斯蒂芬D威廉森宏观经济学第三版第七章Stephen D. Williamson's Macroeconomics, Third Edition chapter7
宏观经济学-课后思考题答案_史蒂芬威廉森013
Chapter 13International Trade in Goods and AssetsTeaching GoalsThere are two basic aspects to international trade. Trade in goods and services allows a nation to benefit from comparative advantage. In the absence of trade, competitive markets allow the economy to reach a Pareto optimum. At this optimum, the marginal rate of substitution for consumers is equal to the marginal rate of transformation in production. These marginal rates are reflected in market prices. If we open up an economy to trade, the country can improve its welfare as long as closed economy relative prices differ from the relative prices in the rest of the world. It does not matter in which direction this difference works. In either case, the representative consumer can reach an indifference curve that lies beyond the one reached in the absence of trade. This is the essence of gains to trade.The second aspect of trade involves trade in financial assets. A closed economy is required to exactly exhaust its total output in each period between consumption, investment, and government spending. An open economy can use either more or less than the output it produces in each period. Differences between production and absorption can occur when the current account is either in surplus or deficit. A common misimpression for students is to think of the current account balance as reflecting competition for sales by firms in different countries. A better insight into the current account balance comes from considering the additional option for consumption smoothing that comes from borrowing and lending activities with those in other countries. One clear case for the benefits of running a current account deficit is for a country that wants to increase its capital stock more quickly than would be possible in the absence of foreign borrowing. Classroom Discussion TopicsSupport for protectionist trade policies comes to the forefront from time to time. Ask students for arguments they have heard that rationalize tariffs or quotas. Ask them if they support such policies, or find the reasons given for protectionist sentiment compelling. What does fair trade as opposed to free trade mean? Guide them in the direction of finding market failures in international trade. Distinctions between free and fair trade only have meaning if there is monopoly power in the markets for traded goods, or if there are externalities that are complicated by the differing rules of different sovereign nations. Monopoly power may be involved in the steel and automotive industries. Is this a concern for students? Trade protection is also proposed because other nations have more lax environmental restrictions. Don’t we benefit from the decision of other countries to specialize in dirty industries?Trade policies usually boil down to attempts by those who are hurt by trade to seek compensation from those who benefit from trade. What are the likely differences in relative prices between a closed United States and the rest of the world? Much of recent concern has its roots in the fact that the value of skilled labor relative to unskilled labor is much higher in the rest of the world than it would be in a closed United States. Are trade policies a relatively efficient or inefficient means to affect the distribution of income? Are students able to see trade policy issues as economists see them? Encourage the students to couch their views of trade policies in the language of economics.Chapter 13 International Trade in Goods and Assets 129Another concern voiced in the popular press relates to the fact that the United States has been running consistent deficits in the current account balance. Are students concerned about the balance of payments? Why or why not? Remind the students that current account surpluses and deficits are equivalent tointernational borrowing and lending. Is it ever a good idea to try to prevent markets from functioning in a competitive manner? Be sure that they understand that encouraging exports and discouraging importscannot solve the problems inherent in the desire to smooth consumption and expand investment as long as the marginal product of capital exceeds the world real interest rate.Regarding modeling strategies, ask students how a closed economy differs from an open economy. With the representative agent construct, just splitting an economy in two would not yield anything interesting. There needs to be something different in the two parts: different realizations of shocks, differencecurrencies, different policies, etc. Also, discuss the distinction between a small open economy and a large open economy (à la two-country model).OutlineI. A Two-Good Model of a Small Open EconomyA. Introduction1. The Small Open Economy Assumption2. Terms of Trade3. The Real Exchange Rate4. The PPFB. Competitive Equilibrium without Trade1. Pareto Optimality: ,,a b a b MRS MRT =2. Efficiency in Consumption: ,,a b a b MRS p =3. Efficiency in Production: ,,a b a b MRT p =C. Effects of Trade1. International Price-Taking2. Efficiency in Consumption: ,a b ab MRS TOT =3. Efficiency in Production: ,a b ab MRT TOT =4. Comparative Advantage5. Trade and WelfareD. A Change in the Terms of Trade1. Trade Effects when Good a Is Imported2. Trade Effects when Good b Is ImportedII. A Two-Period Small Open EconomyA. The Intertemporal Budget ConstraintB. Response of the Current Account to Disturbances1. Current-Period Income and the Current Account2. Current Government Spending and the Current Account3. Taxes and the Current Account4. The Real Interest Rate and the Current AccountC. The Current Account and Consumption SmoothingD. The Twin Deficits130 Williamson • Macroeconomics, Third EditionIII. Production, Investment, and the Current AccountA. Output Supply and Output DemandB. Effects of Disturbances1. An Increase in the World Interest Rate: ,Y CA ↑↑2.A Temporary Increase in Government Spending: ,Y CA ↑↓ 3.A Permanent Increase in Government Spending: ,Y CA ↑↑ 4.An Increase in Current Total Factor Productivity: ,Y CA ↑↑ 5. An Increase in Future Total Factor Productivity: 0,Y CA Δ=↓C. Consumption, Investment, and the Current AccountTextbook Question SolutionsQuestions for Review1. A small open economy is an economy that does not affect the world price of goods.2. The small open economy model is useful in explaining events in the United States because it isrelatively simple, many of the conclusions drawn from the small open economy model are identical to those obtained from more complicated models, and the size of the U.S. economy as a fraction of worldwide GDP is shrinking.3. In the closed economy, the marginal rate of substitution between the two goods must equal themarginal rate of transformation between the two goods. Furthermore, consumption of each individual good must be equal to production of that good.4. In the open economy, the marginal rates of substitution and transformation between the two goodsmust equal the given terms of trade.5. The residents of an open economy must be better off. An open economy has all of the possibilities ofa closed economy, and its options are expanded with the opportunity to trade.6. Production of good a rises and production of good b falls. Consumption of good a falls, butconsumption of good b may either rise or fall.7. Production of good a rises and production of good b falls. Consumption of good b rises, butconsumption of good a may either rise or fall.8. The current account surplus depends upon current period income, current government spending,taxes, and the real interest rate.Chapter 13 International Trade in Goods and Assets 131 9. A current account deficit may help an economy to grow over time if the deficit is used to financeinvestment spending.10. The twin deficits refer to the simultaneous deficits in the government budget and the current account.The large government budget deficit was the result of a simultaneous increase in governmentspending and a reduction in taxes. Unless the reduction in government savings is matched by an equal or larger increase in private savings, the current account deficit must increase.11. An increase in the world real interest rate increases output, reduces absorption, and increases thecurrent account surplus.12. A temporary increase in government spending increases output, increases absorption, and decreasesthe current account surplus. A permanent increase in government spending increases output, has no effect on absorption, and increases the current account surplus.13. An increase in current total factor productivity increases output, has no effect on absorption, andincreases the current account surplus. An increase in future total factor productivity has no effect on output, increases absorption, and decreases the current account surplus.14. A current account deficit used to finance investment spending provides for a larger future capitalstock. The increased capital stock increases future output, which tends to reduce the future current deficit.Problems1. The change in preferences cannot change the terms of trade for a small open economy. Therefore,production of each good is unchanged. The shift in preferences implies increased consumption of good a, and reduced consumption of good b. If good a is originally imported, then imports andexports both increase. If good a is originally exported, then imports and exports both decrease.2. If the marginal rate of transformation increases for every quantity of good a, then there is a shift inthe production possibilities frontier. In particular, there is no change in the maximum amount of goodb that can be produced, so there is no change in the horizontal intercept. The rest of the PPP becomessteeper and lies everywhere else above the original PPP. Production of good b increases, butproduction of good a may either rise or fall. If the increase in the marginal rate of substitution rotated the original PPP around the original production point, then production of good a would decrease.The outward shift in the PPP produces a positive income effect. However, because there can be no change in the terms of trade, there can be no substitution effect in consumption. Consumption of goods a and b both increase. Suppose that, as a first approximation, that production of good a is unchanged. If good b is originally exported, then exports of good b increase along with imports of good a. If good b is originally imported, then imports of good b decrease along with exports ofgood a.132 Williamson • Macroeconomics, Third Edition3. Suppose that the economy starts out as in the figure below. The economy produces 1a units of good aand 1b units of good b . Consumers consume 2a units of good a and 2b units of good b . The economytherefore exports good b and imports good a . Now assume that a quota is placed on imports of good a , and that this quota is, in fact, a binding constraint. Denote the size of the quota as <32.b bThe budget line now becomes vertical at 3.b The new budget line is depicted in the figure below. Theeconomy continues to produce at point 11(,).a b Consumption is at point 33(,).a b Therefore, less of good a is imported and less of good b is exported. Consumers are definitely worse off. They are no longer able to consume at a point on indifference curve, 1.I They are forced to the less desirableindifference curve, 2.IChapter 13 International Trade in Goods and Assets 1334. Government spending with perfect-complements preferences.(a) The net amount of income available from domestic production net of government spending in thefirst period is equal to 100 − 15 = 85, and the net amount of income available from domesticproduction net of government spending in the second period is equal to 120 − 20 = 100. The budget constraint is given by:100851.1 1.1C C ′+=+ Setting first-period and second-period consumption equal, we find that consumption in bothperiods is equal to 92.14. The current account surplus is equal to domestic income, 100 minus consumption, 92.14, minus government spending, 15, so the current account is equal to –7.14, a deficit. The endowment point, E, and the consumption point, F, are depicted in the first figure below.134 Williamson • Macroeconomics, Third Edition(b) Net first-period income now falls to 75. The budget constraint is given by:100751.1 1.1C C ′+=+ Setting first-period and second-period consumption equal, we find that consumption in bothperiods is equal to 87.86. The current account surplus is equal to domestic income, 100 minus consumption, 87.86, minus government spending, 25, so the current account is equal to –12.86, a larger deficit. The endowment point, E, and the consumption point, F, are depicted in the second figure above.(c) In this problem, the increase in government spending leads to a larger current account deficit.The representative consumer increases her borrowing so that first-period consumption need not fall as much as the temporary increase in government spending.5. Different borrowing and lending rates.(a) For levels of first-period consumption less than Y – T , the consumer lends his private savings,and earns the world real rate of interest, r . For levels of first-period consumption greater thanY – T , the consumer must borrow at the higher real rate of interest, r *. The representativeconsumer’s budget line is bowed out, away from the origin. A change in r * steepens the part of the budget line where C > Y – T . If the consumer was originally a saver, the change in r * has no effect on consumption or the current account surplus. If the consumer was originally a borrower, the budget relevant portion of the line rotates through the point (,).Y T Y'T'−− The substitution effect of the change in r * implies lower first-period consumption and higher second-periodconsumption. The income effect of the change in r* decreases both first-period and second-period consumption. Since first-period consumption unambiguously decreases, the currentaccount surplus must increase.(b) A tax cut financed by government borrowing pushes the kink in the budget constraint to the right.If the representative consumer is a lender, there is no effect. If the representative consumer is a borrower, this represents a pure income effect. Both first-period and second-period consumption increase. If the current account is initially in balance, then the current account goes into deficit. The representative consumer is able to get to a higher indifference curve, so welfare increases. The government is able to pass along the ability to lend at the world real interest rate, so theadditional costs of borrowing are eliminated.6.Current account deficit policies.(a) If Ricardian equivalence holds, then the level of lump-sum taxation has no effect on the currentaccount. The first group of advisors would therefore be wrong. A tax on investment shifts theinvestment demand schedule to the left. The output supply curve is unchanged. The outputdemand curve continues to pass through the original equilibrium position at the given world real interest rate. Because investment has decreased, absorption decreases, so the current accountdeficit declines. Therefore, the best advice to take would be to adopt the investment tax.(b) The concern with the current account deficit is misguided in this instance. The deficit is beingused to finance investment spending. Over time, the increase in investment leads to a larger stock of capital, the output supply curve shifts to the right, and the current account deficit eventually disappears. If the policy is implemented, the stated objective could be met, but welfare would be lower, and the policy would continue to be needed, because it would be difficult for the economy to grow its way out of the situation that caused the deficit.Chapter 13 International Trade in Goods and Assets 135 7. The expected future increase in government spending decreases lifetime wealth. The output supplyschedule shifts to the right. At the unchanged real interest rate, investment is unchanged and both current and future consumption decrease. Absorption decreases and output increases, so the current account must increase.8. A persistent increase in total factor productivity would shift both the output supply curve and theoutput demand curve to the right. The supply curve shifts due to higher employment and higherproductivity. Investment demand increases due to the increase in expected future productivity.Consumption increases due to the increases in current and future income. The analysis of Chapter 11 argued that the shift in the supply curve would be larger than the combined effects of the changes in investment and consumption, so the current account balance would also increase. At the given world real interest rate, investment increases. At the given world real interest rate, the increase in domestic income increases consumption. These predictions are in line with the typical business cycle.However, this scenario is inconsistent with Figure 13.10 in the text. In the data, the current account is negatively correlated with output. In this example, output and the current account move in the same direction.9. The increase in future government spending reduces the present value of lifetime income. Laborsupply increases, so the output supply curve shifts to the right, and so output increases. Consumption spending decreases due the decrease in lifetime wealth. Investment is unchanged. Therefore, the current account surplus increases.。
斯蒂芬D威廉森宏观经济学第三版第六章Stephen D. Williamson's Macroeconomics, Third Edition chapter6
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Figure 6.10 Adjustment to the Steady State in the Malthusian Model When z Increases
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Figure 6.7 The Per-Worker Production Function
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Figure 6.8 Determination of the Steady State in the Malthusian Model
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Real Per Capita Income and the Investment Rate
Across countries, real per capita income and the investment rate are positively correlated.
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• There is no tendency for rich countries to grow faster than poor countries, and vice-versa. • Rich countries are more alike in terms of rates of growth than are poor countries.
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威廉森《宏观经济学》(第3版)配套题库【模拟试题】威廉森《宏观经济学》(第3版)模拟试题及详解(一)
威廉森《宏观经济学》（第3版）模拟试题及详解（一）一、名词解释（每小题5分，共计20分）1．IS LM-模型答：IS LM-模型是由英国经济学家希克斯和美国经济学家汉森在凯恩斯宏观经济理论基础上概括出的一个经济分析模式，即“希克斯—汉森模型”，也称“希克斯—汉森综合”或“希克斯—汉森图形”。
IS LM-模型是宏观经济分析的一个重要工具，是描述产品市场和货币市场之间相互联系的理论结构。
在产品市场上，国民收入取决于消费、投资、政府支出和净出口加起来的总支出或者说总需求水平，而总需求尤其是投资需求要受到利率影响，利率则由货币市场供求情况决定，就是说，货币市场要影响产品市场；另一方面，产品市场上所决定的国民收入又会影响货币需求，从而影响利率，这又是产品市场对货币市场的影响。
可见，产品市场和货币市场是相互联系、相互作用的，而收入和利率也只有在这种相互联系、相互作用中才能决定。
IS曲线是描述产品市场达到均衡，即I S=时，国民收入与利率之间存在着反向变动关=时，国民收入和利率之间存在着同系的曲线。
LM曲线是描述货币市场达到均衡，即L M向变动关系的曲线。
把IS曲线和LM曲线放在同一个图上，就可以得出说明两个市场同时均衡时，国民收入与利率决定的IS LM-模型。
2．国内生产总值（gross domestic product，GDP）答：国内生产总值指一个国家（地区）领土范围内，本国（地区）居民和外国居民在一定时期内所生产和提供的最终物品和劳务的市场价值。
GDP一般通过支出法和收入法两种方法进行核算。
用支出法计算的国内生产总值等于消费、投资、政府支出和净出口之和；用收入法计算的国内生产总值等于工资、利息、租金、利润、间接税和企业转移支付和折旧之和。
GDP是一国范围内生产的最终产品的市场价值，因此是一个地域概念，而与此相联系的国民生产总值（GNP）则是一个国民概念，乃指某国国民所拥有的全部生产要素所生产的最终产品的市场价值。
2020年整理宏观经济学第七章习题及答案.doc
第七单元经济周期理论本单元所涉及到的主要知识点：1．经济周期的含义、阶段与种类； 2．经济周期的原因；3．卡尔多经济周期模型； 4．乘数－加速数模型一、单项选择1．经济周期中的两个主要阶段是（）。
a．繁荣和萧条； b．繁荣和衰退； c．萧条和复苏； d．繁荣和复苏。
2．下列对经济周期阶段排序正确的是（）。
a．复苏，繁荣，衰退，萧条； b．复苏，繁荣，萧条，衰退；c．复苏，萧条，衰退，繁荣； d．复苏，衰退，萧条，繁荣。
3．由于经济衰退而形成的失业属于：（）。
a．摩擦性失业； b．结构性失业；c．周期性失业； d．自然失业。
4．下列哪种说法表达了加速原理（）。
a．消费支出随着投资支出增长率的变化而变化；b．投资支出随着国民收入增量的变化而变化；c．国民收入随着投资支出的变化而变化；d．投资支出的减少会造成消费支出一轮一轮地减少。
5．下列哪种说法没有表达加速原理（）。
a．国民收入增长率的变化将导致投资支出的变化；b．消费支出的变化会引起投资支出更大的变化；c．投资支出的减少会造成消费支出一轮一轮地减少；d．投资支出随着国民收入增量的变化而变化。
6．加速原理发生作用的条件是（）。
a．投资的增加会导致国民收入增加；b．消费品的生产需要有一定数量的资本品，因而消费支出的增加会导致投资支出的增加；c．投资的增加会导致消费支出的持续增加；d．投资支出的减少会造成消费支出地减少。
7．经验统计资料表明，在经济周期里，波动最大的一般是（）。
a．资本品的生产； b．农产品的生产； c．日用消费品的生产； d．a和c。
8．所谓资本形成是指（）。
a．净投资； b．总投资； c．更新投资； d．存货的投资。
9．假定某经济连续两年的国民收入都是1200亿美元，在资本－产量比率等于2的条件下，净投资等于（）。
a．1200亿美元； b．2400亿美元； c．2000亿美元； d．0。
10．已知某经济某一年的国民收入是1000亿美元，净投资为零；第二年国民收入增至1200亿美元。
斯蒂芬D威廉森宏观经济学第三版第十一章Stephen D. Williamson's Macroeconomics, Third Edition chapter11
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Figure 11.2 Effects of a Persistent Increase in Total Factor Productivity in the Real Business Cycle Model
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Segmented Markets Model
• Business cycles can be caused in this model by unanticipated shocks to the money supply. • Model exhibits a liquidity effect – the interest rate falls in the short run when the money supply increases. • Monetary policy can only improve the functioning of the economy if the central bank has an informational advantage over the private sector. • Fit to the data is not as good as with the real business cycle model.
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Figure 11.5 Effects of an Unanticipated Increase in the Money Supply in the Segmented Markets Model
宏观经济学-课后思考题答案_史蒂芬威廉森006
Chapter 6Economic Growth: Malthus and SolowTeaching GoalsStudents easily take for granted the much more abundant standard of living of today as opposed to 20, 50, or 100 years ago. Sometimes it is easier to remind students of what their ancestors had to do without, rather than simply referring to per capita income levels over time. Recessions come and go, and yet economic growth swamps the lost output we endure during hard times.The typical student begins study of economic growth against the backdrop of the recent growth experience of the United States. The current standard of living in the United States vastly surpasses the current standard of living in most countries and would have been unimaginable anywhere in the world before the advent of the industrial revolution. Until about 1800, the world economy produced little more than a subsistence level of income for any but the richest individuals. Growth in per capita income was nonexistent. The Malthusian model of growth explains the tendency of increases in population to dilute any gains in productivity.The industrial revolution introduced the possibility of sustained growth in per capita income through the accumulation of physical capital. However, growth experience has varied widely around the world. The richer countries have a sustained record of growth. Per capita income in the United States has proceeded at an average rate of about 2% per year. While 2% growth may seem small, it is important for students to realize that such growth transforms into a more than doubling of per capita GDP per generation. Unfortunately, the poorer countries have remained poor. Furthermore, their growth rates have not generally matched growth rates in the richer countries, so that the poor countries fall farther and farther behind. Such differences in standards of living and growth prospects present puzzles that the study of economic growth hopes to solve.Classroom Discussion TopicsGetting students to relate to differences in standards of living can sometimes be difficult. It is easy to take one’s own standard of living for granted. An interesting discussion topic is whether students would be willing to travel back in time to 100 or 200 years ago, if they could be one of the richest people of those earlier times. Would the tradeoff be worthwhile? While students typically stress factors like antiquated view about freedom of choice, and racial and gender issues, try to encourage students to divide their concerns into those that are more economic as opposed to social. Also point out that higher standards of living allow societies to be more concerned about issues of equality when mere survival is no longer precarious.Chapter 6 Economic Growth: Malthus and Solow 53Students often view population growth as the result of cultural factors and personal preferences. Against the abundance of daily living, it is easy to forget economic factors. Ask the students for examples ofeconomic factors that might impact on fertility decisions. The Malthusian model suggests that growth may only be achieved through population control. In the modern economy, the costs of raising children can be formidable, and so there is tendency for such costs to be a disincentive to fertility. Such costs may attribute to the tendency for low fertility rates in advanced economies. In more primitive societies, having a large family can be a private form of Social Security. The more children a family has, the more family members there will be to provide for the parents in old age. Poor public health conditions may actually enhance fertility. If each child has a small chance for survival to adulthood, more births are required to produce a given-sized family.OutlineI. Economic Growth FactsA. Pre-1800: Constant Per Capita Income across Time and SpaceB. Post-1800: Sustained Growth in the Rich CountriesC. High I nvestment ↔ High Standard of LivingD. High Population Growth ↔ Low Standard of LivingE. Divergence of Per Capita Incomes: 1800–1950F. No Conditional Convergence amongst All CountriesG. Conditional Convergence amongst the Rich CountriesII. The Malthusian ModelA. Production Determined by Labor and Fixed Land SupplyB. Population Growth and Per Capita ConsumptionC. Steady-state Consumption and Population1. Effects of Technological Change2. Effects of Population ControlD. Malthus: Theory and EvidenceIII. Solow’s Model of Exogenous GrowthA. The Representative ConsumerB. The Representative FirmC. Competitive EquilibriumD. Steady-State Growth1. The Steady-State Path2. Adjustment toward EquilibriumE. Savings and Growth1. Equilibrium Effects2. The Golden Rule: K MP n d =+F. Labor Force Growth and Output Per CapitaG. Total Factor Productivity and Output Per CapitaH. Solow: Theory and Evidence54 Williamson • Macroeconomics, Third EditionIV. Growth AccountingA. Solow ResidualsB. The Productivity Slowdown1. Measurement of Services2. The Relative Price of Energy3. Costs of Adopting New TechnologyC. Cyclical Properties of Solow ResidualsTextbook Question SolutionsQuestions for Review1. In exogenous growth models, growth is caused in the model by forces not explained by the modelitself. Endogenous growth models examine the economic factors that cause growth.2. Pre-1800: Constant Per Capita Income across Time and SpacePost-1800: Sustained Growth in the Rich CountriesHigh Investment ↔ High Standard of LivingHigh Population Growth ↔ Low Standard of LivingDivergence of Per Capita Incomes: 1800–1950No Conditional Convergence amongst All CountriesConditional Convergence amongst the Rich Countries3. An increase in total factor productivity increases the size of the population, but has no effect on theequilibrium level of consumption per capita.4. Only a downward shift in the population growth function can increase the standard of living.5. Malthu’s model is quite successful in explaining economic growth prior to the industrial revolution.Malthu’s model has little relevance for more recent growth experience.6. In the steady state, all variables stay constant: per capita capital, output, consumption, savings. Also,this steady state is stable: whatever the initial capital (except zero), the economy will converge to this steady state.7. With an increase in the saving rate, it becomes possible to sustain a higher level of per capita capital,and thus higher output and consumption. With an increase in the population rate, the contraryhappens, as one needs to provide more newborns with the going per capita capital. A higher total factor productivity improves all per capita variables in the steady state.8. To maximize steady-state per capita consumption, the saving rate must be such that the marginalproduct of capital (the slope of the per capita production function) equals the population growth rate plus the depreciation rate.9. The Malthusian model gave no way out of misery, except for measures that reduce the population.Even technological advances would not raise the standard of living. The Solow model shows that it is possible to obtain a stable standard of living with growing population. And if total factor productivity increases, one can even obtain improvements in the standard of living despite population growth.Chapter 6 Economic Growth: Malthus and Solow 55 10. The Cobb-Douglas production function permits a simple decomposition of economic growth into itscomponent sources.11. In a competitive equilibrium, the parameter a is equal to the share of capital income in total income.12. The Solow residual measures increases in real GDP that are not accounted for by increases in capitaland labor. The Solow residual is highly procyclical as it explains the great majority of the cyclical component in GDP.13. The productivity slowdown could be explained by underestimates of output in the growing servicessector, increases in the relative price of energy, and the costs of adopting new technologies.14. American workers then knew how to incorporate the new technologies, in particular informationtechnology. These efficiency gains may have been realized by 2000, which explains the newslowdown, along with higher energy prices.15. Growth in capital, employment, and total factor productivity account for growth in GDP.16. During this period, growth in these countries was much larger than average. Growth rates for thesecountries were about three times as fast as growth in the United States. However, most of this growth can be attributed to increases in the capital stocks in these countries, and such rapid rates of growth of capital cannot be sustained for long periods of time.Problems1. The amount of land increases, and, at first, the size of the population is unchanged. Therefore,consumption per capita increases. However, the increase in consumption per capita increases the population growth rate, see the figure below. In the steady state, neither *c nor *l are affected by the initial increase in land. This fact can be discerned by noting that there will be no changes in either of the panels of Figure 6.8 in the textbook.56 Williamson • Macroeconomics, Third Edition2. A reduction in the death rate increases the number of survivors from the current period who will stillbe living in the future. Therefore, such a technological change in public health shifts the function ()g cupward. In problem #1 there were no effects on the levels of land per capita and consumption per capita. In this case, the ()g c function in the bottom figure below shifts upward. Equilibriumconsumption per capita decreases. From the top figure below, we also see that the decrease inconsumption per capita requires a reduction in the equilibrium level of land per capita. The size of the population has increased, but the amount of available land is unchanged.Chapter 6 Economic Growth: Malthus and Solow 57 3. For the marginal product of capital to increase at every level of capital, the shift in the productionfunction is equivalent to an increase in total factor productivity.(a) The original and new production functions are depicted in the figures below.(b) Equilibrium in the Solow model is at the intersection of ()n d k+szf k with the line segment ().The old and new equilibria are depicted in the bottom panel of the figure above. The newequilibrium is at a higher level of capital per capita and a higher level of output per capita.(c) For a given savings rate, more effective capital implies more savings, and in the steady state thereis more capital and more output. However, if the increase in the marginal product of capital were local, in the neighborhood of the original equilibrium, there would be no equilibrium effects. A twisting of the production function around its initial point does not alter the intersection point.4. An increase in the depreciation rate acts in much the same way as an increase in the populationgrowth rate. More of current savings is required just to keep the amount of capital per capita constant.In equilibrium output per capita and capital per capita decrease.58 Williamson • Macroeconomics, Third Edition5. A destruction of capital.(a) The long-run equilibrium is not changed by an alteration of the initial conditions. If the economystarted in a steady state, the economy will return to the same steady state. If the economy wereinitially below the steady state, the approach to the steady state will be delayed by the loss ofcapital.(b) Initially, the growth rate of the capital stock will exceed the growth rate of the labor force. Thefaster growth rate in capital continues until the steady state is reached.(c) The rapid growth rates are consistent with the Solow model’s predictions about the likelyadjustment to a loss of capital.6. A reduction in total factor productivity reduces the marginal product of capital. The golden rule levelof capital per capita equates the marginal product of capital with .n d + Therefore, for given ,n d + the golden rule amount of capital per capita must decrease as in the figure below. Therefore the golden rule savings rate must decrease.7. Government spending in the Solow model.(a) By assumption, we know that T = G, and so we may write:()(1)(1)K's Y G d K sY gN d K =−+−=−+−Now divide by N and rearrange as:(1)()(1)k'n szf k sg d k +=−+−Divide by (1 + n ) to obtain:()(1)(1)(1)(1)szf k sg d k k'n n n −=−++++Chapter 6 Economic Growth: Malthus and Solow 59Setting k = k ′, we find that:**()().szf k sg n d k =++This equilibrium condition is depicted in the figure below.(b) The two steady states are also depicted in the figure above.(c) The effects of an increase in g are depicted in the bottom panel of the figure above. Capital percapita declines in the steady state. Steady-state growth rates of aggregate output, aggregate consumption, and investment are all unchanged. The reduction in capital per capita isaccomplished through a temporary reduction in the growth rate of capital.8. The golden rule quantity of capital per capita, *,k is such that *().K MP zf k n d ′==+ A decrease in the population growth rate, n , requires a decrease in the marginal product of capital. Therefore, thegolden rule quantity of capital per capita must increase. The golden rule savings rate may either increase or decrease.60 Williamson • Macroeconomics, Third Edition9. (a) First, we need to determine how bN evolves over time:(bN )′ = (1 + f )(1 + n ) bNThen we just need to redo the analysis of the competitive equilibrium and the steady state as inthe book, replacing every N by bN , every (1 + n ) by (1 + f )(1 + n ), and every n by f + n . The new steady-state per efficiency unit capital is then******()(1)(1)(1)(1)(1)szf k d k k f n f n −=+++++ All aggregate variables then grow at the rate of f + n , while per capita aggregates grow at therate f .(b) An increase in f increases the growth rate of per capita income by the same amount, as f is itsgrowth rate. This happens because the exogenous growth in b raises instant capital and income for everyone without a need to invest in capital.10. Production linear in capital:()()Y K z zf k f k k N N==⇒= (a) Recall Equation (20) from the text, and replace ()f k with k to obtain:+−=+((1))(1)sz d k'k n Also recall that 11 and .Y Y Y'zk k k'N z N z N'=⇒== Therefore: ((1))(1)Y'sz d Y N'n N+−=+ As long as((1))1,(1)sz d n +−>+ per capita income grows indefinitely. (b) The growth rate of income per capita is therefore: ((1))1(1)()(1)Y'Y sz d N'N g Y n Nsz n d n −+−==−+−+=+ Obviously, g is increasing in s .(c) This model allows for the possibility of an ever-increasing amount of capital per capita. In theSolow model, the fact that the marginal product of capital is declining in capital is the key impediment to continual increases in the amount of capital per capita.Chapter 6 Economic Growth: Malthus and Solow 6111. Solow residual calculations.(a) To calculate the Solow residuals, we apply the formula, 0.360.64ˆˆˆˆ/,zY K N = to the values in the provided table. Adding a new column for these values, we obtain:Year ˆY ˆK ˆN ˆz 1995 8031.7 25487.3 124.9 9.4781996 8328.9 26222.3 126.7 9.6401997 8703.5 27018.1 129.6 9.8231998 9066.9 27915.9 131.5 10.0191999 9470.3 28899.9 133.5 10.2362000 9817.0 29917.1 136.9 10.3122001 9890.7 30793.4 136.9 10.2822002 10048.8 31599.6 136.5 10.3692003 10301.0 32426.2 137.7 10.4722004 10703.5 33304.9 139.2 10.7032005 11048.6 34191.7 141.7 10.820(b) Next, we compute the percentage changes in each of the table entries. These values arepresented in the table below.Year ˆˆY Y Δ/ (%) ˆˆK K Δ/ (%) ˆˆN N Δ/ (%) ˆˆzz Δ/ (%) 1996 3.70 2.88 1.44 1.71 1997 4.50 3.03 2.29 1.901998 4.18 3.32 1.47 2.001999 4.45 3.52 1.52 2.172000 3.66 3.52 2.55 0.742001 0.75 2.93 0.00 −0.292002 1.60 2.62 −0.29 0.852003 2.51 2.62 0.88 0.992004 3.91 2.71 1.09 2.212005 3.22 2.66 1.80 1.0962 Williamson • Macroeconomics, Third EditionTo compare the contributions to growth, we need to compare the magnitudes,ˆˆˆˆ0.36(/),0.64(/),KKNN ΔΔ and ˆˆ/.z z Δ These values are presented in the table below.Year ˆˆ0.36(Δ/K K) (%) ˆˆ0.64(Δ/N N)(%) ˆˆz z Δ/ (%)1996 1.04 0.92 1.711997 1.09 1.46 1.901998 1.20 0.94 2.001999 1.27 0.97 2.172000 1.27 1.63 0.742001 1.05 0.00 −0.292002 0.94 −0.19 0.852003 0.94 0.56 0.992004 0.98 0.70 2.212005 0.96 1.15 1.09Most often, when output is growing, the biggest contribution to growth comes from increases intotal factor productivity. In 1991 and in 2001, both bad years for growth, total factor productivity decreased. In the other years, growth in total factor productivity is usually the largest contributor to growth, while increases in capital and labor equally share the role of the leading cause of growth in the other years. In the later years, capital growth has come to be relatively more important than in the early years.。
威廉森《宏观经济学》(第3版)配套题库【课后习题】第3章 经济周期的衡量【圣才出品】
第3章经济周期的衡量一、复习题1．经济周期的主要明显特征是什么？答：经济周期的明显特征是：经济周期围绕着实际GDP的趋势波动。
用与现实的实际GDP非常吻合的平滑曲线来表示实际GDP的趋势，这种趋势意味着部分实际GDP可归因于长期增长因素。
其余未分析的，即对趋势的偏离，则用经济周期活动来表示。
表示实际GDP的增长趋势的曲线绕着趋势上下变动，波谷是对趋势的最大负偏离，波峰是对趋势的最大正偏离，从而形成衰退与繁荣的经济周期波动。
2．除持续性外，偏离GDP趋势的三个重要特征是什么？答：偏离GDP趋势的三个重要特征是：（1）偏离实际GDP趋势的时间序列很不稳定。
（2）实际GDP围绕趋势波动的幅度没有规律性。
一些波峰和波谷意味着对趋势的巨大偏离，而另一些波峰和波谷则意味着对趋势的小幅偏离。
（3）实际GDP围绕趋势波动的频率没有规律性。
实际GDP中波峰和波谷之间的时间跨度变化很大。
3．解释预测长期GDP为何困难。
答：预测长期GDP困难的原因：（1）实际GDP围绕趋势波动的幅度没有规律性，一些波峰和波谷意味着对趋势的巨大偏离，而另一些波峰和波谷则意味着对趋势的小幅偏离。
（2）实际GDP围绕趋势波动的频率没有规律性。
实际GDP中波峰和波谷之间的时间跨度变化很大。
（3）偏离实际GDP趋势的时间序列很不稳定。
总之，实际GDP波动的不稳定使这些波动难以预测，而且不稳定性也使得转折点何时发生难以预测，而波幅和频率的无规律则意味着难以预测衰退和繁荣的强度和时间长短。
4．总体经济活动变量的联动为何重要？答：尽管实际GDP波动具有不规律的形式，但宏观经济诸变量一起波动的格局显示出了较强的规律性，这些波动格局称为联动。
通过以时间序列图或散点图的形式为两个经济变量偏离其趋势的百分比作图，或通过计算偏离趋势的百分比标准差，就可判别联动。
联动性很重要，因为联动性的规律表明，经济周期是大同小异的。
经济周期的这一性质可能产生分析经济周期的一般理论，这一可能的新理论不同于以往的理论，即：将每一个经济周期都看作是一系列独特条件的结果再进行经济周期的研究。
宏观经济学第七章ppt课件
❖ 5、M/P= m= m1 + m2
货币供给函数
❖ 6、m=L
货币市场均衡条件
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第一节 总需求曲线
❖ 总需求函数可以从IS-LM曲线中得到。即在表达式
中推导出P与Y的函数关系即可。
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第一节 总需求曲线
AD的来源： IS-LM模型
具体例子见书486
❖ (2)： P↗→ 金融资产实际价值↘→ 个人收入↘→ 消费↘ →AE↘ →y↘ 这种效应称为实际余额效应或财富效应
❖ （影响消费水平）
❖ (3)：P↗→ 名义国民收入↗→ 所得税纳税档次↗→消费支出
↘→AE↘ →y↘ 这种效应称为所得税效应 ❖ （影响消费水平）
m M
P
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第一节 总需求曲线
❖ 2.根据IS-LM图形推导(书P486)：
❖ 价格水平的变化通过产品市场和货币市场的作用 来影响总需求，进而是影响到均衡的产出水平， 当价格水平变动后，产品市场和货币市场会所作 出相应的反应，表现为产量和价格水平之间的反 向关系。
❖ 因此，我们可从IS-LM模型出发，分析价格变化与 总产出水平的关系，从而得到总需求曲线。
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第一节 总需求曲线
三、总需求曲线的斜率 总需求曲线的斜率反映了 既定的价格水平变动所引 起的总需求与国民收入的 不同变动情况。 如图所示：总需求曲线的 越陡，一定价格水平变动 所引起的总需求与国民收 入变动越小；总需求曲线 越平缓，一定的价格水平 变动所引起的总需求与国 民收入变动越大。
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宏观经济学-课后思考题答案_史蒂芬威廉森010
宏观经济学-课后思考题答案_史蒂芬威廉森010Chapter 10A Monetary Intertemporal Model: Money, Prices,and Monetary PolicyTeaching GoalsAnalysis of a monetary economy can become quite complex. Modern economies require significant specialization to function well. Such specialization requires a commonly accepted medium of exchange. Money serves this function. Although it matters quite a lot that we have money, the actual quantity of money in circulation is not very important. This fact emerges because the quantity of money is neutral, if not in the very short run, certainly in the long run.In the monetary intertemporal model, changes in the money supply affect the level of prices, but do not otherwise affect economic outcomes; money is neutral. Real factors may also affect the price level. The price level adjusts to keep money demand and money equal. Disturbances that change the equilibrium levels of output and the real interest rate therefore change the price level. Shifts in preferences for money holding also affect the price level.The principle role of monetary policy in the monetary intertemporal model is to control the level of prices.A popular goal of policy is to stabilize the price level in response to shocks to the economy. However, the central bank’s ability to stabilize prices may be compromised if money demand does not behave in a predictable manner. It is also important for policy to set targets and adhere to particular policy rules.Classroom Discussion TopicsThe payments technology has continually advanced over time, but the rate of advance has acceleratedin the era of computer technology. Ask the students for examples of advances in this technology beyond the routine use of cash and the writing of paper checks. Some obvious possibilities include the use of ATMs, computer and telephone banking, the use of prepaid phone cards and other forms of smartcard technologies. Students are also likely to discuss the existence of credit cards and the ever more sophisticated ways to use credit cards and protect against fraud. As one example, there is the use of credit cards to pay for purchases over the Internet. In discussing these possibilities, it is also important to distinguish the payments technology from the proper measurement of the money supply. For example, it is important to distinguish between payment arrangements that are uses of credit, like the use of credit cards, from uses of money, like cash and transaction deposits.Standard macroeconomic analysis, like that of this chapter, emphasizes central banks’ control of the quantity of money in circulation. However, most contemporary discussions of U.S. monetary policy focus on the Federal Reserve’s control of “interest rates.” This chapter offers plenty of opportunities to discuss real life events. For example, discuss the upcoming meeting of the FOMC, what it decides on, what information it uses, and what it may do.102 Williamson ? Macroeconomics, Third EditionIn the monetary intertemporal model, the real interest rate is market determined and cannot be influenced by central bank behavior. Ask the students whether they believe a simplistic view of popular press coverage that seems to refute the notion that the interest rate is market determined. Note the importance of the distinction between the federal funds rate and the sort of real interest rates that motivate saving and investment choices. Is it possible that the Fed adjusts the federal funds rate to more closely resemble other market interest rates? Is it possible to control the nominal interest rate while being unable to influence the real interest rate? Even if the Fed is able to control one very narrowly defined real interest rate, does this mean that models like those in this chapter are not useful descriptions of reality?OutlineI. Functions of MoneyA. Medium of ExchangeB. Store of ValueC. Unit of AccountII. Measuring the Money SupplyA. The Monetary Base1. Currency Outside the Fed2. Depository Institution Deposits at the FedB. M11. Currency Held by the Public2. Traveler’s Checks3. Demand Deposits4. Other Checkable DepositsC. M21. Savings Deposits2. Small-Denomination Time Deposits3. Retail Money Market Mutual FundsD. M31. Large-Denomination Time Deposits2. Institutional Money Market Mutual Funds3. Repurchase Agreements4. EurodollarsIII. Introduction to the Monetary Intertemporal ModelA. The Need for Money1. Single Coincidence of Wants2. Double Coincidence of Wants3. The Cash-in-Advance ModelB. Real and Nominal Interest Rates1. Nominal Bonds2. The Nominal Interest Rate3. The Fisher RelationshipChapter 10 A Monetary Intertemporal Model: Money, Prices, and Monetary Policy 103C. Representative Consumer1. The Cash-in-Advance Constraint2. Banking Service Cost Function3. Optimal Choice of Banking ServicesD. Representative Firm1. The Cash-in-Advance Constraint2. Banking Service Cost Function3. Optimal Choice of Banking Services E. Money and the Government Budget ConstraintIV. Competitive Equilibrium in the Monetary Intertemporal ModelA. Graphical ApparatusB. A Change in the Level of the Money Supply1. Sources of Changes in the Money Supply a. Helicopter Drops: Taxes/Transfersb. Open-Market Operationsc. Seigniorage2. Classical Dichotomy3. Neutrality of MoneyC. A Change in Current Total Factor Productivity1. Real Effects2. Price-Level EffectsD. Shifts in Money Demand1. Sourcesa. Information Technology and Banking Costsb. New Financial Instrumentsc. Government Regulationsd. Perceived Riskiness of Bankse. Changes in Circumstances in the Banking System2. Neutrality vis-à-vis Real Variables3. Price-L evel EffectsE. Monetary Policy Rules1. Under Perfect Information2. Money Supply Targeting3. Nominal Interest Rate Targeting4. The Taylor RuleTextbook Question SolutionsQuestions for Review1. Money serves as a medium of exchange, a store of value, and a unit of account.2. Measures of the money supply include M 0, M 1, and M 2. The monetary base, M 0, includes all currency outside of currency held by the Federal Reserve, and deposits of depositary institutions at the FederalReserve. M 1 includes all currency held by the public (as opposed to bank vaults, the Fed, and the U.S. Treasury), plus travelers’ checks, demand deposits, and other checkable deposits. M 2 includes all of M 1 plus savings deposits, small-denomination time deposits, and retail money market mutual funds.104 Williamson ? Macroeconomics, Third Edition3. Use of money, as opposed to barter in goods or credit, solves the problem of the double coincidenceof wants.4. The nominal rate of interest is approximately equal to the real rate of interest plus the rate of inflation. The exact relationship is:(1)1(1)R r i ++=+ 5. The real rate of return on money is approximately equal to minus the rate of inflation. If we define thereal rate of return on money as ,m r then the exact relationship is:11(1)m r i +=+ 6. The demand for money stems from the desire of consumers to hold money to make purchases. Thosecan be made with a debit card as well, but this is costly, so the consumer decides in advance how much money to withdraw from the bank account. In addition, firms demand money in a similar way so that they can purchase investment goods.7. A permanent, once-and-for-all increase in the money supply has no effect on the real economy. Thatis, money is neutral. The only effect of the increase in the money supply is a permanent, proportionate increase in the price level.8. The government can change the money supply through a temporary tax cut (a helicopter drop), anopen-market operation, and seigniorage.9. The steady-state effects of an increase in the money growth rate include an increase in the rate ofinflation, a reduction in output, a reduction in employment, an increase in the real wage, and anincrease in the nominal interest rate.10. A change in the cost of banking services alters the trade-off between withdrawing money inadvance for purchases and using the debit card. For example, if the cost decreases, thenconsumers and firms will use debit cards more and will withdraw less cash, thus reducing thedemand for money.11. Money demand can increase if incomes rise (households then want to consume more and thus needmore cash, firms want to buy more investment goods and also need more cash), if the nominalinterest rate is lower, as then the opportunity cost of holding money is lower, and if prices are higher, as money demand is formulated in nominal terms. Money demand can be shifted by anything that would alter the cost of banking services, such as: new information technologies that lower the cost of accessing bank accounts, new financial instruments that lower the cost of banking, changes in bank regulation, changes in the perceived risk of banks, and changes in various circumstances in thebanking system.12. As money is neutral in this model, there is no real goal of any relevance, only a nominal goal. Thiswould be to keep inflation low in order to achieve nominal interest rates as low as possible to prevent households and firms to be constrained by the cash-in-advance constraint.13. A monetary policy rule establishes the money supply as a function of observable aggregates. Threeexamples are money supply targeting, nominal interest rate targeting, and the Taylor rule.Chapter 10 A Monetary Intertemporal Model: Money, Prices, and Monetary Policy 105 14. Money supply targeting implies no change of money supply in response to any of the three shifts,leading to price changes and the failure of the price stability goal. Nominal interest rate targeting achieves price stability in response to money demand shocks, but not to output demand or supply shocks. The Taylor Rule has ambiguous consequences with the model we have studied so far. Problems1. Bank service function with fixed cost.(a) This fix cost can be interpreted as the cost of obtaining a debit card, which is independent of thecost of using it.(b) None, as HXis unaffected.(c) It will change the level of money demand, but it has no impact on the slope of money demand oron its shifts in reaction to various circumstances. Indeed, the slope of H(X), or J(R), is still thesame.(d) With a higher D, households make the same choice of banking services, as X must be such thatHX = R, and HXhas not changed. The same applies to the firm. Thus, there is change to thedemand for money and no change to the price level.2. Zero nominal interest rate.(a) Now HX=0, which can only be achieved at X =0.(b) None. Banks are not used at all.(c) Household and firms have no reason to hold any bonds, as their return is the same as money andit costs to use the debit card. So everything is done with cash, and economic agents are notconstrained by the cash-in-advance constraint anymore. However, in order to achieve a zeronominal interest rate, it implies that the inflation rate should be the opposite of the real interestrate, that is negative. This happens only rarely.3. Government spending in the monetary intertemporal model.(a) The real effects of a temporary increase in government spending are the same as those in the realintertemporal model. Output and employment increase, the real interest rate increases, and thereal wage decreases. The new consideration is the effect on the price level. The increase inincome causes money demand to increase. The increase in the real interest rate causes thedemand for money to decrease. With a fixed supply of money, the price level must change tokeep money supply and money demand equal. If the income effect on money demand is stronger, then prices must decrease. If the interest rate effect on money demand is stronger, then pricesmust increase.(b) The real effects of a permanent increase in government spending are the same as those in the realintertemporal model. Output and employment increase, the real interest rate decreases, and thereal wage decreases. In this case the effects of the increase in income and the decrease in theinterest rate both work to increase money demand. In this case, the price level unambiguouslydeclines.4. The real effects of a decrease in the capital stock are the same as those in the real intertemporalmodel. The decrease in K leads to an increase in the real interest rate and a decrease in the real wage.The effects on output and employment are uncertain, although it may be somewhat more likely that output will decrease. A decrease in output along with an increase in the real interest rate both work to decrease money demand. Therefore, the price level would need to increase to keep money supply and money demand equal.5. The current-period real effects of the future increase in total factor productivity are the same as thosepredicted by the real intertemporal model. Output and employment increase, the real wage decreases, and the real interest rate increases. The increase in output increases money demand and the current price level increases.106 Williamson ? Macroeconomics, Third Edition6. The increased presence of ATMs would allow consumers to get by holding less money. Therefore,this disturbance shifts the money demand curve to the left, so the price level would increase to keep money demand and money supply equal.7. Implementing a nominal interest rate rule.(a) This increase in housing construction may arise from household confidence, for example afteran increase in the stock price. Thus we have a temporary increase in money demand with areduction in prices. To lower the nominal interest rate, the monetary authority increases themoney supply, which raises prices to the previous level. Price stabilization is successful.(b) This is like a drop in current total factor productivity with no consequence for future total factorproductivity. Thus, we have a shift to the left of output supply, reducing output and increasingthe real interest rate. Money demand thus drops and prices increase. The monetary authorityshould react by increasing the money supply to reduce the nominal interest rate to the target, but this increases prices further. Prices are then not stable as intended.(c) We learn that total factor productivity is up, and permanently so. This implies that both outputdemand and supply increase, the real interest rate drops, and that money demand shifts to theright leading to lower prices. Under a nominal interest rate target rule, the monetary authoritywould increase the nominal interest rate by reducing the money supply, thus further reducingprices. Prices are then not stable as intended.8. Textbook Chapter 9 discusses the likely effects of a permanent increase in government spending inthe real intertemporal model. As depicted in textbook Figure 9.18, a permanent increase ingovernment spending increases output. This effect works in the direction of increasing the demand for money. In the figure below, the initial price level is P*. With the money supply fixed at M, the price level decreases to ?.P To keep the price level at P*, the money supply must increase to .M If the central bank were pursuing a policy of price-level stabilization, the central bank would find it useful to be able to accurately predict the advent of this disturbance.。
威廉森宏观经济学有投资的实际跨期模型PPT课件
原文：As we show, a firm invests more the lower its current capital stock, the higher its expected future total factor productivity, and the lower the real interest rate.
9பைடு நூலகம்19
企业的劳动需求
Copyright © 2012 蔡晓陈. All rights reserved.
9-20
全要素生产率或资本存量变化时 的劳动需求需求移动
Copyright © 2012 蔡晓陈. All rights reserved.
9-21
Representative代表性企业投资决 策
9-11
实际利率提高对当期劳动供给 的影响（闲暇的跨期替代效应）
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9-12
一生财富增加对当期劳动供给 曲线的影响
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当前消费需求（参见第八章）
4、第三版，P300，式(10.15)应改为
A P Y P I P H ( X f) B f( 1 R ) B f
5、第三版，P300，式(10.16)应改为
A P Y P X f P H (X f)
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
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第三节 政府
• 政府 ☆假设
1、当期购买G单位的消费品，未来购买G’单位的消费品； 2、当期的总税收是T，未来的总税收是T’； 3、政府当期发行B单位的政府债券；
宏观经济学 斯蒂芬威廉森chap07
Macroeconomics, 3e (Williamson)Chapter 7 I ncome Disparity Among Countries and Endogenous Growth1) I ncome per worker has beenA) c onverging in both the rich countries and the poor countries.B) c onverging in the rich countries, but not converging in the poor countries.C) c onverging in the poor countries, but not converging in the rich countries.D) c onverging in neither the poor nor the rich countries.Answer: BQuestion Status: P revious Edition2) F or the Solow model to accurately explain the observed divergence of growth experiencearound the world would requireA) d ifferences in savings rates across countries.B) d ifferences in population growth rates across countries.C) b arriers to the introduction of new technologies.D) i nadequate educational opportunities in poor countries.Answer: CQuestion Status: P revious Edition3) I n the Solow growth model, countries with identical total factor productivities, identicallabor force growth rates, and identical savings ratesA) a lways have identical levels of capital per worker and output per worker.B) i n equilibrium, have identical levels of capital per worker and output per worker.C) i n equilibrium, have identical levels of capital per worker but not necessarily identicallevels of output per worker.D) i n equilibrium, have identical levels of output per worker but not necessarily identicallevels of capital per worker.Answer: BQuestion Status: P revious Edition4) S uppose that two countries share identical levels of total factor productivity, identical laborforce growth rates and identical savings rates. According to the Solow modelA) t he country with the greater initial level of output per worker will grow more rapidlythan the country with the smaller initial level of output per worker.B) t he country with the smaller initial level of output per worker will grow more rapidlythan the country with the greater initial level of output per worker.C) b oth countries will have the same growth rates of output per worker, even if they startout with different levels of output per worker.D) i f both countries start out with different levels of income per worker, both countriesmay have different growth rates of output per worker, but we cannot be certain whichcountry will have the higher growth rate of output per worker.Answer: BQuestion Status: P revious Edition5) I n the context of the Solow growth model, so-called growth miracles, such as Japan, SouthKorea, Singapore, and Hong Kong, are most easily explained byA) r eductions in the population growth rate.B) i ncreases in the savings rate.C) r emoval of barriers to technology.D) i mprovements in public health.Answer: CQuestion Status: P revious Edition6) S uppose a poor economy inches towards the steady state in Solow's exogenous growthmodel. What happens?A) C onsumption per capita decreases.B) S aving per capita decreases.C) T he depreciation rate increases.D) T he growth rate of output decreases.Answer: DQuestion Status: N ew7) S uppose a poor economy inches towards the steady state in Solow's exogenous growthmodel. What happens?A) C apital grows faster than population.B) C apital grows slower than population.C) C apital grows as fast as population.D) I t depends.Answer: AQuestion Status: N ew8) W hat happens to a poor economy in Solow's exogenous growth model?A) I t becomes poorer.B) I t does not change.C) I ts consumption per capita decreases.D) I ts saving per capita increases.Answer: DQuestion Status: N ew9) W hat happens to a very rich economy in Solow's exogenous growth model?A) I t becomes poorer.B) I t does not change.C) I ts consumption per capita increases.D) I ts saving per capita increases.Answer: AQuestion Status: N ew10) A ccording to Solow's exogenous growth theory, what happens to a country at steady statethat suffered extensive capital destruction due to a war or climate event?A) I t will stay poor forever.B) I t will grow back to be richer than before.C) I t will get back to its original status.D) A nything can happen.Answer: CQuestion Status: N ew11) B arriers to Riches, by S. Parente and E. Prescott, emphasizes the importance ofA) b arriers to technological adoption.B) b arriers to the development of natural resources.C) p ublic education.D) e ndogenous growth.Answer: AQuestion Status: P revious Edition12) T he importance of barriers to the adoption of technologies is supported by research byA) P. Romer.B) R. Lucas.C) S. Parente and E. Prescott.D) G. Glomm and B. Ravikumar.Answer: CQuestion Status: P revious Edition13) I n the endogenous growth models of Lucas and Romer, an increase in a worker's level ofhuman capitalA) i ncreases the amount of additional human capital she can produce, but does notincrease the amount of output she can produce.B) i ncreases the amount of additional output she can produce, but does not increase theamount of human capital she can produce.C) i ncreases both the amount of additional human capital she can produce and theamount of output she can produce.D) i ncreases neither the amount of additional human capital she can produce nor theamount of output she can produce.Answer: CQuestion Status: P revious Edition14) I n the endogenous growth models of Lucas and Romer, workers divide their time betweenmarket work andA) a ccumulating physical capital.B) a ccumulating human capital.C) t rying to invent new production processes.D) w ork at home.Answer: BQuestion Status: P revious Edition15) E ndogenous growth theory is aboutA) t he welfare of indigenous people.B) e xplaining growth.C) s tudying fertility choices.D) g iving more importance to capital accumulation.Answer: BQuestion Status: N ew16) I n the endogenous growth models of Lucas and Romer, human capital accumulation is bestdescribed as a form ofA) c onsumption.B) i nvestment.C) g overnment spending.D) n one of the aboveAnswer: BQuestion Status: P revious Edition17) H uman capital isA) k nowledge found in books.B) k nowledge found in people.C) w ealth.D) m achines owned by people.Answer: BQuestion Status: N ew18) W hich of the following statements best describes the characteristics of accumulatingphysical capital and human capital?A) B oth physical capital accumulation and human capital accumulation are characterizedby decreasing marginal returns.B) P hysical capital accumulation is subject to decreasing marginal returns, but humancapital accumulation is not.C) H uman capital accumulation is subject to decreasing marginal returns, but physicalcapital accumulation is not.D) N either physical capital accumulation nor human capital accumulation ischaracterized by decreasing marginal returns.Answer: BQuestion Status: P revious Edition19) P aul Romer argues that a key feature of knowledge isA) d ivisibility.B) p rivate ownership.C) n onrivalry.D) d urability.Answer: CQuestion Status: P revious Edition20) W hat is a characteristic of human capital?A) r ivalryB) r apid accumulationC) p rivate ownershipD) c oncavityAnswer: CQuestion Status: N ew21) W hat characteristic of human capital is crucial in giving the possibility of sustained growth?A) I t is embodied in people.B) I t has constant returns to scale in production.C) I t takes time to accumulate it.D) I t grows at the same rate as consumption.Answer: BQuestion Status: N ew22) W hat characteristic do human and physical capital share?A) B oth are controlled by the government.B) C urrent costs are incurred for future benefits.C) T heir growth depends crucially on the growth of total factor productivity.D) T he use of both exhibits rivalry.Answer: BQuestion Status: N ew23) W hich of the following is best characterized as being nonrivalrous?A) c onsumption goodsB) s ervicesC) p hysical capitalD) k nowledgeAnswer: DQuestion Status: P revious Edition24) A key characteristic of the production function in the endogenous growth model presentedin the text is thatA) t here are increasing returns to scale in human capital.B) t here are decreasing returns to scale in human capital.C) t here are constant returns to scale in human capital.D) a t low levels of human capital, there are increasing returns to scale in human capital,while at high levels of human capital, there are decreasing returns to scale in humancapital.Answer: CQuestion Status: P revious Edition25) I n the endogenous growth model presented in the text, suppose that u represents thefraction of time spent working (as opposed to accumulating human capital), b represents the efficiency of human capital accumulation, H represents the amount of human capital, and z represents the marginal product of efficiency units of labor. Consumption equalsA) b uH.B) z uH.C) b uz.D) b uzH.Answer: BQuestion Status: R evised26) I n the endogenous growth model presented in the text, suppose that u represents thefraction of time spent working (as opposed to accumulating human capital) and b represents the efficiency of human capital accumulation. The growth rate of human capital equalsA) u(1- b) - 1.B) 1+b(1 -u).C) (1 +b)(1 -u).D) b(1 -u) - 1.Answer: DQuestion Status: P revious Edition27) I n the endogenous growth model presented in the text, suppose that u represents thefraction of time spent working (as opposed to accumulating human capital) and b represents the efficiency of human capital accumulation. The growth rate of consumption equalsA) u(1- b) - 1.B) 1+b(1 -u).C) (1 -b)(1 -u).D) b(1 -u) - 1.Answer: DQuestion Status: P revious Edition28) I n the endogenous growth model presented in the text,A) c onsumption grows faster than human capital.B) h uman capital grows faster than consumption.C) b oth consumption and human capital grow at the same rate.D) n either consumption nor human capital grows in the steady state.Answer: CQuestion Status: P revious Edition29) I n the endogenous growth model presented in the text, an increase in the efficiency ofhuman capital accumulationA) i ncreases the growth rate of human capital and increases the growth rate of output.B) i ncreases the growth rate of human capital and decreases the growth rate of output.C) d ecreases the growth rate of human capital and increases the growth rate of output.D) d ecreases the growth rate of human capital and decreases the growth rate of output.Answer: AQuestion Status: P revious Edition30) I n the endogenous growth model presented in the text, an increase in the fraction of timeaccumulating human capitalA) i ncreases the growth rate of human capital and increases the growth rate of output.B) i ncreases the growth rate of human capital and decreases the growth rate of output.C) d ecreases the growth rate of human capital and increases the growth rate of output.D) d ecreases the growth rate of human capital and decreases the growth rate of output.Answer: AQuestion Status: P revious Edition31) A n example of an increase in b, the efficiency of human capital accumulation, isA) m ore mandatory school years.B) b etter teachers.C) b etter school material.D) b etter total factor productivity.Answer: CQuestion Status: N ew32) W hich of the following policies would increase the growth rate of an economy in theendogenous growth model with human capital?A) M andatory schooling.B) M inimum wages.C) R edistributive taxation.D) L ump-sum taxation.Answer: AQuestion Status: N ew33) A ccording to the endogenous growth model with human capital, what can we say aboutcountries with more efficient schools?A) T hey are richer.B) T hey are richer and grow faster.C) T hey are richer and grow more slowly.D) T hey grow faster.Answer: DQuestion Status: N ew34) T he idea that contact with others with high levels of human capital increases ones ownhuman capital is called human capitalA) c ontagion.B) e xternality.C) t ransference.D) c onvergence.Answer: BQuestion Status: P revious Edition35) S chooling is subsidized in the United States in partA) s o that the golden rule capital level can be reached.B) b ecause otherwise people would not get educated.C) b ecause there is a constitutional right to education.D) b ecause there is a positive externality from schooling.Answer: DQuestion Status: N ew36) A n improvement in school quality translates into an increase in which model parameter?A) HB) zC) bD) 1-uAnswer: CQuestion Status: N ew37) E vidence suggests that income per worker and education areA) n egatively correlated.B) p ositively correlated.C) u ncorrelated.D) p ositively correlated in the richer countries and negatively correlated in the poorercountries.Answer: BQuestion Status: P revious Edition38) W hat immediate consequence does an increase in education time have in the endogenousgrowth model with human capital?A) l ower outputB) l ower output in the futureC) l ower wagesD) l ower human capitalAnswer: AQuestion Status: N ew39) A study by Gerhard Glomm and B. Ravikumar suggests that relying more on privateeducation relative to public education results inA) m ore income inequality and higher per-capita income in the long run.B) m ore income inequality and lower per-capita income in the long run.C) l ess income inequality and higher output per worker in the long run.D) l ess income inequality and lower output per worker in the long run.Answer: AQuestion Status: P revious Edition。
宏观经济学-课后思考题答案_史蒂芬威廉森002
Chapter 2MeasurementTeaching GoalsStudents must understand the importance of measuring aggregate economic activity. Macroeconomics hopes to produce theories that provide useful insights and policy conclusions. To be credible, such theories must produce hypotheses that evidence could possibly refute. Macroeconomic measurement provides such evidence. Without macroeconomic measurements, macroeconomics could not be a social science, and would rather consist of philosophizing and pontificating. Market transactions provide the most simple and direct measurements. Macroeconomists’ most basic measurement is Gross Domestic Product (GDP), the value of final, domestically market output produced during a given period of time.In the United States, the Commerce Department’s National Income and Product Accounts provide official estimates of GDP. These accounts employ their own set of accounting rules to ensure internal consistency and to provide several separate estimates of GDP. These separate estimates are provided by the product accounts, the expenditure accounts, and the income accounts. The various accounting conventions may, at first glance, be rather dry and complicated. However, students can only easily digest the material in later chapters if they have a good grounding in the fundamentals.GDP changes through time because different amounts of goods and services are produced, and such goods and services are sold at different prices. Standards of living are determined by the amounts of goods and services produced, not by the prices they command in the market. While GDP is relatively easy to measure, the decomposition of changes in real GDP into quantity and price components is much more difficult. This kind of problem is less pressing for microeconomists. It is easy to separately measure the number of apples sold and the price of each apple. Because macroeconomics deals with aggregate output, the differentiation of price and quantity is much less easily apparent. It is important to emphasize that while there may be more or less reasonable approaches to this problem, there is no unambiguous best approach. Since many important policy discussions involve debates about output and price measurements, it is very important to understand exactly how such measurements are produced.Classroom Discussion TopicsAs the author demonstrates in presenting this chapter’s material, much of this material is best learned by example. Rather than simply working through the examples from the text or making up your own, the material may resonate better if the students come up with their own examples. They can start by picking a single good, and by the choice of their numbers they provide their own implied decomposition of output into wage and profit income. Later on, encourage them to suggest intermediate input production, inventory adjustments, international transactions, a government sector, and so on. Such an exercise may help assure them that the identities presented in the text are more than simply abstract constructions.If many of your students are familiar with accounting principles, it may also be useful to present the National Income and Product Account with the “T” accounts. Highlighting how every income is an expense elsewhere. Make one account for each of the firms, one for the household and one for the government. Add another account for the rest of the world when discussing the example with international trade. This procedure can highlight how some entities can be inferred from others because accounting10 Williamson • Macroeconomics, Third Editionidentities must hold. It makes it also easier to determine consumption for some student Social Security benefits are indexed to the Consumer Price Index. Explain with an example exactly how these adjustments are made. Ask the students if they think that this procedure is “fair.” Another topic for concern is the stagnation in the growth of measured real wages. Real wages are measured by dividing (for example) average hourly wages paid in manufacturing by the consumer price index. Ask students if measured changes in real wages confirm or conflict with their general beliefs about whether the typical worker is better or worse off than 10 or 20 years ago. How does possible mis-measurement of prices reconcile any apparent differences between casual impressions and statistical evidence?The text discusses why unemployment may or may not be a good measure of labor market tightness. Another interpretation of the unemployment rate is as a(n inverse) measure of economic welfare. Ask the students if they agree with this interpretation. Does the unemployment rate help factor in considerations like equal distribution of income? How can the unemployment rate factor in considerations like higher income per employed worker? Discuss possible pros and cons of using unemployment rather than per capita real GDP as a measure of well-being. Can unemployment be too low? Why or why not?OutlineI. Measuring GDP: The National Income and Product AccountsA. What Is GDP and How Do We Measure It?1. GDP: Value of Domestically Produced Output2. Commerce Department’s National Income and Product Accounts3. Business, Consumer, and Government AccountingB. The Product Approach1. Value Added2. Intermediate Good InputsC. The Expenditure Approach1. Consumption2. Investment3. Government Spending4. Net ExportsD. The Income Approach1. Wage Income2. After-Tax Profits3. Interest Income4. Taxes5. The Income-Expenditure IdentityE. Gross National Product (GNP)1. Treatment of Foreign Income2. GNP = GDP + Net Foreign IncomeF. What Does GDP Leave Out?1. GDP and Welfarea. Income Distributionb. Non-Market Production2. Measuring Market Productiona. The Underground Economyb. Valuing Government ProductionChapter 2 Measurement 11G. Expenditure Components1. Consumptiona. Durable Goodsb. Non-Durable Goodsc. Services2. Investmenta. Fixed Investment: Nonresidential and Residentialb. Inventory Investment3. Net Exportsa. Exportsb. Imports4. Government Expendituresa. Federal Defenseb. Federal Non-Defensec. State and Locald. Treatment of Transfer PaymentsII. Nominal and Real GDP and Price IndicesA. Real GDP1. Output Valued at Base Year Prices2 Chain Weighted Real GDPB. Measures of the Price Level1. Implicit GDP Price Deflator2. Consumer Price Index (CPI)C. Problems Measuring Real GDP and Prices1. Substitution Biases2. Accounting for Quality Changes3. Treatment of Newly Introduced GoodsIII. Savings, Wealth, and CapitalA. Stocks and FlowsB. Private Disposable Income and Private Sector Saving1.d Y Y NFP TR INT T =+++− 2.p d S Y C =− C. Government Surpluses, Deficits, and Government Saving1.g S T TR INT G =−−− 2. g D S =− D. National Saving: p g S S S Y NFP C G =+=+−−E. Saving, Investment, and the Current Account1. NFP NX I S ++=2. CA I S NFP NX CA +=⇒+=F. The Stock of Capital1. Wealth ΔS ⇒2. K I Δ⇒3. Claims on Foreigners CA ⇒12 Williamson • Macroeconomics, Third EditionIV. Labor Market MeasurementA. BLS Categories1. Employed2. Unemployed3. Not in the Labor ForceB. The Unemployment RateNumber unemployed=Unemployment RateLabor forceC. The Participation RateLabor force=Participation RateTotal working age populationD. Unemployment and Labor Force Tightness1. Discouraged Workers2. Job Search IntensityTextbook Question SolutionsQuestions for Review1. Product, income, and expenditure approaches.2. For each producer, value added is equal to the value of total production minus the cost ofintermediate inputs.3. This identity emphasizes the point that all sales of output provide income somewhere in the economy.The identity also provides two separate ways of measuring total output in the economy.4. GNP is equal to GDP (domestic production) plus net factor payments from abroad. Net factorpayments represent income for domestic residents that are earned from production that takes place in foreign countries.5. GDP provides a reasonable approximation of economic welfare. However, GDP ignores the value ofnonmarket economic activity. GDP also measures only total income without reference to how that income is distributed.6. Measured GDP does not include production in the underground economy, which is difficult toestimate. GDP also measures the value of government spending at its cost of production, which may be greater or less than its true value.7. The largest component is consumption, which represents about 2/3 of GDP.8. Investment is equal to private, domestic expenditure on goods and services (Y − G − NX) minusconsumption. Investment includes residential investment, nonresidential investment, and inventory investment.9. National defense spending represents about 5% of GDP.Chapter 2 Measurement 13 10. GDP values production at market prices. Real GDP compares different years’ production at a specificset of prices. These prices are those that prevailed in the base year. Real GDP is therefore a weighted average of individual production levels. The weights are determined according to prevailing relative prices in the base year. Because relative prices change over time, comparisons of real GDP across time can differ according to the chosen base year.11. Chain weighting directly compares production levels only in adjacent years. The price weights aredetermined by averaging the prices of the individual goods and services over the two adjacent years.12. Real GDP is difficult to measure due to changes over time in relative prices, difficulties in estimatingthe extent of quality changes, and how one estimates the value of newly introduced goods.13. Private saving measures additions to private sector wealth. Government saving measures reductionsin government debt (increases in government wealth). National saving measures additions to national wealth. National saving is equal to private saving plus government saving.14. National wealth is accumulated as increases in the domestic stock of capital (domestic investment)and increases in claims against foreigners (the current account surplus).15. Measured unemployment excludes discouraged workers. Measured unemployment only accounts forthe number of individuals unemployed, without reference to how intensively they search for newjobs.Problems1. Product accounting adds up value added by all producers. The wheat producer has no intermediateinputs and produces 30 million bushels at $3/bu. for $90 million. The bread producer produces100 million loaves at $3.50/loaf for $350 million. The bread producer uses $75 million worth ofwheat as an input. Therefore, the bread producer’s value added is $275 million. Total GDP istherefore $90 million + $275 million = $365 million.Expenditure accounting adds up the value of expenditures on final output. Consumers buy100 million loaves at $3.50/loaf for $350 million. The wheat producer adds 5 million bushels ofwheat to inventory. Therefore, investment spending is equal to 5 million bushels of wheat valued at $3/bu., which costs $15 million. Total GDP is therefore $350 million + $15 million = $365 million.2. Coal producer, steel producer, and consumers.(a) (i) Product approach: Coal producer produces 15 million tons of coal at $5/ton, which adds$75 million to GDP. The steel producer produces 10 million tons of steel at $20/ton, whichis worth $200 million. The steel producer pays $125 million for 25 million tons of coal at$5/ton. The steel producer’s value added is therefore $75 million. GDP is equal to$75 million + $75 million = $150 million.(ii) Expenditure approach: Consumers buy 8 million tons of steel at $20/ton, so consumption is $160 million. There is no investment and no government spending. Exports are 2 milliontons of steel at $20/ton, which is worth $40 million. Imports are 10 million tons of coal at$5/ton, which is worth $50 million. Net exports are therefore equal to $40 million −$50 million =−$10 million. GDP is therefore equal to $160 million + (−$10 million) =$150 million.14 Williamson • Macroeconomics, Third Edition(iii) Income approach: The coal producer pays $50 million in wages and the steel producer pays $40 million in wages, so total wages in the economy equal $90 million. The coal producerreceives $75 million in revenue for selling 15 million tons at $15/ton. The coal producerpays $50 million in wages, so the coal producer’s profits are $25 million. The steel producerreceives $200 million in revenue for selling 10 million tons of steel at $20/ton. The steelproducer pays $40 million in wages and pays $125 million for the 25 million tons ofcoal that it needs to produce steel. The steel producer’s profits are therefore equal to$200 million − $40 million − $125 million = $35 million. Total profit income in theeconomy is therefore $25 million + $35 million = $60 million. GDP therefore is equal towage income ($90 million) plus profit income ($60 million). GDP is therefore $150 million.(b) There are no net factor payments from abroad in this example. Therefore, the current accountsurplus is equal to net exports, which is equal to (−$10 million).(c) As originally formulated, GNP is equal to GDP, which is equal to $150 million. Alternatively, ifforeigners receive $25 million in coal industry profits as income, then net factor payments from abroad are (−$25 million), so GNP is equal to $125 million.3. Wheat and Bread(a) Product approach: Firm A produces 50,000 bushels of wheat, with no intermediate goods inputs. At$3/bu., the value of Firm A’s production is equal to $150,000. Firm B produces 50,000 loaves ofbread at $2/loaf, which is valued at $100,000. Firm B pays $60,000 to firm A for 20,000 bushels of wheat, which is an intermediate input. Firm B’s value added is therefore $40,000. GDP is therefore equal to $190,000.(b) Expenditure approach: Consumers buy 50,000 loaves of domestically produced bread at $2/loafand 15,000 loaves of imported bread at $1/loaf. Consumption spending is therefore equal to$100,000 + $15,000 = $115,000. Firm A adds 5,000 bushels of wheat to inventory. Wheat isworth $3/bu., so investment is equal to $15,000. Firm A exports 25,000 bushels of wheat for$3/bu. Exports are $75,000. Consumers import 15,000 loaves of bread at $1/loaf. Imports are$15,000. Net exports are equal to $75,000 − $15,000 = $60,000. There is no governmentspending. GDP is equal to consumption ($115,000) plus investment ($15,000) plus net exports($60,000). GDP is therefore equal to $190,000.(c) Income approach: Firm A pays $50,000 in wages. Firm B pays $20,000 in wages. Total wagesare therefore $70,000. Firm A produces $150,000 worth of wheat and pays $50,000 in wages.Firm A’s profits are $100,000. Firm B produces $100,000 worth of bread. Firm B pays $20,000in wages and pays $60,000 to Firm A for wheat. Firm B’s profits are $100,000 − $20,000 −$60,000 = $20,000. Total profit income in the economy equals $100,000 + $20, 000 = $120,000.Total wage income ($70,000) plus profit income ($120,000) equals $190,000. GDP is therefore$190,000.Chapter 2 Measurement 15 4. Price and quantity data are given as the following.Year 1Good Quanti tyPri ceComputers 20$1,000 Bread 10,000$1.00Year 2Good Quanti tyPri ceComputers 25$1,500Bread 12,000$1.10(a) Year 1 nominal GDP =×+×=20$1,00010,000$1.00$30,000.Year 2 nominal GDP =×+×=25$1,50012,000$1.10$50,700.With year 1 as the base year, we need to value both years’ production at year 1 prices. In the base year, year 1, real GDP equals nominal GDP equals $30,000. In year 2, we need to value year 2’s output at year 1 prices. Year 2 real GDP =×+×=25$1,00012,000$1.00$37,000. The percentage change in real GDP equals ($37,000 − $30,000)/$30,000 = 23.33%.We next calculate chain-weighted real GDP. At year 1 prices, the ratio of year 2 real GDP to year1 real GDP equals g1= ($37,000/$30,000) = 1.2333. We must next compute real GDP using year2 prices. Year 2 GDP valued at year 2 prices equals year 2 nominal GDP = $50,700. Year 1 GDPvalued at year 2 prices equals (20 × $1,500 + 10,000 × $1.10) = $41,000. The ratio of year 2 GDP at year 2 prices to year 1 GDP at year 2 prices equals g2=chain-weighted ratio of real GDP in the two years therefore is equal to 1.23496cg==. The percentage change chain-weighted real GDP from year 1 to year 2 is therefore approximately23.5%.If we (arbitrarily) designate year 1 as the base year, then year 1 chain-weighted GDP equals nominal GDP equals $30,000. Year 2 chain-weighted real GDP is equal to (1.23496 × $30,000) = $37,048.75.(b) To calculate the implicit GDP deflator, we divide nominal GDP by real GDP, and then multiplyby 100 to express as an index number. With year 1 as the base year, base year nominal GDP equals base year real GDP, so the base year implicit GDP deflator is 100. For the year 2, the implicit GDP deflator is ($50,700/$37,000) × 100 = 137.0. The percentage change in the deflator is equal to 37.0%.With chain weighting, and the base year set at year 1, the year 1 GDP deflator equals($30,000/$30,000) × 100 = 100. The chain-weighted deflator for year 2 is now equal to($50,700/$37,048.75) × 100 = 136.85. The percentage change in the chain-weighted deflator equals 36.85%.16 Williamson • Macroeconomics, Third Edition(c) We next consider the possibility that year 2 computers are twice as productive as year1 computers. As one possibility, let us define a “computer” as a year 1 computer. In this case,the 25 computers produced in year 2 are the equivalent of 50 year 1 computers. Each year 1computer now sells for $750 in year 2. We now revise the original data as:Year 1Good Quanti tyPri ceYear 1 Computers 20 $1,000Bread 10,000$1.00Year 2Good Quanti tyPri ceYear 1 Computers 50 $750Bread 12,000$1.10First, note that the change in the definition of a “computer” does not affect the calculations of nominal GDP. We next compute real GDP with year 1 as the base year. Year 2 real GDP in year 1 prices is now ×+×=50$1,00012,000$1.00$62,000. The percentage change in real GDP is equal to ($62,000 − $30,000)/$30,000 = 106.7%.We next revise the calculation of chain-weighted real GDP. From above, g1 equals($62,000/$30,000) = 206.67. The value of year 1 GDP at year 2 prices equals $26,000. Therefore,g 2 equals ($50,700/$26,000) = 1.95. 200.75. The percentage change chain-weighted real GDPfrom year 1 to year 2 is therefore 100.75%.If we (arbitrarily) designate year 1 as the base year, then year 1 chain-weighted GDP equalsnominal GDP equals $30,000. Year 2 chain-weighted real GDP is equal to (2.0075 × $30,000) = $60,225. The chain-weighted deflator for year 1 is automatically 100. The chain-weighteddeflator for year 2 equals ($50,700/$60,225) × 100 = 84.18. The percentage rate of change of the chain-weighted deflator equals −15.8%.When there is no quality change, the difference between using year 1 as the base year and using chain weighting is relatively small. Factoring in the increased performance of year 2 computers, the production of computers rises dramatically while its relative price falls. Compared withearlier practices, chain weighting provides a smaller estimate of the increase in production and a smaller estimate of the reduction in prices. This difference is due to the fact that the relative price of the good that increases most in quantity (computers) is much higher in year 1. Therefore, the use of historical prices puts more weight on the increase in quality-adjusted computer output. 5. Price and quantity data are given as the following:Year 1GoodQuantity(million lbs.)Price(per lb.)Broccoli 1,500 $0.50 Cauliflower 300$0.80Year 2GoodQuantity(million lbs.)Price(per lb.)Broccoli 2,400 $0.60 Cauliflower 350$0.85Chapter 2 Measurement 17(a) Year 1 nominal GDP = Year 1 real GDP =×+×=1,500million$0.50300million$0.80 $990million.Year 2 nominal GDP=×+×=2,400million$0.60350million$0.85$1,730.5million Year 2 real GDP=×+×=2,400million$0.50350million$0.80$1,450million.Year 1 GDP deflator equals 100.Year 2 GDP deflator equals ($1,730.5/$1,450) × 100 = 119.3.The percentage change in the deflator equals 19.3%.(b) Year 1 production (market basket) at year 1 prices equals year 1 nominal GDP = $990 million.The value of the market basket at year 2 prices is equal to ×+×1,500million$0.60300million $0.85= $1,050 million.Year 1 CPI equals 100.Year 2 CPI equals ($1,050/$990) × 100 = 106.1.The percentage change in the CPI equals 6.1%.The relative price of broccoli has gone up. The relative quantity of broccoli has also gone up. The CPI attaches a smaller weight to the price of broccoli, and so the CPI shows less inflation.6. Corn producer, consumers, and government.(a) (i) Product approach: There are no intermediate goods inputs. The corn producer grows30 million bushels of corn. Each bushel of corn is worth $5. Therefore, GDP equals$150 million.(ii) Expenditure approach: Consumers buy 20 million bushels of corn, so consumption equals $100 million. The corn producer adds 5 million bushels to inventory, so investment equals$25 million. The government buys 5 million bushels of corn, so government spendingequals $25 million. GDP equals $150 million.(iii) Income approach: Wage income is $60 million, paid by the corn producer. The corn producer’s revenue equals $150 million, including the value of its addition to inventory. Additions toinventory are treated as purchasing one owns output. The corn producer’s costs includewages of $60 million and taxes of $20 million. Therefore, profit income equals $150 million −$60 million − $20 million = $70 million. Government income equals taxes paid by the cornproducer, which equals $20 million. Therefore, GDP by income equals $60 million +$70 million + $20 million = $150 million.(b) Private disposable income equals GDP ($150 million) plus net factor payments (0) plusgovernment transfers ($5 million is Social Security benefits) plus interest on the government debt ($10 million) minus total taxes ($30 million), which equals $135 million. Private saving equalsprivate disposable income ($135 million) minus consumption ($100 million), which equals$35 million. Government saving equals government tax income ($30 million) minus transferpayments ($5 million) minus interest on the government debt ($10 million) minus governmentspending ($5 million), which equals $10 million. National saving equals private saving($35 million) plus government saving ($10 million), which equals $45 million. The government budget surplus equals government savings ($10 million). Since the budget surplus is positive, the government budget is in surplus. The government deficit is therefore equal to (−$10 million).18 Williamson • Macroeconomics, Third Edition7. Price controls.Nominal GDP is calculated by measuring output at market prices. In the event of effective pricecontrols, measured prices equal the controlled prices. However, controlled prices reflect an inaccurate measure of scarcity values. Nominal GDP is therefore distorted. In addition to distortions in nominal GDP measures, price controls also inject an inaccuracy in attempts to decompose changes in nominal GDP into movements in real GDP and movements in prices. With price controls, there is typically little or no change in white market prices over time. Alternatively, black market or scarcity value prices typically increase, perhaps dramatically. Measures of prices (in terms of scarcity values) understate inflation. Whenever inflation measures are too low, changes in real GDP overstate the extent of increases in actual production.8. Underground economy.Transactions in underground economy are performed with cash exclusively, to exploit the anonymous nature of currency. Thus, once we have established the amount of currency held abroad, we know the portion of $2,474 that is held domestically. Remove from it what is used for recorded transactions, say by using some estimate of the proportion of transactions using cash and applying this to observed GDP. Finally apply a concept of velocity of money to the remaining amount of cash to obtain the size of the underground economy.9. S p– 1 = CA + D(a) By definition:p d S Y C Y NFP TR INT T C =−=+++−− Next, recall that .Y C I G NX =+++ Substitute into the equation above and subtract I to obtain:()()p S I C I G NX NFP INT T C INX NFP G INT TR T CA D −=+++++−−−=++++−=+(b) Private saving, which is not used to finance domestic investment, is either lent to the domesticgovernment to finance its deficit (D ), or is lent to foreigners (CA ).10. Computing capital with the perpetual inventory method.(a) First, use the formula recursively for each year:K 0 = 80K 1 = 0.9 × 80 + 10 = 82K 2 = 0.9 × 82 + 10 = 83.8K 3 = 0.9 × 83.8 + 10 = 85.42K 4 = 0.9 × 85.42 + 10 = 86.88K 5 = 0.9 × 86.88 + 10 = 88.19K 6 = 0.9 × 88.19 + 10 = 89.37K 7 = 0.9 × 89.37 + 10 = 90.43K 8 = 0.9 × 90.43 + 10 = 91.39K 9 = 0.9 × 91.39 + 10 = 92.25K 10 = 0.9 × 92.25 + 10 = 93.03(b) This time, capital stays constant at 100, as the yearly investment corresponds exactly to theamount of capital that is depreciated every year. In (a), we started with a lower level of capital, thus less depreciated than what was invested, as capital kept rising (until it would reach 100).Chapter 2 Measurement 19 11. Assume the following:10540308010520D INT T G C NFP CA S =======−= (a)201080110d p Y S C S D C =+=++=++= (b)103054015D G TR INT T TR D G INT T =++−=−−+=−−+= (c)208030130S GNP C G GNP S C G =−−=++=++= (d)13010120GDP GNP NFP =−=−= (e)Government Surplus 10g S D ==−=− (f)51015CA NX NFP NX CA NFP =+=−=−−=− (g)12080301525GDP C I G NXI GDP C G NX =+++=−−−=−−+=。
宏观经济学-课后思考题答案_史蒂芬威廉森004
Chapter 4Consumer and Firm Behavior: The Work-Leisure Decision and Profit MaximizationTeaching GoalsThe microeconomic approach to macroeconomics stresses the notion that economy-wide events are the result of decisions made by individuals. People work so that they may afford to buy market goods. On the other hand, people generally prefer to work less rather than working more. Although discussions in the popular press often refer to the idea that spending is what drives the economy, an economy cannot produce unless people are willing to work. Therefore, the most basic macroeconomic decision is the decision to choose whether, and how much, to work. Production and willingness to work are intrinsically interconnected.Students often believe that how much a person works is largely determined by the necessities of their circumstances. Students will report that they have to work to survive and pay tuition. Some might point out that some students need not work much or at all because their parents provide more support. However, circumstances need not dictate exactly how much they may choose to work. They may work less if they go to a less costly school. They may sometimes decide to switch to part-time student status and full-time work status if they find a high-paying job. A key message of this chapter is that choice is important and that choice is influenced by changes in circumstances.This chapter demands the mastery of a large body of structure and yet provides little in the way of immediate insights. Students may need frequent assurances that the mastery of this material eventually pays big dividends in providing hope of understanding the phenomenon of business cycles. This is particularly important as this chapter lays critical foundations for the rest of the book: the use of microfoundations in macroeconomics. Students need to be able to justify macroeconomic relationships with microeconomic arguments, like in this chapter. This requires to some extend some boring drills that they will come to appreciate only later. If for many textbooks the strategy is to teach one chapter a week, spend more time on this one, especially if students have not yet mastered intermediate microeconomics. Two key points of this chapter are the concepts of income and substitution effects. Often, students are perplexed at the amount of time spent on this material because nothing in practice is purely an income effect or a substitution effect. However, the two most basic insights of microeconomic analysis are that when we become more well-off we generally want more of everything and that we respond to price incentives at the margin.Classroom Discussion TopicsAsk the students about their work choices and the choices of their parents, friends, and relatives. Does everyone work? Does everyone work the same amount of hours? Then ask the students for examples of the kinds of factors that lead people to work more or less. Try to elicit very specific examples. Thenask the students to categorize these factors that lead to more or less work. Some of these factors are actually the by-products of more complex decision making. For example, if they say that they work more or less because they go to school, point out that going to school is a choice. They may also point to28 Williamson • Macroeconomics, Third Editioncircumstances like whether a married couple has children, and if so, their number and their ages. Point out that these events are also the results of other choices. Then ask the students to try to categorize the remaining factors as being primarily an income effect or a substitution effect. Compare also labor choices across countries, as the Macroeconomics in Action feature, new to the third edition, does.Ask the students to provide examples of factors other than more labor or capital that can allow some countries to be a lot more productive than others. What factors other than growth in capital and labor allow a given economy to produce more (or less) over time? Explain that these are the kinds of factors that we summarize by the concept of total factor productivity. Insist also on the concept of physical capital and what it measures and what it is not.OutlineI. The Representative ConsumerA. Preferences1. Goods: The Consumption Good and Leisure2. The Utility Functiona. More Preferred to Lessb. Preference for Diversityc. Normal Goods3. Indifference Curvesa Downward Slopingb. Convex to the Origin4. Marginal Rate of SubstitutionB. Budget Constraint1. Price-taking Behavior2. The Time Constraint3. Real Disposable Income4. A Graphical RepresentationC. Optimization1. Rational Behavior2. The Optimal Consumption Bundle3. Marginal Rate of Substitution = Relative Price4. A Graphical RepresentationD. Comparative Statics Experiments1. Changes in Dividends and Taxes: Pure Income Effect2. Changes in the Real Wage: Income and Substitution EffectsII. The Representative FirmA. The Production Function1. Constant Returns to Scale2. Monotonicity3. Declining MPN4. Declining MPK5. Changes in Capital and MPN6. Total Factor ProductivityChapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 29B. Profit Maximization1. Profits = Total Revenue − Total Variable Costs2. Marginal Product of Labor = Real Wage3. Labor DemandTextbook Question SolutionsQuestions for Review1. Consumers consume an aggregate consumption good and leisure.2. Consumers’ preferences are summarized in a utility function.3. The first property is that more is always preferred to less. This property assures us that a consumptionbundle with more of one good and no less of the other good than any second bundle will always be preferred to the second bundle.The second property is that a consumer likes diversity in his or her consumption bundle. Thisproperty assures us that a linear combination of two consumption bundles will always be preferred to the two original bundles.The third property is that both consumption and leisure are normal goods. This property assures us that an increase in a consumer’s income will always induce the individual to consume more of both consumption and leisure.4. The first property of indifference curves is that they are downward sloping. This property is a directconsequence of the property that more is always preferred to less. The second property ofindifference curves is that they are bowed toward the origin. This property is a direct consequence of consumers’ preference for diversity.5. Consumers maximize the amount of utility they can derive from their given amount of availableresources.6. The optimal bundle has the property that it represents a point of tangency of the budget line with anindifference curve. An equivalent property is that the marginal rate of substitution of leisure forconsumption and leisure is equal to the real wage.7. In response to an increase in dividend income, the consumer will consume more goods and moreleisure.8. In response to an increase in the real value of a lump-sum tax, the consumer will consume less goodsand less leisure.9. An increase in the real wage makes the consumer more well off. As a result of this pure incomeeffect, the consumer wants more leisure. Alternatively, the increase in the real wage induces asubstitution effect in which the consumer is willing to consume less leisure in exchange for working more hours (consuming less leisure). The net effect of these two competing forces is theoretically ambiguous.10. The representative firm seeks to maximize profits.30 Williamson • Macroeconomics, Third Edition11. As the amount of labor is increased, holding the amount of capital constant, each worker gets asmaller share of the fixed amount of capital, and there is a reduction in each worker’s marginalproductivity.12. An increase in total factor productivity shifts the production function upward.13. The representative firm’s profit is equal to its production (revenue measured in units of goods) minusits variable labor costs (the real wage times the amount of labor input). A unit increase in labor input adds the marginal product of labor to revenue and adds the real wage to labor costs. The amount of labor demand is that amount of labor input that equates marginal revenue with marginal labor costs.This quantity of labor, labor demand, can simply be read off the marginal product of labor schedule.Problems1. Consider the two hypothetical indifference curves in the figure below. Point A is on both indifferencecurves, I1 and I2. By construction, the consumer is indifferent between A and B, as both points are onI 2. In like fashion, the consumer is indifferent between A and C, as both points are on I1. But atpoint C, the consumer has more consumption and more leisure than at point B. As long as the consumer prefers more to less, he or she must strictly prefer C to A. We therefore contradict the hypothesis that two indifference curves can cross.Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 312. u al bC =+(a) To specify an indifference curve, we hold utility constant at u . Next rearrange in the form:u a C l b b=− Indifference curves are therefore linear with slope, −a /b , which represents the marginal rate ofsubstitution. There are two main cases, according to whether /a b w > or /.a b w < The top panelof the left figure below shows the case of /.a b w < In this case the indifference curves are flatterthan the budget line and the consumer picks point A, at which 0l = and .C wh T π=+− Theright figure shows the case of /.a b w > In this case the indifference curves are steeper than thebudget line, and the consumer picks point B, at which l h = and .C T π=− In the coincidentalcase in which /,a b w = the highest attainable indifference curve coincides with the indifference curve, and the consumer is indifferent among all possible amounts of leisure and hours worked.(b) The utility function in this problem does not obey the property that the consumer prefersdiversity, and is therefore not a likely possibility.(c) This utility function does have the property that more is preferred to less. However, the marginalrate of substitution is constant, and therefore this utility function does not satisfy the property ofdiminishing marginal rate of substitution.32 Williamson • Macroeconomics, Third Edition3. When the government imposes a proportional tax on wage income, the consumer’s budget constraintis now given by:(1)(),C w t h l T π=−−+−where t is the tax rate on wage income. In the figure below, the budget constraint for t = 0, is FGH.When t > 0, the budget constraint is EGH. The slope of the original budget line is –w , while the slope of the new budget line is –(1 – t )w . Initially the consumer picks the point A on the original budget line. After the tax has been imposed, the consumer picks point B. The substitution effect of theimposition of the tax is to move the consumer from point A to point D on the original indifference curve. The point D is at the tangent point of indifference curve, I 1, with a line segment that is parallel to EG. The pure substitution effect induces the consumer to reduce consumption and increase leisure (work less).The tax also makes the consumer worse off, in that he or she can no longer be on indifference curve,I 1, but must move to the less preferred indifference curve, I 2. This pure income effect moves the consumer to point B, which has less consumption and less leisure than point D, because bothconsumption and leisure are normal goods. The net effect of the tax is to reduce consumption, but the direction of the net effect on leisure is ambiguous. The figure shows the case in which the substitution effect on leisure dominates the income effect. In this case, leisure increases and hours worked fall. Although consumption must fall, hours worked may rise, fall, or remain the same.4. The increase in dividend income shifts the budget line upward. The reduction in the wage rate flattensthe budget line. One possibility is depicted in the figures below. The original budget constraint HGL shifts to HFE. There are two income effects in this case. The increase in dividend income is a positive income effect. The reduction in the wage rate is a negative income effect. The drawing in the topfigure shows the case where these two income effects exactly cancel out. In this case we are left with a pure substitution effect that moves the consumer from point A to point B. Therefore, consumption falls and leisure increases. As leisure increases, hours of work must fall. The middle figure shows a case in which the increase in dividend income, the distance GF, is larger and so the income effect is positive. The consumer winds up on a higher indifference curve, leisure unambiguously increases,Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 33 and consumption may either increase or decrease. The bottom figure shows a case in which the increase in dividend income, the distance GF, is smaller and so the income effect is negative. The consumer winds up on a lower indifference curve, consumption unambiguously decreases, and leisure may either increase or decrease.34 Williamson • Macroeconomics, Third Edition5. This problem introduces a higher, overtime wage for hours worked above a threshold, q . Thisproblem also abstracts from any dividend income and taxes.(a) The budget constraint is now EJG in the figure below. The budget constraint is steeper for levels ofleisure less than h – q , because of the higher overtime wage. The figure depicts possible choices for two different consumers. Consumer #1 picks point A on her indifference curve, I 1. Consumer #2 picks point B on his indifference curve, I 2. Consumer #1 chooses to work overtime; consumer #2 does not.(b) The geometry of the figure above makes it clear that it would be very difficult to have anindifference curve tangent to EJG close to point J. In order for this to happen, an indifferencecurve would need to be close to right angled as in the case of pure complement. It is unlikely that consumers wish to consume goods and leisure in fixed proportions, and so points like A and Bare more typical. For any other allowable shape for the indifference curve, it is impossible forpoint J to be chosen.(c) An increase in the overtime wage steepens segment EJ of the budget constraint, but has no effecton the segment JG. For an individual like consumer #2, the increase in the overtime wage has no effect up until the point at which the increase is large enough to shift the individual to a point like point A. Consumer #2 receives no income effect because the income effect arises out of a higher wage rate on inframarginal units of work. An individual like consumer #1 has the traditionalincome and substitution effects of a wage increase. Consumer #1 increases her consumption, but may either increase or reduce hours of work according to whether the income effect outweighsthe substitution effect.Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 356. Lump-sum Tax vs. Proportional Tax. Suppose that we start with a proportional tax. Under theproportional tax the consumer’s budget line is EFH in the figure below. The consumer choosesconsumption, *,C and leisure, *,l at point A on indifference curve I 1. A shift to a lump-sum tax steepens the budget line. The absolute value of the slope of the budget line is (1),t w − and t has fallen to zero. The imposition of the lump-sum tax shifts the budget line downward in a parallel fashion. By construction, the lump-sum tax must raise the same amount of revenue as the proportional tax. The consumer must therefore be able to continue to consume *C of the consumption good and *l ofleisure after the change in tax collection. Therefore, the new budget line must also pass through pointA. The new budget line is labeled LGH in the figure below. With the lump-sum tax, the consumer can do better by choosing point B, on the higher indifference curve, I 2. Therefore, the consumer is clearly better off. We are also assured that consumption will be greater at point B than at point A, and that leisure will be smaller at point B than at point A.7. Leisure represents all time used for nonmarket activities. If the government is now providing forsome of those, like providing free child care, households will take advantage of such a program,thereby allowing more time for other activities, including market work. Concretely, this translates in a change of preferences for households. For the same amount of consumption, they are now willing to work more, or in other words, they are willing to forego some additional leisure. On the figure below, the new indifference curve is labeled I 2. It can cross indifference curve I 1 because preferences, as we measure them here, have changed. The equilibrium basket of goods for the household now shifts from A to B. This leads to reduced leisure (from l *1 to l *2), and thus increased hours worked, and increased consumption (from C *1 to C *2) thanks to higher labor income at the fixed wage.36 Williamson • Macroeconomics, Third Edition8. The firm chooses its labor input, N d , so as to maximize profits. When there is no tax, profits for thefirm are given by(,).d d zF K N wN π=−That is, profits are the difference between revenue and costs. In the top figure on the following page,the revenue function is (,)d zF K N and the cost function is the straight line, wN d . The firm maximizes profits by choosing the quantity of labor where the slope of the revenue function equals the slope of the cost function:.N MP w =The firm’s demand for labor curve is the marginal product of labor schedule in the bottom figure on the following page.With a tax that is proportional to the firm’s output, the firm’s profits are given by:(,)(,)(1)(,),d d d d zF K N wN tzF K N t zF K N π=−−=−where the term (1)(,)d t zF K N − is the after-tax revenue function, and as before, wN d is the costfunction. In the top figure below, the tax acts to shift down the revenue function for the firm and reduces the slope of the revenue function. As before, the firm will maximize profits by choosing the quantity of labor input where the slope of the revenue function is equal to the slope of the cost function, but the slope of the revenue function is (1),N t MP − so the firm chooses the quantity of labor where(1).N t MP w −=In the bottom figure below, the labor demand curve is now (1),N t MP − and the labor demand curve has shifted down. The tax acts to reduce the after-tax marginal product of labor, and the firm will hire less labor at any given real wage.9. The firm chooses its labor input N dso as to maximize profits. When there is no subsidy, profits forthe firm are given by (,).d d zF K N wN π=−That is, profits are the difference between revenue and costs. In the top figure on the following page the revenue function is (,)d zF K N and the cost function is the straight line, wN d . The firm maximizes profits by choosing the quantity of labor where the slope of the revenue function equals the slope of the cost function:.N MP w =The firm’s demand for labor curve is the marginal product of labor schedule in the bottom figure below.With an employment subsidy, the firm’s profits are given by:(,)()d d zF K N w s N π=−−where the term (,)d zF K N is the unchanged revenue function, and (w – s )N d is the cost function. The subsidy acts to reduce the cost of each unit of labor by the amount of the subsidy, s . In the top figure below, the subsidy acts to shift down the cost function for the firm by reducing its slope. As before, the firm will maximize profits by choosing the quantity of labor input where the slope of the revenue function is equal to the slope of the cost function, (t – s ), so the firm chooses the quantity of labor where.N MP w s =−In the bottom figure below, the labor demand curve is now ,N MP s + and the labor demand curve has shifted up. The subsidy acts to reduce the marginal cost of labor, and the firm will hire more labor at any given real wage.10. Minimum Employment Requirement. Below *,N no output is produced. Thereafter, the production function has its usual properties. Such a production function is reproduced in the first two figures below. At high wages, the firm’s cost curve is entirely above the revenue curve, so the firm hires no labor, to prevent incurring losses. Only if the wage rate is less than ˆw will the firms choose to hire anyone. At ˆ,N just as it would in the absence of the constraint. Below ˆ,w w w=the firm chooses*,the labor demand curve is unaffected. The labor demand curve is reproduced in the bottom figure.11. The level of output produced by one worker who works h – l hours is given by(,).s Y zF K h l =−This equation is plotted in the figure below. The slope of this production possibilities frontier is simply .N MP −12. As the firm has to internalize the pollution, it realizes that labor is less effective than it previouslythought. It now needs to hire N (1 + x ) workers where N were previously sufficient. This is qualitatively equivalent to a reduction of z , total factor productivity. The figure below highlights the resulting outcome: the firm now hires fewer people for a given wage and thus its labor demand is reduced.13. 0.30.7Y zK n =(a) 0.7.Y n = See the top figure below. The marginal product of labor is positive and diminishing. (b) 0.72.Y n = See the figures below.(c) 0.30.70.72 1.23.Y n n =≈ See the figures below.(d) See the bottom figure below.−−−−==⇒===⇒===⇒=×≈0.30.30.30.30.31,10.72,1 1.41,220.70.86N N N z K MP n z K MP n z K MP n n。
威廉森《宏观经济学》（第5版）笔记和课后习题详解第7章~第8章【圣才出品】
威廉森《宏观经济学》（第5版）笔记和课后习题详解第7章~第8章【圣才出品】第7章经济增长：马尔萨斯和索洛7.1复习笔记考点⼀：七个经济增长事实★1．在1800年前后⼯业⾰命发⽣之前，⽣活⽔平⼏乎长期没有变化，各国的差异也很⼩。
2．⼯业⾰命以来，最富裕国家的⼈均收⼊持续增长。
3．各国的投资率与劳均产出正相关。
4．各国的⼈⼝增长率与劳均产出负相关。
5．1800～1950年，世界各国的⼈均收⼊增长差异很⼤，西欧、美国、加拿⼤、澳⼤利亚和新西兰这些国家拉⼤了与世界其他国家的差距。
6．各国1960年的⼈均产出⽔平与1960～2007年的⼈均产出平均增长率基本不相关。
7．从⼈均实际收⼊的增长率来看，富国之间⽐穷国之间更接近。
考点⼆：马尔萨斯经济增长模型★★1．主要观点马尔萨斯认为，技术进步会拉动⼈⼝增长，⽽更多的⼈⼝会将⽣活⽔平拉低⾄技术进步前。
因此，只有限制⼈⼝增长，才能使⽣活⽔平提⾼。
2．具体模型（1）模型假设①总量⽣产函数为：Y＝zF（L，N）（7.1）其中，z为全要素⽣产率；F的性质与第4章中Y＝zF（K，N d）的性质相同，如：规模报酬不变，不同之处在于⽤⼟地替代资本；Y为社会总产出，可看作⾷物。
函数意义为利⽤当期⼟地投⼊L和当期劳动投⼊N来⽣产当期总产出Y。
②不存在投资和储蓄（封闭经济中I＝S）；③不存在政府⽀出；④⼟地L的供给固定不变；⑤充分就业，即N既是⼈⼝，也是劳动投⼊。
（2）模型分析①模型构建令N′代表下⼀时期的⼈⼝数量，则：N′＝N＋N（出⽣率－死亡率）（7.2）出⽣率＝出⽣⼈数/总⼈⼝，死亡率＝死亡⼈数/总⼈⼝。
⼯业⾰命之前，出⽣率是⼈均消费C/N的增函数，死亡率是⼈均消费C/N的减函数，因此，将等式（7.2）的两边同除以N得：N′/N＝g（C/N）（7.3）g 是⼀个增函数；C 为总消费，N′/N＝1＋⼈⼝增长率。
图7-1说明了等式（7.3）所描述的关系。
图7-1马尔萨斯模型中的⼈⼝增长取决于劳均消费均衡状态下，⽣产出来的所有商品全部⽤于消费，即C＝Y。
宏观经济学-课后思考题答案_史蒂芬威廉森006
Chapter 6Economic Growth: Malthus and SolowTeaching GoalsStudents easily take for granted the much more abundant standard of living of today as opposed to 20, 50, or 100 years ago. Sometimes it is easier to remind students of what their ancestors had to do without, rather than simply referring to per capita income levels over time. Recessions come and go, and yet economic growth swamps the lost output we endure during hard times.The typical student begins study of economic growth against the backdrop of the recent growth experience of the United States. The current standard of living in the United States vastly surpasses the current standard of living in most countries and would have been unimaginable anywhere in the world before the advent of the industrial revolution. Until about 1800, the world economy produced little more than a subsistence level of income for any but the richest individuals. Growth in per capita income was nonexistent. The Malthusian model of growth explains the tendency of increases in population to dilute any gains in productivity.The industrial revolution introduced the possibility of sustained growth in per capita income through the accumulation of physical capital. However, growth experience has varied widely around the world. The richer countries have a sustained record of growth. Per capita income in the United States has proceeded at an average rate of about 2% per year. While 2% growth may seem small, it is important for students to realize that such growth transforms into a more than doubling of per capita GDP per generation. Unfortunately, the poorer countries have remained poor. Furthermore, their growth rates have not generally matched growth rates in the richer countries, so that the poor countries fall farther and farther behind. Such differences in standards of living and growth prospects present puzzles that the study of economic growth hopes to solve.Classroom Discussion TopicsGetting students to relate to differences in standards of living can sometimes be difficult. It is easy to take one’s own standard of living for granted. An interesting discussion topic is whether students would be willing to travel back in time to 100 or 200 years ago, if they could be one of the richest people of those earlier times. Would the tradeoff be worthwhile? While students typically stress factors like antiquated view about freedom of choice, and racial and gender issues, try to encourage students to divide their concerns into those that are more economic as opposed to social. Also point out that higher standards of living allow societies to be more concerned about issues of equality when mere survival is no longer precarious.Chapter 6 Economic Growth: Malthus and Solow 53Students often view population growth as the result of cultural factors and personal preferences. Against the abundance of daily living, it is easy to forget economic factors. Ask the students for examples ofeconomic factors that might impact on fertility decisions. The Malthusian model suggests that growth may only be achieved through population control. In the modern economy, the costs of raising children can be formidable, and so there is tendency for such costs to be a disincentive to fertility. Such costs may attribute to the tendency for low fertility rates in advanced economies. In more primitive societies, having a large family can be a private form of Social Security. The more children a family has, the more family members there will be to provide for the parents in old age. Poor public health conditions may actually enhance fertility. If each child has a small chance for survival to adulthood, more births are required to produce a given-sized family.OutlineI. Economic Growth FactsA. Pre-1800: Constant Per Capita Income across Time and SpaceB. Post-1800: Sustained Growth in the Rich CountriesC. High I nvestment ↔ High Standard of LivingD. High Population Growth ↔ Low Standard of LivingE. Divergence of Per Capita Incomes: 1800–1950F. No Conditional Convergence amongst All CountriesG. Conditional Convergence amongst the Rich CountriesII. The Malthusian ModelA. Production Determined by Labor and Fixed Land SupplyB. Population Growth and Per Capita ConsumptionC. Steady-state Consumption and Population1. Effects of Technological Change2. Effects of Population ControlD. Malthus: Theory and EvidenceIII. Solow’s Model of Exogenous GrowthA. The Representative ConsumerB. The Representative FirmC. Competitive EquilibriumD. Steady-State Growth1. The Steady-State Path2. Adjustment toward EquilibriumE. Savings and Growth1. Equilibrium Effects2. The Golden Rule: K MP n d =+F. Labor Force Growth and Output Per CapitaG. Total Factor Productivity and Output Per CapitaH. Solow: Theory and Evidence54 Williamson • Macroeconomics, Third EditionIV. Growth AccountingA. Solow ResidualsB. The Productivity Slowdown1. Measurement of Services2. The Relative Price of Energy3. Costs of Adopting New TechnologyC. Cyclical Properties of Solow ResidualsTextbook Question SolutionsQuestions for Review1. In exogenous growth models, growth is caused in the model by forces not explained by the modelitself. Endogenous growth models examine the economic factors that cause growth.2. Pre-1800: Constant Per Capita Income across Time and SpacePost-1800: Sustained Growth in the Rich CountriesHigh Investment ↔ High Standard of LivingHigh Population Growth ↔ Low Standard of LivingDivergence of Per Capita Incomes: 1800–1950No Conditional Convergence amongst All CountriesConditional Convergence amongst the Rich Countries3. An increase in total factor productivity increases the size of the population, but has no effect on theequilibrium level of consumption per capita.4. Only a downward shift in the population growth function can increase the standard of living.5. Malthu’s model is quite successful in explaining economic growth prior to the industrial revolution.Malthu’s model has little relevance for more recent growth experience.6. In the steady state, all variables stay constant: per capita capital, output, consumption, savings. Also,this steady state is stable: whatever the initial capital (except zero), the economy will converge to this steady state.7. With an increase in the saving rate, it becomes possible to sustain a higher level of per capita capital,and thus higher output and consumption. With an increase in the population rate, the contraryhappens, as one needs to provide more newborns with the going per capita capital. A higher total factor productivity improves all per capita variables in the steady state.8. To maximize steady-state per capita consumption, the saving rate must be such that the marginalproduct of capital (the slope of the per capita production function) equals the population growth rate plus the depreciation rate.9. The Malthusian model gave no way out of misery, except for measures that reduce the population.Even technological advances would not raise the standard of living. The Solow model shows that it is possible to obtain a stable standard of living with growing population. And if total factor productivity increases, one can even obtain improvements in the standard of living despite population growth.Chapter 6 Economic Growth: Malthus and Solow 55 10. The Cobb-Douglas production function permits a simple decomposition of economic growth into itscomponent sources.11. In a competitive equilibrium, the parameter a is equal to the share of capital income in total income.12. The Solow residual measures increases in real GDP that are not accounted for by increases in capitaland labor. The Solow residual is highly procyclical as it explains the great majority of the cyclical component in GDP.13. The productivity slowdown could be explained by underestimates of output in the growing servicessector, increases in the relative price of energy, and the costs of adopting new technologies.14. American workers then knew how to incorporate the new technologies, in particular informationtechnology. These efficiency gains may have been realized by 2000, which explains the newslowdown, along with higher energy prices.15. Growth in capital, employment, and total factor productivity account for growth in GDP.16. During this period, growth in these countries was much larger than average. Growth rates for thesecountries were about three times as fast as growth in the United States. However, most of this growth can be attributed to increases in the capital stocks in these countries, and such rapid rates of growth of capital cannot be sustained for long periods of time.Problems1. The amount of land increases, and, at first, the size of the population is unchanged. Therefore,consumption per capita increases. However, the increase in consumption per capita increases the population growth rate, see the figure below. In the steady state, neither *c nor *l are affected by the initial increase in land. This fact can be discerned by noting that there will be no changes in either of the panels of Figure 6.8 in the textbook.56 Williamson • Macroeconomics, Third Edition2. A reduction in the death rate increases the number of survivors from the current period who will stillbe living in the future. Therefore, such a technological change in public health shifts the function ()g cupward. In problem #1 there were no effects on the levels of land per capita and consumption per capita. In this case, the ()g c function in the bottom figure below shifts upward. Equilibriumconsumption per capita decreases. From the top figure below, we also see that the decrease inconsumption per capita requires a reduction in the equilibrium level of land per capita. The size of the population has increased, but the amount of available land is unchanged.Chapter 6 Economic Growth: Malthus and Solow 57 3. For the marginal product of capital to increase at every level of capital, the shift in the productionfunction is equivalent to an increase in total factor productivity.(a) The original and new production functions are depicted in the figures below.(b) Equilibrium in the Solow model is at the intersection of ()n d k+szf k with the line segment ().The old and new equilibria are depicted in the bottom panel of the figure above. The newequilibrium is at a higher level of capital per capita and a higher level of output per capita.(c) For a given savings rate, more effective capital implies more savings, and in the steady state thereis more capital and more output. However, if the increase in the marginal product of capital were local, in the neighborhood of the original equilibrium, there would be no equilibrium effects. A twisting of the production function around its initial point does not alter the intersection point.4. An increase in the depreciation rate acts in much the same way as an increase in the populationgrowth rate. More of current savings is required just to keep the amount of capital per capita constant.In equilibrium output per capita and capital per capita decrease.58 Williamson • Macroeconomics, Third Edition5. A destruction of capital.(a) The long-run equilibrium is not changed by an alteration of the initial conditions. If the economystarted in a steady state, the economy will return to the same steady state. If the economy wereinitially below the steady state, the approach to the steady state will be delayed by the loss ofcapital.(b) Initially, the growth rate of the capital stock will exceed the growth rate of the labor force. Thefaster growth rate in capital continues until the steady state is reached.(c) The rapid growth rates are consistent with the Solow model’s predictions about the likelyadjustment to a loss of capital.6. A reduction in total factor productivity reduces the marginal product of capital. The golden rule levelof capital per capita equates the marginal product of capital with .n d + Therefore, for given ,n d + the golden rule amount of capital per capita must decrease as in the figure below. Therefore the golden rule savings rate must decrease.7. Government spending in the Solow model.(a) By assumption, we know that T = G, and so we may write:()(1)(1)K's Y G d K sY gN d K =−+−=−+−Now divide by N and rearrange as:(1)()(1)k'n szf k sg d k +=−+−Divide by (1 + n ) to obtain:()(1)(1)(1)(1)szf k sg d k k'n n n −=−++++Chapter 6 Economic Growth: Malthus and Solow 59Setting k = k ′, we find that:**()().szf k sg n d k =++This equilibrium condition is depicted in the figure below.(b) The two steady states are also depicted in the figure above.(c) The effects of an increase in g are depicted in the bottom panel of the figure above. Capital percapita declines in the steady state. Steady-state growth rates of aggregate output, aggregate consumption, and investment are all unchanged. The reduction in capital per capita isaccomplished through a temporary reduction in the growth rate of capital.8. The golden rule quantity of capital per capita, *,k is such that *().K MP zf k n d ′==+ A decrease in the population growth rate, n , requires a decrease in the marginal product of capital. Therefore, thegolden rule quantity of capital per capita must increase. The golden rule savings rate may either increase or decrease.60 Williamson • Macroeconomics, Third Edition9. (a) First, we need to determine how bN evolves over time:(bN )′ = (1 + f )(1 + n ) bNThen we just need to redo the analysis of the competitive equilibrium and the steady state as inthe book, replacing every N by bN , every (1 + n ) by (1 + f )(1 + n ), and every n by f + n . The new steady-state per efficiency unit capital is then******()(1)(1)(1)(1)(1)szf k d k k f n f n −=+++++ All aggregate variables then grow at the rate of f + n , while per capita aggregates grow at therate f .(b) An increase in f increases the growth rate of per capita income by the same amount, as f is itsgrowth rate. This happens because the exogenous growth in b raises instant capital and income for everyone without a need to invest in capital.10. Production linear in capital:()()Y K z zf k f k k N N==⇒= (a) Recall Equation (20) from the text, and replace ()f k with k to obtain:+−=+((1))(1)sz d k'k n Also recall that 11 and .Y Y Y'zk k k'N z N z N'=⇒== Therefore: ((1))(1)Y'sz d Y N'n N+−=+ As long as((1))1,(1)sz d n +−>+ per capita income grows indefinitely. (b) The growth rate of income per capita is therefore: ((1))1(1)()(1)Y'Y sz d N'N g Y n Nsz n d n −+−==−+−+=+ Obviously, g is increasing in s .(c) This model allows for the possibility of an ever-increasing amount of capital per capita. In theSolow model, the fact that the marginal product of capital is declining in capital is the key impediment to continual increases in the amount of capital per capita.Chapter 6 Economic Growth: Malthus and Solow 6111. Solow residual calculations.(a) To calculate the Solow residuals, we apply the formula, 0.360.64ˆˆˆˆ/,zY K N = to the values in the provided table. Adding a new column for these values, we obtain:Year ˆY ˆK ˆN ˆz 1995 8031.7 25487.3 124.9 9.4781996 8328.9 26222.3 126.7 9.6401997 8703.5 27018.1 129.6 9.8231998 9066.9 27915.9 131.5 10.0191999 9470.3 28899.9 133.5 10.2362000 9817.0 29917.1 136.9 10.3122001 9890.7 30793.4 136.9 10.2822002 10048.8 31599.6 136.5 10.3692003 10301.0 32426.2 137.7 10.4722004 10703.5 33304.9 139.2 10.7032005 11048.6 34191.7 141.7 10.820(b) Next, we compute the percentage changes in each of the table entries. These values arepresented in the table below.Year ˆˆY Y Δ/ (%) ˆˆK K Δ/ (%) ˆˆN N Δ/ (%) ˆˆzz Δ/ (%) 1996 3.70 2.88 1.44 1.71 1997 4.50 3.03 2.29 1.901998 4.18 3.32 1.47 2.001999 4.45 3.52 1.52 2.172000 3.66 3.52 2.55 0.742001 0.75 2.93 0.00 −0.292002 1.60 2.62 −0.29 0.852003 2.51 2.62 0.88 0.992004 3.91 2.71 1.09 2.212005 3.22 2.66 1.80 1.0962 Williamson • Macroeconomics, Third EditionTo compare the contributions to growth, we need to compare the magnitudes,ˆˆˆˆ0.36(/),0.64(/),KKNN ΔΔ and ˆˆ/.z z Δ These values are presented in the table below.Year ˆˆ0.36(Δ/K K) (%) ˆˆ0.64(Δ/N N)(%) ˆˆz z Δ/ (%)1996 1.04 0.92 1.711997 1.09 1.46 1.901998 1.20 0.94 2.001999 1.27 0.97 2.172000 1.27 1.63 0.742001 1.05 0.00 −0.292002 0.94 −0.19 0.852003 0.94 0.56 0.992004 0.98 0.70 2.212005 0.96 1.15 1.09Most often, when output is growing, the biggest contribution to growth comes from increases intotal factor productivity. In 1991 and in 2001, both bad years for growth, total factor productivity decreased. In the other years, growth in total factor productivity is usually the largest contributor to growth, while increases in capital and labor equally share the role of the leading cause of growth in the other years. In the later years, capital growth has come to be relatively more important than in the early years.。
宏观经济学-课后思考题答案-史蒂芬威廉森004.pdf_英中
7.休闲代表所有用于非市场活动的时间。如果政府现在提供其中的一些，比如提供免费的儿童保育，家庭将会利用这样一个项目，从而为包括市场工作在内的其他活动留出更多的时间。具体来说，这意味着家庭偏好的改变。对于同样的消费，他们现在愿意多工作，或者换句话说，他们愿意放弃一些额外的休闲。下图中，新的无差异曲线标记为I2。它可以跨越I1的无差异曲线，因为我们在这里衡量的偏好已经发生了变化。家庭的平衡商品篮子现在从甲转移到乙。这导致休闲减少(从l 1到l 2)，工作时间增加，消费增加(从C1到C2)，这要归功于固定工资下更高的劳动收入。
2.U=al+bc
（a）为了指定一条无差异曲线，我们将效用常数保持在u。下一步以下列形式重新排成线性关系，斜率a/b代表边际替代率。根据是a/b>w还是a/b<w，主要有两种情况。左下图的顶部面板显示了a/b<w。在这种情况下，无差异曲线比预算线更平坦，消费者选择点A，在该点l = 0且C=wh+π-T。右图显示了a/b>w,在这种情况下，无差异曲线比预算线更陡，消费者选择B点，在该点l=h和C=π-T。在巧合的情况下，可达到的最高无差异曲线与无差异曲线一致，消费者对所有可能的休闲和工作时间漠不关心。
第三个特性是消费和休闲都是正常的商品。这一特性向我们保证，消费者收入的增加总是会促使个人消费更多的消费和休闲。
斯蒂芬D威廉森宏观经济学第三版第九章Stephen D. Williamson's Macroeconomics, Third Edition chapter9
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
9-2
Real Intertemporal Model
• Current and future periods. • Representative Consumer – consumption/savings decision • Representative Firm – hires labor and invests in current period, hires labor in future • Government – spends and taxes in present and future, and borrows on the credit market.
9-22
The Representative Firm’s Investment Decision
The firm invests to the point where the marginal benefit from investment equals the marginal cost.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
9-26
Equation 9.16
Simplified optimal investment rule:
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
宏观经济学斯蒂芬威廉森chap09
宏观经济学斯蒂芬威廉森chap09Macroeconomics, 3e (Williamson)Chapter 9 A Real Intertemporal Model with Investment1) A consumer may increase her saving byA) w orking more hours and consuming more goods in the present period.B) w orking more hours and consuming fewer goods in the present period.C) w orking fewer hours and consuming more goods in the present period.D) w orking fewer hours and consuming fewer goods in the present period.Answer: BQuestion Status: P revious Edition2) T he condition, MRS l,C=w, describes the representative consumer'sA) i nvestment decision.B) c onsumption - savings decision.C) c urrent period work - leisure decision.D) f uture period work - leisure decision.Answer: CQuestion Status: P revious Edition3) T he condition, MRS l',C'= w', describes the representative consumer'sA) i nvestment decision.B) c onsumption - savings decision.C) c urrent period work - leisure decision.D) f uture period work - leisure decision.Answer: D4) T he condition, MRS C,C'= 1 +r, describes the representative consumer'sA) i nvestment decision.B) c onsumption - savings decision.C) c urrent period work - leisure decision.D) f uture period work - leisure decision.Answer: BQuestion Status: P revious Edition5) T he assumption that current-period labor supply is positively related to the current-periodreal wage is justified as long as theA) i ncome effect dominates the substitution effect in the short run.B) i ncome effect dominates the substitution effect in the long run.C) s ubstitution effect dominates the income effect in the short run.D) s ubstitution effect dominates the income effect in the long run.Answer: CQuestion Status: P revious Edition6) T he intertemporal substitution of leisure effect is used to justify the assumption that currentlabor supply increases when theA) c urrent real wage increases.B) c urrent real wage decreases.C) r eal interest rate increases.D) r eal interest rate decreases.Answer: C7) W hen drawn against the current wage, the current labor supply shifts to the right ifA) c urrent taxes increase.B) f uture taxes decrease.C) f irms make more profits.D) t otal factor productivity increases.Answer: AQuestion Status: N ew8) A n increase in lifetime wealth is likely toA) i ncrease current labor supply and increase current consumption demand.B) i ncrease current labor supply and decrease current consumption demand.C) d ecrease current labor supply and increase current consumption demand.D) d ecrease current labor supply and decrease current consumption demand.Answer: CQuestion Status: P revious Edition9) A ny increase in the present value of taxes for the consumer impliesA) a n increase in lifetime wealth and an increase in current labor supply.B) a n increase in lifetime wealth and a decrease in current labor supply.C) a decrease in lifetime wealth and an increase in current labor supply.D) a decrease in lifetime wealth and a decrease in current labor supply.Question Status: P revious Edition10) A ny increase in the present value of dividends for the consumer impliesA) a n increase in lifetime wealth and an increase in current labor supply.B) a n increase in lifetime wealth and a decrease in current labor supply.C) a decrease in lifetime wealth and an increase in current labor supply.D) a decrease in lifetime wealth and a decrease in current labor supply.Answer: BQuestion Status: N ew11) T he assumption that current-period consumption demand is positively related to the realinterest rate is justified as long as theA) i ncome effect dominates the substitution effect.B) s ubstitution effect dominates the income effect.C) r epresentative consumer is a borrower.D) r epresentative consumer is a lender.Answer: BQuestion Status: P revious Edition12) T he demand for current consumption, as plotted against current income, shifts to the rightdue to all of the following exceptA) a decrease in current taxes.B) a decrease in future taxes.C) a n increase in current income.D) a n increase in future income.Question Status: P revious Edition13) T he demand for current consumption, as plotted against the interest rate, shifts to the rightdue to all of the following exceptA) a decrease in current taxes.B) a increase in future taxes.C) a n increase in current income.D) a n increase in future income.Answer: BQuestion Status: N ew14) T he marginal propensity to consume out of incomeA) i s larger than one.B) i s equal to one.C) i s smaller than one.D) v aries around one.Answer: CQuestion Status: N ew15) T he marginal propensity to consume helps explaining which stylized fact?A) p rocyclicality of consumptionB) t he lag of consumptionC) t he low relative volatility of consumptionD) c ountercyclical pricesAnswer: CQuestion Status: N ew16) N ext period's capital is equal to current-period investmentA) p lus the amount of current capital left over after depreciation.B) m inus the amount of current capital left over after depreciation.C) p lus the amount of current period depreciation.D) m inus the amount of current period depreciation.Answer: AQuestion Status: P revious Edition17) W hen drawn against the current real wage, the labor demand curve isA) u pward sloping because the marginal product of labor rises with the quantity of laboremployed.B) u pward sloping because the marginal product of labor declines with the quantity oflabor employed.C) d ownward sloping because the marginal product of labor rises with the quantity oflabor employed.D) d ownward sloping because the marginal product of labor declines with the quantity oflabor employed.Answer: DQuestion Status: P revious Edition18) W hen drawn against the current real wage, the labor demand curve shift to the right ifA) t he interest rate increases.B) c urrent taxes increase.C) t otal factor productivity increases.D) f uture capital increases.Answer: CQuestion Status: N ew19) I n determining the benefit of additional investment to the representative firm, we considerthe marginal product ofA) c urrent capital.B) f uture capitalC) c urrent labor.D) f uture labor.Answer: BQuestion Status: N ew20) T he marginal cost of investment for the firm is equal toA) 1.B) -1.C) M P'K .D) -MP'K .Answer: AQuestion Status: P revious Edition21) T he marginal cost of investment for the firm is equal toA) 1.B) 0.C) t he depreciation rate.D) t he depreciation rate plus the interest rate.Answer: AQuestion Status: N ew22) T he marginal benefit from investment for a firm is equal to A) '1(1)K MP d r +++. B) '1(1)K MP d r ?++. C) '1(1)K MP d r +?+. D) '1(1)K MP d r ??+. Answer: CQuestion Status: P revious Edition23) W hen drawn against the real interest rate, the optimal investment schedule shifts to the rightifA) c urrent total factor productivity z increases.B) c urrent total factor productivity z decreases.C) f uture total factor productivity z' increases.D) f uture total factor productivity z' decreases.Answer: CQuestion Status: P revious Edition24) F irms discount future profits at the interest rate r becauseA) i t is the interest rate on their debt.B) i t is the same rate as for households.C) R icardian equivalence holds.D) i t has to equal the marginal productivity of capital in equilibrium.Answer: BQuestion Status: N ew25) W hen drawn against the real interest rate, the optimal investment schedule shifts to the rightif theA) c urrent capital stock K increases.B) c urrent capital stock K decreases.C) f uture capital stock K' increases.D) f uture capital stock K' increases.Answer: BQuestion Status: P revious Edition26) I nvestment will be more variable if the real interest rate isA) m ore variable and future total factor productivity is morevariable.B) m ore variable and future total factor productivity is less variable.C) l ess variable and future total factor productivity is more variable.D) l ess variable and future total factor productivity is less variable.Answer: AQuestion Status: P revious Edition27) I f the interest rate goes up, what happens to the investment demand curve?A) I t shifts to the right.B) I t shift to the left.C) I t stays put.D) W e cannot tell.Answer: CQuestion Status: N ew28) L abor demand depends on the interest rate becauseA) h ousehold savings depend on the interest rate.B) f irms discount future profits.C) o f Ricardian equivalence.D) L abor demand actually does not depend on the interest rate.Answer: DQuestion Status: N ew29) W hen drawn against the real interest rate, the output supply curve is upward slopingbecause labor supply isA) i ncreasing in the real interest rate and labor demand is independent of the real interestrate.B) d ecreasing in the real interest rate and labor demand is independent of the real interestrate.C) i ndependent of the real interest rate and labor demand is increasing in the real interestrate.D) i ndependent of the real interest rate and labor demand is decreasing in the real interestrate.Answer: AQuestion Status: P revious Edition30) O utput supply is increasing in the interest rate becauseA) l abor demand is increasing in the interest rate.B) l abor demand is decreasing in the interest rate.C) l abor supply is increasing in the interest rate.D) l abor supply is decreasing in the interest rate.Answer: CQuestion Status: N ew31) W hen drawn against the real interest rate, the output supply curve unambiguously shifts tothe right if either or both of the following occur.A) a n increase in current government spending and an increase in future governmentspendingB) a n increase in current government spending and a decrease in future governmentspendingC) a decrease in current government spending and an increase in future governmentspendingD) a decrease in current government spending and a decrease in future governmentspendingAnswer: AQuestion Status: P revious Edition32) W hen drawn against the real interest rate, the output supply curve unambiguously shifts tothe right ifA) c urrent capital decreases.B) c urrent total factor productivity decreases.C) f uture total factor productivity decreases.D) c urrent or future taxes increase.Answer: DQuestion Status: N ew33) W hen drawn against the real interest rate, output supply increases ifA) c urrent government expenses increase.B) f uture government expenses increase.C) c urrent total factor productivity increases.D) t he money supply increases.Answer: CQuestion Status: N ew34) W hen drawn against the real interest rate, output supply increases ifA) t he present value of taxes decreases.B) c urrent capital increases.C) t he interest rate decreases.D) f uture total productivity increases.Answer: BQuestion Status: N ew35) I n a model with money neutrality, how much should the money supply be increased toobtain a 1% increase in nominal output?A) -1%B) b etween 0 and 1%C) 1%D) I t cannot be done.Answer: CQuestion Status: N ew36) I n a model with money neutrality, how much should the money supply be increased toobtain a 1% increase in real output?A) -1%B) b etween 0 and 1%C) 1%D) I t cannot be done.Answer: DQuestion Status: N ew37) When drawn against current income, the slope of the Cd (r) + l d (r) + G curve is equal to themarginalA) p roduct of capital.B) p roduct of labor.C) p ropensity to consume.D) p ropensity to save.Answer: CQuestion Status: P revious Edition38) W hen drawn against the real interest rate, the output demand curve unambiguously shiftsto the right if either or both of the following occur.A) a n increase in current taxes and an increase in future taxesB) a n increase in current taxes and a decrease in future taxesC) a decrease in current taxes and an increase in future taxesD) a decrease in current taxes and a decrease in future taxesAnswer: DQuestion Status: P revious Edition39) W hen drawn against the real interest rate, output demand increases ifA) c urrent government expenses increase.B) f uture government expenses increase.C) c urrent taxes increase.D) f uture taxes increase.Answer: AQuestion Status: N ew40) W hen drawn against the real interest rate, the output demand curve unambiguously shiftsto the right ifA) c urrent capital decreases.B) c urrent total factor productivity decreases.C) f uture total factor productivity decreases.D) c urrent or future taxes increase.Answer: AQuestion Status: N ew41) W hich of these curves is directly affected by a change in current capital?A) o utput demandB) o utput supplyC) l abor supplyD) c onsumption demandAnswer: BQuestion Status: N ew42) W hen drawn against the real interest rate, the output demand curve shifts to the right whenA) c urrent total factor productivity z increases.B) c urrent total factor productivity z decreases.C) f uture total factor productivity z' increases.D) f uture total factor productivity z' decreases.Answer: CQuestion Status: P revious Edition43) A temporary increase in government spending that leads to only a small decline in lifetimewealth likely shifts the aggregate demand curve to theA) r ight by more than the rightward shift in aggregate supply.B) r ight by less than the rightward shift in aggregate supply.C) l eft by more than the leftward shift in aggregate supply.D) l eft by less than the leftward shift in aggregate supply.Answer: AQuestion Status: P revious Edition44) A change in current government expenses induces a direct shift in which curve?A) l abor supplyB) l abor demandC) a ggregate supplyD) a ggregate demandAnswer: DQuestion Status: N ew45) A ny increase in the present value of taxes impliesA) a n increase in lifetime wealth and an increase in the current labor supply.B) a n increase in lifetime wealth and a decrease in the current labor supply.C) a decrease in lifetime wealth and an increase in the current labor supply.D) a decrease in lifetime wealth and a decrease in the current labor supply.Answer: CQuestion Status: N ew46) I n response to a temporary increase in government spending, the representative consumerconsumesA) m ore and takes more leisure.B) m ore and takes less leisure.C) l ess and takes more leisure.D) l ess and takes less leisure.Answer: DQuestion Status: P revious Edition47) T he equilibrium effects of a temporary increase in government spending includeA) a n increase in the real wage and an increase in the real interest rate.B) a n increase in the real wage and a decrease in the real interest rate.C) a decrease in the real wage and an increase in the real interest rate.D) a decrease in the real wage and a decrease in the real interest rate.Answer: CQuestion Status: P revious Edition48) T he equilibrium effects of an anticipated increase infuture government spending includeA) a n increase in the real wage and an increase in the real interest rate.B) a n increase in the real wage and a decrease in the real interest rate.C) a decrease in the real wage and an increase in the real interest rate.D) a decrease in the real wage and a decrease in the real interest rate.Answer: DQuestion Status: P revious Edition49) I n response to a permanent increase in government spending, the permanent incomehypothesis would suggest that, to a first approximation, consumption demand shouldA) b e unaffected.B) f all by less than the increase in government spending.C) f all exactly as much as the increase in government spending.D) f all by more than the increase in government spending.Answer: CQuestion Status: P revious Edition50) A ccording to S. Rao Aiyagari, Lawrence Christiano and Martin Eichenbaum, outputA) i ncreases more with a temporary increase in government spending than with apermanent increase in government spending.B) i ncreases less with a temporary increase in government spending than with apermanent increase in government spending.C) d ecreases more with a temporary increase in government spending than with apermanent increase in government spending.D) d ecreases less with a temporary increase in government spending than with apermanent increase in government spending.Answer: BQuestion Status: P revious Edition51) A likely explanation for the extremely large reduction in investment spending during WorldWar II would beA) t he extremely large increase in output during the period.B) t he extremely large increase in real interest rates during the period.C) t hat consumption spending fell very little.D) t hat there was much government control over prices and the distribution of rawmaterials during the period.Answer: DQuestion Status: P revious Edition52) T he response of output following a natural disaster includesA) a n increase in aggregate demand and an increase in aggregate supply.B) a n increase in aggregate demand and a decrease in aggregate supply.C) a decrease in aggregate demand and an increase in aggregate supply.D) a decrease in aggregate demand and a decrease in aggregate supply.Answer: BQuestion Status: P revious Edition53) T he equilibrium effects of a temporary increase in total factor productivity includeA) a n increase in the real wage and an increase in the real interest rate.B) a n increase in the real wage and a decrease in the real interest rate.C) a decrease in the real wage and an increase in the real interest rate.D) a decrease in the real wage and a decrease in the real interest rate.Answer: BQuestion Status: P revious Edition54) H ow many of the following business cycle facts can be explained if the primary cause ofbusiness cycles is temporary changes in total factor productivity: procyclical consumption, procyclical investment, procyclical employment, and procyclical real wages?A) o neB) t woC) t hreeD) f ourAnswer: DQuestion Status: P revious Edition55) T he equilibrium effects of a prospective future increase in total factor productivity includeA) a n increase in the real wage and an increase in the real interest rate.B) a n increase in the real wage and a decrease in the realinterest rate.C) a decrease in the real wage and an increase in the real interest rate.D) a decrease in the real wage and a decrease in the real interest rate.Answer: CQuestion Status: P revious Edition56) I f future total factor productivity increasesA) l abor demand increases.B) g overnment expenses increase.C) c onsumption demand decreases.D) i nvestment demand increases.Answer: DQuestion Status: N ew57) I f consumption demand increases and the labor supply decreases, it must be thatA) t he real wage increases and the interest rate increases.B) t he real wage increases and the interest rate decreases.C) t he real wage decreases and the interest rate increases.D) t he real wage decreases and the interest rate decreases.Answer: BQuestion Status: N ew58) I f consumption demand increases and the labor supply decreases,A) o utput increases.B) o utput decreases.C) o utput does not change.D) o utput may change either way.Answer: DQuestion Status: N ew59) W hat could result in an increase of consumption demand and a decrease in the laborsupply?A) a drop in current taxesB) a n increase in future taxesC) a decrease in total factor productivityD) a n increase in government expensesAnswer: AQuestion Status: N ew60) I n the business cycle models we looked at so far, we assumed that prices (w and r) wereA) c ompletely flexible.B) s omewhat flexible.C) r igid.D) e xogenous.Answer: AQuestion Status: N ew61) I n general equilibriumA) s upply equals demand for all goods in all periods.B) s upply equals demand for most goods in all periods.C) s upply equals demand in present value, but not in all periods.D) p rices are exogenous.Answer: AQuestion Status: N ew。
宏观经济学-课后思考题答案_史蒂芬威廉森016
宏观经济学-课后思考题答案_史蒂芬威廉森016Chapter 16Unemployment: Search and Efficiency WagesTeaching GoalsThus far in the text, the only formal explanation for the phenomenon of unemployment has been in the context of the Keynesian sticky price model. If there is nominal wage rigidity, the real wage may become stuck at a level that implies an excess supply of labor. This chapter supplies two models of unemployment that are more firmly grounded in microeconomic principles.The first model of unemployment is the search model. In this framework, unemployment is a socially useful phenomenon that may improve the quality of matches between workers and firms. When studying the model, it is important to remind students that factors that raise the equilibrium unemployment rate may not be bad, and factors that reduce the equilibrium unemployment may not be good. The focus of the search model is primarily microeconomic in nature. The search model explains what incentives work as households change their behavior in the face of new policies. The microfoundations are very powerful here, as they allow us to experiment at no cost with various policy schemes, yet they give us results of macroeconomic importance: how do taxes or unemployment insurance alter the unemployment rate?The second model of unemployment is the efficiency wage model. This model provides an explanation of unemployment that is hard to empirically distinguish from the Keynesian sticky wage model. In both models, unemployed workers stand willingto accept employment at the prevailing wage rate, and yet cannot find work. However, in the sticky wage model it is plausible to imagine a scenario in which an unemployed worker can successfully agree to work at a wage lower than the prevailing wage. In the efficiency wage model, it is never in the interest of a firm to hire such a “bargain” worker, because the worker cannot commit to put in enough effort to make his employment worthwhile to the firm. The main advantage of this model is that it reconciles such “involuntary” unemployment with optimizing behavior. However, the model is less successful as a part of a consistent explanation of business cycles. The model cannot easily explain the fact that the real wage rate is procyclical.Classroom Discussion TopicsBy now, students should be comfortable with the idea that perfectly competitive markets generate efficient outcomes, as long as there are no externalities. In what sense does the structure of the job search model approximate perfect competition? Are there any possible sources of externalities? Is there some sense in which there may be elements of monopolistic competition? If the job search model is anything like a competitive market, do we have any reason to think that the unemployment rate might be too high or too low relative to a Pareto optimum? If an undistorted market provides the right amount of unemployment, then unemployment insurance leads to an inefficiently high rate of unemployment. Does this line of reasoning make a good case for eliminating unemployment insurance? Where does the desire to avoid risks come in? And moral hazard?152 Williamson ? Macroeconomics, Third EditionIt is useful to point out that the fundamental theorems of welfare economics are worked out in a model in which there is complete information, and where no passage of time is needed to equilibrate the market. Job search is only necessary because workers do not possess complete information, and time is required to acquire additional information. Do these considerations have any relevance for the question of the socially optimum amount of unemployment?The efficiency wage model does not do a very good job of explaining business cycles because it cannot rationalize a procyclical real wage rate. Suppose instead that we had an economy with two sectors. In one sector, firms find it optimal to pay an efficiency wage and there is an excess supply of workers at the optimal efficiency wage. In the other sector, perhaps worker effort and ability are directly observable. Now suppose that there is an increase in total factor productivity. While the wage paid in the efficiency wage sector may be unchanged, what is the likely effect on wages in the rest of the economy? Does this consideration improve the ability of the efficiency wage model to explain business cycle models? Is there likely to be any unemployment in this kind of economy? Why or why not? If there is no unemployment, does the existence of an efficiency wage sector add anything to our understanding of business cycles over and above the explanation given by the real business cycle model?OutlineI. Behavior of Unemployment and Participation RatesA. Determinants of the Unemployment Rate1. Aggregate Economic Activity2. Demography3. Government-Provided Unemployment Insurance4. Sectoral ShiftsB. The Participation Rate1. L ong-Run Trendsa. Participation Rate of Menb. Participation Rate of Women2. Cyclical VariationsII. A Search Model of UnemploymentA. Welfare of Employed Workers1. Real Wage2. Separation Rate3. Wage Income TaxB. Welfare of Unemployed Workers1. Size of Unemployment Insurance Benefit2. Frequency of Job Offers3. Unemployment Insurance Benefit T axC. Reservation Wage1. Welfare of Job Offer ≥ Welfare of Remaining Unemployed2. Increase in Unemployment Insurance Benefit *w ?↑3. Increase in Wage Tax *w ?↑Chapter 16 Unemployment: Search and Efficiency Wages 153D. Determinants of the Equilibrium Unemployment Rate1. Flows out of Employment2. Flows out of Unemployment3. The Wage Offer Distribution4. Effects of Disturbancesa. Increase in Unemployment Insurance Benefits U ?↑b. Increase in Job Offer Rate U ?↓c. Increase in Wage Tax U ?↑d. Increase in Benefit Tax U ?↓5. The Natural Rate of UnemploymentIII. The Efficiency Wage ModelA. Wages and Effort1. Adverse Selection: Unobserved Ability2. Moral Hazard: Unobserved ShirkingB. Optimization by the Firm 1. L abor Demand: ()()e w N e w MP w =2. Efficiency Wage: Maximize()e w wC. Labor Market Equilibrium1. >* Market-Clearing Wage w a. ()d s N N r <b Efficiency Wage Unemployment2. ≤* Market-Clearing Wage wD. Efficiency Wages and Business Cycles1. An Increase in Government Purchases: ,,,0r C I Y w U ↑↓↓Δ=Δ=Δ=2. An Increase in Total Factor Productivity: ,,,,0Y U C I w ↑↓↑↑Δ=3. An Improvement in Monitoring: w ↓Textbook Question SolutionsQuestions for Review1. The four key determinants of the unemployment rate are the level of aggregate economic activity,demographic factors, government intervention, and sectoral shifts.2. The unemployment rate is countercyclical.3. Different demographic groups often experience differing levels of unemployment. The unemploymentrate is higher when the composition of the work force includes a higher percentage of groups that typically experience more unemployment. As one example, younger workers whohave recentlyentered the work force typically experience more unemployment. The aggregate unemployment rate is therefore higher when young workers represent a larger-than-normal proportion of the work force.154 Williamson ? Macroeconomics, Third Edition4. The participation rate is procyclical.5. The welfare of the employed increases when the real wage increases, when the separation ratedecreases, and when taxes on wage income decrease.6. The welfare of the unemployed increases when the unemployment benefit increases, when thefrequency with which the unemployed receive job offers increases, and when the taxes onunemployment benefits decreases.7. The reservation wage is the wage offer that equates the welfare of accepting a job offer with thewelfare of remaining unemployed. The reservation wage increases when the welfare of beingemployed decreases and when the welfare of being unemployed increases.8. An increase in the unemployment benefit increases the welfare of being unemployed and thereforeincreases the reservation wage.9. An increase in the tax on wage income decreases the welfare of being employed and thereforeincreases the reservation wage.10. An increase in the unemployment insurance benefit raises the reservation rate. Therefore, theunemployed require more time to find an acceptable wageoffer, and the equilibrium unemployment rate increases.11. An increase in the job offer rate, holding the reservation wage constant, reduces the amount of time ittakes to find an acceptable job offer. This effect tends to lower the equilibrium unemployment rate.An increase in the job offer rate also increases the reservation wage. This effect tends to increase the equilibrium unemployment rate. The net effect on the unemployment rate is therefore uncertain.An active government role in helping the unemployed to find job offers is likely to increase the job offer rate.12. What matters to the unemployed is the value of the unemployment insurance benefit, net of taxes. Anincrease in taxes on unemployment insurance benefits acts in the same way as a decrease in the gross benefits.13. A higher real wage rate increases the likelihood that more able workers will accept job offers. Ifemployers cannot precisely measure the level of ability, a higher real wage rate increases the average ability level of employees working for the firm. This effect is due to adverse selection.A higher real wage rate increases the potential costs of an employee losing his or her job.If it is costly for firms to monitor the level of effort expended by its workers, a higher real wage reduces the incentives for workers to shirk. This effect is due to moral hazard.14. When the efficiency wage exceeds the market-clearing wage, there will be involuntaryunemployment in the efficiency wage model.15. An increase in government spending increases the realinterest rate, but has no effect on the levels ofoutput and employment.Chapter 16 Unemployment: Search and Efficiency Wages 155 16. An increase in total factor productivity decreases the real interest rate, and increases output andemployment. The increase in total factor productivity does not affect the real wage, unless the change in technology also affects the costs of monitoring workers’ performance.17. The efficiency wage model can account for procyclical employment, consumption, and investment.The efficiency wage model can account for countercyclical unemployment. The efficiency wage model cannot account for the procyclical behavior of the real wage rate.Problems1. An increase in the separation rate lowers the welfare from being employed, and therefore increasesthe efficiency wage. The higher reservation wage shifts the * UpH w curve to the right. The direct()effect of the increase in s shifts the (1)curve to the right. Unemployment therefore increases.s U2. An increase in the average wage paid, holding the reservation wage constant, increases the probabilityof finding an acceptable job offer. However, as long as job searchers are aware of the increase in wage rates, the reservation wage will also increase, because higher wages increase the welfare from being employed. On net, it is likely that at first approximation *H w will be unaffected, and so()there will be no change in the unemployment rate.3. The introduction of unemployment insurance benefits increases the welfare from being unemployedand increases the reservation wage. This effect increases the equilibrium rate of unemployment. If the insurance is paid for from a tax on wage income, then after-tax wages decrease. However, the reduction in the wage rate will likely result in an equal reduction in the reservation wage, so that *H w will be unaffected. Therefore, unemployment increases.()4. There are two channels through which more stringent qualification for unemployment insurancemay operate. For those currently employed, possible difficulties in qualifying would decrease the separation rate. Workers would be more reluctant to quit if they may not qualify for benefits and workers might perform better on the job reducing the incidence of firing. The unemployed who are covered by insurance would be unaffected. However, the pool of the unemployed would now include more potential workers not receiving benefits and these individuals are likely to have lower reservation wages. The average reservation wage would decrease and the long-run unemployment rate would decrease.5. Increased difficulty in distinguishing ability levels is much like an increased difficulty in monitoringworker effort. The effort function therefore shifts down and to the right. The efficiency wagetherefore increases.However, a careful modeling of the adverse selection problem is more complicated than the modeling of the moralhazard problem. If a firm believes that it has some ability to distinguish between high- and low-ability workers, then it is likely to offer different wages to those believed to be of high rather than low ability. In a more complicated model of such a segmented market, it is likely that an increase in the difficulty of distinguishing between workers will lead to an increase in the wages of low-ability workers and a decrease in wages of high-ability workers.156 Williamson ? Macroeconomics, Third Edition6. The destruction of capital is much like a decrease in total factor productivity. The labor demand curveshifts to the left. As long as there is no change in the ability to monitor, there will be no change in the efficiency wage. Output and employment decrease, unemployment increases, and the real interest rate increases.7. The efficiency wage model is a model that predicts real wage rigidity, not nominal wage rigidity. Anincrease in the money supply leads to an equiproportional increase in nominal wages and prices.Money is therefore neutral.8. According to the permanent income hypothesis, a permanent increase in government spending is likely to lead to an equal-sized decrease in consumption spending. The output demand curve therefore does not shift. The wealth effect of the increase in government spending increases labor supply. However, in the efficiency wage model output and employment are determined by labor demand. Therefore, the output supply curve also does not shift. Output, employment, the real wage, investment, and the real interest rate are all unchanged. The only effects of the permanent increase ingovernment spending are a decrease in consumption and an increase in unemployment. There is no crowding out of investment spending. Instead, there is a one-for-one crowding out of consumption spending.。
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7-9
Equation 7.2
Future human capital depends on current human capital and time devoted to training and education.
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Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
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Figure 7.1 Rich and Poor Countries and the Steady State
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Figure 7.8 No Convergence in the Endogenous Growth Model
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Chapter 7
Income Disparity Among Countries and Endogenous Growth
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Chapter 7 Topics
• Convergence • Endogenous growth: a model of human capital accumulation
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7-2
Convergence in the Solow Growth Model
If two countries are initially rich and poor, but identical in all other respects, they will converge in the long run to the same level and rate of growth of per-capita income.
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7-8
Equation 7.1
Consumption is equal to total wage income.
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7-12
Figure 7.5 Determination of the Equilibrium Real Wage in the Endogenous Growth Model
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7-13
Equation 7.5
Equilibrium Consumption:
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7-14
Equation 7.6
Human capital evolves in equilibrium according to:
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7-15
Equation 7.7
Equilibrium growth rate of human capital:
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Figure 7.4 Differences in Total Factor Productivity Can Explain Disparity in Income per Worker Across Countries
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7-16
Figure 7.6 Human Capital Accumulation in the Endogenous Growth Model
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Figure 7.7 Effect of a Decrease in u on the Consumption Path in the Endogenous Growth Model
7-4
Figure 7.2 Convergence in Income per Worker Across Countries in the Solow Growth Model
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7-10
Equation 7.3: Production Function
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7-11
Equation 7.4: Firm’s Profits
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7-5
Figure 7.3 Convergence in Aggregate Output Across Countries in the Solow Growth Model
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7-7
Endogenous Growth: A Model of Human Capital Accumulation
In this model, the growth rate of per capita income is determined by the efficiency with which human capital is accumulated, and the fraction of available time devoted to human capital accumulation.