史蒂芬 威廉森 宏观经济学 第四版 课后题答案 最新Solution_CH5

1 / 66第5章 封闭经济下的一时期宏观经济模型5.1 复习笔记一、政府1．政府行为政府希望购买一定数量的消费品G ，资金来源正是它对典型消费者的征税。

政府在提供公共物品，如国防中应发挥特殊作用。

2．政府预算约束商品在私人部门生产出来后，政府从中购买的数量为G ，剩下的由典型消费者消费，而G 属于外生变量。

外生变量由模型以外的因素决定，而内生变量则由模型本身决定。

在封闭经济模型中，假定政府支出与其他经济部门发生的事情无关，则政府支出是外生变量。

政府必须遵守政府预算约束，它表示为：G ＝T ，即政府的实际购买等于实际税收。

2 / 663．政府政策分析财政政策是指政府对其（购买性）支出、税收、转移性支出和借债的选择。

其中，政府（购买性）支出是用来购买最终商品和服务的，而转移性支出只不过是将购买力从一组人那里重新分配给另一组人。

在预算约束下，政府不能通过借债为其支出筹资，税收收入也不能高于其支出。

政府预算赤字即G －T 总为零。

二、竞争性均衡1．宏观经济模型宏观经济模型是选取外生变量（由模型以外的因素决定，用于模型要解决的问题），来确定内生变量的值，如图5-1所示。

利用模型的过程，就是进行实验以确定外生变量的变化是如何改变内生变量的过程。

图5-1 模型选取外生变量，以确定内生变量3 / 662．竞争性均衡（1）定义竞争性均衡（competitive equilibrium ）是指给定市场价格，经济中每个市场的需求都等于供给的状态。

其中，竞争性是指所有消费者和企业都是价格接受者，当所有消费者和企业的行为一致时，经济就处于均衡中。

市场出清是指所有市场的需求都等于供给。

（2）须满足的四个条件竞争性均衡是在给定外生变量G （政府支出）、z （全要素生产率）和K （资本存量）下，满足下列条件的一组内生数量——C （消费）、N s （劳动供给）、N d （劳动需求）、T （税收）、Y （总产出）以及内生实际工资w 。

宏观经济学第四版课后习题答案第12章国民收入核算1.下列项目是否计入GDP，为什么？（1）政府转移支付；（2）购买一辆用过的卡车；（3）购买普通股票；（4）购买一块地产。

答：（1）不计入。

因为政府转移支付只是简单地通过税收把收入从一个人或一个组织转移到另一个人或另一个组织手中，并没有相应的物品或劳务的交换发生。

（2）不计入。

不是该期的实际生产活动。

（3）不计入。

经济学上所讲的投资是增加或替换资本资产的支出，即购买新厂房、设备和存货的行为，而人们购买债券和股票只是一种交易活动，并不是实际的生产经营活动。

（4）不计入。

同（3）。

2.在统计中，社会保险税增加对GDP、NDP、NI、PI和DPI这五个总量中哪个总量有影响？为什么？答：社会保险税实质上是企业和职工为得到社会保障而支付的保险金，它由政府相关部门按一定比率以税收形式征收。

社会保险税是从NI中扣除的，因此，社会保险税的增加并不影响GDP、NDP和NI，但影响个人收入PI。

3.如果甲乙两国并成一个国家，对GDP总和会有什么影响（假定两国产出不变）？答：有影响。

因为合并前的对外贸易变成合并后的国内贸易。

例如合并前，甲国对乙国有出口200亿，对乙国有进口100亿，顺差100亿。

假定他们分别都没有其他贸易伙伴。

对甲国而言，顺差的100亿为GDP加项；对乙国而言，逆差的100亿为GDP减项，两国GDP的总和中的对外贸易部分因此而抵消，为零。

合并后，甲地生产的产品200亿，乙地生产的产品100亿，对合并后的新国家而言，新增的GDP为300亿，总和增加了。

4.某年发生了以下活动（a）一银矿公司支付7.5万美元给矿工开采了50千克银卖给一银器制造商，售价10万美元；（b）银器制造商支付5万美元工资给工人造了一批项链卖给消费者，售价40万美元。

（1）用最终产品生产法计算GDP；（2）每个生产阶段生产多少价值？用增值法计算GDP。

（3）在生产活动中赚得的工资和利润各共为多少？用收入法计算GDP。

第二部分课后习题第1篇导论和衡量问题第1章导论一、复习题1．宏观经济学的主要鲜明特征是什么？答：（1）宏观经济学的研究对象是众多经济主体的行为。

它关注的是消费者和企业的总体行为、政府的行为、单个国家的经济活动总水平、各国间的经济影响，以及财政政策和货币政策的效应。

（2）宏观经济学侧重于总量研究，强调的问题主要是长期增长和经济周期。

其研究的具体内容包括：①持续经济增长的动力；②经济增长是否有极限；③政府应该如何改变经济增长率，促进经济增长；④经济周期的原因；⑤经济增长在大萧条和第二次世界大战期间发生的剧烈波动是否会重现；⑥政府是否应该采取行动以熨平经济周期。

2．宏观经济学与微观经济学有何异同？答：（1）宏观经济学与微观经济学的联系20世纪70年代以来，微观经济学家与宏观经济学家都在使用非常相似的研究工具。

宏观经济学家用来描述消费者与企业的行为、目标与约束，以及它们之间如何相互影响的经济模型，是根据微观经济学原理建立起来的，而且在分析这些模型和拟合数据时通常都用微观经济学家所用的方法。

宏观经济分析建立在微观经济学原理基础之上。

（2）宏观经济学与微观经济学的区别①研究方法不同微观经济学家侧重个量分析，宏观经济学侧重于总量研究。

②研究内容不同微观经济学研究单个家庭和企业的行为。

因为经济作为一个整体是由许多家庭与企业组成的，在总体水平上的相互影响是单个家庭和企业决策的结果。

宏观经济学有别于微观经济学，因为它涉及的是所有经济主体的选择对经济的总影响，而不是单个消费者或企业的选择对经济的影响，它强调的问题主要是长期增长和经济周期。

3．2011年的普通美国人比1900年的普通美国人富多少？答：2011年的普通的美国人比1900年的普通美国人平均来说富近8倍。

实际人均GDP 是衡量一国居民平均收入水平的指标。

1900年，一个美国人的平均收入是4793美元（以2005年美元计），2011年增加到42733美元（以2005年美元计）。

Chapter 9Credit Market Imperfections: Credit Frictions,Financial Crises and Social SecurityTextbook Question SolutionsQuestions for Review1. Borrowers face higher interest rates than lenders.2. The Ricardian equivalence does not hold. Credit constraint household will not save at least part of thetax cut an consume it.3. Yes, there is room for government intervention, in the form of social security or by holding positivepublic debt.4. Asymmetric information and limited commitment.5. The default premium can increase if more consumers are likely to default.6. As consumers face a higher interest rate when borrowing, they borrow less and thus consume lesstoday.7. Such a borrower must reduce the size of her loan, and thus her consumption. She may also want todefault, thereby increasing the default premium and the interest rate of other borrowers, who also reduce their consumption.8. Pay-as-you-go Social Security always improves the welfare of the first generation to receive benefits.Later generations only see a welfare improvement if the population growth rate exceeds the real rate of interest.9. Fully funded Social Security has no effects as long as taxes collected are less than the optimal amountof saving. If taxes and benefits are larger, then individuals consume less when working and more when retired relative to what they would prefer.10. The government cannot commit not to take care of destitute senior citizens. This leads to an incentivenot to save, at least for the poor. With social security, there should be no destitute senior citizens, and the aggregate savings rate is higher as everyone saves optimally for retirement.Problems1. (a) The government intertemporal budget constraint is, assuming both t and t′ are positive:84 Williamson • Macroeconomics, Fourth Edition 1(1)0(1)bt b at r ′+−=+ (b) We are in a situation where asymmetric information becomes important: the government doesnot know who will be able to pay the future taxes. The relevant interest rate is the onecorresponding to the steeper part of the budget constraint, and the new endowment thus movesthe flatter part down. Consumption choices of the first period consumers are thus impactedthrough a negative income shock, as they have to pay more taxes to compensate for more unpaidtaxes in the future.(c) The Ricardian equivalence does not apply as the change in timing of taxes has changed someconsumption patterns. Indeed, households cannot fully adjust their savings, thus any change inperiodic disposable income has an impact at least for some households.2. (a) The government can only tax in the second period as much as it could get from the collateral:t ′ ≤ pH(b) Now that the government has priority on the collateral, the new collateral constraint is:−s (1 + r ) ≤ pH − t ′which implies(1)/(1)y t pH c r t r −+≤′+−+ (c) As we see from the new collateral constraint, Ricardian equivalence holds, as any shifting oftaxes across periods does not affect the constraint. The consumer makes the same consumptionchoice.3. (a) The bank will be lending so that it will be able to get the loan back in expectation. Thus, the newcollateral constraint isChapter 9 Credit Market Imperfections: Credit Frictions, Financial Crises and Social Security 85−s (1 + r ) ≤ a pHwhich leads to .(1)y t a pH c r −+≤+ This is much like Figure 9.5 in the textbook, simply with a lower collateral value.(b) If the collateral is more likely to be of no value, banks will lend less. Thus, some household willnot be able to borrow as much as they could before, leading for them and in aggregate to areduction of current consumption and an increase in future consumption. Thus we have exactlythe same impact as if we had a reduction in p , as in Figure 9.5 of the textbook.4. Social Security.(a) When the program is first instituted, the current old receive b in benefits and pay nothing.The effect on the current old is as in Figure 9.8 in the text. The current young receive b inbenefits when they are old. This effect is also captured by the shift from BA to FD in thetext’s Figure 9.8. The current young also lend bN to the government in period T and receive(1)r bN + in principal and interest when they are old. In per capita terms, these amounts are/(1)/(1)bN n N b n +=+ and (1)/(1)(1)/(1)r bN n N r b n ++=++ respectively. However, thisborrowing and lending are represented in Figure 9.8 as movements along the budget line.Unless there is a change in the real interest rate, there is no additional shift in the budget line.Therefore, both these generations unambiguously benefit from the program.(b) Once the program is running, it is identical to the pay-as-you-go system in the text. This programbenefits a typical cohort as long as n > r , as is depicted in textbook Figure 9.9. A specialcircumstance applies to the cohort born in period T + 1. These individuals each receive a benefit per capita of b /(1 + r ) in present value terms. However, they pay taxes to support two generations’worth of benefits. They pay taxes to retire the principal and interest on debt incurred in period T . The per capita share of principal and interest on their grandparents’ benefits is equal to(1 + r )b /(1 + n )2. The per capita share of their parents’ benefits is equal to b /(1 + n ). This generation can only benefit if:22(1)(1)1(1)(1)r r n n ++>+++ This requirement is obviously more stringent than .n r >5. Under this regime, disposable income for the young is y , but the price of current consumption is(1 + s ). This implies that the intertemporal budget constraint of the household is now(1)(1)(1)(1)s c c y y b r r r ′′+++=++++ In equibrium, it must be that sc (1 + n ) = b . Thus whether there is going to be a positive income effectis going to depend on n is larger than r . But the is also a substitution effect coming from the change in relative price between c and c ′. This substitution effect has no impact on welfare, though.86 Williamson • Macroeconomics, Fourth Edition6. (a) Consumers born in T are the first ones not to get benefits. The government finances the benefitsof the last generation, bN, with bonds D T. Thus each consumer born in T buys D T/N′ bonds, orb/(1 + n) each. In T +1, the government has to reimburse principal and interest, (1 +r)D T, thuseach old consumer at that time obtains (1 +r)b/(1 +n). This means that for the intertemporalbudget constraint in the figure below, the endowment point is shifted b/(1 + n) to the left and(1 +r)b/(1 +I) up. This is on the same budget constraint as before. However, this household isalso losing the old-age benefits it was expecting, thus the new endowment point shifts anadditional b down. However, this generation does not have to pay, when young, for the benefitsof the previous generation, as they are covered by the debt. Thus, the endowment point shiftsb/(1 +n) to the right. As r> n, the new endowment point is now to the right of the old budgetconstraint, see the figure below, and this household is better of. Essentially, it just the opposite of the situation that made it viable to institute a pay-as-you-go system when n > r. The exact samereasoning applies to all future generations.。

第5章封闭经济下的一时期宏观经济模型一、复习题1．学习封闭经济模型为什么有用？答：封闭经济模型反映的对象是一个单独的国家，与其他国家无关，即没有对外贸易往来。

封闭经济比较容易理解，将一个经济体的经济开放时其经济的大部分性质都不会改变，而且将全世界作为一个整体时封闭经济是一个合理的模型。

同时，可以通过分析在封闭经济中，市场中的消费者和企业是如何互动的，来探讨宏观经济模型的构建方法。

2．政府在一时期封闭经济模型中的作用是什么？答：政府在一时期封闭经济模型中的作用是征税和购买商品。

实践中，政府提供许多不同的产品和服务，包括道路和桥梁、国防、空中交通管制以及教育。

经济学家一般认为，政府在提供公共物品中应发挥特殊作用，因为私人部门难以或不可能提供公共物品。

3．在一时期模型中，政府可以有赤字吗？请解释。

答：在一时期模型中，资金的借、贷行为都无法存在，因此政府无法为其赤字融资，即政府没有赤字。

在预算约束下，政府不能通过借债为其支出筹资，税收收入也不能高于其支出。

政府预算赤字，即G－T≡0。

4．模型中的内生变量有哪些？答：内生变量是由模型本身决定的。

模型中的内生变量包括：C（消费）、N s（劳动供给）、N d（劳动需求）、T（税收）、Y（总产出）和w（市场实际工资）。

5．模型中的外生变量有哪些？答：外生变量是由模型以外的因素决定的。

模型中的外生变量有外生变量G（政府支出）、z（全要素生产率）和K（经济的资本存量）。

6．就这个模型而言，竞争性均衡必须满足哪四个条件？答：竞争性均衡必须满足：（1）典型消费者在他的预算约束下会选择C（消费）和N s（劳动供给），以使其境况尽可能得到改善；（2）典型企业会选择N d（劳动需求），以使其利润最大化；（3）劳动力市场出清，即N d＝N s；（4）政府预算约束得到满足，即G＝T。

7．生产可能性边界的斜率的经济意义是什么？答：生产可能性边界斜率为－MP N，生产可能性边界斜率也被定义为－MRT l，C，MRT l，C为闲暇与消费之间的边际转换率。

Chapter 2MeasurementTextbook 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.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.10 Williamson • Macroeconomics, Fourth Edition11. 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 accountsfor the number of individuals unemployed, without reference to how intensively they search for new jobs.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 of wheat 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 of wheat 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.Chapter 2 Measurement 112. 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.(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 fromabroad are (−$25 million), so GNP is equal to $125 million.3. Wheat and Bread12 Williamson • Macroeconomics, Fourth Edition(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 of bread at $2/loaf, which is valued at $100,000. Firm B pays $60,000 to firm A for 20,000bushels 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 13 4. Price and quantity data are given as the following.Year 1Good QuantityPrice$1,000Computers 20Bread 10,000$1.00Year 2PriceGood QuantityComputers 25$1,500$1.00Bread 10,000(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=×+×=. The output at year 1 prices. Year 2 real GDP 25$1,00012,000$1.00$37,000percentage 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 1.23496g==.cThe 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 equalsnominal 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 GDPequals base year real GDP, so the base year implicit GDP deflator is 100. For the year 2, theimplicit 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 deflatorequals 36.85%.14 Williamson • Macroeconomics, Fourth 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 1PriceGood QuantityYear 1 Computers 20 $1,000Bread 10,000$1.00Year 2PriceGood QuantityYear 1 Computers 50 $750$1.10Bread 12,000First, note that the change in the definition of a “computer” does not affect the calculations ofnominal GDP. We next compute real GDP with year 1 as the base year. Year 2 real GDP in year×+×= The percentage change in real GDP is1 prices is now 50$1,00012,000$1.00$62,000.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, g2 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 usingchain 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, theuse of historical prices puts more weight on the increase in quality-adjusted computer output.Chapter 2 Measurement 15 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 $0.60Cauliflower 350 $0.85(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.16 Williamson • Macroeconomics, Fourth Edition(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. Additionsto inventory are treated as purchasing one owns output. The corn producer’s costsinclude wages of $60 million and taxes of $20 million. Therefore, profit income equals$150 million − $60 million − $20 million = $70 million. Government income equals taxespaid by the corn producer, 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 governmentbudget 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).7. 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 $2,776 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. As for the government sector, the value added in the FIRE sector is difficult to determine with theproduct or the expenditure approach. Thus, this income approach seems most appropriate. However, if wages and profits are not representative of value added, this approach also yields erroneousnumbers. This is especially the case if FIRE income was obtained by hurting costumers, who thereby received no value added. GDP is then overvalued.10. Not all transactions are made with checks or wire transfers. Anything that is paid with cash is notrecorded through Fedwire. Also any transactions with checks between two clients of the same bank do not need to be cleared through Fedwire.Chapter 2 Measurement 17 11. 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 ).12. 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).13. Assume the following:10540308010520D INT T G C NFP CA S =======−= (a) 201080110d p Y S CS D C=+=++=++=18 Williamson • Macroeconomics, Fourth Edition (b) 103054015D G TR INT TTR 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 NX I GDP C G NX =+++=−−−=−−+=14. First some preliminaries. As the unemployment rate is 5% and there are 2.5 million unemployed, itmust be that the labor force is 50 million (2.5/0.05). Thus, the participation rate is 50% (50/100), the labor force 50 million, the number of employed workers 47.5 million (50-2.5), and theemployment/population ratio is 47.5% (47.5/100).。

第3章经济周期的衡量一、复习题1．经济周期的主要特征是什么？答：经济周期的主要特征是：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增长趋势的曲线围绕着趋势上下变动，低谷是对趋势的最大负偏离，高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，GDP偏离趋势的三个重要特征是什么？答：GDP偏离趋势的三个重要特征是：（1）实际GDP偏离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。

一些高峰和低谷意味着对趋势的巨大偏离，而另一些高峰和低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中高峰和低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。

一些高峰和低谷意味着对趋势的巨大偏离，而另一些高峰和低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中高峰和低谷之间的时间跨度变化很大。

（3）实际GDP偏离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。

Macroeconomics, 3e (Williamson)Chapter 5 A Closed-Economy One-Period Macroeconomic Model1) A n economy that has no interaction with the rest of the world is calledA) a n isolated economy.B) a closed economy.C) a parochial economy.D) a rogue nation.Answer: BQuestion Status: P revious Edition2) A n economy that engages in international trade is calledA) a cooperative economy.B) a modern economy.C) a n engaged economy.D) a n open economy.Answer: DQuestion Status: P revious Edition3) G oods and services provided by the government are calledA) g overnment goods.B) p ublic goods.C) f ree goods.D) s ocial goods.Answer: BQuestion Status: P revious Edition4) I n an economic model, an exogenous variable isA) a stand-in for more complicated variables.B) d etermined by the model itself.C) d etermined outside the model.D) a variable that has no effect on the workings of the model.Answer: CQuestion Status: P revious Edition5) I n an economic model, an endogenous variable isA) a stand-in for more complicated variables.B) d etermined by the model itself.C) d etermined outside the model.D) a variable that has no effect on the workings of the model.Answer: BQuestion Status: P revious Edition6) I n a one-period model, government is likely to runA) a deficit but not a surplus.B) a surplus but not a deficit.C) e ither a surplus or a deficit.D) n either a surplus nor a deficit.Answer: DQuestion Status: P revious Edition7) I n a one-period economic model, the government budget constraint requires thatgovernment spendingA) = taxes + transfers.B) = taxes + borrowing.C) > 0.D) = taxes.Answer: DQuestion Status: P revious Edition8) W hich of the following relationships does not hold in the one-period model?A) G=TB) Y=C+GC) Y=zF(K,N)D) π=Y-wN-CAnswer: DQuestion Status: N ew9) F iscal policy refers to a government's choices over itsA) e xpenditures, taxes, transfers, and borrowing.B) e xpenditures, taxes, issuance of money, and borrowing.C) e xpenditures, foreign affairs, issuance of money, and borrowing.D) i ssuance of money, taxes, environmental regulations, and foreign affairs.Answer: AQuestion Status: P revious Edition10) M aking use of an economic model is a process ofA) s olving hundreds of simultaneous equations.B) r unning experiments to determine how changes in the endogenous variables willchange the exogenous variables.C) r unning experiments to determine how changes in the exogenous variables willchange the endogenous variables.D) r esolving inconsistencies in the actions of economic agents.Answer: CQuestion Status: P revious Edition11) A competitive equilibrium is a state of affairs in whichA) m arkets clear, and output is maximized.B) o utput is maximized, and all agents are equally well-off.C) a ll agents are equally well-off and agents are price-takers.D) a gents are price-takers, and markets clear.Answer: DQuestion Status: P revious Edition12) I n a general equilibrium modelA) a ll markets but one clear.B) t here are no fluctuations.C) a ll prices are exogenous.D) a ll prices are endogenous.Answer: DQuestion Status: N ew13) I n a competitive equilibrium all these relationships hold but one. Which one?A) N d= N sB) Y=G+CC) G=TD) w=zAnswer: DQuestion Status: N ew14) I n the one-period competitive model we have been studyingA) b oth consumption and total factor productivity are exogenous.B) c onsumption is exogenous and total factor productivity is endogenous.C) c onsumption is endogenous and total factor productivity is exogenous.D) b oth consumption and total factor productivity are endogenous.Answer: CQuestion Status: P revious Edition15) A relationship that shows the technological possibilities for an economy as a whole is calledaA) p roduction function.B) u tility possibilities frontier.C) p roduction possibilities frontier.D) b udget constraint.Answer: CQuestion Status: P revious Edition16) T he production possibilities frontier in the one-period model is aA) b ehavioral relationship between consumption and leisure.B) b ehavioral relationship between consumption and government spending.C) t echnological relationship between consumption and leisure.D) t echnological relationship between consumption and government spending.Answer: CQuestion Status: P revious Edition17) T he production possibilities frontier representsA) a ll combinations of consumption and leisure for fixed output.B) a ll equally affordable combinations of consumption and leisure for a given wage.C) a ll feasible combinations of consumption and leisure.D) a ll equally liked combinations of consumption and leisure.Answer: CQuestion Status: N ew18) W hich of the following is not a reason for solving the model with a PPF?A) I t merges the household and firm problems into one graph.B) I t is simpler to solve the social planner problem.C) I t highlights the fact that the marginal rate of substitution should equal the marginalrate of transformation.D) I t highlights the fact that firms make no profit in equilibrium.Answer: DQuestion Status: N ew19) T he PPF representsA) a ll possible outcomes for a given wage.B) t he set of feasible outcomes.C) g iven leisure, how much consumption a household wants.D) t he share of consumption in output.Answer: BQuestion Status: N ew20) T he rate at which one good can be converted technologically into another is calledA) t he marginal rate of transformation.B) t he marginal rate of substitution.C) t he marginal product of labor.D) t he rate of conversion.Answer: AQuestion Status: P revious Edition21) P oints on the production possibilities frontier have the property that theyA) a re inherently unattainable.B) s how the maximum amount of leisure that can be consumed for given amounts ofgoods consumed.C) s how the maximum amount of goods that can be consumed for given amounts ofgovernment spending.D) s how the maximum amount of leisure that can be consumed for given amounts ofhours worked.Answer: BQuestion Status: P revious Edition22) A competitive equilibrium has all of the following properties exceptA) M P N= slope of PPF.B) M RS l,C=MRT l,C.C) M RT l,C=MP N.D) M P N=w.Answer: AQuestion Status: P revious Edition23) A competitive equilibrium is Pareto optimal if there is no way to rearrange or to reallocategoods so thatA) a nyone can be made better off.B) n o one can be made worse off.C) s omeone can be made better off without making someone else worse off.D) s omeone can be made better off without making everyone else worse off.Answer: CQuestion Status: P revious Edition24) W hich of the following is not equal to the others in equilibrium?A) t he real wageB) t he marginal rate of substitution between leisure and consumptionC) t he marginal product of laborD) t he price of consumptionAnswer: DQuestion Status: N ew25) A Pareto optimum is a point thatA) a malevolent dictator would choose.B) a cooperative coalition of some altruistic consumers would choose.C) a cooperative coalition of some socially responsible firms would choose.D) a social planner would choose.Answer: DQuestion Status: P revious Edition26) A Pareto optimum requires all of the following exceptA) M P N=-slope of PPF.B) M RS l,C=MRT l,C.C) M RT l,C=MP N.D) M P N=w.Answer: DQuestion Status: P revious Edition27) M uch of the writings of Adam Smith are in close agreement withA) t he necessity of trade restrictions.B) t he first fundamental theorem of welfare economics.C) t he second theorem of welfare economics.D) b oth B and C above.Answer: BQuestion Status: P revious Edition28) T he first fundamental theorem of welfare economics states thatA) u nder certain conditions, a competitive equilibrium is Pareto optimal.B) a competitive equilibrium is always Pareto optimal.C) u nder certain conditions, a Pareto optimum is a competitive equilibrium.D) a Pareto optimum is always a competitive equilibrium.Answer: AQuestion Status: P revious Edition29) T he second fundamental theorem of welfare economics states thatA) u nder certain conditions, a competitive equilibrium is Pareto optimal.B) a competitive equilibrium is always Pareto optimal.C) u nder certain conditions, a Pareto optimum is a competitive equilibrium.D) a Pareto optimum is always a competitive equilibrium.Answer: CQuestion Status: P revious Edition30) T he concept of Pareto optimality is aA) u topian concept.B) u seful concept because it guarantees economic equality.C) u seful concept because it guarantees economic efficiency.D) u seful concept that carefully balances a society's desires for equality and efficiency.Answer: CQuestion Status: P revious Edition31) A competitive equilibrium may fail to be Pareto optimal due to all of the following exceptA) i nequality.B) e xternalities.C) d istorting taxes.D) n on-price-taking firms.Answer: AQuestion Status: P revious Edition32) A n externality is any activity for which an individual firm or consumer does not take intoaccount allA) o f the ramifications of its actions on others.B) a ssociated costs.C) a ssociated benefits.D) a ssociated costs and benefits.Answer: DQuestion Status: P revious Edition33) T he presence of a distorting tax on wage income can result inA) M P N<MRT l,C.B) M RT l,C<MRS l,C.C) M P N<w.D) M RS l,C<MP N.Answer: DQuestion Status: P revious Edition34) R elative to the social optimum, monopoly power directly leads toA) u nderproduction.B) o verproduction.C) t oo much leisure.D) t oo little leisure.Answer: AQuestion Status: P revious Edition35) A n increase in government spending shifts the PPFA) u pward, but does not change its slope.B) u pward, and also changes its slope.C) d ownward, but does not change its slope.D) d ownward, and also changes its slope.Answer: CQuestion Status: P revious Edition36) T he experience of the U.S. economy during World War II confirms the prediction that adramatic increase in government spending is likely toA) i ncrease both real GDP and consumption.B) i ncrease real GDP and decrease consumption.C) d ecrease real GDP and increase consumption.D) d ecrease both real GDP and consumption.Answer: BQuestion Status: P revious Edition37) A n increase in government spendingA) i ncreases consumption, increases hours worked, and increases the real wage.B) r educes consumption, increases hours worked, and increases the real wage.C) r educes consumption, increases hours worked, and reduces the real wage.D) r educes consumption, reduces hours worked, and reduces the real wage.Answer: CQuestion Status: P revious Edition38) A n increase in government spendingA) i ncreases consumption and output.B) i ncreases consumption, decreases output.C) d ecreases consumption, increases output.D) d ecreases consumption and output.Answer: CQuestion Status: N ew39) C hanges in government spending are not likely causes of business cycles becausegovernment spending induced business cycles would counterfactually predictA) c ountercyclical real wages.B) p rocyclical real wages.C) c ountercyclical employment.D) p rocyclical employment.Answer: AQuestion Status: P revious Edition40) C hanges in government spending are not likely causes of business cycles becausegovernment spending induced business cycles would counterfactually predictA) c ountercyclical consumption.B) p rocyclical consumption.C) c ountercyclical employment.D) p rocyclical employment.Answer: AQuestion Status: P revious Edition41) W hich feature of the business cycle does the one-period model replicate with shocks togovernment expenditures?A) p rocyclical employmentB) p rocyclical consumptionC) p rocyclical real wagesD) c ountercyclical pricesAnswer: AQuestion Status: N ew42) A n increase in total factor productivity shifts the PPFA) u pward, but does not change its slope.B) u pward, and also changes its slope.C) d ownward, but does not change its slope.D) d ownward, and also changes its slope.Answer: BQuestion Status: P revious Edition43) A n increase in total factor productivityA) i ncreases consumption, increases output, and increases the real wage.B) r educes consumption, increases output, and increases the real wage.C) r educes consumption, increases output and reduces the real wage.D) r educes consumption, reduces output, and reduces the real wage.Answer: AQuestion Status: P revious Edition44) W hich of the following is wrong with respect to an increase in total factor productivity?A) H ouseholds are better off.B) C onsumption is up.C) T he real wage is down.D) O utput is up.Answer: CQuestion Status: N ew45) I n response to an increase in total factor productivityA) b oth the substitution effect and the income effect suggest that hours worked shouldincrease.B) t he substitution effect suggests that hours worked should increase, while the incomeeffect suggests that hours worked should decrease.C) t he substitution effect suggests that hours worked should decrease, while the incomeeffect suggests that hours worked should increase.D) b oth the substitution effect and the income effect suggest that hours worked shoulddecrease.Answer: BQuestion Status: P revious Edition46) C hanges in total factor productivity are plausible causes of business cycles becauseproductivity-induced business cycles correctly predictA) r eal wages and total hours must be procyclical.B) r eal wages and consumption must be procyclical.C) t otal hours worked and consumption must be procyclical.D) c onsumption and government spending must be procyclical.Answer: BQuestion Status: P revious Edition47) C hanges in total factor productivity are plausible causes of business cycles becauseA) o f the welfare theorems.B) t he U.S. government is following supply-side economic policy.C) t he model matches many stylized facts.D) p rices are countercyclical.Answer: CQuestion Status: N ew48) R eal business cycle theory argues that the primary cause of business cycles is fluctuations inA) p references.B) g overnment spending.C) t he importance of externalities.D) t otal factor productivity.Answer: DQuestion Status: P revious Edition49) J ust prior to the four most recent U.S. recessions, there has been aA) s ignificant contraction of the money supply.B) l arge decrease in government spending.C) l arge increase in the relative price of food.D) s ignificant increase in the relative price of energy.Answer: DQuestion Status: P revious Edition50) I f the government replaces a lump sum tax with a proportional labor income tax, thenA) e mployment and output increase.B) e mployment increases and output decreases.C) e mployment decreases and output increases.D) e mployment and output decrease.Answer: DQuestion Status: N ew51) P roportional income taxation is distorting becauseA) p eople do all they can to avoid paying taxes.B) t he competitive equilibrium is not Pareto optimal.C) f irms do all they can to avoid paying taxes.D) t he government budget constraint does not hold.Answer: BQuestion Status: N ew52) W ith a linear production function in labor only, which of the following must be true?A) T he representative household works as much as possible.B) T he representative firm makes large profits.C) T he real wage equals total factor productivity.D) T he marginal product of labor exceeds the real wage.Answer: CQuestion Status: N ew53) H ow does an increase in the proportional labor income tax modify the budget constraint?A) a parallel move upB) a parallel move downC) a tilting upD) a tilting downAnswer: DQuestion Status: N ew54) A t the competitive equilibrium with a positive proportional labor income taxA) t he real wage after tax exceeds the marginal product of labor.B) t he real wage after tax equals the marginal product of labor.C) t he real wage after tax is lower than the marginal product of labor.D) W e cannot say.Answer: CQuestion Status: N ew55) A t the competitive equilibrium with a positive proportional labor income taxA) t he real wage before tax exceeds the marginal product of labor.B) t he real wage before tax equals the marginal product of labor.C) t he real wage before tax is lower than the marginal product of labor.D) W e cannot say.Answer: BQuestion Status: N ew56) T he tax base isA) t he average tax rate.B) t he tax rate for the base year.C) t he object being taxed.D) t he lowest tax rate.Answer: CQuestion Status: N ew57) W hen the tax rate increases, the tax revenueA) a lways increases.B) d oes not change.C) a lways decreases.D) m ay increase or decrease.Answer: DQuestion Status: N ew58) T he Laffer curve is a curve showingA) o utput as a function of the tax rate.B) t ax revenue as a function of the tax rate.C) g overnment expenses as a function of how liberal the government is.D) t he tax rate as a function of government expenses.Answer: BQuestion Status: N ew59) S upply-side economists argue thatA) o ne should get rid of all taxes.B) t ax rates should not be progressive.C) i ncreasing tax rates always hurts tax revenue.D) o ne can increase tax revenue by decreasing the tax rate.Answer: DQuestion Status: N ew60) I n a competitive equilibrium with a Laffer curve, there are two equilibria that differ in theirA) t ax revenue.B) t otal factor productivity.C) o utput.D) m arginal tax rate.Answer: CQuestion Status: N ew。

1 / 37第1章 导 论1.1 复习笔记一、宏观经济学1．宏观经济学的研究对象宏观经济学的研究对象是众多经济主体的行为。

它关注的是消费者和企业的总体行为、政府的行为、单个国家的经济活动总水平、各国间的经济影响，以及财政政策和货币政策的效应。

2．宏观经济学与微观经济学的联系与区别（1）联系微观经济学家与宏观经济学家都在使用非常相似的研究工具。

宏观经济学家用来描述消费者与企业的行为、目标与约束，以及他们之间如何相互影响的经济模型，是根据微观经济学原理建立起来的，而且在分析这些模型和拟合数据时通常都用微观经济学家所用的方法。

2 / 37（2）区别宏观经济学的研究对象有别于微观经济学，宏观经济学侧重于总量研究，强调的问题主要是长期增长和经济周期。

微观经济学主要针对单个消费者或者企业的行为选择。

二、国内生产总值、经济增长与经济周期1．国内生产总值（gross domestic product ，GDP ）国内生产总值是一国在某一特定时期在境内生产的产品和服务的数量。

GDP 也表示那些对国内产出作出贡献的人挣得的收入总量。

实际GDP 是针对通货膨胀进行调整后的总产出衡量指标。

2．经济增长（long-run growth ）经济增长率是一个国家当年国内生产总值对比往年的增长率。

经济正增长一般被认为是整体经济景气的表现。

长期增长是指一国长期的生产能力和平均生活水平的提高。

3．经济周期（business cycles ）经济周期是指总体经济的短期上下波动，或经济的繁荣与衰退。

3 / 37三、宏观经济模型1．宏观经济模型及其假设宏观经济模型是用来解释长期经济增长、经济周期存在的原因、以及经济政策在宏观经济中应发挥的作用的模型。

确切的说，宏观经济模型的基本构造是用来描述下列特征的：（1）经济中相互影响的消费者与企业。

（2）消费者希望消费的一组商品。

（3）消费者对商品的偏好。

（4）企业生产商品可采用的技术。

（5）可利用的资源。

威廉森《宏观经济学》课后习题（衡量）【圣才出品】第2章衡量⼀、复习题1．衡量GDP的三种⽅法是什么？答：衡量GDP的三种⽅法包括⽣产法、收⼊法和⽀出法。

（1）⽣产法⽣产法也被称作增加值法，是将经济中全部⽣产单位⽣产的产品和服务的增加值加总来计算GDP。

为了⽤⽣产法核算GDP，⾸先将经济体⽣产的所有产品和服务价值相加，然后减去为实现总增加值⽽投⼊⽣产的所有中间产品的价值，以避免重复计算。

（2）⽀出法就⽀出法⽽⾔，GDP是指⽤于经济体⽣产最终产品和最终服务⽅⾯的总⽀出。

不计算⽤于中间产品的⽀出。

总⽀出的计算公式是：总⽀出＝C＋I＋G＋NX。

式中，C为消费⽀出；I为投资⽀出；G为政府⽀出；NX为净出⼝，即出⼝产品和服务的总额减去其进⼝的总额。

（3）收⼊法⽤收⼊法计算GDP，要将各经济主体因参与⽣产⽽获得的全部收⼊加总。

收⼊包括企业实现的利润。

收⼊包括雇员报酬（⼯资、薪⾦和津贴）、业主（⾃营企业的所有者）收⼊、租⾦收⼊、公司利润、净利息、企业间接税（企业缴纳的⼯资税和销售税）和折旧（固定资本损耗）。

折旧是在考虑的时期内⽣产性固定资本（⼯⼚和设备）损耗的价值。

由于计算利润时剔除了折旧，因⽽在计算GDP时需要将此再加进来。

2．解释增加值的概念。

答：⽤⽣产法核算GDP，⾸先应将经济体⽣产的所有产品和服务价值相加，然后减去为实现总增加值⽽投⼊⽣产的所有中间产品的价值，最终得到总增加值。

（1）从私⼈⽣产的⾓度⽽⾔，即对于每个⽣产商，增加值等于总⽣产价值减去中间投⼊的成本。

以饭店服务为例，不应把提供饭店服务过程中投⼊的椰⼦价值算作GDP的⼀部分，⽽是应作为中间产品从GDP中减去，进⽽得到⽣产增加值。

（2）对政府⽣产⽽⾔，由于政府提供的⽣产⼀般⽆法按市场价格销售，以防务的提供为例，其对GDP的贡献就等于提供防务时所需要的劳动⼒的投⼊成本，由此⽽得到提供防务时的国民⽣产增加值。

3．收⼊-⽀出恒等式为什么重要？答：收⼊⽀出恒等式重要的原因：（1）收⼊⽀出恒等式提供了两种单独衡量经济总产出的⽅式，即收⼊法和⽀出法。

Chapter 4Consumer and Firm Behavior: The Work-Leisure Decision and Profit MaximizationTextbook 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.28 Williamson • Macroeconomics, Fourth Edition9. An increase in the real wage makes the consumer more well off. As a result of this pure income effect,the consumer wants more leisure. Alternatively, the increase in the real wage induces a substitution 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.11. 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 on I2. 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 theconsumer prefers more to less, he or she must strictly prefer C to A. We therefore contradict thehypothesis that two indifference curves can cross.2. u al bC=+(a) To specify an indifference curve, we hold utility constant at u Next rearrange in the form:u aC l=−b bChapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 29 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 prefers diversity,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.3. (a) Using the formulas in the example from the textbook, one obtains:l = C = (0.75 × 16 − 0.8 − 6)/(1 + 0.75) = 3.89Given the numbers given, we can precisely determine the coordinates of the points in the figureabove: A is (0,6.8), B is (3.89,3.89), D is (9,07,0), with the slope of ABD being − 0.75.30 Williamson • Macroeconomics, Fourth Edition (b) With the new wage, we obtain: l = C = (1.5 × 16 − 0.8 − 6)/(1 + 1.5) = 7.52where A, B and D have the same coordinates as above, and E is (0, 12.8), F is (7.52, 7.52), H is(12.53,0), and the slope of EFH is − 1.5. As there are no substitution effects when goods areperfect complements, the entire move from point B to point F is due to the income effect.4. 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 the imposition 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). T he tax also makes the consumer worse off, in that he or she can no longer be on indifferencecurve, 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.Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 315. The budget constraint has a kink due to the tax deduction and is represented in the following figuresby ABDh. Reducing the tax deduction pushes the budget constraint to FEDh.First consider a consumer who does not pay taxes. In the old regime, he would have an optimalbundle somewhere between B and D. Two things can happen. If the bundle is between E and D, there is no change. If it is between B and E, say at H, then the household will reoptimize with the new tax deduction. The new bundle is then either somewhere between E and F, and the MRS equals w(1 −t).Or we obtain a corner solution at E, and the MRS is somewhere between w and w(1 −t). The move from H to E is due to the income effect, and if there is an optimal strictly between E and F, the move from E to that point is due to the substitution effect.32 Williamson • Macroeconomics, Fourth EditionFor a consumer who pays taxes, his wage, and thus is MRS does not change. Thus the move from H to J is a pure negative income effect.6. 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 top figure shows the case where these two income effects exactly cancel out. In this case we are left witha pure substitution effect that moves the consumer from point A to point B. Therefore, consumptionfalls 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, and consumption may either increase or decrease. The bottom figure shows a case in which theincrease 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, andleisure may either increase or decrease.Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 33 7. 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 levelsof leisure less than h − q, because of the higher overtime wage. The figure depicts possiblechoices for two different consumers. Consumer #1 picks point A on her indifference curve, I1.Consumer #2 picks point B on his indifference curve, I2. 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.8. 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 I1. A shift to a lump-sum taxsteepens the budget line. The absolute value of the slope of the budget line is (1),− and t has fallent w 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 of leisure after the change in tax collection. Therefore, the new budget line must also pass through point A.The new budget line is labeled LGH in the figure below. With the lump-sum tax, the consumer can34 Williamson • Macroeconomics, Fourth Editiondo better by choosing point B, on the higher indifference curve, I2. 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.9. 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 ina change of preferences for households. For the same amount of consumption, they are now willing towork more, or in other words, they are willing to forego some additional leisure. On the figure below, the new indifference curve is labeled I2. It can cross indifference curve I1 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.Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 3536 Williamson • Macroeconomics, Fourth Edition 10. 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 onthe 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 oflabor 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 curvehas 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.Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 37 11. The firm chooses its labor input N d so 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 pagethe 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 figurebelow.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. Thesubsidy 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 hasshifted up. The subsidy acts to reduce the marginal cost of labor, and the firm will hire more labor at any given real wage.38 Williamson • Macroeconomics, Fourth Edition 12. Minimum Employment Requirement. Below *,N no output is produced. Thereafter, the productionfunction 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 nolabor, to prevent incurring losses. Only if the wage rate is less than ˆwwill the firms choose to hire anyone. At ˆ,w w= the firm chooses *,N just as it would in the absence of the constraint. Below ˆ,w the labor demand curve is unaffected. The labor demand curve is reproduced in the bottom figure.Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization 39 13. 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 −14. 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.40 Williamson • Macroeconomics, Fourth Edition 15. 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 −−−−==⇒===⇒===⇒=×≈。

第十二章国民收入核算1：政府转移支付不计入GDP，因为政府转移支付只是简单地通过税收（包括社会保障税）和社会保险及社会救济等把收入从一个人或一个组织转移到另一个人或另一个组织手中，并没有相应的货物或劳务的交换发生。

例如，政府给残疾人发放救济金，并不是因为残疾人创造了收入；相反，倒是因为他丧失了创造收入的能力从而失去生活来源才给予救济。

购买一辆用过的卡车不计入GDP，因为在生产时已经计入过。

购买普通股票不计入GDP，因为经济学上所讲的投资是增加或替换资本资产的支出，即购买新厂房、设备和存货的行为，而人们购买股票和债券只是一种证券交易活动，并不是实际的生产经营活动。

购买一块地产也不计入GDP，因为购买地产只是一种所有权的转移活动，不属于经济学意义的投资活动，故不计入GDP。

2：社会保险税实质上是企业和职工为得到社会保障而支付的保险金，它由政府有关部门（一般是社会保险局）按一定比率以税收形式征收。

社会保险税是从国民收入中扣除的，因此，社会保险税的增加并不影响GDP、NDP和NI，但影响个人收入PI。

社会保险税的增加并不直接影响可支配收入，因为一旦个人收入决定以后，只有个人所得税的变动才会影响个人可支配收入DPI。

3：如果甲乙两国合并一个国家，对GDP总和会有影响。

因为甲乙两国未合并成一个国家时，双方可能有贸易往来，但这种贸易只会影响甲国或乙国的GDP，对两国GDP总和不会有影响。

举例说，甲国向乙国出口10台机器，价值10万美元，乙国向甲国出口800套服装，价值8万美元，从甲国看，计入GDP的有净出口2万美元，计入乙国的GDP有净出口－2万美元；从两国GDP总和看，计入GDP的价值为零。

如果这两个国家并成一个国家，两国贸易变成两地区间的贸易。

甲地区出售给乙地区10台机器，从收入看，甲地区增加10万美元；从支出看，乙地区增加10万美元。

相反，乙地区出售给甲地区800套服装，从收入看，乙地区增加8万美元；从支出看，甲地区增加8万美元。

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。

宏观经济学-课后思考题答案_史蒂芬威廉森005Chapter 5A Closed-Economy One-PeriodMacroeconomic ModelTeaching GoalsThere are three key points to be learned from this chapter. The first point is that when we allow the consumers and firms that we studied in Chapter 4 to interact with each other and with the government, the economy is able to achieve equilibrium through price adjustment. In this particular case, the “price” is the relative price of leisure, the real wage. The second important point is that the equilibrium that markets settle upon is a favorable one, in the sense of Pareto optimality. This point is in keeping with Adam Smith’s notion that the “invisible hand” of self-interested individuals, meeting in a competitive market, can work for the common good. The third point is that we can directly discover the equilibrium position of a market economy by solving an economic planner problem. Although students may find this point to be somewhat arcane, stress the point that it will be much simpler to solve problems (e.g., exam problems) by working with a planner problem as opposed to directly solving general equilibrium problems. The students, however, need to be aware when this solution method is not applicable. The new section about the Laffer curve is a good way to show when social and private optima do not coincide.Once students have mastered the mechanics of the model, the two problems for which this model is best suited are the analyses of changes in government spending and total factor productivity. In working these problems, stress the applicability of these results to historical applications and as a guide to understanding current events.A key tactic of the textbook’s approach is the critical assessment of the usefulness and credibility of competing models. Therefore, it is important to stress the extent to which models fit the facts. Does this model fit the facts of long-run growth? Does this model fit the facts of the typical business cycle? These kinds of questions come up again and again in the course of macroeconomic study. Stress again and again that scientific study needs to relate to observations, in our case the stylized facts of Chapter 2.Classroom Discussion TopicsAn alternative approach to this material is to start with the example of Robinson Crusoe (or Castaway, Gilligan’s Island, etc.). Does an isolated individual have any economic choices? What would guide these choices? Would you rather be on an island with a more plentiful food supply? A pure income effect can then be presented in the form of extra food (or a volleyball) washing up on shore, or in the form of “pirates” (government?) demanding tribute. An increase in total factor productivity can be in the form of obtaining a fishing net or a ladder to climb coconut trees. A change in capital can be the consequence of a hurricane, etc.The next step would be to ask the students about the likely consequences of additional individuals on the island. If they are all identical, and there are no economies to team production, will there be any reason for markets to exist? Could a market improve things? How and why? Typically, markets improve things only to the extent that people are different. However, these types of differences are what we are willing to ignore when we adopt the fiction of a representative consumer.Chapter 5 A Closed-Economy One-Period Macroeconomic Model 43OutlineI. Com petitive EquilibriumA. A One-Period Model1. No Borrowing or Lending2. G = TB. Equilibrium M odeling1. Endogenous Variables2. Exogenous Variables3. Hypothetical Experiments C. Properties of a Competitive Equilibrium1. Representative Consumer Maximizes Utility Subject to Budget Constraint2. Representative Firm Maximizes Profits3. M arkets Clear4. Government Budget Constraint Satisfied5. ,,l C l C N w MRS MRT MP ===II. O p timalityA. ParetoOptimality B. Welfare Theorems1. 1st Theorem: A Competitive Equilibrium Can Be Pareto Optimal2. 2nd Theorem: A Pareto Optimum Can Be a Competitive EquilibriumC. Inefficiencies1. Externalities2. Distorting Taxes3. M onopoly Power D. Using the Second Theorem1. Pareto Optima Are Easier to Identify2. Effects of Disturbances on Pareto OptimaIII. Effects of an Increase in Government SpendingA. Impact Effect1. Parallel Downward Shift in PPF2. Pure Income EffectB. Equilibrium Effects1. Reduced Consumption2. Reduced Leisure and Increased Hours of Work3. Increased Output4. Lower Real WageC. Crowding-OutD. Government Spending a Source of Business Cycles?1. Government Spending Shocks Wrongly Predict Countercyclical Consumption2. Government Spending Shocks Wrongly Predict Countercyclical Real Wages44 Williamson ? Macroeconomics, Third EditionIV. Effects of an Increase in Total Factor ProductivityA. Impact Effect1. Upward Shift in PPF2. Steeper PPF3. Income and Substitution EffectsB. Equilibrium Effects1. Increased Consumption2. Leisure and Hours Worked May Rise or Fall3. Increased Output4. Higher Real WageC. Productivity and Long-Run Growth1. Consumption Grows over Time2. Hours Worked Remain about Constant3. Output Increases over Time4. Real Wages Rise over TimeD. Productivity as Source of Business Cycles?1. Consumption Is Procyclical2. Cyclical Properties of Hours Workeda. Procyclical Hours Worked Is a Business Cycle Factb. Need Strong Substitution Effect to Predict Procyclical Hoursc. Intertemporal Substitution of Leisure3. Increased Output Defines the Cycle4. Procyclical Real Wage RateV. Income Tax Revenue and the Laffer CurveA. Tax Revenue1. The Tax Base Depends on the Proportional Tax Rate2. The Laffer Curve Measures Tax Revenue as a Function of the Tax Rate3. Unless the Tax Rate Is Optimal, Two Tax Rates Yield the Same Tax Revenue4. Supply-Side Economists Claim the U.S. Economy Is at the Bad Tax Rate5. Empirical Evidence Tends to Prove Supply-Side Economists WrongTextbook Question SolutionsQuestions for Review1. A closed economy is easier to work with. Opening the economy does not change most of theproperties of an economy. The closed economy is the correct model for the world as a whole.2. Government levies taxes and purchases consumption goods.3. In a one-period model, there can be no borrowing or lending. There is therefore no way to finance agovernment deficit.4. Endogenous variables: C, N s, N d, T, Y, and w.5. Exogenous variables: G, z, K.Chapter 5 A Closed-Economy One-Period Macroeconomic Model 456. The representative consumer chooses C and N s to maximize utility.The representative firm chooses N d to maximize profits.M arket-clearing: .s d N N N == Government budget constraint: T = G .7. The slope of the production possibilities frontier is equal to .N MP ? The slope of the productionpossibilities frontier is also identified as ,,l C MRT ? where ,l C MRT is identified as the marginal rate oftransformation between leisure and consumption.8. The competitive equilibrium is Pareto optimal because it lies at a tangency point between theproduction possibilities frontier and a representative consumer’s indifference curve.9. The first theorem: A competitive equilibrium can be Pareto optimal. This theorem assures us that thecompetitive equilibrium is a good outcome. The second theorem: A Pareto optimum is a competitive equilibrium. This theorem allows us to directly analyze Pareto optima with the assurance that these points are also competitive equilibriums. The second theorem is useful because Pareto Optima are often easier to work with than competitive equilibriums.10. Externalities, noncompetitive behavior, and distorting taxes.11. , ,, , and .G Y C N l w ↑?↑↓↑↓↓ 12. Government competes with the private sector in buying goods. An increase in government spendingimplies a negative wealth effect, which results in lower consumption.13. , , and .z Y C w ↑?↑↑↑ The sign of the effects on N and l are ambiguous.14. The substitution effect of an increase in z is that the representative consumer works more hours. Theincome effect of an increase in z is that the representative household works more hours. The sign of the net effect is ambiguous.15. A distorting tax makes that households equalize their marginal rate of substitution between leisureand consumption to the after tax wage, which is different from the before tax wage that firms equalize their marginal rate of transformation to. Thus, one cannot achieve the Pareto optimum where the same wage (before tax) is equal to both marginal rates above.16. The Laffer curve takes into account that higher proportional tax rates give incentives to households towork less. While tax revenue increases with the tax rate for a given tax base, that tax base is reduced by the tax rate.17. When the income tax rate falls, households are willing to supply additional labor more in suchquantities that the tax base increases more than what the tax rate decreases, thus increasing taxrevenue.46 Williamson ? Macroeconomics, Third EditionProblems1. Although we often think about the negative externalities of congestion and pollution in cities, theremay also be some positive externalities. A concentrated population is better able to support the arts and professional sports; cities typically have a greater variety of good restaurants, etc. Perhaps a more basic issue is that there may be some increasing returns to scale at low output levels that makeindustrial production more costly in small towns. There may also be externalities in production in being located close to other producers. One example would be the financial industry in financial centers like New York, London, Tokyo, etc. Another example would be large city medical centers that enhance coordination between primary physicians and specialists.One market test of whether productivity is higher in cities would be to look at the wages in cities versus the wages in smaller towns and rural areas. Wages are often higher in cities for individuals of comparable skills. Market efficiency suggests that the higher wages be reflective of a higher marginal product of labor, and that the higher wages compensate those choosing to live in cities for the negative externalities that they face.2. In a one period model, taxes must be exactly equal to government spending. A reduction in taxes istherefore equivalent to a reduction in government spending. The result is exactly opposite of the case of an increase in government spending that is presented in the text. A reduction in government spending induces a pure income effect that induces the consumer to consume more and work less. At lower employment, the equilibrium real wage is higher because the marginal product of labor rises when employment falls. Output falls, consumption rises, employment falls and the real wage rises.3. The only impact effect of this disturbance is to lower the capital stock. Therefore, the productionpossibility frontier shifts down and the marginal product of labor falls (PPF is flatter).(a) The reduction in the capital stock is depicted in the figure below. The economy starts at point Aon PPF1. The reduction in the capital stock shifts the production possibilities frontier to PPF2.Because PPF2 is flatter, there is a substitution effect that moves the consumer to point D. Theconsumer consumes less of the consumption good and consumes more leisure. Less leisure also means that the consumer works more. Because the production possibilities frontier shifts down, there is also an income effect. The income effect implies less consumption and less leisure (more work). On net, consumption must fall, but leisure could decrease, remain the same, or increase, depending on the relative strengths of the income and substitution effect. The real wage must also fall. To see this, we must remember that, in equilibrium, the real wage must equal the marginal rate of substitution. The substitution effect implies a lower marginal rate of substitution. The income effect is a parallel shift in the production possibilities frontier. As the income effect increases the amount of employment, marginal product of labor must fall from point D topoint B. This reinforces the reduction in the marginal rate of substitution from point A to point D.Chapter 5 A Closed-Economy One-Period Macroeconomic Model 47(b) Changes in the capital stock are not likely candidates for the source of the typical business cycle.While it is easy to construct examples of precipitous declines in capital, it is more difficult toimagine sudden increases in the capital stock. The capital stock usually trends upward, and thisupward trend is important for economic growth. However, the amount of new capital generatedby a higher level of investment over the course of a few quarters, of a few years, is very small in comparison to the existing stock of capital. On the other hand, a natural disaster that decreases the stock of capital implies lower output and consumption, and also implies lower real wages,which are all features of the typical business cycle contraction.4. Government Productivity. First consider the benchmark case in which 1,z= and there is no effect of changes in z on government activities. Now suppose that z increases. This case of an increase in z isdepicted in the figure below. The original production possibilities frontier is labeled PPF1 and thecompetitive equilibrium is at point A. If the increase in z only affects the economy through thechange in (,),zF K N then the new production possibilities frontier is PPF2. The diagram shows acase in which the income and substitution effects on leisure exactly cancel out, and the economy moves to point B. The equation for the production possibilities frontier is (,).C zF K h l T=?? In the benchmark case, T G= and so we have (,).C zF K h l G=?? For this problem, /T G z=, and so the production possibilities frontier is given by (,)/.C zF K h l G z=?? When 1,z= the two PPFs coincide. When z increases, the vertical intercept of the PPF increases by /.G zΔ Therefore, the newPPF is PPF3 in the figure below. The competitive equilibrium is at point C. There is an additionalincome effect that provides an additional increase in equilibrium consumption, and a reinforced income effect that tend to make leisure increase. Therefore, relative to the benchmark case, there is a larger increase in consumption, and either a smaller decrease in leisure or a larger increase in leisure.48 Williamson ? Macroeconomics, Third Edition5. Change in preferences.(a) At the margin, the consumer decides that leisure is more preferred to consumption. That is, theconsumer now requires a bigger increase in consumption to willingly work more (consume lessleisure). In more intuitive language, the consumer is lazier.(b) To work out the effects of this change in tastes, we refer to the figure below. The productionpossibility frontier in this example is unchanged. The consumer now picks a new point at which one of the flatter indifference curves is tangent to the production possibilities frontier. That is,equilibrium will shift from point A to point B. Consumption falls and leisure rises. Therefore, the consumer works less and produces less. Because employment has fallen, it also must be the case that the real wage increases.(c) This disturbance, which some might characterize as a contagious outbreak of laziness, wouldhave the appearance of a recession, as output and employment both fall. The consequentreduction in consumption is also consistent with a typical recession. However, in this case thereal wage would rise, which is inconsistent with the business cycle facts. Therefore, this type ofpreference change is not a cause of recessions.Chapter 5 A Closed-Economy One-Period Macroeconomic Model 496. Production-enhancing aspects of government spending.(a) The increase in government spending in this example has two separate effects on the productionpossibilities frontier. First, the increase in government spending from G1 to G2implies a paralleldownward shift in the production possibilities frontier. Second, the productive nature of government spending is equivalent to an increase in total factor productivity that shifts the production possibilities frontier upward and increases its slope. The figure below draws theoriginal production possibilities frontier as PPF1 and the new production possibilities frontier asPPF2. If the production-enhancing aspects of the increase in government spending are largeenough, representative consumer utility could rise, as in this figure.(b) There are three effects at work in this example. First, there is a negative income effect from theincrease in taxes needed to pay for the increased government spending. This effect tends to lower both consumption and leisure. Second, there is a substitution effect due to the productive effect of the increase in G, which is drawn as the movement from point A to point D. This effect tends to increase both consumption and leisure. Third, there is a positive income effect from theincrease in G on productivity. This effect tends to increase both consumption and leisure. In the figure above, the movement from point D to point B is the net effect of the two income effects. In general, consumption may rise or fall, and leisure may rise or fall. The overall effect on output is the same as in any increase in total factor productivity. Output surely rises.50 Williamson ? Macroeconomics, Third Edition7. The fact that government spending make firms more productive is similar to adding G to theproduction function. There are now two effects to an increase in government expenses: the standard crowding out of consumption, and now also an efficiency effect on production.(a) The figure below illustrates a particular situation where the welfare of the household is improved,as illustrated by a shift to the north-east of the indifference curve. The equilibrium shifts fromA toB as the PPF is lowered by the additional government expenses but is also getting steeperthanks to the same government expenses.(b) From previous results, we know that output increases with the increase in government expenses.This is now reinforced as G increases production efficiency. Regarding consumption and leisure, without this new effect, we obtained that an increase in G lead to a negative income effect andthus to decreases in both consumption and leisure. But as the real wage went down, there wasalso a substitution effect leading to an additional decrease in consumption and increase in leisure.The new effect on the production function adds opposite effects: a positive income effect and awage increase, thus possibly reversing, or not, anything that was concluded without the impact ofG on production.Chapter 5 A Closed-Economy One-Period Macroeconomic Model 51 8. We need to analyze each case separately. Start with the good equilibrium. As government expensesincrease, more tax revenue needs to be raised, and thus the tax rate needs to be increased. As shown in the figure below, this tilts down the linear PPF. The new equilibrium leads to a lower indifference curve. This leads to a negative income effect and a lower wage (remember, it is z(1 ? t)), thus a substitution effect. The income effect lowers consumption and leisure, the substitution effectdecreases consumption and increases leisure. All in all, consumption is lower and leisure is higher, as we know that the substitution effect dominates the income effect. This means that the labor supplyis reduced, and thus equilibrium labor and output.The story is different in the bad equilibrium. To increase tax revenue, one needs to reduce the tax rate. Then all the changes discussed above are exactly in the opposite direction.9. We know from previous analysis that an improvement in total factor productivity pushes up the PPF,and thus leads to an increase in consumption, a decrease in leisure, and thus an increase in thequantity of labor supplied. This increases the tax base, and thus allows to reduce the tax rate toachieve the same tax revenue, or in other words, it pushes the left portion of the Laffer curve to the left. The reduction in the tax rate has then a further impact on the variables of interest: as we saw in question 7, first part with a reversal of all signs: consumption increases even more and leisure decrease yet more, leading to an even higher quantity of labor. All in all, as both labor and total factorproductivity increase, output increases.。

Chapter 3Business Cycle MeasurementTextbook Question SolutionsQuestions for Review1. Business cycles are fluctuations about trend in real GDP.2. The time series of deviations from trend in real GDP is quite choppy. There is no regularity in theamplitude of fluctuations. There is no regularity in the frequency of fluctuations.3. The choppiness of fluctuations makes them difficult to predict. Choppiness also makes it difficult totell when a turning point has occurred. The lack of regularity in amplitude and frequency makes it difficult to predict their severity and length.4. Co-movement is important because the regularity of such co-movements suggests that businesscycles are more alike than different. This property of business cycles suggests that it may be possible to develop a general theory for business cycle analysis. This approach would be in contrast toperforming event studies of each business cycle as if it were a consequence of a unique set ofcircumstances.5. Robert Lucas has suggested, “With respect to qualitative behavior of co-movements among[economic time] series, business cycles are all alike.”6. We may discern correlation in time series by observing whether one series tends to be above (below)trend when the other series is above (below) trend. Series that both tend to be above trend and below trend at the same time are positively correlated. When one series tends to be above (below) trend when the other series is below (above) trend, they are negatively correlated.7. There is an almost endless list of possibilities. Pairs of variables that are positively correlated includethe fraction of the day in sunlight and the average air temperature, and the amount of time spent studying and a student’s grade point average. Pairs of variables that are negatively correlated include the weight of a vehicle and its gasoline mileage, and the amount of home insulation and heating and cooling expenses.Note that pairs of variables may not be perfectly correlated. For example, some students are able to get good grades without studying that much. Also note that correlation says nothing about direct causality. In the sunlight and air temperature example, the direct cause of both phenomena is the fact that the earth is tilted on its axis and revolves around the sun.8. An index of leading indicators is useful because turning points in the index generally precede turningpoints in real GDP.©2011 Pearson Education, Inc. Publishing as Addison Wesley22 Williamson • Macroeconomics, Fourth Edition9. The three characteristics of co-movements that are most interesting to economists are whether a seriesis procyclical or countercyclical, whether the series leads or lags real GDP, and whether the series is more or less volatile than real GDP.10. Consumption and investment are both procyclical. Consumption is less variable than real GDP, whileinvestment is considerably more variable than real GDP. Consumption is coincident with real GDP.Some components of investment (residential investment and inventory investment) lead the business cycle.11. The cyclical behavior of the price level can vary across time periods and across countries. In theUnited States, the price level has been procyclical since the end of World War II. The price also tends to lag the business cycle. The money supply is procyclical and leads the business cycle.12. No. The time period 1947–2009 is best characterized as displaying a reverse Phillips curve.13. Employment is procyclical, employment lags the business cycle, and employment is less variablethan real GDP. The real wage is procyclical.Problems1. The 2008–2009 recession appears more severe than usual due to the more negative deviations fromtrend. If this is a typical recession, it should not drop further. The length of the recession cannot be foretold yet, but if it compares to previous ones it should be over soon. This forecast appears to hold as of this writing (October 2009).2. Government expenses in the cycle.(a) Difficult to tell: government expenses are clearly more variable in the first half of the sample, butthey are less variable in the second half.(b) No clear comovement emerges here. This can be explained by changing policies or by the factthat government expenses take a while to plan, pass the legislature, and execute.(c) Sometimes it leads, sometimes it lags. But lags may be so large that they could be falselyinterpreted as leads of the next cycle, see (b).3. Exports in the cycle.(a) Exports are much more volatile than GDP.(b) Exports appear to be procyclical, but not as strongly as other aggregates.(c) There is definitively a lag.4. Series X clearly lags series Y. The two series are almost identical and are shifted in time.5. Productivity (Y/N) and employment (N) are both procyclical and both are less variable than GDP.By definition, real GDP equals productivity times employment. In an expansion, both productivity and employment increase (both are procyclical). Therefore the variability of real GDP is likely to be greater than the individual volatilities of Y/N and N. Productivity is coincident while employment lags the business cycle. For these facts to be consistent, there must be a dominant coincident factor that affects productivity independently from movements in employment itself.6. Both consumption and investment are procyclical and coincident. The key difference is thatinvestment is much more volatile than consumption. Consumer durables provide services over ahorizon greater than one year. Some consumer nondurable products, like apparel, provide services©2011 Pearson Education, Inc. Publishing as Addison WesleyChapter 3 Business Cycle Measurement 23 well beyond the date of purchase. Services, by definition, are fully utilized at the point of sale. The same kinds of timing considerations that affect business investment are likely to come into playwith consumer durables, and to a lesser extent, consumer nondurables. Therefore, it is logical that consumer durable purchases should be more volatile than consumer nondurable purchases and that consumer nondurable purchases should be more volatile than consumption of services.7. One can see that the amplitude of the deviations from the trend is more moderate for prices, as forGDP. It appears also that the price level is becoming less countercyclical. The fact that both GDP and the price level changed their cyclical behavior indicates that any explanation of the Great Moderation needs to look at more that GDP.©2011 Pearson Education, Inc. Publishing as Addison Wesley。

宏观经济学威廉森答案1 宏观经济学（Macroeconomics）宏观经济学是研究经济发展，尤其是经济政策及其影响方面的学科。

它讨论了国民经济、宏观经济政策、国际贸易、货币政策、财政政策和宏观经济分析等主题。

宏观经济学的研究者经常意在探讨如何促进持续的经济增长和繁荣以及改善国家的国民收入水平，以及资本、人力资本、技术和自然资源等如何增加生产效率。

2 威廉森（Williamson）威廉森是20世纪末知名的经济学家，他对宏观经济学做出重大贡献，推导了克莱顿-史密斯（Coulson-Smith）经济模型、威廉森N条折现，以及威廉森宏测试和宏周期理论，并且在宏观经济思想有着重要影响。

威廉森的理论强调的是经济的动态性，将动态分析应用于稳定的经济现象；他的主要理论概念是威廉森宏测试，该系统密切研究多次估量的结果，检测实际观测值是否具有投资性和现代货币性。

3 重要理论威廉森将宏观经济学——国民经济统计和经济模型——结合到一起，发展出了一种新的方法——威廉森宏测试，该方法用来量化超过数个季度展开的经济变量，根据动态视角研究经济波动；他还推导了威廉森N条折现（Williamson N-discount factor），它是一种金融工具，用来度量未来相当于现在投资的潜力；威廉森宏周期理论则是用来衡量短期内的经济起伏的技术，他认为经济波动往往可以被分解为“指数”和“震荡”，而且他对传统宏观经济学的理论框架也进行了重大更新：他将宏观经济中的“财政政策”和“货币政策”视为一个整体，使它们具备了更大的可能性。

4 对其他经济学家的开拓威廉森的思想和理论为经济研究开创了先河，大大推动了宏观经济学的发展。

他继承并发展了许多古典经济学家的理论基础，强调动态分析，充分发挥了宏观经济学的生物效应和科学方法；同时他也与其他经济学家一起发展，如范一夫、汤普森、埃希尔、梅西斯等等，他们推动了宏观经济学多学科交叉研究，共同推动经济学前进。

5 总结威廉森是世界著名经济学家，他的宏观经济学理论和方法对宏观经济学的发展起到了重要的推动作用。

第4章消费者和企业行为：工作—闲暇决策和利润最大化4.1 复习笔记一、典型消费者1．典型消费者的偏好（1）模型假定①假定消费者想购买的商品只有两种：消费品（Consumption goods）即在经济中表示全部消费品的集合或计算出的总消费；闲暇（leisure）即市场中的非工作时间，包括娱乐活动、睡眠和家务（做饭、庭院杂务，以及打扫房间）等。

②假定所有消费者都是同质的，即典型消费者。

③效用函数（utility function）用来反映典型消费者对闲暇和消费品的偏好，可写成：()，U C l式中，U为效用函数；C为消费量；l为闲暇量。

消费和闲暇的特定组合即为消费束（consumption bundle）。

效用函数表示的是消费者如何对不同的消费束排序。

（2）典型消费者的偏好典型消费者偏好的三个特性：①多总比少好；②消费者偏好多样性；③消费和闲暇是正常品（消费者在收入增加时会增加购买量的商品对此消费者为正常品，反之为低档品）。

（3）无差异曲线与无差异图①无差异曲线（indifference curves）即连接一组表示消费者对各种消费束无差异的点的集合。

②无差异曲线的两个重要特性a．无差异曲线向下倾斜。

无差异曲线的特性1源于偏好的特性1（多总比少好）。

b．无差异曲线凸向原点。

无差异曲线的特性2源于偏好的特性2（消费者喜欢其消费束具有多样性）。

③无差异图（indifference map）是各种无差异曲线的集合，有助于分析典型消费者的偏好。

如图4-1所示。

图4-1 无差异曲线④边际替代率（marginal rate of substitution，MRS）即负的无差异曲线的斜率，即消费者愿意用一种商品替代另一种商品的比率，用MRS表示。

,l c无差异曲线凸向原点这一特性表明，边际替代率是递减的。

也就是说，当沿无差异曲线从左向右移动时，消费者愿意放弃一种商品去替换另一种商品的数量会逐渐减少。

2．典型消费者的预算约束（1）模型假定①典型消费者的行为是竞争性的。