/L.For this problem, we findΔA/A = 1.67% – 0 – (1/3)(5%)= 0.Total factor productivity is the amount of output growth that remains after we have accounted for the determinants of growth that we can measure. In this case,there is no change in technology, so all of the output growth is attributable tomeasured input growth. That is, total factor productivity growth is zero, as expected.b. Between years 1 and 2, the capital stock grows by 1/6, labor input grows by 1/3, andoutput grows by 1/6. We know that the growth in total factor productivity is given byΔA/A = ΔY/Y –αΔK/K – (1 –α)ΔL/L.Substituting the numbers above, and setting α = 2/3, we findΔA/A = (1/6) – (2/3)(1/6) – (1/3)(1/3)= 3/18 – 2/18 – 2/18= – 1/18= –0.056.Total factor productivity falls by 1/18, or approximately 5.6 percent.2. By definition, output Y equals labor productivity Y/L multiplied by the labor force L:Y = (Y/L)L.Using the mathematical trick in the hint, we can rewrite this asD Y Y =D(Y/L)Y/L+D LL.We can rearrange this asD Y Y =D YY-D LL.Substituting for ΔY/Y from the text, we findD(Y/L) Y/L =D AA+aD KK+(1-a)D LL-D LL =D AA+aD KK-aD LL=D AA+aD KK-D LLéëêêùûúúUsing the same trick we used above, we can express the term in brackets asΔK/K –ΔL/L = Δ(K/L)/(K/L)Making this substitution in the equation for labor productivity growth, we conclude thatD(Y/L) Y/L =D AA+aD(K/L)K/L.3. We know the following:ΔY/Y = n + g = 3.6%ΔK/K = n + g = 3.6%ΔL/L = n = 1.8%Capital’s Share = α = 1/3Labor’s Share = 1 –α = 2/3Using these facts, we can easily find the contributions of each of the factors, and then find the contribution of total factor productivity growth, using the following equations:Output = Capital’s+ Labor’s+ Total Factor Growth Contribution Contribution ProductivityD Y Y = aD KK+ (1-a)D LL+ D AA3.6% = (1/3)(3.6%) + (2/3)(1.8%) + ΔA/A.We can easily solve this for ΔA/A, to find that3.6% = 1.2% + 1.2% + 1.2%We conclude that the contribution of capital is 1.2 percent per year, the contribution of labor is 1.2 percent per year, and the contribution of total factor productivity growth is 1.2 percent per year. These numbers match the ones in Table 9-3 in the text for the United States from 1948–2002.。
曼昆《宏观经济学》第9版章节习题精编详解(经济增长Ⅱ：技术、经验和政策)【圣才出品】
曼昆《宏观经济学》（第9版）章节习题精编详解第3篇增长理论：超长期中的经济第9章经济增长Ⅱ：技术、经验和政策一、概念题1．劳动效率（efficiency of labor）答：劳动效率是指单位劳动时间的产出水平，反映了社会对生产方法的掌握和熟练程度。
当可获得的技术改进时，劳动效率会提高。
当劳动力的健康、教育或技能得到改善时，劳动效率也会提高。
在索洛模型中，劳动效率（E）是表示技术进步的变量，反映了索洛模型劳动扩张型技术进步的思想：技术进步提高了劳动效率，就像增加了参与生产的劳动力数量一样，所以在生产函数中的劳动力数量上乘以一个劳动效率变量，形成了有效工人概念，这使得索洛模型在稳态分析中纳入了外生的技术进步。
2．劳动改善型技术进步（labor-augmenting technological progress）答：劳动改善型技术进步是指技术进步提高了劳动效率，就像增加了参与生产的劳动力数量一样，所以在生产函数中的劳动力数量上乘以一个劳动效率变量，以反映外生技术进步对经济增长的影响。
劳动改善型技术进步实际上认为技术进步是通过提高劳动效率而影响经济增长的。
它的引入形成了有效工人的概念，从而使得索洛模型能够以单位有效工人的资本和产量来进行稳定状态研究。
3．内生增长理论（endogenous growth theory）答：内生增长理论是用规模收益递增和内生技术进步来说明一个国家长期经济增长和各国增长率差异的一种经济理论，其重要特征就是试图使增长率内生化。
根据其依赖的基本假定条件的差异，可以将内生增长理论分为完全竞争条件下的内生增长模型和垄断竞争条件下的内生增长模型。
按照完全竞争条件下的内生增长模型，使稳定增长率内生化的两条基本途径就是：①将技术进步率内生化；②如果可以被积累的生产要素有固定报酬，那么可以通过某种方式使稳态增长率受要素的积累影响。
内生增长理论是抛弃了索洛模型外生技术进步的假设，以更好地研究技术进步与经济增长之间的关系的理论。
曼昆宏观经济经济学第九版英文原版复习资料3
Answers to Textbook Questions and ProblemsCHAPTER3 National Income: Where It Comes From and Where It GoesQuestions for Review1. The factors of production and the production technology determine the amount of output an economycan produce. The factors of production are the inputs used to produce goods and services: the most important factors are capital and labor. The production technology determines how much output can be produced from any given amounts of these inputs. An increase in one of the factors of production or an improvement in technology leads to an increase in the economy’s output.2. When a firm decides how much of a factor of production to hire or demand, it considers how thisdecision affects profits. For example, hiring an extra unit of labor increases output and thereforeincreases revenue; the firm compares this additional revenue to the additional cost from the higher wage bill. The additional revenue the firm receives depends on the marginal product of labor (MPL) and the price of the good produced (P). An additional unit of labor produces MPL units of additional output, which sells for P dollars per unit. Therefore, the additional revenue to the firm is P ⨯MPL. The cost of hiring the additional unit of labor is the wage W. Thus, this hiring decision has the following effect on profits:ΔProfit= ΔRevenue –ΔCost= (P ⨯MPL) –W.If the additional revenue, P ⨯MPL, exceeds the cost (W) of hiring the additional unit of labor, then profit increases. The firm will hire labor until it is no longer profitable to do so—that is, until the MPL falls to the point where the change in profit is zero. In the equation above, the firm hires labor until ΔP rofit = 0, which is when (P ⨯MPL) = W.This condition can be rewritten as:MPL = W/P.Therefore, a competitive profit-maximizing firm hires labor until the marginal product of labor equals the real wage. The same logic applies to the firm’s decision regarding how much capital to hire: the firm will hire capital until the marginal product of capital equals the real rental price.3. A production function has constant returns to scale if an equal percentage increase in all factors ofproduction causes an increase in output of the same percentage. For example, if a firm increases its use of capital and labor by 50 percent, and output increases by 50 percent, then the production function has constant returns to scale.If the production function has constant returns to scale, then total income (or equivalently, total output) in an economy of competitive profit-maximizing firms is divided between the return to labor, MPL ⨯L, and the return to capital, MPK ⨯K. That is, under constant returns to scale, economic profit is zero.4. A Cobb–Douglas production function has the form F(K,L) = AKαL1–α. The text showed that theparameter αgives capital’s share of income. So if capital earns one-fourth of total income, then α=0.25. Hence, F(K,L) = AK0.25L0.75.5. Consumption depends positively on disposable income—i.e. the amount of income after all taxes havebeen paid. Higher disposable income means higher consumption.The quantity of investment goods demanded depends negatively on the real interest rate. For an investment to be profitable, its return must be greater than its cost. Because the real interest ratemeasures the cost of funds, a higher real interest rate makes it more costly to invest, so the demand for investment goods falls.6. Government purchases are a measure of the value of goods and services purchased directly by thegovernment. For example, the government buys missiles and tanks, builds roads, and provides services such as air traffic control. All of these activities are part of GDP. Transfer payments are government payments to individuals that are not in exchange for goods or services. They are the opposite of taxes: taxes reduce household disposable income, whereas transfer payments increase it. Examples of transfer payments include Social Security payments to the elderly, unemployment insurance, and veterans’ benefits.7. Consumption, investment, and government purchases determine demand for the economy’s output,whereas the factors of production and the production function determine the supply of output. The real interest rate adjusts to ensure that the demand for the ec onomy’s goods equals the supply. At theequilibrium interest rate, the demand for goods and services equals the supply.8. When the government increases taxes, disposable income falls, and therefore consumption falls as well.The decrease in consumption equals the amount that taxes increase multiplied by the marginalpropensity to consume (MPC). The higher the MPC is, the greater is the negative effect of the tax increase on consumption. Because output is fixed by the factors of production and the production technology, and government purchases have not changed, the decrease in consumption must be offset by an increase in investment. For investment to rise, the real interest rate must fall. Therefore, a tax increase leads to a decrease in consumption, an increase in investment, and a fall in the real interest rate.Problems and Applications1. a. According to the neoclassical theory of distribution, the real wage equals the marginal product oflabor. Because of diminishing returns to labor, an increase in the labor force causes the marginalproduct of labor to fall. Hence, the real wage falls.Given a Cobb–Douglas production function, the increase in the labor force will increase the marginal product of capital and will increase the real rental price of capital. With more workers,the capital will be used more intensively and will be more productive.b. The real rental price equals the marginal product of capital. If an earthquake destroys some of thecapital stock (yet miraculously does not kill anyone and lower the labor force), the marginalproduct of capital rises and, hence, the real rental price rises.Given a Cobb–Douglas production function, the decrease in the capital stock will decrease the marginal product of labor and will decrease the real wage. With less capital, each worker becomes less productive.c. If a technological advance improves the production function, this is likely to increase the marginalproducts of both capital and labor. Hence, the real wage and the real rental price both increase.d. High inflation that doubles the nominal wage and the price level will have no impact on the realwage. Similarly, high inflation that doubles the nominal rental price of capital and the price levelwill have no impact on the real rental price of capital.2. a. To find the amount of output produced, substitute the given values for labor and land into theproduction function:Y = 1000.51000.5 = 100.b. According to the text, the formulas for the marginal product of labor and the marginal product ofcapital (land) are:MPL = (1 –α)AKαL–α.MPK = αAKα–1L1–α.In this problem, α is 0.5 and A is 1. Substitute in the given values for labor and land to find themarginal product of labor is 0.5 and marginal product of capital (land) is 0.5. We know that thereal wage equals the marginal product of labor and the real rental price of land equals the marginal product of capital (land).c. Labor’s share of the output is given by the marginal product of labor times the quantity of labor, or50.d. The new level of output is 70.71.e. The new wage is 0.71. The new rental price of land is 0.35.f. Labor now receives 35.36.3. A production function has decreasing returns to scale if an equal percentage increase in all factors ofproduction leads to a smaller percentage increase in output. For example, if we double the amounts of capital and labor output increases by less than double, then the production function has decreasing returns to scale. This may happen if there is a fixed factor such as land in the production function, and this fixed factor becomes scarce as the economy grows larger.A production function has increasing returns to scale if an equal percentage increase in all factorsof production leads to a larger percentage increase in output. For example, if doubling the amount of capital and labor increases the output by more than double, then the production function has increasing returns to scale. This may happen if specialization of labor becomes greater as the population grows.For example, if only one worker builds a car, then it takes him a long time because he has to learn many different skills, and he must constantly change tasks and tools. But if many workers build a car, then each one can specialize in a particular task and become more productive.4. a. A Cobb–Douglas production function has the form Y = AKαL1–α. The text showed that the marginalproducts for the Cobb–Douglas production function are:MPL = (1 –α)Y/L.MPK = αY/K.Competitive profit-maximizing firms hire labor until its marginal product equals the real wage, and hire capital until its marginal product equals the real rental rate. Using these facts and theabove marginal products for the Cobb–Douglas production function, we find:W/P = MPL = (1 –α)Y/L.R/P = MPK = αY/K.Rewriting this:(W/P)L = MPL ⨯L = (1 –α)Y.(R/P)K = MPK ⨯K = αY.Note that the terms (W/P)L and (R/P)K are the wage bill and total return to capital, respectively.Given that the value of α = 0.3, then the above formulas indicate that labor receives 70 percent of total output (or income) and capital receives 30 percent of total output (or income).b. To determine what happens to total output when the labor force increases by 10 percent, considerthe formula for the Cobb–Douglas production function:Y = AKαL1–α.Let Y 1 equal the initial value of output and Y 2 equal final output. We know that α = 0.3. We also know that labor L increases by 10 percent:Y 1 = AK 0.3L 0.7. Y 2 = AK 0.3(1.1L )0.7.Note that we multiplied L by 1.1 to reflect the 10-percent increase in the labor force. To calculate the percentage change in output, divide Y 2 by Y 1:Y 2Y 1=AK 0.31.1L ()0.7AK 0.3L 0.7=1.1()0.7=1.069.That is, output increases by 6.9 percent.To determine how the increase in the labor force affects the rental price of capital, consider the formula for the real rental price of capital R/P :R/P = MPK = αAK α–1L 1–α.We know that α = 0.3. We also know that labor (L ) increases by 10 percent. Let (R/P )1 equal the initial value of the rental price of capital, and let (R/P )2 equal the final rental price of capital after the labor force increases by 10 percent. To find (R/P )2, multiply L by 1.1 to reflect the 10-percent increase in the labor force:(R/P )1 = 0.3AK –0.7L 0.7. (R/P )2 = 0.3AK –0.7(1.1L )0.7.The rental price increases by the ratioR /P ()2R /P ()1=0.3AK -0.71.1L ()0.70.3AK -0.7L 0.7=1.1()0.7=1.069So the rental price increases by 6.9 percent. To determine how the increase in the labor forceaffects the real wage, consider the formula for the real wage W/P :W/P = MPL = (1 – α)AK αL –α.We know that α = 0.3. We also know that labor (L ) increases by 10 percent. Let (W/P )1 equal the initial value of the real wage, and let (W/P )2 equal the final value of the real wage. To find (W/P )2, multiply L by 1.1 to reflect the 10-percent increase in the labor force:(W/P )1 = (1 – 0.3)AK 0.3L –0.3. (W/P )2 = (1 – 0.3)AK 0.3(1.1L )–0.3.To calculate the percentage change in the real wage, divide (W/P )2 by (W/P )1:W /P ()2W /P ()1=1-0.3()AK 0.31.1L ()-0.31-0.3()AK 0.3L-0.3=1.1()-0.3=0.972That is, the real wage falls by 2.8 percent.c. We can use the same logic as in part (b) to setY 1 = AK 0.3L 0.7. Y 2 = A (1.1K )0.3L 0.7.Therefore, we have:Y 2Y 1=A 1.1K ()0.3L 0.7AK 0.3L 0.7=1.1()0.3=1.029This equation shows that output increases by about 3 percent. Notice that α < 0.5 means thatproportional increases to capital will increase output by less than the same proportional increase to labor.Again using the same logic as in part (b) for the change in the real rental price of capital:R /P ()2R /P ()1=0.3A 1.1K ()-0.7L 0.70.3AK -0.7L 0.7=1.1()-0.7=0.935The real rental price of capital falls by 6.5 percent because there are diminishing returns to capital; that is, when capital increases, its marginal product falls.Finally, the change in the real wage is:W /P ()2W /P ()1=0.7A 1.1K ()0.3L -0.30.7AK 0.3L -0.3=1.1()0.3=1.029Hence, real wages increase by 2.9 percent because the added capital increases the marginalproductivity of the existing workers. (Notice that the wage and output have both increased by the same amount, leaving the labor share unchanged —a feature of Cobb –Douglas technologies.)d. Using the same formula, we find that the change in output is:Y 2Y 1=1.1A ()K 0.3L 0.7AK 0.3L 0.7=1.1This equation shows that output increases by 10 percent. Similarly, the rental price of capital and the real wage also increase by 10 percent:R /P ()2R /P ()1=0.31.1A ()K -0.7L 0.70.3AK -0.7L 0.7=1.1W /P ()2W /P ()1=0.71.1A ()K 0.3L -0.30.7AK 0.3L -0.3=1.15. Labor income is defined asW P ´L =WLP Labor’s share of income is defined asWL P æèççöø÷÷/Y =WL PYFor example, if this ratio is about constant at a value of 0.7, then the value of W /P = 0.7*Y /L . Thismeans that the real wage is roughly proportional to labor productivity. Hence, any trend in laborproductivity must be matched by an equal trend in real wages. O therwise, labor’s share would deviate from 0.7. Thus, the first fact (a constant labor share) implies the second fact (the trend in real wages closely tracks the trend in labor productivity).6. a. Nominal wages are measured as dollars per hour worked. Prices are measured as dollars per unitproduced (either a haircut or a unit of farm output). Marginal productivity is measured as units of output produced per hour worked.b. According to the neoclassical theory, technical progress that increases the marginal product offarmers causes their real wage to rise. The real wage for farmers is measured as units of farm output per hour worked. The real wage is W /P F , and this is equal to ($/hour worked)/($/unit of farm output).c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged. The realwage for barbers is measured as haircuts per hour worked. The real wage is W /P B , and this is equal to ($/hour worked)/($/haircut).d. If workers can move freely between being farmers and being barbers, then they must be paid thesame wage W in each sector.e. If the nominal wage W is the same in both sectors, but the real wage in terms of farm goods isgreater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods. We know that W /P = MPL so that W = P MPL . This means that P F MPL F = P H MPL B , given that the nominal wages are the same. Since the marginal product of labor for barbers has not changed and the marginal product of labor for farmers has risen, the price of a haircut must have risen relative to the price of the farm output. If we express this in growth rate terms, then the growth of the farm price + the growth of the marginal product of the farm labor = the growth of the haircut price.f. The farmers and the barbers are equally well off after the technological progress in farming, giventhe assumption that labor is freely mobile between the two sectors and both types of peopleconsume the same basket of goods. Given that the nominal wage ends up equal for each type ofworker and that they pay the same prices for final goods, they are equally well off in terms of what they can buy with their nominal income. The real wage is a measure of how many units of output are produced per worker. Technological progress in farming increased the units of farm outputproduced per hour worked. Movement of labor between sectors then equalized the nominal wage.7. a. The marginal product of labor (MPL)is found by differentiating the production function withrespect to labor:MPL=dY dL=13K1/3H1/3L-2/3An increase in human capital will increase the marginal product of labor because more human capital makes all the existing labor more productive.b. The marginal product of human capital (MPH)is found by differentiating the production functionwith respect to human capital:MPH=dY dH=13K1/3L1/3H-2/3An increase in human capital will decrease the marginal product of human capital because there are diminishing returns.c. The labor share of output is the proportion of output that goes to labor. The total amount of outputthat goes to labor is the real wage (which, under perfect competition, equals the marginal product of labor) times the quantity of labor. This quantity is divided by the total amount of output to compute the labor share:Labor Share=(13K1/3H1/3L-2/3)LK1/3H1/3L1/3=1 3We can use the same logic to find the human capital share:Human Capital Share=(13K1/3L1/3H-2/3)HK1/3H1/3L1/3=1 3so labor gets one-third of the output, and human capital gets one-third of the output. Since workers own their human capital (we hope!), it will appear that labor gets two-thirds of output.d. The ratio of the skilled wage to the unskilled wage is:Wskilled Wunskilled =MPL+MPHMPL=13K1/3L-2/3H1/3+13K1/3L1/3H-2/31K1/3L-2/3H1/3=1+LHNotice that the ratio is always greater than 1 because skilled workers get paid more than unskilled workers. Also, when H increases this ratio falls because the diminishing returns to human capitallower its return, while at the same time increasing the marginal product of unskilled workers.e. If more colleges provide scholarships, it will increase H, and it does lead to a more egalitariansociety. The policy lowers the returns to education, decreasing the gap between the wages of more and less educated workers. More importantly, the policy even raises the absolute wage of unskilled workers because their marginal product rises when the number of skilled workers rises.8. The effect of a government tax increase of $100 billion on (a) public saving, (b) private saving, and (c)national saving can be analyzed by using the following relationships:National Saving = [Private Saving] + [Public Saving]= [Y –T –C(Y –T)] + [T –G]= Y –C(Y –T) –G.a. Public Saving—The tax increase causes a 1-for-1 increase in public saving. T increases by $100billion and, therefore, public saving increases by $100 billion.b. Private Saving—The increase in taxes decreases disposable income, Y –T, by $100 billion. Sincethe marginal propensity to consume (MPC) is 0.6, consumption falls by 0.6 $100 billion, or $60 billion. Hence,ΔPrivate Saving = –$100b – 0.6 (–$100b) = –$40b.Private saving falls $40 billion.c. National Saving—Because national saving is the sum of private and public saving, we canconclude that the $100 billion tax increase leads to a $60 billion increase in national saving.Another way to see this is by using the third equation for national saving expressed above, that national saving equals Y –C(Y –T) –G. The $100 billion tax increase reduces disposableincome and causes consumption to fall by $60 billion. Since neither G nor Y changes, nationalsaving thus rises by $60 billion.d. Investment—To determine the effect of the tax increase on investment, recall the nationalaccounts identity:Y = C(Y –T) + I(r) + G.Rearranging, we findY –C(Y –T) –G = I(r).The left side of this equation is national saving, so the equation just says that national savingequals investment. Since national saving increases by $60 billion, investment must also increaseby $60 billion.How does this increase in investment take place? We know that investment depends on thereal interest rate. For investment to rise, the real interest rate must fall. Figure 3-1 illustrates saving and investment as a function of the real interest rate.The tax increase causes national saving to rise, so the supply curve for loanable funds shifts to the right. The equilibrium real interest rate falls, and investment rises.9. If consumers increase the amount that they consume today, then private saving and, therefore, nationalsaving will fall. We know this from the definition of national saving:National Saving = [Private Saving] + [Public Saving]= [Y –T –C(Y –T)] + [T –G].An increase in consumption decreases private saving, so national saving falls.Figure 3-2 illustrates saving and investment as a function of the real interest rate. If national saving decreases, the supply curve for loanable funds shifts to the left, thereby raising the real interest rate and reducing investment.10. a. Private saving is the amount of disposable income, Y – T, that is not consumed:S private= Y – T – C= 8,000 – 2,000 – [1,000 + (2/3)(8,000 – 2,000)]= 1,000.Public saving is the amount of taxes the government has left over after it makes its purchases:S public= T – G= 2,000 – 2,500= –500.National saving is the sum of private saving and public saving:S national= S private+ S public= 1,000 + (500)= 500.b. The equilibrium interest rate is the value of r that clears the market for loanable funds. We alreadyknow that national saving is 500, so we just need to set it equal to investment:S national= I500 = 1,200 – 100rSolving this equation for r, we find:r = 0.07 or 7%.c. When the government increases its spending, private saving remains the same as before (noticethat G does not appear in the S private equation above) while government saving decreases. Puttingthe new G into the equations above:S private= 1,000S public= T – G= 2,000 – 2,000= 0.Thus,S national= S private+ S public= 1,000 + (0)= 1,000.d. Once again the equilibrium interest rate clears the market for loanable funds:S national= I1,000 = 1,200 – 100rSolving this equation for r, we find:r = 0.02 or 2%.11. To determine the effect on investment of an equal increase in both taxes and government spending,consider the national income accounts identity for national saving:National Saving = [Private Saving] + [Public Saving]= [Y –T –C(Y –T)] + [T –G].We know that Y is fixed by the factors of production. We also know that the change in consumption equals the marginal propensity to consume (MPC) times the change in disposable income. This tells us thatΔNational Saving= {–ΔT – [MPC ⨯ (–ΔT)]} + [ΔT –ΔG]= [–ΔT + (MPC ⨯ΔT)] + 0= (MPC – 1) ΔT .The above expression tells us that the impact on national saving of an equal increase in T and G depends on the size of the marginal propensity to consume. The closer the MPC is to 1, the smaller is the fall in saving. For example, if the MPC equals 1, then the fall in consumption equals the rise in government purchases, so national saving [Y – C (Y – T ) – G ] is unchanged. The closer the MPC is to 0 (and therefore the larger is the amount saved rather than spent for a one-dollar change in disposable income), the greater is the impact on saving. Because we assume that the MPC is less than 1, we expect that national saving falls in response to an equal increase in taxes and government spending.The reduction in saving means that the supply of loanable funds curve will shift to the left in Figure 3-3. The real interest rate rises, and investment falls.12. a. The demand curve for business investment shifts out to the right because the subsidy increases thenumber of profitable investment opportunities for any given interest rate. The demand curve for residential investment remains unchanged.b. The total demand curve for investment in the economy shifts out to the right since it represents thesum of business investment, which shifts out to the right, and residential investment, which isunchanged. As a result the real interest rate rises as in Figure 3-4.c. The total quantity of investment does not change because it is constrained by the inelastic supply of savings. The investment tax credit leads to a rise in business investment, but an offsetting fall in residential investment. That is, the higher interest rate means that residential investment falls (a movement along the curve), whereas the rightward shift of the business investment curve leads business investment to rise by an equal amount. Figure 3-5 shows this change. Note that I 1B +I 1R +I 2B +I 2R =S .13. In this chapter, we concluded that an increase in government expenditures reduces national saving andraises the interest rate. The increase in government expenditure therefore crowds out investment by the full amount of the increase. Similarly, a tax cut increases disposable income and hence consumption.This increase in consumption translates into a fall in national saving, and the increase in consumption crowds out investment by the full amount of the increase.If consumption depends on the interest rate, then saving will also depend on it. The higher the interest rate, the greater the return to saving. Hence, it seems reasonable to think that an increase in the interest rate might increase saving and reduce consumption. Figure 3-6 shows saving as an increasing function of the interest rate.Consider what happens when government purchases increase. At any given level of the interest rate, national saving falls by the change in government purchases, as shown in Figure 3-7. The figure shows that if the saving function slopes upward, investment falls by less than the amount thatgovernment purchases rises by. This happens because consumption falls and saving increases inresponse to the higher interest rate. Hence, the more responsive consumption is to the interest rate, the less investment is crowded out by government purchases.14. a. Figure 3-8 shows the case where the demand for loanable funds is stable but the supply of funds(the saving schedule) fluctuates perhaps reflecting temporary shocks to income, changes ingovernment spending, or changes in consumer confidence. In this case, when interest rates fall,investment rises; when interest rates rise, investment falls. We would expect a negative correlation between investment and interest rates.b. Figure 3-9 shows the case where the supply of loanable funds (saving) is stable, whereas thedemand for loanable funds fluctuates, perhaps reflecting ch anges in firms’ expectations about the marginal product of capital. We would now find a positive correlation between investment and the interest rate—when demand for funds rises, it pushes up the interest rate, so we observe thatinvestment and the real interest rate increase at the same time.c. If both curves shift, we might generate a scatter plot as in Figure 3-10, where the economyfluctuates among points A, B, C, and D. Depending on how often the economy is at each of these points, we might find little clear relationship between investment and interest rates.d. Situation (c) seems fairly reasonable—as both the supply of and demand for loanable fundsfluctuate over time in response to changes in the economy.。
曼昆宏观经济经济学第九版英文原版答案完整版
曼昆宏观经济经济学第九版英文原版答案完整版曼昆宏观经济经济学第九版英文原版答案集团标准化办公室：[VV986T-J682P28-JP266L8-68PNN]A n s w e r s t o T e x t b o o k Q u e s t i o n s a n d P r o b l e m sCHAPTER 7Unemployment and the Labor MarketQuestions for Review1. The rates of job separation and job finding determine the naturalrate of unemployment. The rate of job separation is the fraction of people who lose their job each month. The higher the rate of jobseparation, the higher the natural rate of unemployment. The rate of job finding is the fraction of unemployed people who find a job each month. The higher the rate of job finding, the lower the natural rate of unemployment.2. Frictional unemployment is the unemployment caused by the time ittakes to match workers and jobs. Finding an appropriate job takes time because the flow of information about job candidates and job vacancies is not instantaneous. Because different jobs requiredifferent skills and pay different wages, unemployed workers may not accept the first job offer they receive.In contrast, structural unemployment is the unemployment resulting from wage rigidity and job rationing. These workers are unemployed not because they are actively searching for a job that best suits their skills (as in the case of frictional unemployment), but because at the prevailing real wage thequantity of labor supplied exceeds the quantity of labor demanded. If the wage does not adjust to clear the labor market, then these workers must wait for jobs to become available. Structural unemployment thus arises because firms fail to reduce wages despite an excess supply of labor.3. The real wage may remain above the level that equilibrates laborsupply and labor demand because of minimum wage laws, the monopoly power of unions, and efficiency wages.Minimum-wage laws cause wage rigidity when they prevent wages from falling to equilibrium levels. Although most workers are paid a wage above the minimum level, for some workers, especially the unskilled and inexperienced, the minimum wage raises their wage above theequilibrium level. It therefore reduces the quantity of their labor that firms demand, and creates an excess supply of workers, which increases unemployment.The monopoly power of unions causes wage rigidity because the wages of unionized workers are determined not by the equilibrium of supply and demand but by collective bargaining between union leaders and firm management. The wage agreement often raises the wage abovethe equilibrium level and allows the firm to decide how many workers to employ. These high wages cause firms to hire fewer workers than at the market-clearing wage, so structural unemployment increases.Efficiency-wage theories suggest that high wages make workers more productive. The influence of wages on worker efficiency may explain why firms do not cut wages despite an excess supply of labor. Even though a wage reduction decreasesthe firm’s wage bill, it may also lower worker productivity and therefore the firm’s profits.4. Depending on how one looks at the data, most unemployment can appearto be either short term or long term. Most spells of unemployment are short; that is, most of those who became unemployed find jobs quickly.On the other hand, most weeks of unemployment are attributable to the small number of long-term unemployed. By definition, the long-term unemployed do not find jobs quickly, so they appear on unemployment rolls for many weeks or months.5. Europeans work fewer hours than Americans. One explanation is thatthe higher income tax rates in Europe reduce the incentive to work. A second explanation is a larger underground economy in Europe as aresult of more people attempting to evade the high tax rates.A third explanation is the greater importance of unions in Europe and their ability to bargain for reduced work hours. A final explanation isbased on preferences, whereby Europeans value leisure more thanAmericans do, and therefore elect to work fewer hours.Problems and Applications1. a. In the example that follows, we assume that during the school yearyou look for a part-time job, and that, on average, it takes 2 weeks to find one. We also assume that the typical job lasts 1semester, or 12 weeks.b. If it takes 2 weeks to find a job, then the rate of job finding in weeks isf = (1 job/2 weeks) = 0.5 jobs/week.If the job lasts for 12 weeks, then the rate of job separation in weeks iss = (1 job/12 weeks) = 0.083 jobs/week.c. From the text, we know that the formula for the natural rate of unemployment is(U/L) = [s/(s + f )],where U is the number of people unemployed, and L is the number of people in the labor force.Plugging in the values for f and s that were calculated in part (b), we find(U/L) = [0.083/(0.083 + 0.5)] = 0.14.Thus, if on average it takes 2 weeks to find a job that lasts 12 weeks, the natural rate of unemployment for this population ofcollege students seeking part-time employment is 14 percent.2. Call the number of residents of the dorm who are involved I, thenumber who are uninvolved U, and the total number of students T = I + U. In steady state the total number of involved students is constant.For this to happen we need the number of newly uninvolved students,(0.10)I, to be equal to the number of students who just becameinvolved, (0.05)U. Following a few substitutions:(0.05)U = (0.10)I= (0.10)(T – U),soWe find that two-thirds of the students are uninvolved.3. To show that the unemployment rate evolves over time to thesteady-state rate, let’s begin by defining how the number of people unemployed changes over time. The change in the number of unemployed equals the number of people losing jobs (sE) minus the number finding jobs (fU). In equation form, we can express this as:U–U t= ΔU t + 1 = sE t–fU t.t + 1Recall from the text that L = E t + U t, or E t = L –U t, where L is the total labor force (we will assume that L is constant). Substituting for E t in the above equation, we findΔU t + 1 = s(L –U t) –fU t.Dividing by L, we get an expression for the change in the unemployment rate from t to t + 1:ΔU t + 1/L = (U t + 1/L) –(U t/L) = Δ[U/L]t + 1 = s(1 –U t/L) –fU t/L.Rearranging terms on the right side of the equation above, we end up with line 1 below. Now take line 1 below, multiply the right side by (s + f)/(s + f) and rearrange terms to end up with line 2 below:Δ[U/L]t + 1= s – (s + f)U t/L= (s + f)[s/(s + f) – U/L].tThe first point to note about this equation is that in steady state, when the unemployment rate equals its natural rate, the left-handside of this expression equals zero. This tells us that, as we found in the text, the natural rate of unemployment (U/L)n equals s/(s + f).We can now rewrite the above expression, substituting (U/L)n for s/(s + f), to get an equation that is easier to interpret: Δ[U/L]t + 1 = (s + f)[(U/L)n–U t/L].This expression shows the following:If U t/L > (U/L)n (that is, the unemployment rate is above its natural rate), then Δ[U/L]t + 1 is negative: the unemployment rate falls.If U t/L < (U/L)n (that is, the unemployment rate is below its natural rate), then Δ[U/L]t + 1 is positive: the unemployment raterises.This process continues until the unemployment rate U/L reaches the steady-state rate (U/L)n.4. Consider the formula for the natural rate of unemployment,If the new law lowers the chance of separation s, but has no effect on the rate of job finding f, then the natural rate of unemployment falls.For several reasons, however, the new law might tend to reduce f.First, raising the cost of firing might make firms more careful about hiring workers, since firms have a harder time firing workers who turn out to be a poor match. Second, if job searchers think that the new legislation will lead them to spend a longer period of time on a particular job, then they might weigh morecarefully whether or not to take that job. If the reduction in f is large enough, then the new policy may even increase the natural rate of unemployment.5. a. The demand for labor is determined by the amount of labor that aprofit-maximizing firm wants to hire at a given real wage. The profit-maximizing condition is that the firm hire labor until the marginal product of labor equals the real wage,The marginal product of labor is found by differentiating the production function with respect to labor (see Chapter 3 for more discussion),In order to solve for labor demand, we set the MPL equal to the real wage and solve for L:Notice that this expression has the intuitively desirable feature that increases in the real wage reduce the demand for labor.b. We assume that the 27,000 units of capital and the 1,000 units oflabor are supplied inelastically (i.e., they will work at anyprice). In this case we know that all 1,000 units of labor and 27,000 units of capital will be used in equilibrium, so we can substitute these values into the above labor demand function and.solve for WPIn equilibrium, employment will be 1,000, and multiplying this by10 we find that the workers earn 10,000 units of output. The totaloutput is given by the production function:Y=5Y13Y23Y=5(27,00013)(1,00023)Y=15,000.Notice that workers get two-thirds of output, which is consistent with what we know about the Cobb–Douglas production function from Chapter 3.c. The real wage is now equal to 11 (10% above the equilibrium levelof 10).Firms will use their labor demand function to decide how manyworkers to hire at the given real wage of 11 and capital stock of 27,000:So 751 workers will be hired for a total compensation of 8,261units of output. To find the new level of output, plug the new value for labor and the value for capital into the production function and you will find Y = 12,393.d. The policy redistributes output from the 249 workers who becomeinvoluntarily unemployed to the 751 workers who get paid more than before. The lucky workers benefit less than the losers lose as the total compensation to the working class falls from 10,000 to 8,261 units of output.e. This problem does focus on the analysis of two effects of theminimum-wage laws: they raise the wage for some workers whiledownward-sloping labor demand reduces the total numberof jobs.Note, however, that if labor demand is less elastic than in this example, then the loss of employment may be smaller, and thechange in worker income might be positive.6. a. The labor demand curve is given by the marginal product of laborschedule faced by firms. If a country experiences a reduction inproductivity, then the labor demand curve shifts to the left as in Figure 7-1. If labor becomes less productive, then at any givenreal wage, firms demand less labor.b. If the labor market is always in equilibrium, then, assuming afixed labor supply, an adverse productivity shock causes adecrease in the real wage but has no effect on employment orunemployment, as in Figure 7-2.c. If unions constrain real wages to remain unaltered, then asillustrated in Figure 7-3, employmentfalls to L1 and unemployment equals L –L1.This example shows that the effect of a productivity shock on aneconomy depends on the role of unions and the response of collective bargaining to such a change.7. a. If workers are free to move between sectors, then the wage in each sector will be equal. If thewages were not equal then workers would have an incentive to move to the sector with the higherwage and this would cause the higher wage to fall, and the lower wage to rise until they wereequal.b. Since there are 100 workers in total, L S = 100 – L M. We cansubstitute this expression into the labor demand for services equation, and call the wage w since it is the same in bothsectors:L S = 100 – LM= 100 – 4wLM= 4w.Now set this equal to the labor demand for manufacturing equation and solve for w:4w = 200 – 6ww = $20.Substitute the wage into the two labor demand equations to find L M is 80 and L S is 20.c. If the wage in manufacturing is equal to $25 then L M is equal to 50.d. There are now 50 workers employed in the service sector and the wage w S is equal to $12.50.e. The wage in manufacturing will remain at $25 and employment will remain at 50. If thereservation wage for the service sector is $15 then employment in the service sector will be 40. Therefore, 10 people are unemployed and the unemployment rate is 10 percent.8. Real wages have risen over time in both the United Statesand Europe,increasing the reward for working (the substitution effect) but also making people richer, so they want to “buy” more leisure (theincome effect). If the income effect dominates, then people want to work less as real wages go up. This could explain the Europeanexperience, in which hours worked per employed person have fallen over time. If the income and substitution effects approximatelycancel, then this could explain the U.S. experience, in which hours worked per person have stayed about constant. Economists do not have good theories for why tastes might differ, so they disagree onwhether it is reasonable to think that Europeans have a larger income effect than do Americans.9. The vacant office space problem is similar to the unemploymentproblem; we can apply the same concepts we used in analyzingunemployed labor to analyze why vacant office space exists. There isa rate of office separation: firms that occupy offices leave, eitherto move to different offices or because they go out of business.There is a rate of office finding: firms that need office space (either to start up or expand) find empty offices. It takes time to match firms with available space. Different types of firms require spaces with different attributes depending on what theirspecific needs are. Also, because demand for different goods fluctuates, there are “sectoral shifts”—changes in the composition of demand among industries and regions that affect the profitability and office needs of different firms.。
(完整版)曼昆宏观经济学原理答案
第一篇导言复习题第一章宏观经济学的科学1、解释宏观经济学和微观经济学之间的差距，这两个领域如何相互关联？【答案】微观经济学研究家庭和企业如何作出决策以及这些决策在市场上的相互作用。
微观经济学的中心原理是家庭和企业的最优化——他们在目的和所面临的约束条件下可以让自己的境况更好。
而相对的，宏观经济学研究经济的整体情况，它主要关心总产出、总就业、一般物价水平和国际贸易等问题，以及这些宏观指标的波动趋势与规律。
应该看到，宏观经济学研究的这些宏观经济变量是以经济体系中千千万万个体家庭和企业之间的相互作用所构成的。
因此，微观经济决策总是构成宏观经济模型的基础，宏观经济学必然依靠微观经济基础。
2、为什么经济学家建立模型？【答案】一般来说，模型是对某些具体事物的抽象，经济模型也是如此。
经济模型可以简洁、直接地描述所要研究的经济对象的各种关系。
这样，经济学家可以依赖模型对特定的经济问题进行研究；并且，由于经济实际不可控，而模型是可控的，经济学家可以根据研究需要，合理、科学的调整模型来研究各种经济情况。
另外，经济模型一般是数学模型，而数学是全世界通用的科学语言，使用规范、标准的经济模型也有利于经济学家正确表达自己的研究意图，便于学术交流。
3、什么是市场出清模型？什么时候市场出清的假设是适用的？【答案】市场出清模型就是供给与需求可以在价格机制调整下很快达到均衡的模型。
市场出清模型的前提条件是价格是具有伸缩性的（或弹性）。
但是，我们知道价格具有伸缩性是一个很强的假设，在很多实际情况下，这个假设都是不现实的。
比如：劳动合同会使劳动力价格在一段时期内具有刚性。
因此，我们必须考虑什么情况下价格具有伸缩性是合适的。
现在一般认为，在研究长期问题时，假设价格具有伸缩性是合理的；而在研究短期问题时，最好假设价格具有刚性。
因为，从长期看，价格机制终将发挥作用，使市场供需平衡，即市场出清，而在短期，价格机制因其他因素制约，难以很快使市场出清。
曼昆经济学原理宏观经济学分册英文原版
REAL VERSUS NOMINAL GDP
• An accurate view of the economy requires adjusting nominal to real GDP by using the GDP deflator.
第17页/共264页
Table 2 Real and Nominal GDP
The GDP Deflator
• The GDP deflator is calculated as follows:
GDP deflator = Nominal GDP 100 Real GDP
第22页/共264页
The GDP Deflator
• Nominal GDP is converted to real GDP as follows:
第3页/共264页
THE ECONOMY’S INCOME AND EXPENDITURE
• For an economy as a whole, income must equal expenditure because: • Ever y transaction has a buyer and a seller. • Ever y dollar of spending by some buyer is a dollar of income for some seller.
第18页/共264页
Table 2 Real and Nominal GDP
第19页/共264页
Table 2 Real and Nominal GDP
第20页/共264页
The GDP Deflator
• The GDP deflator is a measure of the price level calculated as the ratio of nominal GDP to real GDP times 100.
曼昆《宏观经济学》第9版章节习题精编详解(金融系统：机会与危险)【圣才出品】
曼昆《宏观经济学》（第9版）章节习题精编详解第6篇宏观经济政策专题第20章金融系统：机会与危险一、关键概念1．金融系统（financial system）答：金融系统是指代经济中促进储蓄者和投资者之间资金流动的机构的概括性术语，其主要职能是将来自储蓄者的资源引导到各种形式的投资中去。
金融系统的一个部分是金融市场的集合，另一个部分是金融中介的集合。
2．金融市场（financial markets）答：金融市场是指资金融通市场，资金供给者和资金需求者双方通过信用工具进行交易而融通资金的市场。
广义的金融市场是指实现货币借贷、资金融通、办理各种票据和有价证券交易活动的场所。
通过金融市场，家庭能够直接为投资提供资源。
两个重要的金融市场是债券市场和股票市场。
3．债券（bonds）答：债券代表债券持有人给企业的贷款。
通过发行债券来筹集投资资金称为债券融资。
债券是直接融资形式之一，发行者通常是公司或政府。
4．股票（stocks）答：股票代表企业股东的所有权要求。
通过发行股票来筹集资金称为股权融资。
股票是直接融资形式之一。
5．债务融资（debt finance）答：债务融资是指企业通过发行债券来筹集投资资金，资金供给者作为债权人享有到期收回本息的一种融资方式。
债务融资属于直接融资，其经营风险较小，预期收益也相对较小。
6．股权融资（equity finance）答：股权融资是指通过发行股票，引进新股东来筹集资金，企业无须还本付息，但是新老股东共享企业的收益。
股权融资属于直接融资，主要用于解决企业运营资金短缺的问题。
7．金融中介（financial intermediaries）答：金融系统是金融中介的集合，通过金融中介，家庭能够间接地为投资提供资源。
金融中介连接市场的两端，帮助金融资源流向它们的最佳用途。
商业银行是最广为人知的金融中介类型。
它们从储蓄者那里吸收存款，用这些存款给那些需要为投资项目融资的人放贷。
8．厌恶风险（risk averse）答：投资天生是有风险的。
国际经济学第九版英文课后答案 第9单元
*CHAPTER 9(Core Chapter)NONTARIFF TRADE BARRIERS AND THE NEW PROTECTIONISM OUTLINE9.1 Introduction9.2 Import Quotas9.2a Effects of an Import QuotaCase Study 9-1: The Economic Effects of the U.S. Quota on Sugar Imports9.2b Comparison of an Import Quota to an Import Tariff9.3 Other Nontariff Barriers and the New Protectionism9.3a Voluntary Export RestraintsCase Study 9-2: Voluntary Export Restraints on Japanese Autos to the United States9.3b Technical, Administrative, and Other Regulations9.3c International Cartels9.3d DumpingCase Study 9-3: Antidumping Measures in Force in 20049.3e Export SubsidiesCase Study 9-4: Agricultural Subsidies in Developed NationsCase Study 9-5: Countervailing Measures in Force in 2004Case Study 9-6: The Pervasiveness of Nontariff Barriers9.4 The Political Economy of Protectionism9.4a Fallacious and Questionable Arguments for Protection9.4b Infant-Industry and Other Qualified Arguments for Protection9.4c Who Gets Protected?Case Study 9-7: Welfare Effects on the U.S. Economy of Removing All ImportRestraintsCase Study 9-8: Effects on the World Economy of Removing All ImportRestraints9.5 Strategic Trade and Industrial Policies9.5a Strategic Trade Policy9.5b Strategic Trade and Industrial Policies with Game Theory9.5c The U.S. Response to Foreign Industrial Targeting and Strategic TradePolicy9.6 History of U.S. Commercial Policy9.6a The Trade Agreements Act of 19349.6b The General Agreements on Tariffs and Trade (GATT)9.6c The 1962 Trade Agreements Act and the Kennedy Round9.6d The Trade Reform Act of 1974 and the Tokyo Round9.6e The 1984 and 1988 Trade Acts9.7 The Uruguay Round and Outstanding Trade Problems9.7a The Uruguay RoundCase Study 9-9: Gains from the Uruguay RoundCase Study 9-10: The Multilateral Rounds of Trade Negotiations9.7b Outstanding Trade ProblemsCase Study 9-11: Benefits from a “Likely” Doha ScenarioAppendix: A9.1 Centralized CartelsA9.2 International Price DiscriminationA9.3 Tariffs, Subsidies and Domestic GoalsKey TermsQuota Smoot-Hawley Tariff Act of 1930 Nontariff trade barrier (NTBs) Trade Agreements Act of 1934New protectionism Most-favored-nation principleVoluntary export restraints (VERs) Bilateral TradeTechnical, administrative, and General Agreement on Tariff andother regulations Trade (GATT)International cartel Multilateral Trade NegotiationsDumping International Trade Organization (ITO) Persistent dumping Peril-point provisionsPredatory dumping Escape clauseSporadic dumping National security clauseTrigger-price mechanism Trade Expansion Act of 1962Export subsidies Trade Adjustment Assistance (TAA) Export-Import bank Kennedy RoundForeign Sales Corporations Trade Reform Act of 1974 Countervailing duties (CVDs) Tokyo RoundScientific tariff Trade and Tariff Act of 1984Infant-industry argument Omnibus Trade and Competitiveness Act of 1988Strategic trade policy Uruguay RoundIndustrial Policy World Trade Organization (WTO)Game theory GlobalizationAnti-Globalization MovementLecture Guide:1.This is an important core chapter examining some of the most recentdevelopments in international trade policy.2.I would cover sections 1 and 2 in lecture 1. I would pay particular attention toFigure 9-1, which examines the partial equilibrium effects of an import quota. 3.I would cover section 3 in lecture 2. Here I would clearly explain the differencebetween a regular import quota and a voluntary export restraint. I would alsoclearly explain dumping and Figure 9-2 (which deals with export subsidies). The five case studies serve to highlight the theory and show the relevance of thetheory in today's world.4.I would cover section 4 in lecture 3. Here I would give special attention to thefallacious arguments for protection since they are often heard in commondiscussions of trade matters. I would also clearly explain the importance ofstrategic trade and industrial policy and the political economy of who getsprotected.5.I would cover section 5 in lecture 4, which examines strategic trade andindustrial policies policies with game theory. This is not difficult and thestudents will find it very interesting.6.Sections 6 and 7 can be covered in lecture 5. Here I would stress the UruguayRound and the outstanding international trade problems.Answer to Problems:1. Nations restrict trade either in response to lobbying by the producers of acommodity in which the nation has a comparative disadvantage or to gain astrategic advantage in relation to other nations. The first leads to a welfare loss for he nation as a whole. The second is very difficult to achieve.2. The partial equilibrium effects of the import quota are:P x=$1.50; consumption is 45X, of which 15X are produced domestically;by auctioning off import licenses, the revenue effect would be $15.3. The partial equilibrium effects of the import quota are:P x=$2.50; consumption is 40X, of which 10X are produced domestically;the revenue effect is $45.4. The partial equilibrium effects of the quota are:P x=$2; domestic production and consumption are 50X; The revenue is zero.5. The partial equilibrium effects of the quota are:P x=$1; consumption is 70X, production is 30X, and revenue is zero.6. The partial equilibrium effects of a negotiated export quota of 30X are:P x=$4; domestic production is 40X, of which 10X are consumed at home.7.An export tariff or quota, as an import tariff or quota, affects the price of thecommodity and domestic consumption and production. But the effects are theopposite.8. See Figure 1.The equilibrium price of the commodity is P x=OC and the equilibrium quantity is Q x=OB in Figure 1.9.If the supply curve of the commodity in Figure 1 referred to a cartel ofexporters acting as a monopolist, P x=OF and Q x=OA (see Figure 1).10. P x is higher and Q x smaller when exporters behave as a monopolist.11. a) The monopolist should charge P1=$4 in the domestic market and P2=$3 inFigure 9-5 in Appendix A9.2.b) This represents the best, or optimal distribution of sales between the twomarkets because any other distribution of sales in the two markets gives lessrevenue.12. See Figure 2. To the left of point A, the domestic firm faces higher long-run average costs of production (LAC D) than the foreign firm (LAC F). To theright of point A the opposite is the case.13.a) If the entries in the top left-hand corner of Table 9-5 were changed to +10,+10, then both Boeing and Airbus would produce the aircraft without anysubsidy, and so no strategic trade and industrial policy would be needed in theU.S. or Europe.b)If the entries in the top left-hand corner of Table 9-5 were changed to +5, +0,then both Boeing and Airbus would produce the aircraft without any subsidy, and so no strategic trade and industrial policy would be needed in the U.S. or Europe.*Note that even though Airbus only breaks even, in economics we includea normal return on investment as part of costs. Thus, Airbus wouldremain in business because it would earn a normal return on investment.c)If the entries in the top left-hand corner of Table 9-5 were changed to +5, -10,then both Boeing produces and Airbus does not produce without any subsidy.With a subsidy of at least $10 million per year, however, Airbus would enterthe market and lead to a loss of $100 million for Boeing unless the U.S.government would provide a subsidy of at least $5 million per year to Boeing.14. The answer to part (a) and (b) are presented in Appendix A9.3.App. 1. See Figure 3 on page 90.App. 2. In order to maximize to maximize total profits the domestic monopolist practicing international price discrimination should sell at theprice of P d=$20 in the domestic market and at the price of P f=$15 in theforeign market.App. 3. By imposing a 100% tax on the production of commodity X andgiving it as a subsidy to producers of commodity Y.Multiple-choice Questions:1. An import quota:a. increases the domestic price of the imported commodityb. reduces domestic consumptionc. increases domestic production*d. all of the above2. An increase in the demand of the imported commodity subject to a given import quota:a. reduces the domestic quantity demanded of the commodity*b. increases the domestic production of the commodityc. reduces the domestic price of the commodityd. reduces the producers' surplus3.Adjustment to any shift in the domestic demand or supply of an importablecommodityoccurs:a. in domestic price with an import quotab. in the quantity of imports with a tariffc. through the market mechanism with an import tariff but not with an import quota *d. all of the above4. An international cartel refers to:a. dumping*b. an organization of exportersc. an international commodity agreementd. voluntary export restraints5.The temporary sale of a commodity at below cost or at a lower price abroad in orderto drive foreign producers out of business is called:*a. predatory dumpingb. sporadic dumpingc. continuous dumpingd. voluntary export restraints6.The type of dumping which would justify antidumping measures by the countrysubject to the dumping is:*a. predatory dumpingb. sporadic dumpingc. continuous dumpingd. all of the above7. A fallacious argument for protection is:a. the infant industry argumentb. protection for national defense*c. the scientific tariffd. to correct domestic distortions8. Which of the following is true with respect to the infant-industry argument forprotection:a. it refers to temporary protection to establish a domestic industryb. to be valid, the return to the grown-up industry must be sufficiently high also to repay for the higher prices paid by domestic consumers of the commodity during the infancy periodc. is inferior to an equivalent production subsidy to the infant industry*d. all of the above9. Which of the following is false with respect to strategic trade policy?a. it postulates that a nation can gain by an activist trade policy*b. it is practiced to some extent by most industrial nationsc. it can easily be carried outd. all of the above10.Industrial policy refers to:a. an activist policy by the government of an industrial country to stimulate the development of an industryb. the granting of a subsidy to a domestic industry to stimulate the development of an industryc. the granting of a subsidy to a domestic industry to counter a foreign subsidy*d. all of the above11. Game theory refers to:*a. a method of choosing the optimal strategy in conflict situationsb. the granting of a subsidy to correct a domestic distortionc. the theory of tariff protectiond. none of the above12. Trade protection in the United States is usually provided to:a. low-wage workersb. well-organized industries with large employmentc. industries producing consumer products*d. all of the above13. The most-favored-nation principle refers to:*a. extension to all trade partners of any reciprocal tariff reduction negotiated by the U.S. with any of its trade partnersb. multilateral trade negotiationc. the General Agreement on Tariffs and Traded. the International Trade Organization14. On which of the following principles does GATT rest?a. nondiscriminationb. elimination of nontariff barriersc. consultation among nations in solving trade disputes*d. all of the above15. Which of the following was not negotiated under the Uruguay Round?a. reduction of tariffs on industrial goodsb. replacement of quotas with tariffsc. reduction of subsidies on industrial products and on agricultural exports*d. liberalization in trade in most services。
曼昆《宏观经济学》第9版章节习题精编详解（政府债务和预算赤字）【圣才出品】
曼昆《宏观经济学》第9版章节习题精编详解（政府债务和预算⾚字）【圣才出品】曼昆《宏观经济学》（第9版）章节习题精编详解第6篇宏观经济政策专题第19章政府债务和预算⾚字⼀、概念题1．资本预算（capital budgeting）答：资本预算是⼀种既衡量负债⼜衡量资产的预算程序，它考虑到了资本的变动。
采⽤资本预算，净国债等于政府资产减去政府负债。
按现⾏的预算程序，当政府出售其资产时，预算⾚字会减少。
但在资本预算中，从出售中得到的收⼊并没有减少⾚字，因为债务的减少被资产的减少所抵消了。
同样，在资本预算中，政府借贷为购买资本品筹资并不会增加⾚字。
经济学家对资本预算的看法不⼀。
资本预算的反对者认为，虽然这个体系在原则上优于现⾏体系，但它在实践中难以实施。
资本预算的⽀持者认为，即使对资本资产的不完善处理也⽐完全忽略资本资产好。
2．周期调整性预算⾚字（cyclically adjusted budget deficit）答：周期调整性预算⾚字有时称为充分就业预算⾚字，它的计算是根据对经济在其产出和就业⾃然率运⾏时政府⽀出与税收收⼊的估算⽽作出的。
周期调整性预算⾚字是⼀个有⽤的衡量指标，因为它反映了政策的变动⽽不是经济周期的当前阶段。
3．李嘉图等价（Ricardian equivalence）答：李嘉图等价定理是英国经济学家李嘉图提出，并由新古典主义学者巴罗根据理性预期重新进⾏论述的⼀种理论。
该理论认为，在政府⽀出⼀定的情况下，政府采取征税或发⾏公债来为政府筹措资⾦，其效应是相同的。
李嘉图等价理论的思路是：假设政府预算在初始时是平衡的。
政府实⾏减税以图增加私⼈部门和公众的⽀出，扩⼤总需求，但减税导致财政⾚字。
如果政府发⾏债券来弥补财政⾚字，由于在未来某个时点，政府将不得不增加税收，以便⽀付债务和积累的利息。
具有前瞻性的消费者知道，政府今天借债意味着未来更⾼的税收。
⽤政府债务融资的减税并没有减少税收负担，它仅仅是重新安排税收的时间。
曼昆 宏观经济经济学第九版 英文原版答案9(完整资料).doc
【最新整理，下载后即可编辑】Answers to Textbook Questions and ProblemsCHAPTER 9 Economic Growth II: Technology, Empirics, and Policy Questions for Review1. In the Solow model, we find that only technological progress canaffect the steady-state rate of growth in income per worker. Growth in the capital stock (through high saving) has no effect on the steady-state growth rate of income per worker; neither does population growth.But technological progress can lead to sustained growth.2. In the steady state, output per person in the Solow model grows at the rate of technological progress g. Capital per person also grows at rate g. Note that this implies that output and capital per effective worker are constant in steady state. In the U.S. data, output and capital per worker have both grown at about 2 percent per year for the past half-century.3. To decide whether an economy has more or less capital than theGolden Rule, we need to compare the marginal product of capital net of depreciation (MPK –δ) with the growt h rate of total output (n + g). The growth rate of GDP is readily available. Estimating the netmarginal product of capital requires a little more work but, as shown in the text, can be backed out of available data on the capital stockrelative to GDP, the total amount of depreciation relative to GDP, and capital’s share in GDP.4. Economic policy can influence the saving rate by either increasingpublic saving or providing incentives to stimulate private saving. Public saving is the difference between government revenue and government spending. If spending exceeds revenue, the government runs a budget deficit, which is negative saving. Policies that decrease the deficit (such as reductions in government purchases or increases in taxes) increase public saving, whereas policies that increase the deficit decrease saving.A variety of government policies affect private saving. The decision bya household to save may depend on the rate of return; the greater thereturn to saving, the more attractive saving becomes. Tax incentives such as tax-exempt retirement accounts for individuals and investment tax credits for corporations increase the rate of return and encourage private saving.5. The legal system is an example of an institutional difference betweencountries that might explain differences in income per person.Countries that have adopted the English style common law systemtend to have better developed capital markets, and this leads to more rapid growth because it is easier for businesses to obtain financing. The quality of government is also important. Countries with moregovernment corruption tend to have lower levels of income per person.6. Endogenous growth theories attempt to explain the rate oftechnological progress by explaining the decisions that determine the creation of knowledge through research and development. By contrast, the Solow model simply took this rate as exogenous. In the Solowmodel, the saving rate affects growth temporarily, but diminishingreturns to capital eventually force the economy to approach a steady state in which growth depends only on exogenous technologicalprogress. By contrast, many endogenous growth models in essenceassume that there are constant (rather than diminishing) returns tocapital, interpreted to include knowledge. Hence, changes in the saving rate can lead to persistent growth.Problems and Applications1. a. In the Solow model with technological progress, y is defined asoutput per effective worker, and k is defined as capital per effective worker. The number of effective workers is defined as L E (orLE), where L is the number of workers, and E measures theefficiency of each worker. To find output per effective worker y,divide total output by the number of effective workers:Y LE =K12(LE)12LEY LE =K12L12E12LEY LE =K12 L12E12Y LE =KLE æèççöø÷÷12y=k1b. To solve for the steady-state value of y as a function of s, n, g, andδ, we begin with the equation for the change in the capital stock in the steady state:Δk = sf(k) –(δ + n + g)k = 0.The production function ycan also be rewritten as y2 = k.Plugging this production function into the equation for the changein the capital stock, we find that in the steady state:sy –(δ + n + g)y2 = 0.Solving this, we find the steady-state value of y:y* = s/(δ + n + g).c. The question provides us with the following information about each country:Atlantis: s = 0.28 Xanadu: s = 0.10n = 0.01 n = 0.04g = 0.02 g = 0.02δ = 0.04δ = 0.04Using the equation for y* that we derived in part (a), we cancalculate the steady-state values of y for each country.Developed country: y* = 0.28/(0.04 + 0.01 + 0.02) = 4Less-developed country: y* = 0.10/(0.04 + 0.04 + 0.02) = 1 2. a. In the steady state, capital per effective worker is constant, and thisleads to a constant level of output per effective worker. Given that the growth rate of output per effective worker is zero, this means the growth rate of output is equal to the growth rate of effective workers (LE). We know labor grows at the rate of population growth n and the efficiency of labor (E) grows at rate g. Therefore, output grows at rate n+g. Given output grows at rate n+g and labor grows at rate n,output per worker must grow at rate g. This follows from the rule that the growth rate of Y/L is equal to the growth rate of Y minus the growth rate of L.b. First find the output per effective worker production function by dividing both sides of the production function by the number of effective workers LE:Y LE =K13(LE)23LEYLE=K13L23E23LEYLE=K13L13E13YLE=KLEæèçöø÷13y=k13To solve for capital per effective worker, we start with the steady state condition:Δk = sf(k) –(δ + n + g)k = 0.Now substitute in the given parameter values and solve for capital per effective worker (k):Substitute the value for k back into the per effective workerproduction function to find output per effective worker is equal to2. The marginal product of capital is given bySubstitute the value for capital per effective worker to find themarginal product of capital is equal to 1/12.c. According to the Golden Rule, the marginal product of capital isequal to (δ + n + g) or 0.06. In the current steady state, the marginal product of capital is equal to 1/12 or 0.083. Therefore, we have less capital per effective worker in comparison to the Golden Rule. Asthe level of capital per effective worker rises, the marginal product of capital will fall until it is equal to 0.06. To increase capital pereffective worker, there must be an increase in the saving rate.d. During the transition to the Golden Rule steady state, the growth rateof output per worker will increase. In the steady state, output perworker grows at rate g. The increase in the saving rate will increaseoutput per effective worker, and this will increase output pereffective worker. In the new steady state, output per effective worker is constant at a new higher level, and output per worker is growing at rate g. During the transition, the growth rate of output per workerjumps up, and then transitions back down to rate g.3. To solve this problem, it is useful to establish what we know about the U.S. economy:• A Cobb–Douglas production function has the form y = kα, where α is capital’s share of income. The question tells us that α = 0.3,so we know that the production function is y = k0.3.•In the steady state, we know that the growth rate of output equals 3 percent, so we know that (n + g) = 0.03.•The deprec iation rate δ = 0.04.•The capital–output ratio K/Y = 2.5. Because k/y =[K/(LE)]/[Y/(LE)] = K/Y, we also know that k/y = 2.5. (That is, the capital–output ratio is the same in terms of effective workers as it is in levels.)a. Begin with the steady-state condition, sy = (δ + n + g)k. Rewritingthis equation leads to a formula for saving in the steady state:s = (δ + n + g)(k/y).Plugging in the values established above:s = (0.04 + 0.03)(2.5) = 0.175.The initial saving rate is 17.5 percent.b. We know from Chapter 3 that with a Cobb–Douglas production function, capital’s share of income α = MPK(K/Y). Rewriting, we haveMPK = α/(K/Y).Plugging in the values established above, we findMPK = 0.3/2.5 = 0.12.c. We know that at the Golden Rule steady state:MPK = (n + g + δ).Plugging in the values established above:MPK = (0.03 + 0.04) = 0.07.At the Golden Rule steady state, the marginal product of capital is 7 percent, whereas it is 12 percent in the initial steady state. Hence, from the initial steady state we need to increase k to achieve theGolden Rule steady state.d. We know from Chapter 3 that for a Cobb–Douglas production function, MPK = α (Y/K). Solving this for the capital–outputratio, we findK/Y = α/MPK.We can solve for the Golden Rule capital–output ratio using this equation. If we plug in the value 0.07 for the Golden Rule steady-state marginal product of capital, and the value 0.3 for α, we findK/Y = 0.3/0.07 = 4.29.In the Golden Rule steady state, the capital–output ratio equals4.29, compared to the current capital–output ratio of 2.5.e. We know from part (a) that in the steady states = (δ + n + g)(k/y),where k/y is the steady-state capital–output ratio. In theintroduction to this answer, we showed that k/y = K/Y, and in part(d) we found that the Golden Rule K/Y = 4.29. Plugging in thisvalue and those established above:s = (0.04 + 0.03)(4.29) = 0.30.To reach the Golden Rule steady state, the saving rate must risefrom 17.5 to 30 percent. This result implies that if we set the saving rate equal to the share going to capital (30 percent), we will achieve the Golden Rule steady state.4. a. In the steady state, we know that sy = (δ + n + g)k. This implies thatk/y = s/(δ + n + g).Since s, δ, n, and g are constant, this means that the ratio k/y is also constant. Since k/y = [K/(LE)]/[Y/(LE)] = K/Y, we can conclude that in the steady state, the capital–output ratio is constant.b. We know that capital’s share of income = MPK (K/Y). In thesteady state, we know from part (a) that the capital–output ratioK/Y is constant. We also know from the hint that the MPK is afunction of k, which is constant in the steady state; therefore theMPK itself must be constant. Thus, capital’s share of income isconstant. Labor’s share of income is 1 – [C apital’s Share].Hence, if capital’s share is constant, we see that labor’s share of income is also constant.c. We know that in the steady state, total income grows at n + g,defined as the rate of population growth plus the rate oftechnological change. In part (b) we showed that labor’s andcapital’s share of income is constant. If the shares are constant,and total income grows at the rate n + g, then labor income andcapital income must also grow at the rate n + g.d. Define the real rental price of capital R asR = Total Capital Income/Capital Stock= (MPK K)/K= MPK.We know that in the steady state, the MPK is constant becausecapital per effective worker k is constant. Therefore, we canconclude that the real rental price of capital is constant in the steady state.To show that the real wage w grows at the rate of technological progress g, defineTLI = Total Labor IncomeL = Labor ForceUsing the hint that the real wage equals total labor income divided by the labor force:w = TLI/L.Equivalently,wL = TLI.In terms of percentage changes, we can write this asΔw/w + ΔL/L = ΔTLI/TLI.This equation says that the growth rate of the real wage plus thegrowth rate of the labor force equals the growth rate of total labor income. We know that the labor force grows at rate n, and, frompart (c), we know that total labor income grows at rate n + g. We, therefore, conclude that the real wage grows at rate g.5. a. The per worker production function isF(K, L)/L = AKαL1–α/L = A(K/L)α = Akαb. In the steady state, Δk = sf(k) –(δ + n + g)k = 0. Hence, sAkα = (δ + n + g)k, or, after rearranging:k*=sAd+n+géëêêùûúúa1-aæèççöø÷÷.Plugging into the per-worker production function from part (a) givesy *=A a 1-a æèççöø÷÷s d +n +g éëêêùûúúa 1-a æèççöø÷÷.Thus, the ratio of steady-state income per worker in Richland to Poorland isy *Richland /y *Poorland ()=s Richland d +n Richland +g /s Poorland d +n Poorland +g éëêêùûúúa 1-a=0.320.05+0.01+0.02/0.100.05+0.03+0.02éëêêùûúúa 1-ac. If α equals 1/3, then Richland should be 41/2, or two times, richer than Poorland.d. If 4a 1-æèççöø÷÷= 16, then it must be the case that a 1-a æèççöø÷÷, which in turnrequires that α equals 2/3. Hence, if the Cobb –Douglasproduction function puts 2/3 of the weight on capital and only 1/3 on labor, then we can explain a 16-fold difference in levels ofincome per worker. One way to justify this might be to think about capital more broadly to include human capital —which must also be accumulated through investment, much in the way one accumulates physical capital.6. How do differences in education across countries affect the Solowmodel? Education is one factor affecting the efficiency of labor , which we denoted by E . (Other factors affecting the efficiency of laborinclude levels of health, skill, and knowledge.) Since country 1 has amore highly educated labor force than country 2, each worker in country 1 is more efficient. That is, E1 > E2. We will assume that both countries are in steady state.a. In the Solow growth model, the rate of growth of total income is equal to n + g, which is independent of the work force’s level of education. The two countries will, thus, have the same rate ofgrowth of total income because they have the same rate ofpopulation growth and the same rate of technological progress. b. Because both countries have the same saving rate, the samepopulation growth rate, and the same rate of technological progress, we know that the two countries will converge to the same steady-state level of capital per effective worker k*. This is shown in Figure 9-1.Hence, output per effective worker in the steady state, which is y* = f(k*), is the same in both countries. But y* = Y/(L E) or Y/L = y* E. We know that y* will be the same in both countries, but that E1> E2. Therefore, y*E1 > y*E2. This implies that (Y/L)1 > (Y/L)2.Thus, the level of income per worker will be higher in the countrywith the more educated labor force.c. We know that the real rental price of capital R equals the marginalproduct of capital (MPK). But the MPK depends on the capitalstock per efficiency unit of labor. In the steady state, both countries have k*1= k*2= k* because both countries have the same saving rate, the same population growth rate, and the same rate of technological progress. Therefore, it must be true that R1 = R2 = MPK. Thus, the real rental price of capital is identical in both countries.d. Output is divided between capital income and labor income.Therefore, the wage per effective worker can be expressed asw = f(k) –MPK • k.As discussed in parts (b) and (c), both countries have the samesteady-state capital stock k and the same MPK. Therefore, the wage per effective worker in the two countries is equal.Workers, however, care about the wage per unit of labor, not the wage per effective worker. Also, we can observe the wage per unitof labor but not the wage per effective worker. The wage per unitof labor is related to the wage per effective worker by the equationWage per Unit of L = wE.Thus, the wage per unit of labor is higher in the country with the more educated labor force.7. a. In the two-sector endogenous growth model in the text, theproduction function for manufactured goods isY = F [K,(1 –u) EL].We assumed in this model that this function has constant returns to scale. As in Section 3-1, constant returns means that for anypositive number z, zY = F(zK, z(1 –u) EL). Setting z = 1/EL, we obtainY EL =FKEL,(1-u)æèççöø÷÷.Using our standard definitions of y as output per effective worker and k as capital per effective worker, we can write this asy = F[k,(1 –u)]b. To begin, note that from the production function in research universities, the growth rate of labor efficiency, ΔE/E, equals g(u).We can now follow the logic of Section 9-1, substituting the function g(u) for the constant growth rate g. In order to keep capital per effective worker (K/EL) constant, break-even investment includes three terms: δk is needed to replace depreciating capital, nk is needed to provide capital for new workers, and g(u) is needed to provide capital for the greater stock of knowledge E created by research universities. That is, break-even investment is [δ +n + g(u)]k.c. Again following the logic of Section 9-1, the growth of capital pereffective worker is the difference between saving per effectiveworker and break-even investment per effective worker. We now substitute the per-effective-worker production function from part (a) and the function g(u) for the constant growth rate g, to obtainΔk = sF [k,(1 –u)] – [δ + n + g(u)]kIn the steady state, Δk = 0, so we can rewrite the equation above assF [k,(1 –u)] = [δ + n + g(u)]k.As in our analysis of the Solow model, for a given value of u, we can plot the left and right sides of this equationThe steady state is given by the intersection of the two curves. d. The steady state has constant capital per effective worker k as givenby Figure 9-2 above. We also assume that in the steady state, there is a constant share of time spent in research universities, so u is constant. (After all, if u were not constant, it wouldn’t be a“steady” state!). Hence, output per effective worker y is also constant. Output per worker equals yE, and E grows at rate g(u). Therefore, output per worker grows at rate g(u). The saving ratedoes not affect this growth rate. However, the amount of timespent in research universities does affect this rate: as more time is spent in research universities, the steady-state growth rate rises.e. An increase in u shifts both lines in our figure. Output per effectiveworker falls for any given level of capital per effective worker, since less of each worker’s time is spent producing manufactured goods. This is the immediate effect of the change, since at the time u rises, the capital stock K and the efficiency of each worker E are constant.Since output per effective worker falls, the curve showing savingper effective worker shifts down.At the same time, the increase in time spent in research universities increases the growth rate of labor efficiency g(u). Hence, break-even investment [which we found above in part (b)] rises at any given level of k, so the line showing breakeven investment also shifts up.Figure 9-3 shows these shifts.In the new steady state, capital per effective worker falls from k1 to k2. Output per effective worker also falls.f. In the short run, the increase in u unambiguously decreasesconsumption. After all, we argued in part (e) that the immediateeffect is to decrease output, since workers spend less timeproducing manufacturing goods and more time in researchuniversities expanding the stock of knowledge. For a given saving rate, the decrease in output implies a decrease in consumption.The long-run steady-state effect is more subtle. We found in part(e) that output per effective worker falls in the steady state. But welfare depends on output (and consumption) per worker, not per effective worker. The increase in time spent in research universities implies that E grows faster. That is, output per worker equals yE. Although steady-state y falls, in the long run the faster growth rate of E necessarily dominates. That is, in the long run, consumption unambiguously rises.Nevertheless, because of the initial decline in consumption, theincrease in u is not unambiguously a good thing. That is, apolicymaker who cares more about current generations than aboutfuture generations may decide not to pursue a policy of increasing u.(This is analogous to the question considered in Chapter 8 ofwhether a policymaker should try to reach the Golden Rule level ofcapital per effective worker if k is currently below the Golden Rulelevel.)8. On the World Bank Web site (), click on the datatab and then the indicators tab. This brings up a large list of dataindicators that allows you to compare the level of growth anddevelopment across countries. To explain differences in income per person across countries, you might look at gross saving as a percentage of GDP, gross capital formation as a percentage of GDP, literacy rate, life expectancy, and population growth rate. From the Solow model, we learned that (all else the same) a higher rate of saving will lead to higher income per person, a lower population growth rate will lead to higher income per person, a higher level of capital per worker will lead to a higher level of income per person, and more efficient orproductive labor will lead to higher income per person. The selected data indicators offer explanations as to why one country might have a higher level of income per person. However, although we mightspeculate about which factor is most responsible for the difference in income per person across countries, it is not possible to say for certain given the large number of other variables that also affect income per person. For example, some countries may have more developed capital markets, less government corruption, and better access to foreigndirect investment. The Solow model allows us to understand some of the reasons why income per person differs across countries, but givenit is a simplified model, it cannot explain all of the reasons why income per person may differ.More Problems and Applications to Chapter 91. a. The growth in total output (Y) depends on the growth rates oflabor (L), capital (K), and total factor productivity (A), assummarized by the equationΔY/Y = αΔK/K + (1 –α)ΔL/L + ΔA/A, where α is capital’s share of output. We can look at the effect onoutput of a 5-percent increase in labor by setting ΔK/K = ΔA/A =0. Since α = 2/3, this gives usΔY/Y = (1/3)(5%)= 1.67%.A 5-percent increase in labor input increases output by 1.67 percent.Labor productivity is Y/L. We can write the growth rate in labor productivity asD Y Y =D(Y/L)Y/L-D LL.Substituting for the growth in output and the growth in labor, we findΔ(Y/L)/(Y/L) = 1.67% – 5.0%= –3.34%.Labor productivity falls by 3.34 percent.To find the change in total factor productivity, we use the equationΔA/A = ΔY/Y –αΔK/K – (1 –α)ΔL/L.For this problem, we findΔA/A = 1.67% – 0 – (1/3)(5%)= 0.Total factor productivity is the amount of output growth that remains after we have accounted for the determinants of growththat we can measure. In this case, there is no change in technology, so all of the output growth is attributable to measured input growth.That is, total factor productivity growth is zero, as expected.b. Between years 1 and 2, the capital stock grows by 1/6, labor inputgrows by 1/3, and output grows by 1/6. We know that the growthin total factor productivity is given byΔA/A = ΔY/Y –αΔK/K – (1 –α)ΔL/L.Substituting the numbers above, and setting α = 2/3, we findΔA/A = (1/6) – (2/3)(1/6) – (1/3)(1/3)= 3/18 – 2/18 – 2/18= – 1/18= –0.056.Total factor productivity falls by 1/18, or approximately 5.6 percent.2. By definition, output Y equals labor productivity Y/L multiplied by the labor force L:Y = (Y/L)L.Using the mathematical trick in the hint, we can rewrite this asD Y Y =D(Y/L)Y/L+D LL.We can rearrange this asD Y Y =D YY-D LL.Substituting for ΔY/Y from the text, we findD(Y/L) Y/L =D AA+aD KK+(1-a)D LL-D LL =D AA+aD KK-aD LL=D AA+aD KK-D LLéëêêùûúúUsing the same trick we used above, we can express the term in brackets asΔK/K –ΔL/L = Δ(K/L)/(K/L) Making this substitution in the equation for labor productivity growth, we conclude thatD(Y/L) Y/L =D AA+aD(K/L)K/L.3. We know the following:ΔY/Y = n + g = 3.6%ΔK/K = n + g = 3.6%ΔL/L = n = 1.8%Capital’s Share = α = 1/3Labor’s Share = 1 –α = 2/3Using these facts, we can easily find the contributions of each of the factors, and then find the contribution of total factor productivitygrowth, using the following equations:Output = Capital’s+ Labor’s+ Total FactorGrowth Contribution ContributionProductivityD Y Y = aD KK+ (1-a)D LL+ D AA3.6% = (1/3)(3.6%) + (2/3)(1.8%) +ΔA/A.We can easily solve this for ΔA/A, to find that3.6% = 1.2% + 1.2% + 1.2%We conclude that the contribution of capital is 1.2 percent per year, the contribution of labor is 1.2 percent per year, and the contribution of total factor productivity growth is 1.2 percent per year. These numbers match the ones in Table 9-3 in the text for the United States from 1948–2002.。
曼昆-宏观经济经济学第九版-英文原版答案3强烈推荐.docx
Answers to Textbook Questions and ProblemsCHAPTER3 National Income: Where It Comes From and Where It GoesQuestions for Review1. The factors of production and the production technology determine the amount of output an economycan produce. The factors of production are the inputs used to produce goods and services: the most important factors are capital and labor. The production technology determines how much output can be produced from any given amounts of these inputs. An increase in one of the factors of production or an improvement in technology leads to an increase in the economy’s output.2. When a firm decides how much of a factor of production to hire or demand, it considers how thisdecision affects profits. For example, hiring an extra unit of labor increases output and thereforeincreases revenue; the firm compares this additional revenue to the additional cost from the higher wage bill. The additional revenue the firm receives depends on the marginal product of labor (MPL) and the price of the good produced (P). An additional unit of labor produces MPL units of additional output, which sells for P dollars per unit. Therefore, the additional revenue to the firm is P ⨯MPL. The cost of hiring the additional unit of labor is the wage W. Thus, this hiring decision has the following effect on profits:ΔProfit= ΔRevenue –ΔCost= (P ⨯MPL) –W.If the additional revenue, P ⨯MPL, exceeds the cost (W) of hiring the additional unit of labor, then profit increases. The firm will hire labor until it is no longer profitable to do so—that is, until the MPL falls to the point where the change in profit is zero. In the equation above, the firm hires labor until ΔProfit = 0, which is when (P ⨯MPL) = W.This condition can be rewritten as:MPL = W/P.Therefore, a competitive profit-maximizing firm hires labor until the marginal product of labor equals the real wage. The same logic applies to the firm’s decision regarding how much capital to hire: the firm will hire capital until the marginal product of capital equals the real rental price.3. A production function has constant returns to scale if an equal percentage increase in all factors ofproduction causes an increase in output of the same percentage. For example, if a firm increases its use of capital and labor by 50 percent, and output increases by 50 percent, then the production function has constant returns to scale.If the production function has constant returns to scale, then total income (or equivalently, total output) in an economy of competitive profit-maximizing firms is divided between the return to labor, MPL ⨯L, and the return to capital, MPK ⨯K. That is, under constant returns to scale, economic profit is zero.4. A Cobb–Douglas production function has the form F(K,L) = AKαL1–α. The text showed that theparameter αgives capital’s share of income. So if capital earns one-fourth of total income, then α=0.25. Hence, F(K,L) = AK0.25L0.75.5. Consumption depends positively on disposable income—i.e. the amount of income after all taxes havebeen paid. Higher disposable income means higher consumption.The quantity of investment goods demanded depends negatively on the real interest rate. For an investment to be profitable, its return must be greater than its cost. Because the real interest ratemeasures the cost of funds, a higher real interest rate makes it more costly to invest, so the demand for investment goods falls.6. Government purchases are a measure of the value of goods and services purchased directly by thegovernment. For example, the government buys missiles and tanks, builds roads, and provides services such as air traffic control. All of these activities are part of GDP. Transfer payments are government payments to individuals that are not in exchange for goods or services. They are the opposite of taxes: taxes reduce household disposable income, whereas transfer payments increase it. Examples of transfer payments include Social Security payments to the elderly, unemployment insurance, and veterans’ benefits.7. Consumption, investment, and government purchases determine demand for the economy’s output,whereas the factors of production and the production function determine the supply of output. The real interest rate adjusts to ensure that the demand for t he economy’s goods equals the supply. At theequilibrium interest rate, the demand for goods and services equals the supply.8. When the government increases taxes, disposable income falls, and therefore consumption falls as well.The decrease in consumption equals the amount that taxes increase multiplied by the marginalpropensity to consume (MPC). The higher the MPC is, the greater is the negative effect of the tax increase on consumption. Because output is fixed by the factors of production and the production technology, and government purchases have not changed, the decrease in consumption must be offset by an increase in investment. For investment to rise, the real interest rate must fall. Therefore, a tax increase leads to a decrease in consumption, an increase in investment, and a fall in the real interest rate.Problems and Applications1. a. According to the neoclassical theory of distribution, the real wage equals the marginal product oflabor. Because of diminishing returns to labor, an increase in the labor force causes the marginalproduct of labor to fall. Hence, the real wage falls.Given a Cobb–Douglas production function, the increase in the labor force will increase the marginal product of capital and will increase the real rental price of capital. With more workers,the capital will be used more intensively and will be more productive.b. The real rental price equals the marginal product of capital. If an earthquake destroys some of thecapital stock (yet miraculously does not kill anyone and lower the labor force), the marginalproduct of capital rises and, hence, the real rental price rises.Given a Cobb–Douglas production function, the decrease in the capital stock will decrease the marginal product of labor and will decrease the real wage. With less capital, each worker becomes less productive.c. If a technological advance improves the production function, this is likely to increase the marginalproducts of both capital and labor. Hence, the real wage and the real rental price both increase.d. High inflation that doubles the nominal wage and the price level will have no impact on the realwage. Similarly, high inflation that doubles the nominal rental price of capital and the price levelwill have no impact on the real rental price of capital.2. a. To find the amount of output produced, substitute the given values for labor and land into theproduction function:Y = 1000.51000.5 = 100.b. According to the text, the formulas for the marginal product of labor and the marginal product ofcapital (land) are:MPL = (1 –α)AKαL–α.MPK = αAKα–1L1–α.In this problem, α is 0.5 and A is 1. Substitute in the given values for labor and land to find themarginal product of labor is 0.5 and marginal product of capital (land) is 0.5. We know that thereal wage equals the marginal product of labor and the real rental price of land equals the marginal product of capital (land).c. Labor’s share of the output is given by the marginal product of labor times the quantity of labor, o r50.d. The new level of output is 70.71.e. The new wage is 0.71. The new rental price of land is 0.35.f. Labor now receives 35.36.3. A production function has decreasing returns to scale if an equal percentage increase in all factors ofproduction leads to a smaller percentage increase in output. For example, if we double the amounts of capital and labor output increases by less than double, then the production function has decreasing returns to scale. This may happen if there is a fixed factor such as land in the production function, and this fixed factor becomes scarce as the economy grows larger.A production function has increasing returns to scale if an equal percentage increase in all factorsof production leads to a larger percentage increase in output. For example, if doubling the amount of capital and labor increases the output by more than double, then the production function has increasing returns to scale. This may happen if specialization of labor becomes greater as the population grows.For example, if only one worker builds a car, then it takes him a long time because he has to learn many different skills, and he must constantly change tasks and tools. But if many workers build a car, then each one can specialize in a particular task and become more productive.4. a. A Cobb–Douglas production function has the form Y = AKαL1–α. The text showed that the marginalproducts for the Cobb–Douglas production function are:MPL = (1 –α)Y/L.MPK = αY/K.Competitive profit-maximizing firms hire labor until its marginal product equals the real wage, and hire capital until its marginal product equals the real rental rate. Using these facts and theabove marginal products for the Cobb–Douglas production function, we find:W/P = MPL = (1 –α)Y/L.R/P = MPK = αY/K.Rewriting this:(W/P)L = MPL ⨯L = (1 –α)Y.(R/P)K = MPK ⨯K = αY.Note that the terms (W/P)L and (R/P)K are the wage bill and total return to capital, respectively.Given that the value of α = 0.3, then the above formulas indicate that labor receives 70 percent of total output (or income) and capital receives 30 percent of total output (or income).b. To determine what happens to total output when the labor force increases by 10 percent, considerthe formula for the Cobb–Douglas production function:Y = AKαL1–α.Let Y 1 equal the initial value of output and Y 2 equal final output. We know that α = 0.3. We also know that labor L increases by 10 percent:Y 1 = AK 0.3L 0.7. Y 2 = AK 0.3(1.1L )0.7.Note that we multiplied L by 1.1 to reflect the 10-percent increase in the labor force. To calculate the percentage change in output, divide Y 2 by Y 1:Y 2Y 1=AK 0.31.1L ()0.7AK 0.3L 0.7=1.1()0.7=1.069.That is, output increases by 6.9 percent.To determine how the increase in the labor force affects the rental price of capital, consider the formula for the real rental price of capital R/P :R/P = MPK = αAK α–1L 1–α.We know that α = 0.3. We also know that labor (L ) increases by 10 percent. Let (R/P )1 equal the initial value of the rental price of capital, and let (R/P )2 equal the final rental price of capital after the labor force increases by 10 percent. To find (R/P )2, multiply L by 1.1 to reflect the 10-percent increase in the labor force:(R/P )1 = 0.3AK –0.7L 0.7. (R/P )2 = 0.3AK –0.7(1.1L )0.7.The rental price increases by the ratioR /P ()2R /P ()1=0.3AK -0.71.1L ()0.70.3AK -0.7L 0.7=1.1()0.7=1.069So the rental price increases by 6.9 percent. To determine how the increase in the labor forceaffects the real wage, consider the formula for the real wage W/P :W/P = MPL = (1 – α)AK αL –α.We know that α = 0.3. We also know that labor (L ) increases by 10 percent. Let (W/P )1 equal the initial value of the real wage, and let (W/P )2 equal the final value of the real wage. To find (W/P )2, multiply L by 1.1 to reflect the 10-percent increase in the labor force:(W/P )1 = (1 – 0.3)AK 0.3L –0.3. (W/P )2 = (1 – 0.3)AK 0.3(1.1L )–0.3.To calculate the percentage change in the real wage, divide (W/P )2 by (W/P )1:W /P ()2W /P ()1=1-0.3()AK 0.31.1L ()-0.31-0.3()AK 0.3L-0.3=1.1()-0.3=0.972That is, the real wage falls by 2.8 percent.c. We can use the same logic as in part (b) to setY 1 = AK 0.3L 0.7. Y 2 = A (1.1K )0.3L 0.7.Therefore, we have:Y 2Y 1=A 1.1K ()0.3L 0.7AK 0.3L 0.7=1.1()0.3=1.029This equation shows that output increases by about 3 percent. Notice that α < 0.5 means thatproportional increases to capital will increase output by less than the same proportional increase to labor.Again using the same logic as in part (b) for the change in the real rental price of capital:R /P ()2R /P ()1=0.3A 1.1K ()-0.7L 0.70.3AK -0.7L 0.7=1.1()-0.7=0.935The real rental price of capital falls by 6.5 percent because there are diminishing returns to capital; that is, when capital increases, its marginal product falls.Finally, the change in the real wage is:W /P ()2W /P ()1=0.7A 1.1K ()0.3L -0.30.7AK 0.3L -0.3=1.1()0.3=1.029Hence, real wages increase by 2.9 percent because the added capital increases the marginalproductivity of the existing workers. (Notice that the wage and output have both increased by the same amount, leaving the labor share unchanged —a feature of Cobb –Douglas technologies.)d. Using the same formula, we find that the change in output is:Y 2Y 1= 1.1A ()K 0.3L 0.7AK 0.3L 0.7=1.1This equation shows that output increases by 10 percent. Similarly, the rental price of capital and the real wage also increase by 10 percent:R /P ()2R /P ()1=0.31.1A ()K -0.7L 0.70.3AK -0.7L 0.7=1.1W /P ()2W /P ()1=0.71.1A ()K 0.3L -0.30.7AK 0.3L -0.3=1.15. Labor income is defined asW P ´L =WLP Labor’s share of income is defined asWL P æèççöø÷÷/Y =WL PYFor example, if this ratio is about constant at a value of 0.7, then the value of W /P = 0.7*Y /L . Thismeans that the real wage is roughly proportional to labor productivity. Hence, any trend in laborproductivity must be matched by an equal trend in real wages. Otherwise, labor’s share would deviate from 0.7. Thus, the first fact (a constant labor share) implies the second fact (the trend in real wages closely tracks the trend in labor productivity).6. a. Nominal wages are measured as dollars per hour worked. Prices are measured as dollars per unitproduced (either a haircut or a unit of farm output). Marginal productivity is measured as units of output produced per hour worked.b. According to the neoclassical theory, technical progress that increases the marginal product offarmers causes their real wage to rise. The real wage for farmers is measured as units of farm output per hour worked. The real wage is W /P F , and this is equal to ($/hour worked)/($/unit of farm output).c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged. The realwage for barbers is measured as haircuts per hour worked. The real wage is W /P B , and this is equal to ($/hour worked)/($/haircut).d. If workers can move freely between being farmers and being barbers, then they must be paid thesame wage W in each sector.e. If the nominal wage W is the same in both sectors, but the real wage in terms of farm goods isgreater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods. We know that W /P = MPL so that W = P MPL . This means that P F MPL F = P H MPL B , given that the nominal wages are the same. Since the marginal product of labor for barbers has not changed and the marginal product of labor for farmers has risen, the price of a haircut must have risen relative to the price of the farm output. If we express this in growth rate terms, then the growth of the farm price + the growth of the marginal product of the farm labor = the growth of the haircut price.f. The farmers and the barbers are equally well off after the technological progress in farming, giventhe assumption that labor is freely mobile between the two sectors and both types of peopleconsume the same basket of goods. Given that the nominal wage ends up equal for each type ofworker and that they pay the same prices for final goods, they are equally well off in terms of what they can buy with their nominal income. The real wage is a measure of how many units of output are produced per worker. Technological progress in farming increased the units of farm outputproduced per hour worked. Movement of labor between sectors then equalized the nominal wage.7. a. The marginal product of labor (MPL)is found by differentiating the production function withrespect to labor:MPL=dY dL=11/3H1/3L-2/3An increase in human capital will increase the marginal product of labor because more human capital makes all the existing labor more productive.b. The marginal product of human capital (MPH)is found by differentiating the production functionwith respect to human capital:MPH=dY dH=13K1/3L1/3H-2/3An increase in human capital will decrease the marginal product of human capital because there are diminishing returns.c. The labor share of output is the proportion of output that goes to labor. The total amount of outputthat goes to labor is the real wage (which, under perfect competition, equals the marginal product of labor) times the quantity of labor. This quantity is divided by the total amount of output to compute the labor share:Labor Share=(13K1/3H1/3L-2/3)LK1/3H1/3L1/3=1 3We can use the same logic to find the human capital share:Human Capital Share=(13K1/3L1/3H-2/3)HK1/3H1/3L1/3=1 3so labor gets one-third of the output, and human capital gets one-third of the output. Since workers own their human capital (we hope!), it will appear that labor gets two-thirds of output.d. The ratio of the skilled wage to the unskilled wage is:Wskilled Wunskilled =MPL+MPHMPL=13K1/3L-2/3H1/3+13K1/3L1/3H-2/313K1/3L-2/3H1/3=1+LHNotice that the ratio is always greater than 1 because skilled workers get paid more than unskilled workers. Also, when H increases this ratio falls because the diminishing returns to human capitallower its return, while at the same time increasing the marginal product of unskilled workers.e. If more colleges provide scholarships, it will increase H, and it does lead to a more egalitariansociety. The policy lowers the returns to education, decreasing the gap between the wages of more and less educated workers. More importantly, the policy even raises the absolute wage of unskilled workers because their marginal product rises when the number of skilled workers rises.8. The effect of a government tax increase of $100 billion on (a) public saving, (b) private saving, and (c)national saving can be analyzed by using the following relationships:National Saving = [Private Saving] + [Public Saving]= [Y –T –C(Y –T)] + [T –G]= Y –C(Y –T) –G.a. Public Saving—The tax increase causes a 1-for-1 increase in public saving. T increases by $100billion and, therefore, public saving increases by $100 billion.b. Private Saving—The increase in taxes decreases disposable income, Y –T, by $100 billion. Sincethe marginal propensity to consume (MPC) is 0.6, consumption falls by 0.6 $100 billion, or $60 billion. Hence,ΔPrivate Saving = –$100b – 0.6 (–$100b) = –$40b.Private saving falls $40 billion.c. National Saving—Because national saving is the sum of private and public saving, we canconclude that the $100 billion tax increase leads to a $60 billion increase in national saving.Another way to see this is by using the third equation for national saving expressed above, that national saving equals Y –C(Y –T) –G. The $100 billion tax increase reduces disposableincome and causes consumption to fall by $60 billion. Since neither G nor Y changes, nationalsaving thus rises by $60 billion.d. Investment—To determine the effect of the tax increase on investment, recall the nationalaccounts identity:Y = C(Y –T) + I(r) + G.Rearranging, we findY –C(Y –T) –G = I(r).The left side of this equation is national saving, so the equation just says that national savingequals investment. Since national saving increases by $60 billion, investment must also increaseby $60 billion.How does this increase in investment take place? We know that investment depends on thereal interest rate. For investment to rise, the real interest rate must fall. Figure 3-1 illustrates saving and investment as a function of the real interest rate.The tax increase causes national saving to rise, so the supply curve for loanable funds shifts to the right. The equilibrium real interest rate falls, and investment rises.9. If consumers increase the amount that they consume today, then private saving and, therefore, nationalsaving will fall. We know this from the definition of national saving:National Saving = [Private Saving] + [Public Saving]= [Y –T –C(Y –T)] + [T –G].An increase in consumption decreases private saving, so national saving falls.Figure 3-2 illustrates saving and investment as a function of the real interest rate. If national saving decreases, the supply curve for loanable funds shifts to the left, thereby raising the real interest rate and reducing investment.10. a. Private saving is the amount of disposable income, Y – T, that is not consumed:S private= Y – T – C= 8,000 – 2,000 – [1,000 + (2/3)(8,000 – 2,000)]= 1,000.Public saving is the amount of taxes the government has left over after it makes its purchases:S public= T – G= 2,000 – 2,500= –500.National saving is the sum of private saving and public saving:S national= S private+ S public= 1,000 + (500)= 500.b. The equilibrium interest rate is the value of r that clears the market for loanable funds. We alreadyknow that national saving is 500, so we just need to set it equal to investment:S national= I500 = 1,200 – 100rSolving this equation for r, we find:r = 0.07 or 7%.c. When the government increases its spending, private saving remains the same as before (noticethat G does not appear in the S private equation above) while government saving decreases. Puttingthe new G into the equations above:S private= 1,000S public= T – G= 2,000 – 2,000= 0.Thus,S national= S private+ S public= 1,000 + (0)= 1,000.d. Once again the equilibrium interest rate clears the market for loanable funds:S national= I1,000 = 1,200 – 100rSolving this equation for r, we find:r = 0.02 or 2%.11. To determine the effect on investment of an equal increase in both taxes and government spending,consider the national income accounts identity for national saving:National Saving = [Private Saving] + [Public Saving]= [Y –T –C(Y –T)] + [T –G].We know that Y is fixed by the factors of production. We also know that the change in consumption equals the marginal propensity to consume (MPC) times the change in disposable income. This tells us thatΔNational Saving= {–ΔT – [MPC ⨯ (–ΔT)]} + [ΔT –ΔG]= [–ΔT + (MPC ⨯ΔT)] + 0= (MPC – 1) ΔT .The above expression tells us that the impact on national saving of an equal increase in T and G depends on the size of the marginal propensity to consume. The closer the MPC is to 1, the smaller is the fall in saving. For example, if the MPC equals 1, then the fall in consumption equals the rise in government purchases, so national saving [Y – C (Y – T ) – G ] is unchanged. The closer the MPC is to 0 (and therefore the larger is the amount saved rather than spent for a one-dollar change in disposable income), the greater is the impact on saving. Because we assume that the MPC is less than 1, we expect that national saving falls in response to an equal increase in taxes and government spending.The reduction in saving means that the supply of loanable funds curve will shift to the left in Figure 3-3. The real interest rate rises, and investment falls.12. a. The demand curve for business investment shifts out to the right because the subsidy increases thenumber of profitable investment opportunities for any given interest rate. The demand curve for residential investment remains unchanged.b. The total demand curve for investment in the economy shifts out to the right since it represents thesum of business investment, which shifts out to the right, and residential investment, which isunchanged. As a result the real interest rate rises as in Figure 3-4.c. The total quantity of investment does not change because it is constrained by the inelastic supply of savings. The investment tax credit leads to a rise in business investment, but an offsetting fall in residential investment. That is, the higher interest rate means that residential investment falls (a movement along the curve), whereas the rightward shift of the business investment curve leads business investment to rise by an equal amount. Figure 3-5 shows this change. Note that I 1B +I 1R +I 2B +I 2R =S .13. In this chapter, we concluded that an increase in government expenditures reduces national saving andraises the interest rate. The increase in government expenditure therefore crowds out investment by the full amount of the increase. Similarly, a tax cut increases disposable income and hence consumption.This increase in consumption translates into a fall in national saving, and the increase in consumption crowds out investment by the full amount of the increase.If consumption depends on the interest rate, then saving will also depend on it. The higher the interest rate, the greater the return to saving. Hence, it seems reasonable to think that an increase in the interest rate might increase saving and reduce consumption. Figure 3-6 shows saving as an increasing function of the interest rate.Consider what happens when government purchases increase. At any given level of the interest rate, national saving falls by the change in government purchases, as shown in Figure 3-7. The figure shows that if the saving function slopes upward, investment falls by less than the amount thatgovernment purchases rises by. This happens because consumption falls and saving increases inresponse to the higher interest rate. Hence, the more responsive consumption is to the interest rate, the less investment is crowded out by government purchases.14. a. Figure 3-8 shows the case where the demand for loanable funds is stable but the supply of funds(the saving schedule) fluctuates perhaps reflecting temporary shocks to income, changes ingovernment spending, or changes in consumer confidence. In this case, when interest rates fall,investment rises; when interest rates rise, investment falls. We would expect a negative correlation between investment and interest rates.b. Figure 3-9 shows the case where the supply of loanable funds (saving) is stable, whereas thedemand for loanable funds fluctuates, perhaps reflecting changes in firms’ expectations about the marginal product of capital. We would now find a positive correlation between investment and the interest rate—when demand for funds rises, it pushes up the interest rate, so we observe thatinvestment and the real interest rate increase at the same time.c. If both curves shift, we might generate a scatter plot as in Figure 3-10, where the economyfluctuates among points A, B, C, and D. Depending on how often the economy is at each of these points, we might find little clear relationship between investment and interest rates.d. Situation (c) seems fairly reasonable—as both the supply of and demand for loanable fundsfluctuate over time in response to changes in the economy.。
曼昆《宏观经济学》第9版章节习题精编详解(总供给与通货膨胀和失业之间的短期权衡)【圣才出品】
圣才电子书 十万种考研考证电子书、题库视频学习平台
的变动。这种混淆影响了供给多少的决策，并导致价格水平与产出之间在短期的正相关关系。 当价格水平发生了未预期到的上升时，经济中所有供给者都观察到了自己所生产的产品价格 的上升。他们都错误地推断，他们生产的产品的相对价格上升了。他们更努力地工作，并生 产得更多。
新古典综合派经济学家把菲利普斯曲线作为调节经济的依据，即当失业率高时，实行扩 张性财政政策与货币政策，以承受一定通货膨胀率为代价换取较低的失业率；当通货膨胀率 高时，实行紧缩性的财政政策与货币政策，借助提高失业率以降低通货膨胀率。
货币主义者对菲利普斯曲线所表示的通货膨胀率与失业率之间的交替关系提出了质疑， 并进一步论述了短期菲利普斯曲线、长期菲利普斯曲线和附加预期的菲利普斯曲线，以进一 步解释在不同条件下，通货膨胀率与失业率之间的关系。
3 / 28
圣才电子书 十万种考研考证电子书、题库视频学习平台
古典宏观经济学的批判，认为它缺乏微观经济学基础。适应性预期的权数分布是既定的几何 级数，没有利用与被测变量相关的其他变量，对经济预期方程的确定基本上是随意的，没有 合理的经济解释。因此，新古典宏观经济学派的“理性预期”逐渐取代了“适应性预期”。
5．需求拉动型通货膨胀（demand-pull inflation） 答：需求拉动型通货膨胀，又称为超额需求通货膨胀，指总需求超过总供给所引起的一 般价格水平的持续显著上涨，可解释为“过多货币追求过少的商品”。 需求拉动型通货膨胀的原因是：在总产量达到一定水平后，当需求增加时，供给会增加 一部分，但供给的增加会遇到生产过程中的瓶颈现象，即由于劳动、原料、生产设备的不足 使成本提高，从而引起价格上升；或者在产量达到最大时，即为充分就业的产量时，当需求 增加，供给也不会增加，总需求增加只会引起价格的上涨。消费需求、投资需求或来自政府 的需求、国外需求都会导致需求拉动型通货膨胀，需求方面的原因或冲击主要包括财政政策、 货币政策、消费习惯的改变和国际市场的需求变动等。 引起需求扩大的因素有两大类：一类是实际因素，即消费需求、投资需求的扩大，政府 支出的增加、减税，净出口增加等（通过 IS 曲线右移），它们都会导致总需求的增加，需求 曲线右移；另一类是货币因素，即货币供给量的增加或实际货币需求量的减少即实际货币余 额增加（通过 LM 曲线右移），导致总需求增加。
曼昆《经济学原理》(宏观经济学分册)英文原版
Con ps riin uc d m P eer o e x b if rcae o s g fk o a eo s n td e dr s 1 v0 ic Pr ob ifcae is b nk a ye s ete ar
© 2007 Thomson South-Western
THE CONSUMER PRICE INDEX
• The consumer price index (CPI) is a measure of the overall cost of the goods and services bought by a typical consumer.
© 2007 Thomson South-Western
How the Consumer Price Index Is Calculated • The inflation rate is calculated as follows:
I n f l a t i o n R a t e i n Y e a r 2 = C P I i n Y e a r 2 C P I i n Y e a r 1 1 0 0 C P I i n Y e a r 1
© 2007 Thomson South-Western
How the Consumer Price Index Is Calculated
4. Choose a base year and compute the index.
曼昆经济学原理Chapter 9
PowerPoint Slides prepared by: Andreea CHIRITESCU Eastern Illinois University
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
4
The Determinants of Trade
• World price
– Price of a good that prevails in the world market for that good
• Domestic price
– Opportunity cost of the good on the domestic market
Quantity of textiles
When an economy cannot trade in world markets, the price adjusts to balance domestic supply and demand. This figure shows consumer and producer surplus in an equilibrium without international trade for the textile market in the imaginary country of Isoland.
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Answers to Textbook Questions and ProblemsCHAPTER 9 Economic Growth II: Technology, Empirics, and PolicyQuestions for Review1. In the Solow model, we find that only technological progress can affect the steady-state rate of growthin income per worker. Growth in the capital stock (through high saving) has no effect on the steady-state growth rate of income per worker; neither does population growth. But technological progress can lead to sustained growth.2. In the steady state, output per person in the Solow model grows at the rate of technological progress g.Capital per person also grows at rate g. Note that this implies that output and capital per effectiveworker are constant in steady state. In the U.S. data, output and capital per worker have both grown at about 2 percent per year for the past half-century.3. To decide whether an economy has more or less capital than the Golden Rule, we need to compare themarginal product of capital net of depreciation (MPK –δ) with the growth rate of total output (n + g).The growth rate of GDP is readily available. Estimating the net marginal product of capital requires a little more work but, as shown in the text, can be backed out of available data on the capital stock relative to GDP, the total amount o f depreciation relative to GDP, and capital’s share in GDP.4. Economic policy can influence the saving rate by either increasing public saving or providingincentives to stimulate private saving. Public saving is the difference between government revenue and government spending. If spending exceeds revenue, the government runs a budget deficit, which is negative saving. Policies that decrease the deficit (such as reductions in government purchases or increases in taxes) increase public saving, whereas policies that increase the deficit decrease saving. A variety of government policies affect private saving. The decision by a household to save may depend on the rate of return; the greater the return to saving, the more attractive saving becomes. Taxincentives such as tax-exempt retirement accounts for individuals and investment tax credits forcorporations increase the rate of return and encourage private saving.5. The legal system is an example of an institutional difference between countries that might explaindifferences in income per person. Countries that have adopted the English style common law system tend to have better developed capital markets, and this leads to more rapid growth because it is easier for businesses to obtain financing. The quality of government is also important. Countries with more government corruption tend to have lower levels of income per person.6. Endogenous growth theories attempt to explain the rate of technological progress by explaining thedecisions that determine the creation of knowledge through research and development. By contrast, the Solow model simply took this rate as exogenous. In the Solow model, the saving rate affects growth temporarily, but diminishing returns to capital eventually force the economy to approach a steady state in which growth depends only on exogenous technological progress. By contrast, many endogenous growth models in essence assume that there are constant (rather than diminishing) returns to capital, interpreted to include knowledge. Hence, changes in the saving rate can lead to persistent growth. Problems and Applications1. a. In the Solow model with technological progress, y is defined as output per effective worker, and kis defined as capital per effective worker. The number of effective workers is defined as L E (or LE), where L is the number of workers, and E measures the efficiency of each worker. To findoutput per effective worker y, divide total output by the number of effective workers:Y LE =K12(LE)12LEY LE =K12L12E12LEY LE =K12 L1E1Y LE =KLE æèççöø÷÷12y=k12b. To solve for the steady-state value of y as a function of s, n, g, and δ, we begin with the equationfor the change in the capital stock in the steady state:Δk = sf(k) –(δ + n + g)k = 0.The production function ycan also be rewritten as y2 = k. Plugging this production functioninto the equation for the change in the capital stock, we find that in the steady state:sy –(δ + n + g)y2 = 0.Solving this, we find the steady-state value of y:y* = s/(δ + n + g).c. The question provides us with the following information about each country:Atlantis: s = 0.28 Xanadu: s = 0.10n = 0.01 n = 0.04g = 0.02 g = 0.02δ = 0.04δ = 0.04Using the equation for y* that we derived in part (a), we can calculate the steady-state values of yfor each country.Developed country: y* = 0.28/(0.04 + 0.01 + 0.02) = 4Less-developed country: y* = 0.10/(0.04 + 0.04 + 0.02) = 12. a. In the steady state, capital per effective worker is constant, and this leads to a constant level ofoutput per effective worker. Given that the growth rate of output per effective worker is zero, this means the growth rate of output is equal to the growth rate of effective workers (LE). We know labor grows at the rate of population growth n and the efficiency of labor (E) grows at rate g. Therefore, output grows at rate n+g. Given output grows at rate n+g and labor grows at rate n, output perworker must grow at rate g. This follows from the rule that the growth rate of Y/L is equal to thegrowth rate of Y minus the growth rate of L.b. First find the output per effective worker production function by dividing both sides of theproduction function by the number of effective workers LE:Y LE =K 13(LE )23LE YLE =K 13L 23E 23LEY LE =K 13L 13E 13Y LE =K LE æèçöø÷13y =k 13To solve for capital per effective worker, we start with the steady state condition:Δk = sf (k ) – (δ + n + g )k = 0.Now substitute in the given parameter values and solve for capital per effective worker (k ):Substitute the value for k back into the per effective worker production function to find output per effective worker is equal to 2. The marginal product of capital is given bySubstitute the value for capital per effective worker to find the marginal product of capital is equal to 1/12.c. According to the Golden Rule, the marginal product of capital is equal to (δ + n + g) or 0.06. In the current steady state, the marginal product of capital is equal to 1/12 or 0.083. Therefore, we have less capital per effective worker in comparison to the Golden Rule. As the level of capital per effective worker rises, the marginal product of capital will fall until it is equal to 0.06. To increase capital per effective worker, there must be an increase in the saving rate.d. During the transition to the Golden Rule steady state, the growth rate of output per worker will increase. In the steady state, output per worker grows at rate g . The increase in the saving rate will increase output per effective worker, and this will increase output per effective worker. In the new steady state, output per effective worker is constant at a new higher level, and output per worker is growing at rate g . During the transition, the growth rate of output per worker jumps up, and then transitions back down to rate g .3. To solve this problem, it is useful to establish what we know about the U.S. economy: • A Cobb –Douglas production function has the form y = k α, where α is capital’s share of income.The question tells us that α = 0.3, so we know that the production function is y = k 0.3.• In the steady state, we know that the growth rate of output equals 3 percent, so we know that (n +g ) = 0.03.• The deprec iation rate δ = 0.04. • The capital –output ratio K/Y = 2.5. Because k/y = [K /(LE )]/[Y /(LE )] = K/Y , we also know that k/y =2.5. (That is, the capital –output ratio is the same in terms of effective workers as it is in levels.)a. Begin with the steady-state condition, sy = (δ + n + g)k. Rewriting this equation leads to a formulafor saving in the steady state:s = (δ + n + g)(k/y).Plugging in the values established above:s = (0.04 + 0.03)(2.5) = 0.175.The initial saving rate is 17.5 percent.b. We know from Chapter 3 that with a Cobb–Douglas production function, capital’s share ofincome α = MPK(K/Y). Rewriting, we haveMPK = α/(K/Y).Plugging in the values established above, we findMPK = 0.3/2.5 = 0.12.c. We know that at the Golden Rule steady state:MPK = (n + g + δ).Plugging in the values established above:MPK = (0.03 + 0.04) = 0.07.At the Golden Rule steady state, the marginal product of capital is 7 percent, whereas it is 12 percent in the initial steady state. Hence, from the initial steady state we need to increase k to achieve the Golden Rule steady state.d. We know from Chapter 3 that for a Cobb–Douglas production function, MPK = α (Y/K). Solvingthis for the capital–output ratio, we findK/Y = α/MPK.We can solve for the Golden Rule capital–output ratio using this equation. If we plug in the value0.07 for the Golden Rule steady-state marginal product of capital, and the value 0.3 for α, we findK/Y = 0.3/0.07 = 4.29.In the Golden Rule steady state, the capital–output ratio equals 4.29, compared to the current capital–output ratio of 2.5.e. We know from part (a) that in the steady states = (δ + n + g)(k/y),where k/y is the steady-state capital–output ratio. In the introduction to this answer, we showed that k/y = K/Y, and in part (d) we found that the Golden Rule K/Y = 4.29. Plugging in this value and those established above:s = (0.04 + 0.03)(4.29) = 0.30.To reach the Golden Rule steady state, the saving rate must rise from 17.5 to 30 percent. Thisresult implies that if we set the saving rate equal to the share going to capital (30 percent), we will achieve the Golden Rule steady state.4. a. In the steady state, we know that sy = (δ + n + g)k. This implies thatk/y = s/(δ + n + g).Since s, δ, n, and g are constant, this means that the ratio k/y is also constant. Since k/y =[K/(LE)]/[Y/(LE)] = K/Y, we can conclude that in the steady state, the capital–output ratio isconstant.b. We know that capital’s share of income = MPK ⨯ (K/Y). In the steady state, we know from part (a)that the capital–output ratio K/Y is constant. We also know from the hint that the MPK is afunction of k, which is constant in the steady state; therefore the MPK itself must be constant.Thus, capital’s share of income is constant. Labor’s share of income is 1 – [C apital’s Share].Hence, if capital’s share is constant, we see that labor’s share of income is also constant.c. We know that in the steady state, total income grows at n + g, defined as the rate of populationgrowth plus the rate of technological change. In part (b) we showed that labor’s and capital’s share of income is constant. If the shares are constant, and total income grows at the rate n + g, thenlabor income and capital income must also grow at the rate n + g.d. Define the real rental price of capital R asR = Total Capital Income/Capital Stock= (MPK ⨯K)/K= MPK.We know that in the steady state, the MPK is constant because capital per effective worker k isconstant. Therefore, we can conclude that the real rental price of capital is constant in the steadystate.To show that the real wage w grows at the rate of technological progress g, defineTLI = Total Labor IncomeL = Labor ForceUsing the hint that the real wage equals total labor income divided by the labor force:w = TLI/L.Equivalently,wL = TLI.In terms of percentage changes, we can write this asΔw/w + ΔL/L = ΔTLI/TLI.This equation says that the growth rate of the real wage plus the growth rate of the labor forceequals the growth rate of total labor income. We know that the labor force grows at rate n, and,from part (c), we know that total labor income grows at rate n + g. We, therefore, conclude that the real wage grows at rate g.5. a. The per worker production function is F (K, L )/L = AK α L 1–α/L = A (K/L )α = Ak α b. In the steady state, Δk = sf (k ) – (δ + n + g )k = 0. Hence, sAk α = (δ + n + g )k , or, after rearranging:k *=sA d +n +g éëêêùûúúa 1-a æèççöø÷÷.Plugging into the per-worker production function from part (a) givesy *=A a 1-a æèççöø÷÷s d +n +g éëêêùûúúa 1-a æèççöø÷÷.Thus, the ratio of steady-state income per worker in Richland to Poorland isy *Richland/y *Poorland ()=s Richland d +n Richland +g /s Poorlandd +n Poorland +g éëêêùûúúa1-a =0.320.05+0.01+0.02/0.100.05+0.03+0.02éëêêùûúúa1-c. If α equals 1/3, then Richland should be 41/2, or two times, richer than Poorland.d. If 4a 1-a æèççöø÷÷= 16, then it must be the case that a 1-a æèççöø÷÷, which in turn requires that α equals 2/3.Hence, if the Cobb –Douglas production function puts 2/3 of the weight on capital and only 1/3 on labor, then we can explain a 16-fold difference in levels of income per worker. One way to justify this might be to think about capital more broadly to include human capital —which must also be accumulated through investment, much in the way one accumulates physical capital.6. How do differences in education across countries affect the Solow model? Education is one factoraffecting the efficiency of labor , which we denoted by E . (Other factors affecting the efficiency of labor include levels of health, skill, and knowledge.) Since country 1 has a more highly educated labor force than country 2, each worker in country 1 is more efficient. That is, E 1 > E 2. We will assume that both countries are in steady state. a. In the Solow growth model, the rate of growth of total income is equal to n + g , which isindependent of the work force’s level of education. The two countries will, thus, have the same rate of growth of total income because they have the same rate of population growth and the same rate of technological progress.b. Because both countries have the same saving rate, the same population growth rate, and the samerate of technological progress, we know that the two countries will converge to the same steady-state level of capital per effective worker k *. This is shown in Figure 9-1.Hence, output per effective worker in the steady state, which is y* = f(k*), is the same in bothcountries. But y* = Y/(L E) or Y/L = y*E. We know that y* will be the same in both countries, but that E1 > E2. Therefore, y*E1 > y*E2. This implies that (Y/L)1 > (Y/L)2. Thus, the level of incomeper worker will be higher in the country with the more educated labor force.c. We know that the real rental price of capital R equals the marginal product of capital (MPK). Butthe MPK depends on the capital stock per efficiency unit of labor. In the steady state, bothcountries have k*1= k*2= k* because both countries have the same saving rate, the same population growth rate, and the same rate of technological progress. Therefore, it must be true that R1 = R2 = MPK. Thus, the real rental price of capital is identical in both countries.d. Output is divided between capital income and labor income. Therefore, the wage per effectiveworker can be expressed asw = f(k) –MPK • k.As discussed in parts (b) and (c), both countries have the same steady-state capital stock k and the same MPK. Therefore, the wage per effective worker in the two countries is equal.Workers, however, care about the wage per unit of labor, not the wage per effective worker.Also, we can observe the wage per unit of labor but not the wage per effective worker. The wageper unit of labor is related to the wage per effective worker by the equationWage per Unit of L = wE.Thus, the wage per unit of labor is higher in the country with the more educated labor force.7. a. In the two-sector endogenous growth model in the text, the production function for manufacturedgoods isY = F [K,(1 –u) EL].We assumed in this model that this function has constant returns to scale. As in Section 3-1,constant returns means that for any positive number z, zY = F(zK, z(1 –u) EL). Setting z = 1/EL,we obtainY EL =FKEL,(1-u)æèççöø÷÷.Using our standard definitions of y as output per effective worker and k as capital per effective worker, we can write this asy = F[k,(1 –u)]b. To begin, note that from the production function in research universities, the growth rate of laborefficiency, ΔE/E, equals g(u). We can now follow the logic of Section 9-1, substituting thefunction g(u) for the constant growth rate g. In order to keep capital per effective worker (K/EL) constant, break-even investment includes three terms: δk is needed to replace depreciating capital, nk is needed to provide capital for new workers, and g(u) is needed to provide capital for thegreater stock of knowledge E created by research universities. That is, break-even investment is [δ + n + g(u)]k.c. Again following the logic of Section 9-1, the growth of capital per effective worker is thedifference between saving per effective worker and break-even investment per effective worker.We now substitute the per-effective-worker production function from part (a) and the function g(u) for the constant growth rate g, to obtainΔk = sF [k,(1 –u)] – [δ + n + g(u)]kIn the steady state, Δk = 0, so we can rewrite the equation above assF [k,(1 –u)] = [δ + n + g(u)]k.As in our analysis of the Solow model, for a given value of u, we can plot the left and right sides of this equationThe steady state is given by the intersection of the two curves.d. The steady state has constant capital per effective worker k as given by Figure 9-2 above. We alsoassume that in the steady state, there is a constant share of time spent in research universities, so u is constant. (After all, if u were not constant, it wouldn’t be a ―steady‖ state!). Hence, output per effective worker y is also constant. Output per worker equals yE, and E grows at rate g(u).Therefore, output per worker grows at rate g(u). The saving rate does not affect this growth rate.However, the amount of time spent in research universities does affect this rate: as more time is spent in research universities, the steady-state growth rate rises.e. An increase in u shifts both lines in our figure. Output per effective worker falls for any givenlevel of capital per effective worker, since less of each worker’s time is spent producingmanufactured goods. This is the immediate effect of the change, since at the time u rises, thecapital stock K and the efficiency of each worker E are constant. Since output per effective worker falls, the curve showing saving per effective worker shifts down.At the same time, the increase in time spent in research universities increases the growth rate of labor efficiency g(u). Hence, break-even investment [which we found above in part (b)] rises at any given level of k, so the line showing breakeven investment also shifts up.Figure 9-3 shows these shifts.In the new steady state, capital per effective worker falls from k1 to k2. Output per effective worker also falls.f. In the short run, the increase in u unambiguously decreases consumption. After all, we argued inpart (e) that the immediate effect is to decrease output, since workers spend less time producingmanufacturing goods and more time in research universities expanding the stock of knowledge.For a given saving rate, the decrease in output implies a decrease in consumption.The long-run steady-state effect is more subtle. We found in part (e) that output per effective worker falls in the steady state. But welfare depends on output (and consumption) per worker, not per effective worker. The increase in time spent in research universities implies that E grows faster.That is, output per worker equals yE. Although steady-state y falls, in the long run the fastergrowth rate of E necessarily dominates. That is, in the long run, consumption unambiguously rises.Nevertheless, because of the initial decline in consumption, the increase in u is not unambiguously a good thing. That is, a policymaker who cares more about current generationsthan about future generations may decide not to pursue a policy of increasing u. (This is analogous to the question considered in Chapter 8 of whether a policymaker should try to reach the GoldenRule level of capital per effective worker if k is currently below the Golden Rule level.)8. On the World Bank Web site (), click on the data tab and then the indicators tab.This brings up a large list of data indicators that allows you to compare the level of growth anddevelopment across countries. To explain differences in income per person across countries, you might look at gross saving as a percentage of GDP, gross capital formation as a percentage of GDP, literacy rate, life expectancy, and population growth rate. From the Solow model, we learned that (all else the same) a higher rate of saving will lead to higher income per person, a lower population growth rate will lead to higher income per person, a higher level of capital per worker will lead to a higher level of income per person, and more efficient or productive labor will lead to higher income per person. The selected data indicators offer explanations as to why one country might have a higher level of income per person. However, although we might speculate about which factor is most responsible for thedifference in income per person across countries, it is not possible to say for certain given the largenumber of other variables that also affect income per person. For example, some countries may have more developed capital markets, less government corruption, and better access to foreign directinvestment. The Solow model allows us to understand some of the reasons why income per person differs across countries, but given it is a simplified model, it cannot explain all of the reasons why income per person may differ.More Problems and Applications to Chapter 91. a. The growth in total output (Y) depends on the growth rates of labor (L), capital (K), and totalfactor productivity (A), as summarized by the equationΔY/Y = αΔK/K + (1 –α)ΔL/L + ΔA/A,where α is capital’s share of output. We can look at the effect on output of a 5-percent increase in labor by setting ΔK/K = ΔA/A = 0. Since α = 2/3, this gives usΔY/Y = (1/3)(5%)= 1.67%.A 5-percent increase in labor input increases output by 1.67 percent.Labor productivity is Y/L. We can write the growth rate in labor productivity asD Y Y =D(Y/L)Y/L-D LL.Substituting for the growth in output and the growth in labor, we findΔ(Y/L)/(Y/L) = 1.67% – 5.0%= –3.34%.Labor productivity falls by 3.34 percent.To find the change in total factor productivity, we use the equationΔA/A = ΔY/Y –αΔK/K – (1 –α)ΔL/L.For this problem, we findΔA/A = 1.67% – 0 – (1/3)(5%)= 0.Total factor productivity is the amount of output growth that remains after we have accounted for the determinants of growth that we can measure. In this case, there is no change in technology, so all of the output growth is attributable to measured input growth. That is, total factorproductivity growth is zero, as expected.b. Between years 1 and 2, the capital stock grows by 1/6, labor input grows by 1/3, and output growsby 1/6. We know that the growth in total factor productivity is given byΔA/A = ΔY/Y –αΔK/K – (1 –α)ΔL/L.Substituting the numbers above, and setting α = 2/3, we findΔA/A = (1/6) – (2/3)(1/6) – (1/3)(1/3)= 3/18 – 2/18 – 2/18= – 1/18= –0.056.Total factor productivity falls by 1/18, or approximately 5.6 percent.2. By definition, output Y equals labor productivity Y/L multiplied by the labor force L:Y = (Y/L)L.Using the mathematical trick in the hint, we can rewrite this asD Y Y =D(Y/L)Y/L+D LL.We can rearrange this asD Y Y =D YY-D LL.Substituting for ΔY/Y from the text, we findD(Y/L) Y/L =D AA+aD KK+(1-a)D LL-D LL =D AA+aD KK-aD LL=D AA+aD KK-D LLéëêêùûúúUsing the same trick we used above, we can express the term in brackets asΔK/K –ΔL/L = Δ(K/L)/(K/L)Making this substitution in the equation for labor productivity growth, we conclude thatD(Y/L) Y/L =D AA+aD(K/L)K/L.3. We know the following:ΔY/Y = n + g = 3.6%ΔK/K = n + g = 3.6%ΔL/L = n = 1.8%Capital’s Share = α = 1/3Labor’s Share = 1 –α = 2/3Using these facts, we can easily find the contributions of each of the factors, and then find the contribution of total factor productivity growth, using the following equations:Output = Capital’s+ Labor’s+ Total FactorGrowth Contribution Contribution ProductivityD Y Y =aD KK+(1-a)D LL+D AA3.6% = (1/3)(3.6%) + (2/3)(1.8%) + ΔA/A.We can easily solve this for ΔA/A, to find that3.6% = 1.2% + 1.2% + 1.2%Chapter 9—Economic Growth II: Technology, Empirics, and Policy 81We conclude that the contribution of capital is 1.2 percent per year, the contribution of labor is 1.2 percent per year, and the contribution of total factor productivity growth is 1.2 percent per year. These numbers match the ones in Table 9-3 in the text for the United States from 1948–2002.Chapter 9—Economic Growth II: Technology, Empirics, and Policy 82。