中级微观经济学补充练习题 (1)

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中级微观经济学考题

中级微观经济学考题《中级微观经济学》习题第一章绪论1、英国古典经济学家大卫·李嘉图在《政治经济学及税赋原理》一书中认为，市场经济是商业完全自由的经济制度，如果没有外在干预的影响，它会自然地、有序地发展下去。

李嘉图指出：“在没有政府的干预时，农业、商业和制造业最为繁荣。

”国家需要做的全部事情，就是避免一切干预，既不要鼓励生产的一个源泉，也不要抑制另一个源泉。

对此观点，你有什么看法？请予以系统论述。

2、微观经济学研究极大满足人类需要的方式，但这真的是一个切合实际的目标吗？比如，假设人民需要不好的东西，如吸毒、酗酒等等。

尽可能满足人们的这些需要仍是切合实际的吗？微观经济学对人们的需要的假设有什么问题？你认为应怎样改进？3、对大多数经济政策问题，人们可以发现经济学家之间存在很大的分歧，这能证明经济学不是一门科学吗？4、在评价经济学家的论述的准确性时，你是否能够区分：（1）经济学家的那些论述是描述性的？（2）那些是它们关于究竟应采取何种政策的论述。

5、西方有一种“奥卡姆剃刀”原则：如无必要，勿增实体。

如果两个模型预测的准确度相同，我们应选择不太复杂的那个？你是否赞成这种观点？你如何去判断一个模型的复杂程度？6、为什么一个不能通过经验事实来验证的理论不是一个好的理论？第二章供给和需求的基本原理1、需求的价格弹性有哪些类型？它们是怎样划分的？2、什么是价格控制？政府干预市场价格的后果是什么？3、短期弹性与长期弹性的区别？4、影响需求弹性与价格弹性的因素分别有哪些？5、假定需求函数为N=，其中M不是收入，P表示水平价格，N（N>0）Q-MP为常数。

求：需求的价格点弹性和需求的收入点弹性。

6、若某商品市场是有100个消费者，其中，60个消费者购买该市场1/3的商品，且每个消费者的需求的价格弹性为3；另外40个消费者购买该市场2/3的商品，且每个消费者的需求的价格弹性为6。

求：按照100个消费者合计的需求的价格弹性是多少？7、画图说明蛛网模型的三种情况。

中级微观经济学45道题（含答案）

中级微观经济学45道题（含答案）中级微观经济学期末考试复习题（版权归13企业管理班所有，翻版必究，哈哈！）1.实现委托代理最优合约设计的两个约束条件是什么、答：⼀种是代理⼈的个⼈理性约束，即委托⼈得保证让代理⼈不跳槽，安于经理岗位。

另⼀种是对代理⼈的激励相容约束，即让代理⼈⾃⼰去选择⾏动值a，使其期望的边际效⽤值达到最⼤。

2、为何需求的价格弹性⼤于1时，降价能增加收益，⽽需求的价格弹性⼩于1时，涨价能增加收益，请给出数学证明。

答：需求的价格弹性公式为：由公式可知，当|e|>1，即富于弹性时，MR<0，边际收益为负，即提⾼价格，收益降低，相反，降低价格则收益升⾼。

当|e|<1，即缺乏弹性时，MR>0，边际收益为正，即提⾼价格，收益升⾼，相反，降低价格，收益变少。

3.简述公共产品与私⼈产品的差异。

（微观经济学⼗⼋讲P352）答：公共品是指由公共部门提供⽤来满⾜社会公共需要的商品和服务。

公共品具有不可分割性、⾮竞争性和⾮排他性。

但是必须明确并不是全部的公共品都应由公共部门提供。

私⼈品是指那些具有效⽤上的可分割性，消费上的竞争性和受益上的排他性的产品。

公共品和私⼈品的区别在于，公共品是可以让⼀群⼈同时消费的物品，⽽私⼈品在任何时候只能为⼀个使⽤者提供效⽤。

%4、毕加索油画的供给价格弹性是多少，为什么答：弹性0，因为供给的价格弹性反映价格变动对供给数量变动的影响。

毕加索的油画是唯⼀的，因此，不管价格如何变动，供给为1，即供给不随价格变动⽽变动，弹性为0。

5、完全竞争市场条件下，为什么⾏业中所有⼚商的经济利润在长期均衡时都会为零这是否意味着⼚商的⽣产变得没有意义西⽅经济学中所谓长期均衡时利润为零，是指经济利润为零，并不是会计利润为零。

所谓经济利润，通常也叫超额利润，就是⼀个⼚商赚取了较之⼀般利润⽔平更⾼的利润。

之所以如此，这是因为，在西⽅经济学理论上，会计利润被计⼊⼚商投⼊⾃有要素所应获得的报酬，是产品的隐含成本。

中级微观经济学练习

中级微观经济学练习中级微观经济学练习题1、吴兵有一份每小时￥15的工作，如果他每周工作超过40小时，他将得到50%的超时奖金，即工资上升到￥元/小时。

他只偏好单一商品消费和娱乐，而且他每周可以利用80小时。

假定单一商品的价格是￥6/单位。

请画出他的预算线。

2、某个消费者的效用函数为U(x1,x2)=x12x2。

令P1,P2与m分别表示商品1的价格、商品2的价格和收入。

如果m=24, p1=1, p2=1 , 现在P1的价格上升为2，求此消费者关于商品1的斯勒茨基替代效应和收入效应。

请根据计算，验证恩格尔加总规则。

3、消费者对的效用函数是拟线性的效用函数U＝x1＋x21/2，x1的价格为1，x2的价格为p2，消费者的收入为m。

求x1，x2的需求函数收入变化是否影响对x1和x2的消费？设m＝100，p2从1变化到2，计算该消费者从消费x2商品获得的消费者剩余的变化？4、设消费者对的效用函数是U=x1+x2，x1的价格为2，x2的价格为1。

消费者的收入是m=100. 计算当p1从2变为1/2时对x1的需求的变化。

计算该变化的斯勒茨基替代效应和收入效应，并用图表示出来。

5、利用效用函数u(x1,x2)=x1x2,预算约束m=p1x1+p2x2。

计算X(p,m),γ(p,m),h(p,u)和e(p,u) 6、假设一个人对面包和可乐的偏好可以用下列效用函数来表达，U(x1,x2)=x11/2x21/2。

初始状态下，px=1/2, py=2，m=4。

现在假设可乐的价格px1/2上升到2，计算于px变化引起的补偿性变化CV、等值性变化EV。

1 1/31/27、消费者的效用函数为u=(c1,c2)=? 。

在第一期和第二期的收入分别为100元和180元，利率为r。

求：第一期和第二期的消费分别为多少？r取什么值时，该消费者在第一期将储蓄、贷款或不借贷。

当利率变化时对c1,c2的影响是什么？8、设某人的每天时间分为工作时间和闲暇时间，其效用函数为u?80L?Ly?L2，这里的Y为收入。

中级微观经济学习题及部分答案

中级微观经济学习题及部分答案第一篇：中级微观经济学习题及部分答案一、单项选择题（每题0.5分，共15分，将正确答案填入答题纸上）1.有下列因素除哪一种外都会使需求曲线移动？（B）a 消费者收入变化；b 商品价格变化；c消费者偏好变化； d 其他相关商品价格变化。

2.假定某耐用消费品的需求函数Qd=400-5P时的均衡价格为50，当需求函数变为Qd=600-5P时，（供给不变）均衡价格将（B）a 低于50b 高于50c 等于50d 不变3.下列命题中哪个是规范经济学的命题?(A)a.征税对中等收入家庭是不公平的c.1982年8月政府把贴现率降到10％b.1981年失业率超过9％d.社会保险税的课税依据现已超过30000美元4.当供求力量自由作用时，一次谷物歉收通过什么显示在市场上？（B）a.政府规定的购买量限制b.谷物价格上涨c.劝说人们减少购买量的广告d.谷物贸易量的增加5.某月内，X商品的替代品的价格上升和互补品的价格上升，分别引起X商品的需求变动量为50单位和80单位，则在它们共同作用下该月X商品需求数量：（B）。

a.增加30单位b.减少30单位c.增加130单位d.减少130单位6.在完全竞争市场中，（C）。

a.消费者是价格接受者，而企业不是b.消费者和企业都不是价格接受者c.消费者和企业都是价格接受者d.企业是价格接受者，而消费者不是C曲线（A）。

a.当LMC＜LAC时下降，而当LMC＞LAC时上升b.随LMC曲线下降而下降c．随LMC曲线上升而上升d.通过LMC曲线的最低点8．一个企业在以下哪种情况下应该关闭？（A）a.P＜AVCb.P＜SACc.发生亏损时d.SMC＞MR 9.寡头垄断和垄断竞争之间的主要区别是（C）。

a.厂商的广告开支不同b.非价格竞争的种类不同c.厂商之间相互影响的程度不同d.以上都不对10.短期内，完全竞争厂商只能通过对（D）调整来实现最大利润。

a.生产规模b.价格c.全部生产要素d.产量11.不完全竞争市场中出现低效率的资源配置是因为产品价格（A）边际成本a．大于b．小于等于d．大于或等于12．当市场处于长期均衡状态时，向右下方倾斜的需求曲线相切于长期平均成本的最低点的左边，产品的价格等于生产的平均成本，产品产量较高但存在多余的生产能力，则该市场属于下列哪一类(B)。

中级微观经济学题库(1-10章)

中级微观经济学题库第一章市场1.1 假定市场中最初有5单位公寓，而其中的一个单位变成了公共品。

（a）假设需求者A决定买下该公共物品。

使得公寓的需求等于供给的最高价格是多少？最低价格是多少？在表中的A列中填入你的答案。

然后计算一下，如果B，C，…决定购买该公共品时公寓的均衡价格。

（b）假设在每个保留价格下有两个需求者，共有10套公寓。

供给等于需求的最高价格是多少？假设这些公寓中的一套变成了公共品，这一最高价格还是均衡价格吗？需求者 A B C D E F G H最高价最低价1.2 现在假定有一个垄断者拥有所有的公寓，他要决定能够最大化他的收入的价格和数量。

（a）如果该垄断者租出1，2，…，8套公寓，在下表中填写他能获得的最高价格和收入。

（假定他必须对所有的公寓索要同样的价格。

）（b）从A到F中，哪些人租到了公寓？（c）如果法律要求垄断者刚好租出5套公寓，为了最大化收入，他索要的价格将是多少？（d）哪些人会租到公寓？（e）假定该房东可以向每个人索要不同的价格，并且他知道每个人的保留价格。

如果他将5套公寓全部租出，他能获得的最大收入是多少？（f）如果5套公寓都租出去了，哪些人租到了公寓？数量 1 2 3 4 5 6 7 8价格收入第二章预算约束2.1 在波罗的海附近的一个小国中，只有三种商品：土豆、肉丸和果酱。

在过去的近50年里，价格都十分稳定。

土豆每袋2克朗，肉丸每坛4克朗，果酱每罐6克朗。

（a）一个叫Gunnar的公民，他每年有360克朗的收入，写出他的预算方程。

令P、M、J分别代表Gunnar在一年中所消费的土豆的袋数、肉丸的坛数和果酱的罐数。

（b）该国的公民一般都十分聪明，但是他们不擅长乘以2的计算。

这使得购买土豆成为了一件令许多公民痛苦的困难事情。

因此该国决定引入一种新的货币单位，使得土豆成为计价物。

一代土豆要花费一单位的新货币，但相对价格与过去一样。

用新货币表示的肉丸价格是多少？（c）用新货币表示的果酱价格是多少？（d）要使Gunnar能够买得起变革之前他所消费的相同的商品束，他以新货币表示的收入必须是多少？（e）写出Gunnar的新预算方程。

中级微观经济学补充练习题-(1)

1.税收对消费者福利的影响：假设政府要征收一定总额的税收T，一种方法是征收从量税，另一种方法是征收所得税，并假设这两种方法征收的总税额相等，即tx1*=R=T,那么消费者在哪种税收下境况更好？2.写出下列情形下的效用函数，画出无差异曲线，并求最优解。

（1）X1=一支铅笔，x2=一对铅笔（2）一杯咖啡加两勺糖一起消费3.求解如下效用函数的最优选择（1）u(x1,x2)= x12 x2（2）u= （x1）1/2+ x24.消费者对(x1,x2)的效用函数是拟线性的效用函数U= x1+ （x2）1/2，x1的价格为1，x2的价格为P2，消费者收入是m。

（1）求x1，x2的需求函数（注意分情况讨论，比如角点和内部解）。

（2）收入变化是否影响对x1，x2的消费？（3）设m=100，P2从1变到2，计算该消费者从消费x2这种商品获得的消费者剩余的变化。

5.已知某消费者每月用于购买X商品和Y商品的货币收入为M=9000美元，这两种商品的价格分别为P X=30美元、P Y=40美元，该消费者的效用函数为U=2XY2，试求该消费者每月购买这两种商品的数量分别是多少？他每月从中获得的总效用是多少？6.用下列效用函数推导对商品1的需求函数、反需求函数、恩格尔曲线；在图上大致画出价格提供曲线、收入提供曲线；说明商品1是否为正常商品、劣质品、一般商品、吉芬商品？商品2与商品1是替代还是互补关系？（1）u=2 x1+ x2（2）u=min(x1,2 x2)（3）u= x1a x2b（4）u=ln x1+ x27.一辆自行车和一把车锁总是捆在一起消费，消费者对自行车（x1）和车锁（x2）的效用函数可以表示为：U= x1+ x2。

请问这个说法正确吗？8.若某个消费者的偏好可以由效用函数U(x1，x2)= （x1+ x2）3-5表示，那么对于该消费者而言，x1和x2是完全替代品。

请问这个说法正确吗？9.假定篮球赛的门票需求可表示为P=50-0.00166Q。

中级微观经济学补充练习题图文稿

中级微观经济学补充练习题集团文件发布号：（9816-UATWW-MWUB-WUNN-INNUL-DQQTY-1.税收对消费者福利的影响：假设政府要征收一定总额的税收T，一种方法是征收从量税，另一种方法是征收所得税，并假设这两种方法征收的总税额相等，即tx1*=R=T,那么消费者在哪种税收下境况更好？2.写出下列情形下的效用函数，画出无差异曲线，并求最优解。

（1）X1=一支铅笔，x2=一对铅笔（2）一杯咖啡加两勺糖一起消费3.求解如下效用函数的最优选择（1）u(x1,x2)= x12 x2（2）u= （x1）1/2+ x24.消费者对(x1,x2)的效用函数是拟线性的效用函数U= x1+（x2）1/2，x1的价格为1，x2的价格为P2，消费者收入是m。

（1）求x1，x2的需求函数（注意分情况讨论，比如角点和内部解）。

（2）收入变化是否影响对x1，x2的消费？（3）设m=100， P2从1变到2，计算该消费者从消费x2这种商品获得的消费者剩余的变化。

5.已知某消费者每月用于购买X商品和Y商品的货币收入为M=9000美元，这两种商品的价格分别为PX=30美元、PY=40美元，该消费者的效用函数为U=2XY2，试求该消费者每月购买这两种商品的数量分别是多少他每月从中获得的总效用是多少6.用下列效用函数推导对商品1的需求函数、反需求函数、恩格尔曲线；在图上大致画出价格提供曲线、收入提供曲线；说明商品1是否为正常商品、劣质品、一般商品、吉芬商品？商品2与商品1是替代还是互补关系？（1）u=2 x1+ x2（2）u=min(x1,2 x2)（3）u= x1a x2b（4）u=ln x1+ x27.一辆自行车和一把车锁总是捆在一起消费，消费者对自行车（x1）和车锁（x2）的效用函数可以表示为：U= x1+x2。

请问这个说法正确吗？8.若某个消费者的偏好可以由效用函数U(x1，x2)= （x1+ x2）3-5表示，那么对于该消费者而言，x1和x2是完全替代品。

中级微观经济学习题与答案

1 The Market 1. Suppose that there were 25 people who had a reservation price of $500, and the 26th person had a reservation price of $200. What would the demand curve look like? 1.1. It would be constant at $500 for 25 apartments and then drop to $200.
8. If our model of rent control allowed for unrestricted subletting, who would end up getting apartments in the inner circle? Would the outcome be Pareto eﬃcient? 1.8. Everyone who had a reservation price higher than the equilibrium price in the competitive market, so that the ﬁnal outcome would be Pareto eﬃcient. (Of course in the long run there would probably be fewer new apartments built, which would lead to another kind of ineﬃciency.)
2. In the above example, what would the equilibrium price be if there were 24 apartments to rent? What if there were 26 apartments to rent? What if there were 25 apartments to rent? 1.2. In the ﬁrst case, $500, and in the second case, $200. In the third case, the equilibrium price would be any price between $200 and $500.

中级微观经济学题库及参考答案

中级微观经济学题库及参考答案⼀、名词辨析1.规范分析与实证分析；实证分析⽅法：实证分析不涉及价值判断，只讲经济运⾏的内在规律，也就是回答“是什么”的问题；实证分析⽅法的⼀个基本特征它提出的问题是可以测试真伪的，如果⼀个命题站得住脚，它必须符合逻辑并能接受经验数据的检验。

规范分析⽅法：规范分析以价值判断为基础，以某种标准为分析处理经济问题的出发点，回答经济现象“应当是什么”以及“应当如何解决”的问题，其命题⽆法证明真伪。

2.⽆差异曲线与等产量线；⽆差异曲线是指这样⼀条曲线，尽管它上⾯的每⼀点所代表的商品组合是不同的，但消费者从中得到的满⾜程度却是相同的。

等产量线表⽰曲线上每⼀点的产量都相等，是由⽣产出同⼀产量的不同投⼊品组合所形成的曲线。

3.希克斯补偿与斯卢茨基补偿;希克斯补偿是指当商品价格发⽣变化后，要维持原有效⽤⽔平所需补偿的货币数量。

斯卢茨基补偿是指当商品价格发⽣变化后，要维持原有消费⽔平所需补偿的货币数量。

4.边际替代率与边际技术替代率；边际替代率是指，消费者在增加额外⼀单位商品X之后，若要保持满⾜⽔平不变⽽必须放弃的商品Y的数量。

边际替代率就等于⽆差异曲线在该点的斜率的绝对值。

边际技术替代率是指，当只有⼀种投⼊品可变时，要增加产量，企业必须投⼊更多的另⼀种投⼊品；当两种投⼊品都可变时，企业往往会考虑⽤⼀种投⼊品来替代另⼀种投⼊品。

等产量线斜率的绝对值就是两种投⼊品的边际技术替代率。

5.边际产出与边际收益产出边际产出，就是指在其他⽣产资源的投⼊量不变的条件下,由于增加某种⽣产资源⼀个单位的投⼊,相应增加的产出量。

当产出以产量表⽰时,即为边际产量;当产出以产值表⽰时,即为边际产值。

边际收益产出是指，额外单位劳动给企业带来的额外收益是劳动的边际产品与产品的边际收益的乘积。

6.显性成本与隐性成本；显性成本：是指⼚商在⽣产要素市场上购买或租⽤所需要的⽣产要素的实际⽀出；隐性成本：是指⼚商本⾝所拥有的且被⽤于该企业⽣产过程的那些⽣产要素的总价格。

中级微观经济学习题集

三、论述下列各题
1、分析保险市场的逆向选择问题。
2、总结信号传递博弈的分析框架。
3、分析委托代理理论的现实意义。
6、设效用函数为，其中，。求对应的希克斯需求函数。
第三章需求分析
一、解释下列概念
1、需求价格弹性，2、需求收入弹性，3、需求交叉弹性，4、替代效应，5、收入效应，6、斯勒茨基方程，7、期望效用函数，8、货币彩票的的期望，9、确定性等价，10、风险溢价，11、用货币度量的效用函数，12、消费者剩余，13、等价变化，14、补偿变化
（3）请计算出价格变化的收入效应。
5、假设效用函数为，其中，Q为商品的消费量，M为消费者收入。求：（1）需求函数。（2）P=0.05，Q=25时的消费者剩余。
第四章技术与生产
一、解释下列概念
1、生产集，2、转换函数，3、生产函数，4、边际技术替代率，5、替代弹性，6、产出弹性，7、生产力弹性，8、成本函数，9、条件要素需求函数，10、成本弹性，11、支出弹性，12、利润弹性，13、利润函数，14、要素需求函数。
乙
甲
左
中
右
上
2，0
1，1
4，2
中
3，4
1，2
2，3
下
1，3
0，2
3，0
2、考虑一个二人序贯博弈，局中人甲先行动，它可以在“上”或“下”中选择其一；局中人乙看到对方行动之后决定选“左”或者“右”。如果甲选“上”，乙选“左”时双方的支付向量为（2，1），选“右”时是（0，0）；如果甲选“下”，乙作何选择都无关紧要，双方的支付都是（1，2）。要求：
二、简答下列各题
1、占优战略均衡，2、纳什均衡，3、混合战略纳什均衡，4、子博弈精炼纳什均衡，5、无名氏定理，6、贝叶斯纳什均衡，7、精炼贝叶斯纳什均衡。

中级微观经济学考题及答案

中级微观经济学考题及答案
1. 何为微观经济学？
微观经济学是研究个体之间的经济行为的学科，旨在了解单个人、家庭、公司和其他组织如何做出经济决定，以及如何受到政府政策和
其他因素的影响。

该学科利用统计技术和模型，以及涉及决策行为的
理论分析，来分析经济活动。

它也研究如何应用经济政策来影响经济
绩效和人民生活。

2. 市场均衡与价格敏感
市场均衡是指市场中购买者和销售者都在一定价格下能获得最大
利益的一种经济状态。

价格敏感性是指消费者在价格的变动性的程度，也就是说，当价格上升时，消费者购买的量会减少。

市场均衡和价格
敏感性之间存在直接关系，当价格敏感性增大时，消费者对价格变化
会有密切关注，进而影响市场均衡。

3. 动态效用和信息不对称
动态效用指的是由于消费者向高效用的货物和服务偏爱的行为，
使其短期的满意度增加而长期的满意度降低的状态。

信息不对称指的
是消费者在购买时无法获得完整的可靠信息，导致其在决策过程中受到巨大的影响的状况。

动态效用和信息不对称之间存在联系，当消费者在购买中缺乏信息时，他们会关注动态效用，从而做出更糟糕的决策。

4. 最优消费艺术和最优生产艺术
最优消费艺术是指消费者以最大限度满足他们欲望的最有效价格分配货物和服务的方式，可以以最少成本实现最大收益。

最优生产艺术指的是采取最有效的生产方式和技术，以最小的成本获得最大的收益。

最优消费艺术和最优生产艺术的实现都受到道德和法律的限制，二者之间也存在着联系，一方面，最优生产需要有效的资源配置，来满足消费需求；另一方面，最优消费除了遵循经济模型外，还需考虑在效用函数中考虑善恶和道德行为等因素。

中级微观经济学习题及答案

ANSWERS1 The Market1. Suppose that there were 25 people who had a reservation price of $500, and the 26th person had a reservation price of $200. What would the demand curve look like?1.1. It would be constant at $500 for 25 apartments and then drop to $200.2. In the above example, what would the equilibrium price be if there were 24 apartments to rent? What if there were 26 apartments to rent?What if there were 25 apartments to rent?1.2. In the ﬁrst case, $500, and in the second case, $200. In the third case, the equilibrium price would be any price between $200 and $500.3. If people have diﬀerent reservation prices, why does the market demand curve slope down?1.3. Because if we want to rent one more apartment, we have to oﬀer a lower price. The number of people who have reservation prices greater than p must always increase as p decreases.4. In the text we assumed that the condominium purchasers camefrom the inner-ring people—people who were already renting apartments. What would happen to the price of inner-ring apartments if all of the condominium purchasers were outer-ring people—the people who were not currently renting apartments in the inner ring?1.4. The price of apartments in the inner ring would go up since demand for apartments would not change but supply would decrease.5. Suppose now that the condominium purchasers were all inner-ring people, but that each condominium was constructed from two apartments. What would happen to the price of apartments? 1.5. The price of apartments in the inner ring would rise.6. What do you suppose the eﬀect of a tax would be on the number of apartments that would be built in the long run?1.6. A tax would undoubtedly reduce the number of apartments supplied in the long run.7. Suppose the demand curve is D(p) = 100−2p. What price would the monopolist set if he had 60 apartments? How many would he rent? What price would he set if he had 40 apartments? How manywould he rent?1.7. He would set a price of 25 and rent 50 apartments. In the second case he would rent all 40 apartments at the maximum price the market would bear. This would be given by the solution to D(p) = 100−2p = 40, which is p∗ = 30.8. If our model of rent control allowed for unrestricted subletting, who would end up getting apartments in the inner circle? Would the outcome be Pareto eﬃcient?1.8. Everyone who had a reservation price higher than the equilibrium price in the competitive market, so that the ﬁnal outcome would be Pareto eﬃcient. (Of course in the long run there would probably be fewer new apartments built, which would lead to another kind of ineﬃciency.)2 Budget Constraint1. Originally the consumer faces the budget line p1x1 + p2x2 = m. Then the price of good 1 doubles, the price of good 2 becomes 8 times larger, and income becomes 4 times larger. Write down an equation for the new budget line in terms of the original prices and income.2.1. The new budget line is given by 2p1x1 +8p2x2 =4m.2. What happens to the budget line if the price of good 2 increases, but the price of good 1 and income remain constant?2.2. The vertical intercept (axis) decreases and the horizontal intercept (axis) stays the same. Thus the budget line becomes ﬂatter.3. If the price of good 1 doubles and the price of good 2 triples, does the budget line become ﬂatter or steeper?2.3. Flatter. The slope is −2/3.4. What is the deﬁnition of a numeraire good?2.4. A good whose price has been set to 1; all other goods’ prices are measured relative to the numeraire good’s price.5. Suppose that the government puts a tax of 15 cents a gallon on gasoline and then later decides to put a subsidy on gasoline at a rate of 7 cents a gallon. What net tax is this combination equivalent to? 2.5. A tax of 8 cents a gallon.6. Suppose that a budget equation is given by+= m. The government decides to impose a lump-sum tax of u, a quantity tax on good 1 of t, and a quantity subsidy ongood 2 of s. What is the formula for the new budget line?2.6. (+ t)+(−s)= m−u.7. If the income of the consumer increases and one of the prices decreases at the same time, will the consumer necessarily be at least as well-oﬀ?2.7. Yes, since all of the bundles the consumer could aﬀord before are aﬀordable at the new prices and income.3 Preferences1. If we observe a consumer choosing (,)when(,) is available one time, are we justiﬁed in concludingthat (,)>(,)?3.1. No. It might be that the consumer was indiﬀerent between the two bundles. All we are justiﬁed in concluding is that(,)> (,).2. Consider a group of people A, B, C and the relation “at least as tall as,” as in “A is at least as tall as B.” Is this relation transitive? Is it complete?3.2. Yes to both.3. Take the same group of people and consider the relation “strictly taller than.” Is this relation transitive? Is it reﬂexive? Is it complete?3.3. It is transitive, but it is not complete—two people might be the same height. It is not reﬂexive since it is false that a person is strictly taller than himself.4. A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. Is this preference relation transitive? Is it complete?3.4. It is transitive, but not complete. What if A were bigger but slower than B? Which one would he prefer?5. Can an indiﬀerence curve cross itself? For example, could Figure3.2 depict a single indiﬀerence curve?3.5. Yes. An indiﬀerence curve can cross itself, it just can’t cross another distinct indiﬀerence curve.6. Could Figure 3.2 be a single indiﬀerence curve if preferences are monotonic?3.6. No, because there are bundles on the indiﬀerence curve that have strictly more of both goods than other bundles on the (alleged) indiﬀerence curve.7. If both pepperoni and anchovies are bads, will the indiﬀerence curve have a positive or a negative slope?3.7. A negative slope. If you give the consumer more anchovies, you’ve made him worse oﬀ, so you have to take away some pepperoni to get him back on his indiﬀerence curve. In this case the direction of increasing utility is toward the origin.8. Explain why convex preferences means that “averages are preferred to extremes.”3.8. Because the consumer weakly prefers the weighted average of two bundles to either bundle.9. What is your marginal rate of substitution of $1 bills for $5 bills? 3.9. If you give up one $5 bill, how many $1 bills do you need to compensate you? Five $1 bills will do nicely. Hence the answer is −5 or−1/5, depending on which good you put on the horizontal axis.10. If good 1 is a “neutral,” what is its marginal rate of substitution for good 2?3.10. Zero—if you take away some of good 1, the consumer needs zero units of good 2 to compensate him for his loss.ANSWERS A1311. Think of some other goods for which your preferences might be concave.3.11. Anchovies and peanut butter, scotch and Kool Aid, and other similar repulsive combinations.4 Utility1. The text said that raising a number to an odd power was a monotonic transformation. What about raising a number to an even power? Is this a monotonic transformation? (Hint: consider the case f(u)=u^2.)4.1. The function f(u)=u^2 is a monotonic transformation for positive u, but not for negative u.2. Which of the following are monotonic transformations?(1) u =2 v−13; (2) u = −1/v^2; (3)u =1/v^2; (4)u = ln v; (5)u = −e^−v; (6)u = v^2; (7) u = v^2 for v>0; (8) u = v^2 for v<0.4.2. (1) Yes. (2) No (works for v positive). (3) No (works for v negative). (4) Yes (only deﬁned for v positive). (5) Yes. (6) No. (7) Yes. (8) No.3. We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indiﬀerence curve exactly once. Can you prove this rigorously? (Hint: what would happen if it intersected some indiﬀerence curve twice?)4.3. Suppose that the diagonal intersected a given indiﬀerence curve at two points, say (x,x) and (y,y). Then either x>y or y>x, which means that one of the bundles has more of both goods. But if preferences are monotonic, then one of the bundles would have to be preferred to the other.4. What kind of preferences are represented by a utility function of the form u(x1,x2)=? What about the utility function v(x1,x2)= 13x1 + 13x2?4.4. Both represent perfect substitutes.5. What kind of preferences are represented by a utility function of the form u(x1,x2)=x1 +? Is the utility function v(x1,x2)=x2 1 +2x1+x2 a monotonic transformation of u(x1,x2)?4.5. Quasilinear preferences. Yes.6. Consider the utility function u(x1,x2)=. What kind of pref- erences does it represent? Is the function v(,)=a monotonic transformation of u(,)? Is the function w(,)= a monotonic transformation ofu(,)?4.6. The utility function represents Cobb-Douglas preferences. No. Yes.7. Can you explain why taking a monotonic transformation of a utility function doesn’t change the marginal rate of substitution? 4.7. Because the MRS is measured along an indiﬀerence curve, and utility remains constant along an indiﬀerence curve.5 Choice1. If two goods are perfect substitutes, what is the demand function for good 2?5.1.=0 when>, = m/when<, and anything between 0 and m/p2 when = .2. Suppose that indiﬀerence curves are described by straight lines with a slope of −b. Given arbitrary prices and money income p1, p2, and m, what will the consumer’s optimal choices look like?5.2. The optimal choices will be x1 = m/p1 and x2 = 0 ifp1/p2 <b ,x1 = 0 andx2 = m/p2 if p1/p2 >b, and any amount on the budget line if p1/p2 = b.3. Suppose that a consumer always consumes 2 spoons of sugar with each cup of coﬀee. If the price of sugar is p1 per spoonful and the price of coﬀee is p2 per cup and the consumer has m dollars to spend on coﬀee and sugar, how much will he or she want to purchase?5.3. Let z be the number of cups of coﬀee the consumer buys. Then we know that 2z is the number of teaspoons of sugar he or she buys. We must satisfy the budget constraint2z + z = m.Solving for z we havez =.4. Suppose that you have highly nonconvex preferences for ice cream and olives, like those given in the text, and that you face prices p1, p2 and have m dollars to spend. List the choices for the optimal consumption bundles.5.4. We know that you’ll either consume all ice cream or all olives. Thus the two choices for the optimal consumption bundles will be x1 = m/, x2 = 0, or x1 = 0, x2 = m/.5. If a consumer has a utility function u(x1,x2)=x1x4 2, what fraction of her income will she spend on good 2?5.5. This is a Cobb-Douglas utility function, so she will spend 4/(1 + 4) = 4/5 of her income on good 2.6. For what kind of preferences will the consumer be just as well-oﬀfacing a quantity tax as an income tax?5.6. For kinked preferences, such as perfect complements, where the change in price doesn’t induce any change in demand.6 Demand1. If the consumer is consuming exactly two goods, and she is always spending all of her money, can both of them be inferior goods?6.1. No. If her income increases, and she spends it all, she must be purchasing more of at least one good.2. Show that perfect substitutes are an example of homothetic preferences.6.2. The utility function for perfect substitutes is u(,)=+ . Thus ifu(,) >u (,), we have + >+ . It follows that t+ t> t+ t, so that u(t,t) >u (t, t).3. Show that Cobb-Douglas preferences are homothetic preferences.6.3. The Cobb-Douglas utility function has the property that u(t,t)==2 = t 2 = t*u(x1,).Thus if u(,) >u (,), we know that u(t,t) >u (t,), so that Cobb-Douglas preferences are indeed homothetic.4. The income oﬀer curve is to the Engel curve as the price oﬀer curve is to ...?6.4. The demand curve.5. If the preferences are concave will the consumer ever consume both of the goods together?6.5. No. Concave preferences can only give rise to optimal consumption bundles that involve zero consumption of one of the goods.6. Are hamburgers and buns complements or substitutes?6.6. Normally they would be complements, at least for non-vegetarians.7. What is the form of the inverse demand function for good 1 in the case of perfect complements?6.7. We know that x1 = m/(p1 + p2). Solving for p1 as a function of the other variables, we have p1 = m x1 −p2.8. True or false? If the demand function is x1 = −p1, then the inverse demand function is x = −1/p1.6.8. False.7 Revealed Preference1. When prices are (p1,p2) = (1 ,2) a consumer demands (x1,x2) =(1 ,2), and when prices are ( q1,q2) = (2 ,1) the consumer demands (y1,y2) = (2 ,1). Is this behavior consistent with the model of maximizing behavior?7.1. No. This consumer violates the Weak Axiom of Revealed Preference since when he bought (x1,x2) he could have bought (y1,y2) and vice versa. In symbols:p1x1 + p2x2 =1×1+2×2=5> 4=1×2+2×1=p1y1 + p2y2andq1y1 + q2y2 =2×2+1×1=5> 4=2×1+1×2=q1x1 + q2x2.2. When prices are (p1,p2) = (2 ,1) a consumer demands (x1,x2) = (1 ,2), and when prices are ( q1,q2) = (1 ,2) the consumer demands (y1,y2) = (2 ,1). Is this behavior consistent with the model of maximizing behavior?7.2. Yes. No violations of WARP are present, since the y-bundle is not aﬀordable when the x-bundle was purchased and vice versa.3. In the preceding exercise, which bundle is preferred by the consumer, the x-bundle or the y-bundle?7.3. Since the y-bundle was more expensive than the x-bundle when the x-bundle was purchased and vice versa, there is no way to tell which bundle is preferred.4. We saw that the Social Security adjustment for changing prices would typically make recipients at least as well-oﬀas they were at the base year. What kind of price changes would leave them just as well-oﬀ, no matter what kind of preferences they had?7.4. If both prices changed by the same amount. Then the base-year bundle would still be optimal.5. In the same framework as the above question, what kind of preferences would leave the consumer just as well-oﬀas he was in the base year, for all price changes?7.5. Perfect complements.8 Slutsky Equation1. Suppose a consumer has preferences between two goods that are perfect substitutes. Can you change prices in such a way that the entire demand response is due to the income eﬀect?8.1. Yes. To see this, use our favorite example of red pencils and blue pencils. Suppose red pencils cost 10 cents a piece, and blue pencils cost 5 cents a piece, and the consumer spends $1 on pencils. She would then consume 20 blue pencils. If the price of blue pencils falls to 4 cents a piece, she would consume 25 blue pencils, a change which is entirely due to the income eﬀect.2. Suppose that preferences are concave. Is it still the case that the substitution eﬀect is negative?8.2. Yes.3. In the case of the gasoline tax, what would happen if the rebate to the consumers were based on their original consumption of gasoline, x, rather than on their ﬁnal consumption of gasoline, x’?8.3. Then the income eﬀect would cancel out. All that would be left would be the pure substitution eﬀect, which would automatically be negative.4. In the case described in the preceding question, would the government be paying out more or less than it received in tax revenues?8.4. They are receiving tx’ in revenues and paying out tx, so they are losing money.5. In this case would the consumers be better oﬀ or worse oﬀ if the tax with rebate based on original consumption were in eﬀect?8.5. Since their old consumption is aﬀordable, the consumers would have to be at least as well-oﬀ. This happens because the governmentis giving them back more money than they are losing due to the higher price of gasoline.9 Buying and Selling1. If a consumer’s net demands are (5,−3) and her endowment is (4,4), what are her gross demands?9.1. Her gross demands are (9,1).2. The prices are (p1,p2) = (2 ,3), and the consumer is currently consuming (x1,x2) = (4 ,4). There is a perfect market for the two goods in which they can be bought and sold costlessly. Will the consumer necessarily prefer consuming the bundle (y1,y2) = (3 ,5)? Will she necessarily prefer having the bundle (y1,y2)?9.2. The bundle (y1,y2) = (3 ,5) costs more than the bundle (4,4) at the current prices. The consumer will not necessarily prefer consuming this bundle, but would certainly prefer to own it, since she could sell it and purchase a bundle that she would prefer.3. The prices are (p1,p2) = (2 ,3), and the consumer is currently consuming (x1,x2) = (4 ,4). Now the prices change to (q1,q2) = (2 ,4). Could the consumer be better oﬀ under these new prices?9.3. Sure. It depends on whether she was a net buyer or a net seller of the good that became more expensive.4. The U.S. currently imports about half of the petroleum that it uses. The rest of its needs are met by domestic production. Could the price of oil rise so much that the U.S. would be made better oﬀ?9.4. Yes, but only if the U.S. switched to being a net exporter of oil.5. Suppose that by some miracle the number of hours in the day increased from 24 to 30 hours (with luck this would happen shortly before exam week). How would this aﬀect the budget constraint?9.5. The new budget line would shift outward and remain parallel to the old one, since the increase in the number of hours in the day is a pure endowment eﬀect.6. If leisure is an inferior good, what can you say about the slope of the labor supply curve?9.6. The slope will be positive.10 Intertemporal Choice1. How much is $1 million to be delivered 20 years in the future worth today if the interest rate is 20 percent?10.1. According to Table 10.1, $1 20 years from now is worth 3 cents today at a 20 percent interest rate. Thus $1 million is worth .03×1,000,000 = $30,000 today.2. As the interest rate rises, does the intertemporal budget constraint be- come steeper or ﬂatter?10.2. The slope of the intertemporal budget constraint is equal to −(1+r). Thus as r increases the slope becomes more negative (steeper).3. Would the assumption that goods are perfect substitutes be valid in a study of intertemporal food purchases?10.3. If goods are perfect substitutes, then consumers will only purchase the cheaper good. In the case of intertemporal food purchases, this implies that consumers only buy food in one period, which may not be very realistic.4. A consumer, who is initially a lender, remains a lender even aftera decline in interest rates. Is this consumer better oﬀor worse oﬀafter the change in interest rates? If the consumer becomes a borrower after the change is he better oﬀ or worse oﬀ?10.4. In order to remain a lender after the change in interest rates, the consumer must be choosing a point that he could have chosen under the old interest rates, but decided not to. Thus the consumer must be worse oﬀ. If the consumer becomes a borrower after thechange, then he is choosing a previously unavailable point that cannot be compared to the initial point (since the initial point is no longer available under the new budget constraint), and therefore the change in the consumer’s welfare is unknown.5. What is the present value of $100 one year from now if the interest rate is 10%? What is the present value if the interest rate is 5%?10.5. At an interest rate of 10%, the present value of $100 is $90.91. At a rate of 5% the present value is $95.24.11 Asset Markets1. Suppose asset A can be sold for $11 next period. If assets similar toA are paying a rate of return of 10%, what must be asset A’s current price?11.1. Asset A must be selling for 11/(1 + 0.10) = $10.2. A house, which you could rent for $10,000 a year and sell for $110,000 a year from now, can be purchased for $100,000. What is the rate of return on this house?11.2. The rate of return is equal to (10,000 + 10,000)/100,000 = 20%.3. The payments of certain types of bonds (e.g., municipal bonds) are not taxable. If similar taxable bonds are paying 10% and everyone faces a marginal tax rate of 40%, what rate of return must the nontaxable bonds pay?11.3. We know that the rate of return on the nontaxable bonds, r, must be such that (1−t)= r, therefore (1−0.40)*0.10 =0 .06 = r.4. Suppose that a scarce resource, facing a constant demand, will be exhausted in 10 years. If an alternative resource will be available at a price of $40 and if the interest rate is 10%, what must the price of the scarce resource be today?11.4. The price today must be 40/(1 +0 .10)^10 = $15.42.12 Uncertainty1. How can one reach the consumption points to the left of the endowment in Figure 12.1?12.1. We need a way to reduce consumption in the bad state and increase consumption in the good state. To do this you would have to sell insurance against the loss rather than buy it.2. Which of the following utility functions have the expected utility property? (a) u(c1,c2,π1,π2)=a(π1c1 + π2c2), (b) u(c1,c2,π1,π2)=π1c1 + π2c2 2, (c)u(c1,c2,π1,π2)=π1 lnc1 + π2 lnc2 + 17.12.2. Functions (a) and (c) have the expected utility property (they are aﬃne transformations of the functions discussed in the chapter), while (b) does not.3. A risk-averse individual is oﬀered a choice between a gamble that pays $1000 with a probability of 25% and $100 with a probability of 75%, or a payment of $325. Which would he choose?12.3. Since he is risk-averse, he prefers the expected value of the gamble, $325, to the gamble itself, and therefore he would take the payment.4. What if the payment was $320?12.4. If the payment is $320 the decision will depend on the form of the utility function; we can’t say anything in general.5. Draw a utility function that exhibits risk-loving behavior for small gambles and risk-averse behavior for larger gambles.12.5. Your picture should show a function that is initially convex, but then becomes concave.6. Why might a neighborhood group have a harder time self insuring for ﬂood damage versus ﬁre damage?12.6. In order to self-insure, the risks must be independent. However, this does not hold in the case of ﬂood damage. If one house in the neighborhood is damaged by a ﬂood it is likely that all of the houses will be damaged.13 Risky Assets1. If the risk-free rate of return is 6%, and if a risky asset is available with a return of 9% and a standard deviation of 3%, what is the maximum rate of return you can achieve if you are willing to accept a standard deviation of 2%? What percentage of your wealth would have to be invested in the risky asset?13.1. To achieve a standard deviation of 2% you will need to invest x = σx/σm =2 /3 of your wealth in the risky asset. This will result in a rate of return equal to (2/3)0.09 + (1−2/3)0.06 = 8%.2. What is the price of risk in the above exercise?13.2. The price of risk is equal to (rm − rf)/σm = (9− 6)/3 = 1. That is, for every additional percent of standard deviation you can gain 1% of return.3. If a stock has a β of 1.5, the return on the market is 10%, and the risk- free rate of return is 5%, what expected rate of return should this stock oﬀer according to the Capital Asset Pricing Model? If theexpected value of the stock is $100, what price should the stock be selling for today?13.3. According to the CAPM pricing equation, the stock should oﬀer an expected rate of return of rf + β(rm −rf)=0.05 + 1.5(0.10−0.05) =0 .125 or 12.5%. The stock should be selling for its expected present value, which is equal to 100/1.125 = $88.89.14 Consumer’s Surplus1. A good can be produced in a competitive industry at a cost of $10 per unit. There are 100 consumers are each willing to pay $12 each to consume a single unit of the good (additional units have no value to them.) What is the equilibrium price and quantity sold? The government imposes a tax of $1 on the good. What is the deadweight loss of this tax?14.1. The equilibrium price is $10 and the quantity sold is 100 units. If the tax is imposed, the price rises to $11, but 100 units of the good will still be sold, so there is no deadweight loss.2. Suppose that the demand curve is given by D(p) = 10−p. What is the gross beneﬁt from consuming 6 units of the good?14.2. We want to compute the area under the demand curve to the left of the quantity 6. Break this up into the area of a triangle with a base of 6 and a height of 6 and a rectangle with base 6 and height 4.Applying the formulas from high school geometry, the triangle has area 18 and the rectangle has area 24. Thus gross beneﬁt is 42.3. In the above example, if the price changes from 4 to 6, what is the change in consumer’s surplus?14.3. When the price is 4, the consumer’s surplus is given by the area of a triangle with a base of 6 and a height of 6; i.e., the consumer’s surplus is 18. When the price is 6, the triangle has a base of 4 and a height of 4, giving an area of 8. Thus the price change has reduced consumer’s surplus by $10.4. Suppose that a consumer is consuming 10 units of a discrete good and the price increases from $5 per unit to $6. However, after the price change the consumer continues to consume 10 units of the discrete good. What is the loss in the consumer’s surplus from this price change?14.4. Ten dollars. Since the demand for the discrete good hasn’t changed, all that has happened is that the consumer has had to reduce his expenditure on other goods by ten dollars.15 Market Demand1. If the market demand curve is D(p) = 100 − .5p, what is the inverse demand curve?15.1. The inverse demand curve is P(q) = 200−2q.2. An addict’s demand function for a drug may be very inelastic, but the market demand function might be quite elastic. How can this be?15.2. The decision about whether to consume the drug at all could well be price sensitive, so the adjustment of market demand on the extensive margin would contribute to the elasticity of the market demand.3. If D(p) = 12−2p, what price will maximize revenue?15.3. Revenue is R(p) = 12 p−2p2, which is maximized at p = 3.4. Suppose that the demand curve for a good is given by D(p) = 100/p. What price will maximize revenue?15.4. Revenue is pD(p) = 100, regardless of the price, so all prices maximize revenue.5. True or false? In a two good model if one good is an inferior good the other good must be a luxury good.15.5. True. The weighted average of the income elasticities must be 1, so if one good has a negative income elasticity, the other good musthave an elasticity greater than 1 to get the average to be 1.16 Equilibrium1. What is the eﬀect of a subsidy in a market with a horizontal supply curve? With a vertical supply curve?16.1. The entire subsidy gets passed along to the consumers if the supply curve is ﬂat, but the subsidy is totally received by the producers when the supply curve is vertical.2. Suppose that the demand curve is vertical while the supply curve slopes upward. If a tax is imposed in this market who ends up paying it?16.2. The consumer.3. Suppose that all consumers view red pencils and blue pencils as perfect substitutes. Suppose that the supply curve for red pencils is upward sloping. Let the price of red pencils and blue pencils be and . What would happen if the government put a tax only on red pencils?16.3. In this case the demand curve for red pencils is horizontal at the price , since that is the most that they would be willing to pay for a red pencil. Thus, if a tax is imposed on red pencils, consumers will end up paying for them, so the entire amount of the tax will end。

中级微观经济学(1-4章习题及答案)

（1）将 1代入 CES 函数，立即得到 y A1x1 A 2x 2 ，这是线性函数。
（2）当 0 时，CES 函数成为不定式，为求其极限，对 CES 函数取对数。
ln
y A

ln(
1x
1

2
x
2
)

利用洛必达法则：
lim lim 0
ln
y A

0
币；假设他现在处于均衡状态，即是说目前的市价下他不想买进也不想卖出。证明：无论钱
币市场上钱币的价格上涨还是下跌，这个人的效用水平总会增加。（该题是关于显示偏好的
内容，参照显示偏好内容进行理解）
提示：假设现在收藏家在（ M* ， X* ）处达到均衡，其中 M 指钱币数量， X 是所有其他消费
品（的支出）。在图中，预算线与一条无差异曲线I* 相切。如果 pM 上升， pM/pX 增大，预算约束线较以前陡峭，但它必然还通过（ M* ，X* ）点，因为这点的坐标满足预算线方程[注
ln(
1x
1

2
x
2
)

lim
1x
1
ln
x1

2
x
2
ln
x2
0

1x
1

2
x
2
1 ln x1 2 ln x 2 1 2

ln
x 1a
x
b 2
其中 a

1 1 2
,b

2 ，故 y 1 2

Ax
a 1
x
b 2
（3）对 CES 函数取对数，求极限，利用洛必达法则

中级微观经济学习题

中级微观经济学习题习题课21.假定消费者的收入为m，他要消费两种商品1和2，其价格分别为p1和p2,。

这个消费者的效用函数为：U(x1,x2)=x12+4x22其中，x1和x2分别为这两种商品的消费量，请计算消费者的消费决策。

2.某人仅消费x和y两种商品，其效用函数为：U=50x?0.5x2+100y?y2其收入I=672，P x=4。

（1）推导出此人对y的需求函数。

（2）如果P y=14。

，此人将消费多少x。

+100/m，3.假设某个学生的月收入为m=1000元，他对面包的需求函数为x(p,m)=20p 面包的价格p=4。

（1）当价格从4上涨为5时，为使该学生买得起面包消费量，他的收入应当增加多少？（2）计算斯勒茨基替代效应。

（3）请计算收入效应。

4.某消费者的效用函数为：U=xy其中，P x=1，P y=2，收入m=40,。

现在如果商品y的价格下降到1，请回答下列问题：（1）y 价格下降的替代效应应使y 的购买量变化多少？（2）y 价格下降的收入效应应使y 的购买量变化多少？5. 假定一个消费者的效用函数为：U (x 1,x 2)=x 11/2x 21/2他开始面对的价格是（1,1），所有的收入是100。

然后商品1的价格上升到2，问补偿变化和等价变化各是多少。

6. 已知112212u x x =，m=100，110p =,25p =; （1）求效用最大化下的1x 和2x（2）当商品1价格下降为15p =时，求收入效应和替代效应7. 某消费者消费X 和Y 两种商品的效用函数为U=X 2Y 3，消费者收入M 为100。

（1）求该消费者对X 商品的需求函数；（2）若Y 商品的价格为P Y =3，求当X 商品的价格P X 由2 变为1时产生的替代效应和收入效应。

张元鹏《微观经济学》(中级教程)模拟试题及详解(一)(圣才出品)

商品的价格。他们可以通过获得食物券以实际 px (1− s) 的价格来购买食物（当食物消费数量
不足 x 单位时）。如果他们购买的食物数量超过 x ，他们要承担的价格是 px 。他们每周的收
入多于 px (1− s) x* ，那么他们能购买的食物数量最多为（）。
A． x + m px
B． m + x px
px
px
2．边际收益递减规律是指（）。 A．任何一种投入的总产量最终一定会达到最大，且随着该投入单位数的增加而减少 B．任何一种投入的平均产量最终一定会达到最小，且随着所有投入的增加而成比例的增加 C．任何一种投入的边际产量应该最终都会随着该投入单位数的增加而减少 D．任何一种投入的边际产量应该最终都会随着该投入的单位数增加而成比例的减少【答案】C 【解析】边际收益递减指在其他投入不变的情况下，随着可变投入的不断增加边际产量最终会下降。但并不反映边际产量的减少与可变投入的增加在量上是否成比例。
2．边际替代率
答：边际替代率（margina1 rate of substitution， MRS ），即无差异曲线的斜率，是
指在维持效用水平不变的前提下，消费者增加一单位某种商品的消费数量时所需要放弃的另
一种商品的消费数量。商品 1 பைடு நூலகம்商品 2 的边际替代率的定义公式为：
MRS12
=
−
x2 x1
py
3 / 19
圣才电子书十万种考研考证电子书、题库视频学习平台

总收入减去购买 OE = x* 所花费的就是花费在 EC 上的，故 EC = m − px (1− s) x* = m − (1− s) x* 。
px
px
从而： OC = x + m − (1− s) x = sx + m 。

中级微观经济学试题I资料讲解

中级微观经济学试题IINTERMEDIATE MICROECONOMICSExercise I1. The demand curve of movie is Q=500−5P. If the current price of tickets is 35, the price elasticity of demand at the current price isa. -0.2b. -0.54c. -0.68d. -12. Which of the following utility functions would not be consistent with the notion that x and y are both “goods” with positive marginal utilities?a.(,)2U x y = y x . b.U(x, y) = x + y .c.(,)U x y d. U(x, y) = x/y .3. If two goods are perfect complements:a. there is a bliss point and the indifference curves surround this point.b. consumers will only buy the cheaper of the two goods.c. indifference curves have a positive slope.d. none of the above.4. According to the graph shown, if the government imposes a price ceiling in this market at a price of $5.00, the result would bea. a shortage of 20 units.b. a shortage of 30 units.c. a surplus of 20 units.d. a surplus of 40 units.5. If utility is given by22(,)2U x y xy yx=++, this person’s indifference curves area. parabolas.（抛物线）b. hyperbolas.（双曲线）c. concentric circles. （同心圆）d. straight lines.6. Which of the following is an example of a normative, as opposed to positive, statement?a. The price of gasoline came down sharply during the second half of 2006.b. If the government were to set a maximum legal price on gasoline, then there would be a shortage of gasoline.c. Income taxes should be reduced.d. The federal government obtains much of its revenue from income taxes.7. If an individual’s utility function for coffee (x) and cream (y) is given by U(x, y) = min (x, 5y), the demand function for coffee is given bya. X = I/2p x .b. X = I/(p x + p y).c. X = I/(p x + 0.2p y).d. X = I/(p x + p y)2.1.Engel curves always slope upwards.2.If there are two goods, if a consumer prefers more of each good to less, and if shehas diminishing marginal rate of substitution, then her preferences are convex. 3.If someone has a utility function U=2min{x,y},then x and y are perfect substitutesfor that person.4.An increase in an individual’s income without changing relative prices will shiftthe indifference curves outward.5.Tangencies of indifference curves to the budget constraint must be points of utilitymaximization.II.Calculation and Graph1.Draw graphs with quantities of pizza on the horizontal axis and coca on thevertical axis to illustrate the following situations. In each case draw two different indifference curves and make a little arrow pointing in the direction of greater preference.a. Marvin loves pizza and hates coca.b. Marvin hates coca and is completely indifference about pizza.2.Patrick has a utility function U(x1, x2)=48x11/2+ x2, where x1 is his consumption ofnuts and x2 is his consumption of berries. His income is 217, the price of nuts is 3 and the price of berries is 1. How many units of berries will Patrick demand? If his income doubles and prices stay unchanged, will his demand for both goods double?3.Justin has the utility function U = xy. The price of x is 2, the price of y is p y, andhis income is 40. When he maximizes utility subject to his budget constraint, he purchases 5 units of y. What must be the price of y and the amount of x consumed?。

中级微观练习题及参考答案

中级微观练习题及参考答案中级微观练习题及参考答案第一部分消费者选择理论1.有两种商品，x1和x2，价格分别为p1和p2，收入为m 。

当11x x时，政府加数量税t,画出预算集并写出预算线2. 消费者消费两种商品（x1，x2），如果花同样多的钱可以买（4，6）或（12，2），写出预算线的表达式。

3．重新描述中国粮价改革（1）假设没有任何市场干预，中国的粮价为每斤0。

4元，每人收入为100元。

把粮食消费量计为x ，在其它商品上的开支为y ，写出预算线，并画图。

（2）假设每人得到30斤粮票，可以凭票以0。

2元的价格买粮食，再写预算约束，画图。

（3）假设取消粮票，补贴每人6元钱，写预算约束并画图。

4．证两条无差异曲线不能相交5．一元纸币（x1）和五元纸币（x2）的边际替代率是多少6．若商品1为中性商品，则它对商品2的边际替代率 7. 写出下列情形的效用函数，画出无差异曲线，并在给定价格（p 1，p 2）和收入（m ）的情形下求最优解。

（1）x 1=一元纸币，x 2=五元纸币。

（2）x 1=一杯咖啡，x 2=一勺糖, 消费者喜欢在每杯咖啡加两勺糖。

8. 解最优选择（1）21212(,)u x x x x =?（2）2u x =+9. 对下列效用函数推导对商品1的需求函数，反需求函数，恩格尔曲线；在图上大致画出价格提供曲线，收入提供曲线；说明商品一是否正常品、劣质品、一般商品、吉芬商品，商品二与商品一是替代还是互补关系。

（1）212x x u +=（2）()212,m in x x u =（3）ba x x u 21?=（4） 12ln u x x =+,10. 当偏好为完全替代时，计算当价格变化时的收入效用和替代效用（注意分情况讨论）。

11. 给定效用函数 (,)x y xy =，p x =3，p y =4，m=60，求当p y降为3时价格变化引起的替代效应和收入效应。

12. 用显示偏好的弱公理说明为什么Slutsky 替代效应为负。

中级微观经济学习题（消费者理论部分）

中级微观经济学习题消费者理论部分【尼克尔森3、4、5、6章】1. 【尼克尔森3.1】画出下列效用函数的无差异曲线，并判断他们是否是凸的（及边际替代率MRS是否是随着x的增加而递减）。

（1）U(x,y)=3x+y（2）U(x,y)=xy（3）U(x,y)=x+y（4）U(x,y)= x2−y2（5）U(x,y)=xyx+y2. 某大学生仅有6天时间复习经济学、高等数学、英语三门课，要使这三门客的期末考试取得尽可能高的总成绩，他必须安排好每门课程的复习时间。

如果每门可得复习时间与相应的考试分数用下表表示，请问该学生应该如何分配复习时间才能取得尽可能搞得成绩？他可能得到的最高总分是多少？3. 【尼克尔森3.3】对于如下效用函数，请证明尽管这些效用函数具有递减的MRS，但是它们分别显示出边际效用不变、递增、递减。

（1）U(x,y)=xy（2）U(x,y)=x2y2（3）U(x,y)=lnx+lny4. 【尼克尔森3.5】Phillie Phanatic总是喜欢以一种特定的方式来吃Ballpark Franks牌热狗：他将1英尺长的热狗，恰好配以半块小圆面包，1盎司芥末以及2盎司的咸菜调味品同时食用。

他的效用是以上四种食品的函数，亲切额外一种食品的数量增加而其他食品不变是不会增加他的效用的。

（1）Phillie Phanatic对这四种食品的效用函数的形式是什么？（2）我们可以如何将Phillie Phanatic的效用视为一种商品的函数来简化问题？这种商品是什么？（3）假设每英尺热狗的价格为1元，小圆面包价格为0.5元，每盎司芥末的价格为0.05元，每盎司咸菜调味品的价格为0.15元，那么第（2）问中定义的商品价格是多少？（4）如果每英尺热狗的价格增加50%（即增至1.5元），那么该商品的价格增加的百分比是多少？（5）小圆面包的价格上涨50%将如何影响该商品的价格？观察此答案与（4）的答案有什么不同？（6）如果政府对Phillie Phanatic购买的每单位商品征税1元，则税收将如何在这4中商品中分担，从而使Phillie Phanatic的效用成本最小化？5. 【尼克尔森3.6】许多广告语是会表明了人们的某些偏好，你将如何用效用函数来描述下列广告语？（1）人造黄油与真黄油一样好。