史蒂芬 威廉森 宏观经济学 第四版 课后题答案 最新Solution_CH2
宏观经济学第四版课后习题答案
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。
威廉森《宏观经济学》【课后习题】 第1篇 导论和衡量问题【圣才出品】
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）。
史蒂芬 威廉森 宏观经济学 第四版 课后题答案 最新Solution_CH9
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.。
威廉森《宏观经济学》课后习题(封闭经济下的一时期宏观经济模型)【圣才出品】
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。
威廉森《宏观经济学》课后习题(经济周期的衡量)【圣才出品】
第3章经济周期的衡量一、复习题1．经济周期的主要特征是什么？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。
威廉森《宏观经济学》笔记和课后习题详解(导论)【圣才出品】
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】
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。
史蒂芬 威廉森 宏观经济学 第四版 课后题答案 最新Solution_CH4
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 −−−−==⇒===⇒===⇒=×≈。
宏观经济学(第四版)课后习题答案
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。
威廉森《宏观经济学》笔记和课后习题详解(搜寻和失业)【圣才出品】
1 / 46第6章 搜寻和失业6.1 复习笔记一、劳动力市场事实1．失业率、参与率和就业-人口比率（1）失业率、参与率和就业-人口比率的定义失业率＝U/Q参与率＝Q/N就业-人口比率＝（Q －U ）/N式中，N 为适龄就业人口数；Q 是劳动力人数（就业人数加上失业人数）；U 是失业人口数。
（2）失业率、参与率和就业-人口比率的特征失业率是一个逆周期变量，当实际GDP 高（低）于趋势时，失业率往往就低（高）于趋势。
参与率是顺周期变量，但要比实际GDP 的变化稳定得多。
同就业-人口比率相2 / 46比，劳动力参与率没那么像周期性变量。
在经济衰退时期，失业者要去找其他的工作，虽然处于失业但仍属劳动力。
2．职位空缺率与贝弗里奇曲线（1）职位空缺率的定义在任何时点上，只要企业出现了想要填补的职位空缺，就可以通过做广告，招聘新工人。
如果令A 代表整个经济体系的职位空缺数量，那么，职位空缺率就可定义为： 职业空缺率＝A/（A ＋Q －U ）即职位空缺数占职位空缺数加上就业数的百分比。
（2）贝弗里奇曲线（Beveridge curve ）的定义贝弗里奇曲线是一条向下倾斜的曲线，反映的是失业率与职位空缺率之间可观察到的关系。
失业率和职位空缺率负相关，且职位空缺率是顺周期的。
二、戴蒙德—莫特森—皮萨里迪斯的搜寻与失业模型（DMP 模型）总体假设：假定只有一个时期，有N 个消费者，都是潜在工人，即N 为适龄就业人口。
企业的数量是内生的，由模型决定。
3 / 461．消费者（1）假设N 个消费者均可以选择在市场之外工作（市场外工作一般都属于家务生产），或者寻找市场工作。
（2）分析令Q 代表决定寻找工作的消费者数量，则N －Q 就是选择家务生产的消费者数量。
将Q 看作是劳动力，N －Q 看作是不属于劳动力的适龄就业人员；令P （Q ）界定选择寻找市场工作的工人的供给曲线，故P （Q ）代表能诱使Q 个消费者寻找市场工作的预期报酬。
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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).。