范里安中级微观经济学题目

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范里安_中级微观经济学Ch16

第十六章
均衡
市场均衡
当所有买者的总需求量等于所有卖者的
供给量时，我们称市场达到均衡状态。
市场均衡
p衡
p 市场供给 q=S(p)
S(p)
市场均衡
p 市场需求市场供给 q=S(p)
q=D(p) D(p), S(p)
市场均衡
p 市场需求市场供给 q=S(p)
p D
* 1
(q ) S
*
1
ac (q ) . bd
*
市场均衡
D-1(q), 市场需求 S-1(q)
市场供给 S-1(q) = (-c+q)/d
p ac bd
D-1(q) = (a-q)/b
*
ad bc q bd
*
q
市场均衡
两种特殊情况:
供给量固定，与市场价格无关或者供给量对市场价格相当敏感。
*
供给量固定，与市场价格无关
ac p b
*
q* c.
市场均衡
两种特殊情况

供给量固定，与市场价格无关供给量对市场价格十分敏感。
市场均衡
p 供给量对市场价格十分敏感
q
市场均衡
p 供给量对市场价格十分敏感 S-1(q) = p*. p*
q
市场均衡
p 市场需求供给量对市场价格十分敏感 S-1(q) = p*. p* D-1(q) = (a-q)/b q
市场均衡
p 市场需求市场供给 q=S(p) p’ p* q=D(p) D(p’) S(p’) D(p), S(p) D(p’) < S(p’); 供给量大于需求量
市场价格会下降至p*
市场均衡
p 市场需求市场供给 q=S(p) D(p”) > S(p”); 需求量大于供给量 p* p” S(p”) D(p”) q=D(p) D(p), S(p)

《中级微观经济学》第一二章作业

《中级微观经济学》第一二章作业1.1.假设25个人的保留价格为500美元，第26个人持有的保留价格为200美元，需求曲线呈什么形状？1.2.在上述例子中，假如只有24套房可以出租，均衡价格是多少？如果有26套房可出租，均衡价格又是多少？如果有25套房可以出租，均衡价格是多少？1.3.假定持有不同的保留价格，为什么市场需求曲线向下倾斜？1教材为范里安《微观经济学：现代观点》第九版，习题可能与第八版略有不同1.4.在本书中，我们假设公寓购买者都者来自内城区的人。

如果公寓购买者都来自于外城区的人，内城区住房的价格会发生怎么样的变化？.1.5.假设现在公寓的购买者都是内城区的人，但是每一公寓由两套住房构成，住房的价格会发生什么样的变化。

1.6.设想一下，征税会对长期内的建房数量产生什么影响。

1.7.假设需求曲线为D(p)=100-2p.如果垄断者有60个公寓，他将如何定价？他将租出多少公寓？如果他有40个公寓，他将如何定价？他将租出多少公寓？1.8.如果我们的租金管制模型允许不受限制地转租，谁最终获得内环的公寓？这个结果是帕累托有效率的吗？2.1.消费者的初始预算线为p1某1+p2某2-m。

现在商品1的价格提高了1倍，商品2的价格提升了7倍，收入提升了3倍。

根据原先的价格和收入写出新的预算线方程。

2.2.如果商品2的价格上升，但商品1的价格和收入保持不变，那么预算线如何变动？2.3.如果商品1的价格上涨了1倍，商品2的价格上涨了2倍，预算线变得更平坦还是更陡峭？2.4.计价物的定义是什么？2.5.假设政府最初对每加仑汽油征税15分钱，后来又决定对每加仑汽油给与7分钱的补贴。

这种税收和补贴联合使用的方式等价于对每加仑汽油征多少税？2.6.假设预算线方程为p1某1+p2某2=m现在政府决定：对消费者征收定额税，税额为u；对每单位商品1征收t元从量税；对每单位商品2给与元补贴。

求新预算线的表达式。

2.7.如果消费者的收入增加，同时其中一种商品价格下降，消费者的状况必然至少与原来一样好吗？2.4.计价物的定义是什么？2.5.假设政府最初对每加仑汽油征税15分钱，后来又决定对每加仑汽油给与7分钱的补贴。

范里安中级微观经济学题目

范⾥安中级微观经济学题⽬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,min x x u =（3）b a 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。

中级微观经济学范里安课后答案

中级微观经济学范里安课后答案第1章市场说明：作为范里安《微观经济学：现代观点》教材的第一章，本章通过考察一个特定的市场模型——住房市场进行实例分析。

对于本章内容，建议学员简单了解即可。

钟根元《中级微观经济学学习指南》（第4版）未添加相关的练习题。

第2章预算约束一、判断题1考虑某消费者消费价格均为正的两种商品。

如果其中一种商品的价格下降了，而收入和另一种商品的价格保持不变，那么预算集范围缩小了。

（）【答案】F查看答案【解析】设消费者消费x和y两种商品，价格分别为px和py，收入为m。

设商品x的价格由px下降为px′，那么，如图2-1所示，预算线与横轴的交点由m/px右移至m/px′，预算线与纵轴的交点未变，显然，预算集的范围扩大了。

图2-1 价格下降引起的预算集变化2以横轴代表商品1，纵轴代表商品2，商品1价格为p1，商品2价格为p2，那么预算线的斜率为－p2/p1。

（）【答案】F查看答案【解析】如图2-2所示，预算线的斜率k＝－OA/OB，A为预算线与纵轴的交点，表示的是收入全部用于购买商品2时的消费量，即OA ＝m/p2，同理，OB＝m/p1，因此预算线的斜率为k＝－（m/p2）/（m/p1）＝－p1/p2。

图2-2 预算线3如果所有的商品价格都变为原来的两倍，而收入保持不变，那么预算集没有变化，因为相对价格没有变化。

（）【答案】F查看答案【解析】预算线方程为px＋py＝I，价格变为原来的两倍后，预算线变为2px＋2py＝I，或者px＋py＝I/2，显然，预算线斜率不变，但预算集范围缩小了。

4考虑两种商品，如果一种商品价格为正，而另一种商品价格为负（例如把“拾垃圾”也看成是“商品”，负的价格表示对消费者的补贴），那么预算线斜率为正。

（）【答案】T查看答案【解析】预算线的斜率为k＝－p1/p2，若一种商品价格为正，另一种商品价格为负，那么－p1/p2＞0，即预算线斜率为正。

5如果所有商品价格变为原来的两倍，收入变为原来的三倍，则预算线会更加陡峭。

中级微观经济学(范里安)期末复习

目录一、简答题（3道） (2)1.期望效用与风险态度（需要计算和判断） (2)2.由显示偏好判断消费行为是否满足显示偏好弱公理（消费者是否理性） (8)3.举例说明正负外部性（消费或生产） (10)二、计算题（5选3，3必做，1和2选一个，4和5选一个） (13)1.禀赋收入效应、普通收入效应和替代效应 (13)2.消费者剩余的变化、补偿变换和等价变换 (18)3.税收和补贴对均衡的影响，税收或补贴的归宿 (21)4.古诺模型、卡特尔及囚徒困境博弈 (25)5.子博弈精炼纳什均衡 (27)三、分析题（2选1，一道大题一道小题） (30)差别定价（价格歧视） (30)两部收费制：案例分析题，企业如何运用两部收费制（垄断PPT43页） (36)一、简答题（3道）1.期望效用与风险态度（需要计算和判断）引入（1）期望效用的概念期望效用指的是消费者在不确定条件下可能获得的各种结果的效用的加权平均数，假设πa 表示结果a发生的概率，πna表示结果na发生的概率，c a表示结果a发生时的消费，c na表示结果na发生时的消费，则期望效用EU=πa U(c a)+πna U(c na)期望效用函数的特点①状态独立性（人们在一种自然状态下做出的选择，将独立于他们在另一种自然状态下做出的选择）②状态可加性③概率加权（因为效用与概率相关，赋予小概率事件更小的权重）*注意：期望效用仅仅是对个人偏好的一种假设，它是可以被推翻的（当人们考虑在两种东西中进行选择时，他们拥有的第三件东西的数量会影响其选择。

比如咖啡和茶的选择，在相当程度上取决于你拥有多少冰激凌）（2）根据效用函数判断风险态度①风险厌恶（更偏好财富的期望值而不是赌博本身）凹函数（凹向原点）u (12×15+12×5)=u (10)>12u (15)+12u (5)②风险偏好（更偏好的是财富的随机分布而不是财富的期望值）凸函数（凸向原点）u (12×15+12×5)=u (10)<12u (15)+12u (5)效用函数是严格凸的，风险偏好效用函数是严格凹的，风险厌恶效用函数是一条直线，风险中性定理：一个投资者是（严格）风险厌恶的，其充要条件是他的确定性效用函数u( )是（严格）凹函数。

范里安《微观经济学：现代观点》（章节题库-选择）【圣才出品】

范⾥安《微观经济学：现代观点》（章节题库-选择）【圣才出品】第5章选择⼀、判断题 1．某消费者的效⽤函数为u （x ，y ）＝（x ＋2）（y ＋1），如果他所消费的商品x 和商品y 都增加⼀倍，那么商品x 和商品y 的边际替代率仍保持不变。

（）【答案】F【解析】边际替代率为：//u x MRS u y ??=-??当u （x ，y ）＝（x ＋2）（y ＋1）时，MRS ＝－（y ＋1）/（x ＋2）；当u （x ，y ）＝（2x ＋2）（2y ＋1）时，MRS ＝－2（2y ＋1）/[2（2x ＋2）]＝－（2y ＋1）/[2（x ＋1）]。

商品x 和商品y 的边际替代率发⽣变化。

2．在最优选择处，消费者的⽆差异曲线和预算线⼀定是相切的。

（）【答案】F【解析】最优选择处，⽆差异曲线和预算线可以相切，也可以不相切。

在凸性偏好和内部最优的条件下，相切是最优选择的充分条件，即相切处⼀定是最优选择，但最优选择不⼀定是相切的。

在边界最优的情况下，如商品完全替代的情况下，⽆差异曲线与预算线是相交的，⽽不是相切的。

3．已知⼀元钱的边际效⽤为5个单位，⼀⽀钢笔的边际效⽤为35个单位，则消费者需要⽤6元来买这⽀钢笔。

（）【答案】F 【解析】基数效⽤论中效⽤最⼤化条件为MU/P ＝λ，本题中35/6＞5，消费者需要7元来购买这⽀钢笔。

4．某消费者的效⽤函数为u （x ，y ）＝x ＋4y 1/2，商品x 的价格为1元/单位，商品y 的价格为2元/单位。

如果他的收⼊从100元增加到150元，他对商品y 的消费将增加超过10%，但少于50%。

（）【答案】F【解析】根据效⽤最⼤化的条件//x y P u x P u y= 可得：1/（2y －1/2）＝1/2，即y ＝1。

当收⼊变动时，消费者对y 的消费不变。

5．某消费者效⽤函数为u （x ，y ）＝max{x ，y}，如果商品x 的价格与商品y 的价格相等，该消费者会选择购买等量的x 和y 。

中级微观考试题型(范里安版本)

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q p
q 1
p q
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当商品具有弹性需求，即（p） 1时，商品价格上升会导致收益减少；
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由①知，p pq qp
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微观经济学：现代观点(范里安著)48题及答案

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pl 和p2，收入为m 当X iX 1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. 一兀纸币（x1）和五兀纸币（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=—杯咖啡， 8.解最优选择X 2= 一勺糖，消费者喜欢在每杯咖啡加两勺糖。

(1) U (X 1,X 2) 2 X 1X 29. 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) u2x 1X 2 (2) umin X 1,2xa b(3) u X 1 X 2(4) u In x-i X 2,10. 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。

微观经济学：现代观点(范里安著)48题及答案

第一部分消费者选择理论有两种商品，和，价格分别为和，收入为。

当11x x ≥时，政府加数量税画出预算集并写出预算线消费者消费两种商品（，），如果花同样多的钱可以买（，）或（，），写出预算线的表达式。

．重新描述中国粮价改革（）假设没有任何市场干预，中国的粮价为每斤。

元，每人收入为元。

把粮食消费量计为，在其它商品上的开支为，写出预算线，并画图。

（）假设每人得到斤粮票，可以凭票以。

元的价格买粮食，再写预算约束，画图。

（）假设取消粮票，补贴每人元钱，写预算约束并画图。

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

（）一元纸币，五元纸币。

（）一杯咖啡，一勺糖消费者喜欢在每杯咖啡加两勺糖。

解最优选择（） 21212(,)u x x x x =⋅（）2u x =对下列效用函数推导对商品的需求函数，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。

（）212x x u +=（）()212,m in x x u =（）b a x x u 21⋅=（） 12ln u x x =+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）。

给定效用函数 (,)x y xy =，，，，求当降为时价格变化引起的替代效应和收入效应。

用显示偏好的弱公理说明为什么替代效应为负。

设元小时，=R 小时，元，cR c R u =),(求）??,?,===***L c R ）12='w 元，求'*R 和'*L．121212(,),2000,1000,u c c c c m m ==⋅== 两期的价格都是，利息率。

范里安中级微观经济学题库

范里安中级微观经济学题库在范里安中级微观经济学题库中，涵盖了微观经济学的多个重要主题，包括供给与需求、消费者行为、生产者行为、市场结构等等。

通过学习和解答这些题目，可以加深对微观经济学理论的理解，并提高解决经济问题的能力。

下面是一些范里安中级微观经济学题库中的样例题目及其解答，供大家参考。

1. 供给与需求题目：某种商品的市场需求曲线为Qd = 1000 - 2P，市场供给曲线为Qs = 500 + 3P。

求市场平衡时的价格和数量。

解答：市场平衡时，供给量等于需求量，即Qs = Qd。

代入供给和需求的曲线方程，得到500 + 3P = 1000 - 2P。

整理方程，得到5P = 500，解得P = 100。

将P = 100代入需求曲线，得到Qd = 1000 - 2×100 = 800。

所以市场平衡时的价格为100，数量为800。

2. 消费者行为题目：某消费者的收入为500元，某商品的价格为5元，该消费者对该商品的需求量与价格之间的关系如下：Qd = 10 - 2P。

求该消费者对该商品的需求函数，并判断该商品是否为正常商品或劣质商品。

解答：需求函数表示需求量与价格之间的关系，根据题目中的信息可得到需求函数为Qd = 10 - 2P。

当收入增加时，需求量随之增加，所以该商品为正常商品。

3. 生产者行为题目：某企业的生产函数为Q = L^0.5K^0.5，其中Q为产量，L为劳动力投入，K为资本投入。

该企业的生产函数是否具有规模报酬递减性？请给出理由。

解答：生产函数具有规模报酬递减性意味着当生产要素投入增加时，边际产量递减。

我们可以对生产函数进行计算，得到边际产量函数。

边际产量函数为dQ/dL = 0.5L^(-0.5)K^0.5。

可以看出，当L增加时，边际产量递减；当K增加时，边际产量也递减。

因此，该企业的生产函数具有规模报酬递减性。

4. 市场结构题目：某市场上有4家企业，市场需求曲线为Qd = 1000 - 2P，每家企业的成本函数为TC = 100Q + 1000。

《中级微观经济学》作业二

《中级微观经济学》作业二本次作业包括范里安教材第6章末尾的习题5，以及以下附加题。

除特殊说明外，消费束的可行范围（效用函数的定义域）为R +2。

对教材第6章习题5，偏好满足弱凹性/强凹性的定义如下：弱凹性：如果1212(,)(,)x x y y ，则对任意01t ≤≤，都满足12(,)x x 弱偏好于12((),())z t z t ，其中111()(1)z t tx t y =+-，222()(1)z t tx t y =+- 强凹性：如果1212(,)(,)x x y y ，则对任意01t <<，都满足12(,)x x 严格偏好于12((),())z t z t ，其中111()(1)z t tx t y =+-，222()(1)z t tx t y =+-1. 某消费者的效用函数为2(,)462u x y x y y =+-，他的收入为135元，如果商品x 的价格为1元/单位，商品y 的价格为18元/单位，他对两种商品的最优选择量分别是多少？2. 某消费者的效用函数为(,)(2)(1)u x y x y =++，如果他消费14个单位的商品x ，并且此时的边际替代率为-4，那么他消费多少个单位的商品y ？3. 某消费者的效用函数为2(,)u x y x y =，假设他的收入为100元，商品y 的价格为1元/单位。

（1）考虑以下价格变化：商品x 的价格从2元/单位下降到1元/单位，计算Slutsky 替代效应和收入效应；Hicks 替代效应和收入效应（2）考虑以下价格变化：商品x的价格从1元/单位上升到2元/单位，计算Slutsky替代效应和收入效应。

得到的结果与（1）中的Slutsky 替代效应和收入效应的计算结果相同吗？4. 考查真实收入水平的改变：假设消费者的初始最优选择为消费束（3,5），两种商品的初始价格分别为（2,3）假设消费者的收入是固定的：（1）当商品价格变为（3,2）时消费者的真实收入水平如何变化？（2）当商品价格变为（1,4）时消费者的真实收入水平如何变化？假设消费者的初始禀赋为（0,7）：（3）当商品价格变为（3,2）时消费者的真实收入水平如何变化？（4）当商品价格变为（1,4）时消费者的真实收入水平如何变化？5. 某消费者的效用函数为(,)=，假设他的收入为100元，商品u x y xyy的价格固定为1元/单位。

范里安中级微观经济学习题集答案

Chapter1NAMEThe MarketIntroduction.The problems in this chapter examine some variations on the apartment market described in the text.In most of the problems we work with the true demand curve constructed from the reservation prices of the consumers rather than the“smoothed”demand curve that we used in the text.Remember that the reservation price of a consumer is that price where he is just indiﬀerent between renting or not renting the apartment. At anyprice below the reservation price the consumer will demand one apartment,at anyprice above the reservation price the consumer will de-mand zero apartments,and exactlyat the reservation price the consumer will be indiﬀerent between having zero or one apartment.You should also observe that when demand curves have the“stair-case”shape used here,there will typically be a range of prices where supplyequals demand.Thus we will ask for the the highest and lowest price in the range.1.1(3)Suppose that we have8people who want to rent an apartment. Their reservation prices are given below.(To keep the numbers small, think of these numbers as being dailyrent pay ments.)Person=A B C D E F G HPrice=402530351018155(a)Plot the market demand curve in the following graph.(Hint:When the market price is equal to some consumer i’s reservation price,there will be two diﬀerent quantities of apartments demanded,since consumer i will be indiﬀerent between having or not having an apartment.)2THE MARKET(Ch.1)012345678102030406050PriceApartments(b)Suppose the supplyof apartments isﬁxed at5units.In this case there is a whole range of prices that will be equilibrium prices.What is the highest price that would make the demand for apartments equal to5 units?$18.(c)What is the lowest price that would make the market demand equal to5units?$15.(d)With a supplyof4apartments,which of the people A–H end up getting apartments?A,B,C,D.(e)What if the supplyof apartments increases to6units.What is the range of equilibrium prices?$10to$15.1.2(3)Suppose that there are originally5units in the market and that 1of them is turned into a condominium.(a)Suppose that person A decides to buythe condominium.What will be the highest price at which the demand for apartments will equal the supplyof apartments?What will be the lowest price?Enter y our an-swers in column A,in the table.Then calculate the equilibrium prices of apartments if B,C,...,decide to buythe condominium.NAME3Person A B C D E F G H High price1818181825252525 Low price1515151518151818 (b)Suppose that there were two people at each reservation price and10 apartments.What is the highest price at which demand equals supply?18.Suppose that one of the apartments was turned into a condo-minium.Is that price still an equilibrium price?Yes.1.3(2)Suppose now that a monopolist owns all the apartments and thathe is trying to determine which price and quantity maximize his revenues.(a)Fill in the box with the maximum price and revenue that the monop-olist can make if he rents1,2,...,8apartments.(Assume that he must charge one price for all apartments.)Number12345678 Price403530251815105 Revenue40709010090907040(b)Which of the people A–F would get apartments?A,B,C,D.(c)If the monopolist were required bylaw to rent exactly5apartments, what price would he charge to maximize his revenue?$18.(d)Who would get apartments?A,B,C,D,F.(e)If this landlord could charge each individual a diﬀerent price,and heknew the reservation prices of all the individuals,what is the maximum revenue he could make if he rented all5apartments?$148.(f)If5apartments were rented,which individuals would get the apart-ments?A,B,C,D,F.1.4(2)Suppose that there are5apartments to be rented and that the cityrent-control board sets a maximum rent of$9.Further suppose that people A,B,C,D,and E manage to get an apartment,while F,G,andH are frozen out.4THE MARKET(Ch.1)(a)If subletting is legal—or,at least,practiced—who will sublet to whomin equilibrium?(Assume that people who sublet can evade the cityrent-control restrictions.)E,who is willing to payonly$10for an apartment would sublet to F,who is willing to pay$18.(b)What will be the maximum amount that can be charged for the sublet payment?$18.(c)If you have rent control with unlimited subletting allowed,which ofthe consumers described above will end up in the5apartments?A,B,C,D,F.(d)How does this compare to the market outcome?It’s the same.1.5(2)In the text we argued that a tax on landlords would not getpassed along to the renters.What would happen if instead the tax wasimposed on renters?(a)To answer this question,consider the group of people in Problem1.1.What is the maximum that theywould be willing to payto the landlordif theyeach had to paya$5tax on apartments to the city?Fill in thebox below with these reservation prices.Person A B C D E F G H Reservation Price35202530513100 (b)Using this information determine the maximum equilibrium price ifthere are5apartments to be rented.$13.(c)Of course,the total price a renter pays consists of his or her rent plusthe tax.This amount is$18.(d)How does this compare to what happens if the tax is levied on the landlords?It’s the same.Chapter 2NAMEBudget ConstraintIntroduction.These workouts are designed to build your skills in de-scribing economic situations with graphs and algebra.Budget sets are a good place to start,because both the algebra and the graphing are very easy.Where there are just two goods,a consumer who consumes x 1units of good 1and x 2units of good 2is said to consume the consumption bun-dle ,(x 1,x 2).Anyconsumption bundle can be represented bya point on a two-dimensional graph with quantities of good 1on the horizontal axis and quantities of good 2on the vertical axis.If the prices are p 1for good 1and p 2for good 2,and if the consumer has income m ,then she can aﬀord anyconsumption bundle,(x 1,x 2),such that p 1x 1+p 2x 2≤m .On a graph,the budget line is just the line segment with equation p 1x 1+p 2x 2=m and with x 1and x 2both nonnegative.The budget line is the boundary of the budget set .All of the points that the consumer can aﬀord lie on one side of the line and all of the points that the consumer cannot aﬀord lie on the other.If you know prices and income,you can construct a consumer’s bud-get line byﬁnding two commoditybundles that she can “just aﬀord”and drawing the straight line that runs through both points.Example:Myrtle has 50dollars to spend.She consumes only apples and bananas.Apples cost 2dollars each and bananas cost 1dollar each.You are to graph her budget line,where apples are measured on the horizontal axis and bananas on the vertical axis.Notice that if she spends all of her income on apples,she can aﬀord 25apples and no bananas.Therefore her budget line goes through the point (25,0)on the horizontal axis.If she spends all of her income on bananas,she can aﬀord 50bananas and no apples.Therfore her budget line also passes throught the point (0,50)on the vertical axis.Mark these two points on your graph.Then draw a straight line between them.This is Myrtle’s budget line.What if you are not told prices or income,but you know two com-moditybundles that the consumer can just aﬀord?Then,if there are just two commodities,you know that a unique line can be drawn through two points,so you have enough information to draw the budget line.Example:Laurel consumes onlyale and bread.If she spends all of her income,she can just aﬀord 20bottles of ale and 5loaves of bread.Another commoditybundle that she can aﬀord if she spends her entire income is 10bottles of ale and 10loaves of bread.If the price of ale is 1dollar per bottle,how much moneydoes she have to spend?You could solve this problem graphically.Measure ale on the horizontal axis and bread on the vertical axis.Plot the two points,(20,5)and (10,10),that you know to be on the budget line.Draw the straight line between these points and extend the line to the horizontal axis.This point denotes the amount of6BUDGET CONSTRAINT (Ch.2)ale Laurel can aﬀord if she spends all of her moneyon ale.Since ale costs 1dollar a bottle,her income in dollars is equal to the largest number of bottles she can aﬀord.Alternatively,you can reason as follows.Since the bundles (20,5)and (10,10)cost the same,it must be that giving up 10bottles of ale makes her able to aﬀord an extra 5loaves of bread.So bread costs twice as much as ale.The price of ale is 1dollar,so the price of bread is 2dollars.The bundle (20,5)costs as much as her income.Therefore her income must be 20×1+5×2=30.When you have completed this workout,we hope that you will be able to do the following:•Write an equation for the budget line and draw the budget set on a graph when you are given prices and income or when you are given two points on the budget line.•Graph the eﬀects of changes in prices and income on budget sets.•Understand the concept of numeraire and know what happens to the budget set when income and all prices are multiplied bythe same positive amount.•Know what the budget set looks like if one or more of the prices is negative.•See that the idea of a “budget set”can be applied to constrained choices where there are other constraints on what you can have,in addition to a constraint on moneyexpenditure.NAME 72.1(0)You have an income of $40to spend on two -modity1costs $10per unit,and commodity2costs $5per unit.(a)Write down your budget equation.10x 1+5x 2=40.(b)If you spent all your income on commodity 1,how much could you buy?4.(c)If you spent all of your income on commodity 2,how much could you buy?8.Use blue ink to draw your budget line in the graphbelow.02468246x1x28(d)Suppose that the price of commodity1falls to $5while every thing else stays the same.Write down your new budget equation.5x 1+5x 2=40.On the graph above,use red ink to draw your new budget line.(e)Suppose that the amount you are allowed to spend falls to $30,while the prices of both commodities remain at $5.Write down your budget equation.5x 1+5x 2=30.Use black ink to draw this budget line.(f)On your diagram,use blue ink to shade in the area representing com-moditybundles that y ou can aﬀord with the budget in Part (e)but could not aﬀord to buywith the budget in Part (a).Use black ink or pencil to shade in the area representing commoditybundles that y ou could aﬀord with the budget in Part (a)but cannot aﬀord with the budget in Part (e).2.2(0)On the graph below,draw a budget line for each case.8BUDGET CONSTRAINT (Ch.2)(a)p 1=1,p 2=1,m =15.(Use blue ink.)(b)p 1=1,p 2=2,m =20.(Use red ink.)(c)p 1=0,p 2=1,m =10.(Use black ink.)(d)p 1=p 2,m =15p 1.(Use pencil or black ink.Hint:How much of good 1couldyou aﬀord if you spend your entire budget on good 1?)0510152051015x1x2202.3(0)Your budget is such that if you spend your entire income,youcan aﬀord either 4units of good x and 6units of good y or 12units of x and 2units of y .(a)Mark these two consumption bundles and draw the budget line in the graph below.04812164812xy 16(b)What is the ratio of the price of x to the price of y ?1/2.(c)If you spent all of your income on x ,how much x could you buy?16.(d)If you spent all of your income on y ,how much y could you buy?8.(e)Write a budget equation that gives you this budget line,where the price of x is 1.x +2y =16.(f)Write another budget equation that gives you the same budget line,but where the price of x is 3.3x +6y =48.2.4(1)Murphywas consuming 100units of X and 50units of Y .Theprice of X rose from 2to 3.The price of Y remained at 4.(a)How much would Murphy’s income have to rise so that he can still exactlyaﬀord 100units of X and 50units of Y ?$100.2.5(1)If Amyspent her entire allowance,she could aﬀord 8candybars and 8comic books a week.She could also just aﬀord 10candybars and 4comic books a week.The price of a candybar is 50cents.Draw her budget line in the box below.What is Amy’s weekly allowance?$6.0816243281624Candy barsComic books3212 2.6(0)In a small countrynear the Baltic Sea,there are onlythree commodities:potatoes,meatballs,and jam.Prices have been remark-ablystable for the last 50y ears or so.Potatoes cost 2crowns per sack,meatballs cost 4crowns per crock,and jam costs 6crowns per jar.(a)Write down a budget equation for a citizen named Gunnar who has an income of 360crowns per year.Let P stand for the number of sacks of potatoes,M for the number of crocks of meatballs,and J for the number of jars of jam consumed byGunnar in a y ear.2P +4M +6J =360.(b)The citizens of this countryare in general veryclever people,but they are not good at multiplying by 2.This made shopping for potatoes excru-ciatinglydiﬃcult for manycitizens.Therefore it was decided to introduce a new unit of currency,such that potatoes would be the numeraire.A sack of potatoes costs one unit of the new currencywhile the same rel-ative prices applyas in the past.In terms of the new currency ,what is the price of meatballs?2crowns.(c)In terms of the new currency,what is the price of jam?3crowns.(d)What would Gunnar’s income in the new currencyhave to be for him to be exactlyable to aﬀord the same commoditybundles that he could aﬀord before the change?180crowns.(e)Write down Gunnar’s new budget equation.P +2M +3J =180.Is Gunnar’s budget set anydiﬀerent than it was before the change?No.2.7(0)Edmund Stench consumes two commodities,namelygarbage and punk rock video cassettes.He doesn’t actuallyeat the former but keeps it in his backy ard where it is eaten bybillygoats and assorted vermin.The reason that he accepts the garbage is that people payhim $2per sack for taking it.Edmund can accept as much garbage as he wishes at that price.He has no other source of income.Video cassettes cost him $6each.(a)If Edmund accepts zero sacks of garbage,how manyvideo cassettescan he buy?0.NAME 11(b)If he accepts 15sacks of garbage,how manyvideo cassettes can he buy?5.(c)Write down an equation for his budget line.6C −2G =0.(d)Draw Edmund’s budget line and shade in his budget set.0510152051015Video cassettesGarbage 202.8(0)If you think Edmund is odd,consider his brother Emmett.Emmett consumes speeches bypoliticians and universityadministrators.He is paid $1per hour for listening to politicians and $2per hour for listening to universityadministrators.(Emmett is in great demand to help ﬁll emptychairs at public lectures because of his distinguished appearance and his abilityto refrain from making rude noises.)Emmett consumes one good for which he must pay.We have agreed not to disclose what that good is,but we can tell you that it costs $15per unit and we shall call it Good X .In additionto what he is paid for consuming speeches,Emmett receives a pension of $50per week.0255075100255075Politician speechesAdministrator speeches10012BUDGET CONSTRAINT (Ch.2)(a)Write down a budget equation stating those combinations of the three commodities,Good X ,hours of speeches bypoliticians (P ),and hours of speeches byuniversityadministrators (A )that Emmett could aﬀord to consume per week.15X −1P −2A =50.(b)On the graph above,draw a two-dimensional diagram showing the locus of consumptions of the two kinds of speeches that would be possible for Emmett if he consumed 10units of Good X per week.2.9(0)Jonathan Livingstone Yuppie is a prosperous lawyer.He has,in his own words,“outgrown those conﬁning two-commoditylim-its.”Jonathan consumes three goods,unblended Scotch whiskey,de-signer tennis shoes,and meals in French gourmet restaurants.The price of Jonathan’s brand of whiskeyis $20per bottle,the price of designer tennis shoes is $80per pair,and the price of gourmet restaurant meals is $50per meal.After he has paid his taxes and alimony,Jonathan has $400a week to spend.(a)Write down a budget equation for Jonathan,where W stands for the number of bottles of whiskey,T stands for the number of pairs of tennis shoes,and M for the number of gourmet restaurant meals that he consumes.20W +80T +50M =400.(b)Draw a three-dimensional diagram to show his budget bel the intersections of the budget set with each axis.(c)Suppose that he determines that he will buyone pair of designer tennis shoes per week.What equation must be satisﬁed bythe combinations of restaurant meals and whiskeythat he could aﬀord?20W +50M =320.2.10(0)Martha is preparing for exams in economics and sociology.She has time to read 40pages of economics and 30pages of sociology.In the same amount of time she could also read 30pages of economics and 60pages of sociology.(a)Assuming that the number of pages per hour that she can read of either subject does not depend on how she allocates her time,how many pages of sociologycould she read if she decided to spend all of her time on sociologyand none on economics?150pages.(Hint:You have two points on her budget line,so you should be able to determine the entire line.)(b)How manypages of economics could she read if she decided to spend all of her time reading economics?50pages.2.11(1)HarryHy pe has $5,000to spend on advertising a new kind ofdehydrated sushi.Market research shows that the people most likely to buythis new product are recent recipients of M.B.A.degrees and lawy ers who own hot tubs.Harryis considering advertising in two publications,a boring business magazine and a trendyconsumer publication for people who wish theylived in California.Fact 1:Ads in the boring business magazine cost $500each and ads in the consumer magazine cost $250each.Fact 2:Each ad in the business magazine will be read by1,000recent M.B.A.’s and 300lawyers with hot tubs.Fact 3:Each ad in the consumer publication will be read by300recent M.B.A.’s and 250lawyers who own hot tubs.Fact 4:Nobodyreads more than one ad,and nobodywho reads one magazine reads the other.(a)If Harryspends his entire advertising budget on the business pub-lication,his ad will be read by10,000recent M.B.A.’s and by3,000lawyers with hot tubs.(b)If he spends his entire advertising budget on the consumer publication,his ad will be read by 6,000recent M.B.A.’s and by5,000lawyers with hot tubs.(c)Suppose he spent half of his advertising budget on each publication.His ad would be read by 8,000recent M.B.A.’s and by4,000lawyers with hot tubs.(d)Draw a “budget line”showing the combinations of number of readings byrecent M.B.A.’s and bylawy ers with hot tubs that he can obtain if he spends his entire advertising budget.Does this line extend all the way to the axes?No.Sketch,shade in,and label the budget set,which includes all the combinations of MBA’s and lawyers he can reach if he spends no more than his budget.(e)Let M stand for the number of instances of an ad being read byan M.B.A.and L stand for the number of instances of an ad being read by a lawyer.This budget line is a line segment that lies on the line with equation M +2L =16.With a ﬁxed advertising budget,how manyreadings byM.B.A.’s must he sacriﬁce to get an additional reading bya lawy er with a hot tub?2.04812164812Lawyers x 1000MBA's x 10001610262.12(0)On the planet Mungo,theyhave two kinds of money ,blue moneyand red money .Everycommodityhas two prices—a red-money price and a blue-moneyprice.EveryMungoan has two incomes—a red income and a blue income.In order to buyan object,a Mungoan has to paythat object’s red-moneyprice in red moneyand its blue-moneyprice in blue money .(The shops simplyhave two cash registers,and y ou have to payat both registers to buyan object.)It is forbidden to trade one kind of moneyfor the other,and this prohibition is strictlyenforced byMungo’s ruthless and eﬃcient monetarypolice.•There are just two consumer goods on Mungo,ambrosia and bubble gum.All Mungoans prefer more of each good to less.•The blue prices are 1bcu (bcu stands for blue currencyunit)per unit of ambrosia and 1bcu per unit of bubble gum.•The red prices are 2rcus (red currencyunits)per unit of ambrosia and 6rcus per unit of bubble gum.(a)On the graph below,draw the red budget (with red ink)and the blue budget (with blue ink)for a Mungoan named Harold whose blue income is 10and whose red income is 30.Shade in the “budget set”containing all of the commoditybundles that Harold can aﬀord,givenNAME 15its ∗two budget constraints.Remember,Harold has to have enough blue money and enough red moneyto payboth the blue-moneycost and the red-moneycost of a bundle ofgoods.0510152051015AmbrosiaGum 20(b)Another Mungoan,Gladys,faces the same prices that Harold faces and has the same red income as Harold,but Gladys has a blue income of 20.Explain how it is that Gladys will not spend its entire blue income no matter what its tastes maybe.(Hint Draw Glady s’s budget lines.)The blue budget line lies strictlyoutside the red budget line,so to satisfyboth budgets,one must be strictlyinside the red budget line.(c)A group of radical economic reformers on Mungo believe that the currencyrules are unfair.“Whyshould every one have to paytwo prices for every thing?”theyask.Theypropose the following scheme.Mungo will continue to have two currencies,everygood will have a blue price and a red price,and everyMungoan will have a blue income and a red income.But nobodyhas to payboth prices.Instead,every one on Mungo must declare itself to be either a Blue-MoneyPurchaser (a “Blue”)or a Red-Money Purchaser (a “Red”)before it buys anything at all.Blues must make all of their purchases in blue moneyat the blue prices,spending onlytheir blue incomes.Reds must make all of their purchases in red money,spending only their red incomes.Suppose that Harold has the same income after this reform,and that prices do not change.Before declaring which kind of purchaser it will be,∗We refer to all Mungoans bythe gender-neutral pronoun,“it.”Al-though Mungo has two sexes,neither of them is remotelylike either of ours.16BUDGET CONSTRAINT (Ch.2)Harold contemplates the set of commoditybundles that it could aﬀord bymaking one declaration or the other.Let us call a commoditybundle “attainable”if Harold can aﬀord it bydeclaring itself to be a “Blue”and buying the bundle with blue money or if Harold can aﬀord the bundle bydeclaring itself to be a “Red”and buy ing it with red money .On the diagram below,shade in all of the attainable bundles.0510152051015AmbrosiaGum202.13(0)Are Mungoan budgets reallyso fanciful?Can y ou think of sit-uations on earth where people must simultaneouslysatisfymore than onebudget constraint?Is moneythe onlyscarce resource that people use up when consuming?Consumption of manycommoditiestakes time as well as money.People have to simultaneouslysatisfya time budget and a moneybudget.Other examples--people mayhave a calorie budget or a cholesterol budget or an alcohol-intake budget.Chapter 3NAMEPreferencesIntroduction.In the previous section you learned how to use graphs toshow the set of commoditybundles that a consumer can aﬀord.In this section,you learn to put information about the consumer’s preferences on the same kind of graph.Most of the problems ask you to draw indiﬀerence curves.Sometimes we give you a formula for the indiﬀerence curve.Then all you have to do is graph a known equation.But in some problems,we give you only “qualitative”information about the consumer’s preferences and ask you to sketch indiﬀerence curves that are consistent with this information.This requires a little more thought.Don’t be surprised or disappointed if you cannot immediately see the answer when you look at a problem,and don’t expect that you will ﬁnd the answers hiding somewhere in your textbook.The best way we know to ﬁnd answers is to “think and doodle.”Draw some axes on scratch paper and label them,then mark a point on your graph and ask yourself,“What other points on the graph would the consumer ﬁnd indiﬀerent to this point?”If possible,draw a curve connecting such points,making sure that the shape of the line you draw reﬂects the features required by the problem.This gives you one indiﬀerence curve.Now pick another point that is preferred to the ﬁrst one you drew and draw an indiﬀerence curve through it.Example:Jocasta loves to dance and hates housecleaning.She has strictly convex preferences.She prefers dancing to anyother activityand never gets tired of dancing,but the more time she spends cleaning house,the less happyshe is.Let us tryto draw an indiﬀerence curve that is consistent with her preferences.There is not enough information here to tell us exactlywhere her indiﬀerence curves go,but there is enough information to determine some things about their shape.Take a piece of scratch paper and draw a pair of bel the horizontal axis “Hours per dayof housecleaning.”Label the vertical axis “Hours per dayof dancing.”Mark a point a little ways up the vertical axis and write a 4next to it.At this point,she spends 4hours a daydancing and no time housecleaning.Other points that would be indiﬀerent to this point would have to be points where she did more dancing and more housecleaning.The pain of the extra housekeeping should just compensate for the pleasure of the extra dancing.So an indiﬀerence curve for Jocasta must be upward sloping.Because she loves dancing and hates housecleaning,it must be that she prefers all the points above this indiﬀerence curve to all of the points on or below it.If Jocasta has strictlyconvex preferences,then it must be that if you draw a line between any two points on the same indiﬀerence curve,all the points on the line (except the endpoints)are preferred to the endpoints.For this to be the case,it must be that the indiﬀerence curve slopes upward ever more steeplyas y ou move to the right along it.You should convince yourself of this by making some drawings on scratch18PREFERENCES (Ch.3)paper.Draw an upward-sloping curve passing through the point (0,4)and getting steeper as one moves to the right.When you have completed this workout,we hope that you will be able to do the following:•Given the formula for an indiﬀerence curve,draw this curve,and ﬁnd its slope at anypoint on the curve.•Determine whether a consumer prefers one bundle to another or is indiﬀerent between them,given speciﬁc indiﬀerence curves.•Draw indiﬀerence curves for the special cases of perfect substitutes and perfect complements.•Draw indiﬀerence curves for someone who dislikes one or both com-modities.•Draw indiﬀerence curves for someone who likes goods up to a point but who can get “too much”of one or more goods.•Identifyweaklypreferred sets and determine whether these are con-vex sets and whether preferences are convex.•Know what the marginal rate of substitution is and be able to deter-mine whether an indiﬀerence curve exhibits “diminishing marginal rate of substitution.”•Determine whether a preference relation or anyother relation be-tween pairs of things is transitive,whether it is reﬂexive,and whether it is complete.3.1(0)Charlie likes both apples and bananas.He consumes nothing else.The consumption bundle where Charlie consumes x A bushels of apples per year and x B bushels of bananas per year is written as (x A ,x B ).Last year,Charlie consumed 20bushels of apples and 5bushels of bananas.It happens that the set of consumption bundles (x A ,x B )such that Charlie is indiﬀerent between (x A ,x B )and (20,5)is the set of all bundles such that x B =100/x A .The set of bundles (x A ,x B )such that Charlie is just indiﬀerent between (x A ,x B )and the bundle (10,15)is the set of bundles such that x B =150/x A .(a)On the graph below,plot several points that lie on the indiﬀerence curve that passes through the point (20,5),and sketch this curve,using blue ink.Do the same,using red ink,for the indiﬀerence curve passing through the point (10,15).(b)Use pencil to shade in the set of commoditybundles that Charlie weaklyprefers to the bundle (10,15).Use blue ink to shade in the set of commoditybundles such that Charlie weaklyprefers (20,5)to these bundles.NAME 19010203040102030ApplesBananas 40For each of the following statements about Charlie’s preferences,write “true”or “false.”(c)(30,5)∼(10,15).True.(d)(10,15) (20,5).True.(e)(20,5) (10,10).True.(f)(24,4) (11,9.1).False.(g)(11,14) (2,49).True.(h)A set is convex if for anytwo points in the set,the line segment between them is also in the set.Is the set of bundles that Charlie weakly prefers to (20,5)a convex set?Yes.(i)Is the set of bundles that Charlie considers inferior to (20,5)a convex set?No.(j)The slope of Charlie’s indiﬀerence curve through a point,(x A ,x B ),is known as his marginalrateofsubstitutionat that point.20PREFERENCES (Ch.3)(k)Remember that Charlie’s indiﬀerence curve through the point (10,10)has the equation x B =100/x A .Those of you who know calculus will remember that the slope of a curve is just its derivative,which in this case is −100/x 2A .(If you don’t know calculus,you will have to take our word for this.)Find Charlie’s marginal rate of substitution at the point,(10,10).−1.(l)What is his marginal rate of substitution at the point (5,20)?−4.(m)What is his marginal rate of substitution at the point (20,5)?(−.25).(n)Do the indiﬀerence curves you have drawn for Charlie exhibit dimin-ishing marginal rate of substitution?Yes.3.2(0)Ambrose consumes onlynuts and berries.Fortunately ,he likes both goods.The consumption bundle where Ambrose consumes x 1units of nuts per week and x 2units of berries per week is written as (x 1,x 2).The set of consumption bundles (x 1,x 2)such that Ambrose is indiﬀerent between (x 1,x 2)and (1,16)is the set of bundles such that x 1≥0,x 2≥0,and x 2=20−4√x 1.The set of bundles (x 1,x 2)such that (x 1,x 2)∼(36,0)is the set of bundles such that x 1≥0,x 2≥0and x 2=24−4√x 1.(a)On the graph below,plot several points that lie on the indiﬀerence curve that passes through the point (1,16),and sketch this curve,using blue ink.Do the same,using red ink,for the indiﬀerence curve passing through the point (36,0).(b)Use pencil to shade in the set of commoditybundles that Ambrose weaklyprefers to the bundle (1,16).Use red ink to shade in the set of all commoditybundles (x 1,x 2)such that Ambrose weaklyprefers (36,0)to these bundles.Is the set of bundles that Ambrose prefers to (1,16)a convex set?Yes.(c)What is the slope of Ambrose’s indiﬀerence curve at the point (9,8)?(Hint Recall from calculus the wayto calculate the slope of a curve.If you don’t know calculus,you will have to draw your diagram carefully and estimate the slope.)−2/3.。

（完整版）范里安中级微观经济学

（完整版）范⾥安中级微观经济学中级微观经济学1. 维克⾥拍卖定义：维克⾥拍卖的⽅式类似密封拍卖，但有⼀个重要区别：商品由报价最⾼的竞价⼈获得，但他只需要按第⼆⾼的报价⽀付。

换句话说，报价最⾼的投标⼈得到了拍卖商品，但是他不需要按照他⾃⾝的报价⽀付，⽽是按照报价第⼆⾼的⼈的报价⽀付。

特点：密封报、同时报价、价⾼者得、赢家⽀付次⾼价分析：我们分析⼀个只有两个投标⼈的特殊情形。

这两⼈的对商品的评价分别为 1v 和2v ，他们在纸条上写下的报价分别为1b 和2b 。

投标⼈1的期望收益为：如果21v ＞v ，最⼤化胜出的概率；也就是设置11v b =。

如果21v ＜v ，最⼩化胜出的概率；也就是设置11v b =。

任意情况，Telling the truth is best 。

2. 帕累托有效率如果可以找到⼀种配置，在其他⼈的境况没有变坏的情况下，的确能使⼀些⼈的境况变得更好⼀些，那么，这就叫做帕累托改进；如果⼀种配置⽅法存在帕累托改进，他就称为帕累托低效率；如果⼀种配置⽅法不存在任何的帕累托改进，他就称为帕累托有效率的。

3. 价格歧视，第⼀、⼆、三级价格歧视1.价格歧视：按不同价格销售不同单位产品的做法称为价格歧视 2.⼀、⼆、三级价格歧视：第⼀级价格歧视：是指垄断企业按不同价格出售不同产量，⽽且这些价格可能因⼈⽽异。

这种价格歧视有时⼜称为完全价格歧视。

第⼆级价格歧视：是指，垄断企业按不同价格出售不同产量，但是购买相同数量的每个⼈⽀付价格是相同的。

因此，价格按购买数量制定，⽽不是因⼈⽽异。

最常见的情形是⼤宗购买时可以享受折扣。

第三级价格歧视：是指垄断企业的销售价格因⼈⽽异，但对于同⼀个⼈来说，每单位产品的售价是相同的。

这种价格歧视最常见。

例如:对⽼年⼈打折，对学⽣打折等。

4. 消费者剩余消费者剩余：是指购买者的⽀付意愿减去购买者的实际⽀付量。

消费者剩余衡量了购买者⾃⼰感觉到所获得的额外收益。

5. 显⽰偏好原理1.显⽰偏好：假定：（1）所有消费者的偏好都是严格凸性的，因此对于⼀个预算线来说都有且只有⼀个最优消费束。

微观经济学：现代观点(范里安著)48题及答案

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 。

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。

13. 设w=9元/小时，=R 18小时，m=16元，cR c R u =),( 求1）??,?,===***L c R 2）12='w 元，求'*R 和'*L14．121212(,),2000,1000,u c c c c m m ==⋅== 两期的价格都是p=1，利息率r=10%。

范里安中级微观经济学习题集答案

范里安中级微观经济学习题集答案在范里安中级微观经济学习题集中，以下是答案解析：1. 供给和需求对于供给和需求的理解，我们可以从市场上某个商品的定价和交易量来进行分析。

供给表示某个商品或服务在一定时间内，卖方愿意以不同价格提供的数量。

需求表示某个商品或服务在一定时间内，买方愿意以不同价格购买的数量。

供给和需求的交互作用决定了市场上商品的价格和交易量。

在供需关系中，如果供给增加，需求不变，价格会下降，交易量会增加。

相反，如果供给减少，需求不变，价格会上升，交易量会减少。

如果需求增加，供给不变，价格会上升，交易量会增加。

相反，如果需求减少，供给不变，价格会下降，交易量会减少。

2. 市场均衡市场均衡是指在供求关系下，商品的价格和交易量达到一种稳定状态的情况。

当供给和需求达到均衡时，市场上的商品价格不再发生明显的变化。

市场均衡是通过供给曲线和需求曲线的相交来确定的。

在市场均衡的状态下，供给量等于需求量，市场价格也就是均衡价格。

这个均衡价格和交易量反映了供需双方的心理预期。

3. 稀缺性和选择稀缺性是指人们的需求超过可用资源的总量。

由于资源是有限的，人们不得不做出选择。

选择性是指在有限的资源下，人们必须做出取舍来满足自己的需求。

例如，一个人在有限的时间内可以选择看电视、读书还是锻炼身体。

人们在做出选择时，会比较不同选择之间的成本和收益，并选择能够最大化收益的选项。

4. 机会成本机会成本是指在做出某种选择时，放弃的最好的替代选择所产生的成本。

换句话说，机会成本是指因选择某种行动而放弃的下一最有价值的选择。

例如，一个人在选择上班的同时，放弃了进行休闲娱乐的时间。

这段放弃休闲娱乐的时间的价值就是他的机会成本。

5. 弹性在微观经济学中，弹性是指需求或供给对价格或收入变化的敏感程度。

需求弹性分为价格弹性和收入弹性。

价格弹性衡量了需求对价格变化的敏感程度，收入弹性衡量了需求对收入变化的敏感程度。

供给弹性衡量了供给对价格变化的敏感程度。

范里安中级微观经济学第八版习题

1 BUDGET CONSTRAINT1.A poor person who has an income of $1000 receives $100 worth offood stamps. Draw the budget constraint if the food stamp recipient can sell these coupons on the black market for less than their face value.2.Since 1979, recipients have been given food stamps. Before 1979,however, people bought food stamps at a subsidized rate. For example, to get $1 worth of food stamps, a household paid about 15￠(the exact amount varied by household characteristics and other factors). What is the budget constraint facing an individual if that individual may buy up to $100 per month in food stamps at 15￠per each $1 coupon. 3.During his first year at school, Ximing buys eight new collegetextbooks at a cost of $50 each. Used books cost $30 each. When the bookstore announces a 20% increase in new texts and a 10% increase in used texts next year, Ximing’s father offers him $80 extra. Is Ximing better off, the same, or worse off after the price change? Why?2 PREFERENCES1. Julia consumes cans of anchovies, A, and boxes of biscuits, B. Each ofher indifference curves reflects strictly diminishing marginal rates of substitution. Where A = 2 and B = 2, her marginal rate of substitution between cans of anchovies and boxes of biscuits equals -1. Will sheprefer a bundle with three cans of anchovies and a box of biscuits to a bundle with two of each? Why?2. What assumption or assumptions rule out the following phenomenon:Geoffrey has a bundle consisting of 6 apples and 8 raspberries. He states that if he is given 1 more apple, he will ask for 3 more raspberries to keep him indifferent between his old bundle and the new bundle that he will have after he receives the 1 additional apple.3. Draw indifference curves for the following people:a) John says: “I get no satisfaction from 1 ounce of vermouth or 3 ouncesof gin, but 1 ounce of vermouth and 3 ounces of gin (a martini) really turn me on.”b) Steve says: “I will not cut my hair to please my boss unless she paysme. My price is $300 plus $1 for every 1/8 inch of hair that is cut. In other words, for every $1 above $300 that the boss pays me, I will cut 1/8 inch off my hair.”c) In Part b of this problem, what is the marginal rate of substitutionbetween dollars and hair in the region below and above $300?d) Ann says: “I enjoy beer and pretzels, but after 12 beers, any additionalbeer makes me sick.”4. Jeffrey is five years old. He likes candy and hates spinach. He isallowed 2 candy bars a day, but his mother offers him 1 additional candy bar for every 2 ounce of spinach he eats.a) On these terms, Jeffrey eats 3 ounces of spinach and 3.5 candy barseach day. Using indifference curves, illustrate his optional choice.b) Suppose that Jeffrey’s mother does not give him 2 “free” candy barseach day but still gives him 1 candy bar for every 2 ounce of spinach he eats. Would his spinach consumption be greater or smaller than in Part a? Explain your answer.4 CHOICE1. Tara has a utility function U(B, Z) = ABαZβ, Where A, α, andβareconstraints, B is burritos, and Z is pizzas. If the price of burritos, p B is $2 and the price of pizzas, p Z is $1, what is Tara’s optimal bundle?2. Assume that there are two goods in the world: apples and raspberries.Say that Geoffrey has a utility function for these goods of the following type, where r denotes the quantity of raspberries and a the quantity if apples: U = r·a.a)Draw an indifference curve that is defined by this utility function andhas a utility level of 2500.b)What is the marginal rate of substitution between the raspberries andthe apples when Geoffrey consumes 50 raspberries and 50 apples?What is the marginal rate of substitution between these two goods when Geoffrey consumes 100 raspberries and 50 apples?c)If the price of raspberries is $1 per unit and the price of apples is $1per unit and Geoffrey has $100 to spend, what bundle of raspberries and apples will he buy? Is the marginal rate of substitution equal to the ratio of the prices of these goods in the optimal bundle? If not, why not?d)If the unit prices of the raspberries and the apples are $4 and $3,respectively, what bundle of raspberries and apples will Geoffrey buy with his income of $100?3. Steve’s utility function is U = BC, where B = veggie burgers per weekand C= packs of cigarettes per week. What is his marginal rate of substitution if veggie burgers are on the vertical axis and cigarettes are on the horizontal axis? Steve’s income is $120, the price of a veggie burger is $2, and that of a pack of cigarettes is $1. How many burgers and how many packs of cigarettes does Steve consume to maximize his utility? When a new tax raises the price of a burger to $3, what is his new optimal bundle? Illustrate your answers in a graph.5 DEMAND1.Roger’s utility function is U = B1/4Z3/4, his income is Y, the price of Bis p B, and the price of Z is p Z. Derive his demand curves.2.Derive Roger’s Engel curve for B for the utility given in problem 2.7 CONSUMER’S SUPPLUS1.If the inverse demand function is p = a–bQ, what is the consumersurplus if price is a/2?2.If the supply function is Q = Apη, what is the producer surplus if priceis p*?9 EQUILIBRIUM1.In 1998, a virus killed more than half the oysters used to producepearls in the world’s busiest undersea factory. Use a diagram to indicate why the price of pearls rose 18%. How did the equilibrium quantity change?2.Increasingly, instead of advertising in newspapers, individuals andfirms use Web sites that offer free classified ads, such as , , , and portals like Yahoo and America Online.Using a supply-and-demand model, explain what will happen to the equilibrium levels of newspaper advertising as the use of the Internet grows. Will the growth of the Internet affect the supply curve, the demand curve or both? Why?3.The U.S. supply of frozen orange juice comes from Florida and Brazil.What is the effect of a freeze that damages oranges in Florida on the price of frozen orange juice in the U.S. and on the quantities of orange juice sold by Floridian and Brazilian firms?4.The supply of corn by the U.S. is Q a= a + bp, and the supply by therest of the world is Q r = c + ep. What is the world supply?5. A rent control law limits the price of an apartment. What is the likelyeffect of such a law in the short run? What is the likely effect of the law in the long run? Be sure to discuss the quantity and quality of apartments available for rent.6.The government wants to drive the price of soybeans above theequilibrium price, p1 to p2. It offers growers a payment of x to reduce their output from Q1(the equilibrium level) to Q2, which is the quantity demanded by consumers at p2. How large must x be for growers to reduce output to this level? What are the effects of this program on consumers, farmers, and total welfare? Compare this approach to (a) offering a price support of p2, (b) offering a price support and a quota set at Q1, and (c) offering a price support and a quota set at Q2.10 TECHNOLOGY1.Michelle’s business produces ceramic cups using labor, clay, and akiln. She can manufacture 25 cups a day with one worker and 35 with two workers. Does her production process illustrate diminishing returns to scale or diminishing marginal returns to scale? What is the likely explanation for why output doesn’t increase proportionatelywith the number of workers?2. Suppose that the production function is q = L 3/4K 1/4.a. What is the average product of labor ，holding capital fixed at K ?b. What is the marginal product of labor?c. Does this production function have increasing, constant, or decreasing returns to scale?3. A good recipe for a French dish called ceviche requires 16 ounces of fillet of red snapper, 3 ounces of lime juice, 1 ounce of coriander, and 8 ounces of Bermuda onion. This combination of inputs is expressed in the following production function:1243min ,,,1638z z z y z ⎧⎫=⎨⎬⎩⎭ In this production function, z 1 is fillet of red snapper, z 2 is lime juice, z 3 is coriander, and z 4 is Bermuda onion. The unit of measure for each input is the ounce, and the unit of measure for ceviche (the output) is the quantity produced by the recipe. If a restaurant has on hand 32 ounces of snapper, 9 ounces of lime juice, 5 ounces of coriander, and 48 ounces of onion, how many “units ” of ceviche can it produce?4. Construct a total product curve for a function that exhibits diminishing marginal product throughout. Then construct another total product curve for a function that exhibits initially constant and subsequently diminishing marginal product. Below the graphs of these two total products curve, derive the corresponding average and marginalfunctions. Check to see that the curves you have drawn are consistent with what you know about the relationship between the average and marginal product curves.11 PROFIT MAXIMIZATION1.You have 60 minutes to take an exam with two questions. You want tomaximize your score. Toward the end of the exam, the more time you spend on either question, the fewer extra points per minutes you get for that question. How should you allocate time between the two questions?(Hint: Think about producing an output of a score on the exam using inputs of time spent on each of the problem)2. A competitive firm’s production function is y = L + 2LK + K. What isits marginal revenue product of labor?3.A firm’s production function is y = ALαKβ. What is the firm’s marginalrevenue product of labor?1L2, 4.A competitive firm has the production of function Q= 20L–4 where Q is the number of units of output produced and L is the number of units of labor (the only input) used. The output price is $2, the wage rate is $1, and the firm faces a fixed cost of $100.a)What is the profit-maximizing quantity of labor demanded by thefirm?b)What is the firm’s profit in the short run?c)If, in the long run, the output price changes so that profits are zero,what is the quantity of labor demanded in the long run?5.A competitive firm has the production function. Q = LαKβ, where Q isthe number of units of output produced, L is the number of units of labor used, and K is the number of units of capital used. The output price p, the wage rate w, and the cost of capital r are given. Assume that α > 0, β > 0, and 0 < ( α + β ) < 1.a)What is the firm’s profit-maximizing quantity of labor if the quantityof capital is fixed at K?b)What is the firm’s profit-maximizing level of capital if both capitaland labor are variable? (Hint: Use the profit-maximizing capital-labor ratio K/L to substitute for the level of labor.)12 COST MINIMIZATION1.Assume that a firm produces 90 units of output using 9 units of inputX and 9 units of input Y. The f irm’s technological possibilities can be represented by the production function Q = 10X1/2Y1/2.a)If the price of X is $8 and the price of Y is $16, is the inputcombination of 9 units of X and 9 units of Y the most efficient way to produce 90 units of output?b)What must the ratio of input prices be for this input combination to beefficient?c)Assume that the price of X is $1 and the price of Y is $2. Derive theleast-cost way to produce 400 units of output.2.A medical center produces health services using two inputs: hospitalbeds and labor. There is a government regulation restricting the number of beds to B. Assume that the medical center is currently usingB beds and L units of labor to produce Q1 units of health services. Alsoassume that the medical center plans to expand its output to Q2 units of health services. Prepare a diagram to show how this government regulation restricting the number of hospital beds would affect the efficiency of delivering health services.3.A trucking firm’s output is measured by the number m of truck-milesmoved per day. The firm’s operating costs are as follows:i.wages of trucks, $w per hourii.cost of gasoline, $p per galloniii.fuel consumption, g= A+ Bs, where g is gallons of gasoline per truck-mile, s is the speed at which a truck is driven, and A and B are constantsa)Derive the total variable cost function of the firm if it has an unlimitednumber of trucks.b)What does the cost function look like if the firm has only one truckand that truck can be driven for a maximum of ten hours per day?4.A college student is considering whether to operate a lawn-mowingbusiness for the summer or work in a business owned by her family.Her time is worth $w1 per hour and she can work as many hours as she chooses in the family business at this rate. If she starts her own business, she will have to buy gasoline for her lawn mower at a price of $w2 per gallon. She can rent a small mower for $w3 per hour. The mower cuts a 12-inch swath of lawn and uses 1/3 gallon of gasoline per hour. With this mower, she can cut 10,000 square feet of lawn in an hour. (Use 10,000 square feet as the units of measurement for output.) Our college student can rent a large mower for $w4 per hour.This mower uses 1 gallon of gasoline per hour and cuts 3 units of lawn per hour.a)Verify that the production function for the two mowers are as follows:y = min{z1, 3z2, z3}y = 3min{z1, z2, z4}Assume that z1 is hours of labor, z2 is gallons of gasoline, and z3 and z4are the hours of the small mower and the large mower, respectively.b)Derive the cost functions.c)Show that using the small mower is a cheaper way to cut grass if 2w1 <w4 – 3w3. Why is this result independent of the price of gasoline?d)How high a price must our college student receive for cutting a unit oflawn in order to induce her to set up her own lawn-mowing firm ratherthan work in the family business?e)Assume that a firm uses two types of input in the production of acertain commodity. What is the maximum output if the marginal product of input is MP1 = 100X2 –X1 and the marginal product of input2 is MP2 = 100X1 –X2, the total amount that can be spent on inputs is$1,000, the price of input 1 is $2, and the price of 2 is $5?13 COST CURVES1.The only variable input a janitorial service firm uses to clean offices isworkers who are paid a wage, w, of $8 an hour. Each worker can clean four offices in an hour. Use math to determine the variable cost, the average variable cost, and the marginal cost of cleaning one more office. Draw a diagram to show the average cost, and marginal cost curves.2.Gail works in a flower shop, where she produces 10 floralarrangements per hour. She is paid $10 an hour for the first eight hours she works and $15 an hour for each additional hour she works. What is the firm’s cost function? What are its AC, AVC, and MC functions?Draw the AC, AVC, and MC curves.3.A firm has two plants that produce identical output. The cost functionsare C1 = 10y– 4y2 + y3and C2 = 10y– 2y2 + y3.b.At what output levels does the average cost curve of each plant reachits minimum?c. If the firm wants to produce 4 units of output, how much should it produce in each plant?4. A firm that makes widgets must build a plan that will cost $10,000. The plant will be able to produce up to 10,000 units, at which point its capacity will be reached and a new plant will be needed. The total cost function for each plant (including the fixed cost of building the plant) is C (y ) = 10,000 – x 1/2/100.a) Determine the cost function for this firm.b) Is this cost function subadditive over the range of outputs from 1 unit to 10,000 units? Is it subadditive for all levels of output?14 FIRM SUPPLY1. If a competitive firm ’s cost function is C (y ) = 100 + 10y – y 2 + 31y 3, what is the firm ’s marginal cost function? What is the firm ’s profit- maximizing condition?2. If a competitive firm ’s cost function is C (y ) = a + by + cy 2 + dy 3, where a , b , c , and d are constants, what is the firm ’s marginal cost function? What is the firm ’s profit-maximizing condition?3. Consider a firm with a total cost curve of TC = 1,000 + q 3/3 – 2q 2 + 6q . a) What is the lowest price at which this firm will want to supply a positive amount to the market in the short run?b) At the “lowest price”, how much will be supplied?c) How much will be supplied in the short run if the price is $10?4. What is the effect on firm and market equilibrium of a law requiring afirm to give its workers six months’ notice before it can shut down its plant?15 INDUSTRY SUPPLY1. Each firm in a competitive market has a cost function of C = 16 + y2.The market demand function is Q = 24–y. Determine the equilibrium price, quantity per firm, market quantity, and number of firms.2. Assume that the taxi industry in the town of New City is perfectlycompetitive. Also assume that the constant marginal cost of a taxi ride is $5 per trip and that each taxi is capable of making 20 trips a day. We will let the demand function for taxi rides each day be D(p) = 1,100 –20p.a)What is the perfectly competitive price of a taxi ride?b)How many rides will the citizens of New City make every day?c)How many taxis will operate in New City?Assume that every taxi that operates in New City has a special license. Therefore, the number of such licenses is the same as the number of taxis that you calculated in Part c of this problem. Further assume that the demand for taxi rides has increased and is now D(p) =1,200 - 20p. The cost of operating a taxi is still $5 per ride, and the number of taxis has not changed.d)Calculate the price that will equate demand with supply.e)Calculate the profit that each taxi will earn on a ride.f)Calculate the daily profit of each taxi. (Hint: Continue to assume thateach taxi can make only 20 rides a day)3. A competitive market has an unlimited number of potential suppliersproducing the same output, and each supplier has a long-run average cost function of AC= q2 –4q+ 6 and a long-run marginal cost function of MC = 3q2 – 8q + 6.a) Find the equilibrium quantity q produced by each firm in the long run.b) Find the long-run equilibrium price.4. Assume that a very large number of firms in an industry all have accessto the same production technology. The total cost function associated with this technology is TC(Q) = 40Q–24Q2 + 4Q3. If the demand function for the industry’s product is Q = 19 –P, how many firms will produce positive amounts of output at a competitive (that is, zero profit) equilibrium?5. Assume that a certain small town contains a large number ofwidget-producing firms. All the firms buy oil from the same refinery.Firm 1 is situated very close to the refinery, and the other firms are located 50 miles away. Firm 1 pays $18 per barrel for the oil, while theother firms pay $18 per barrel plus a transportation charge of $.05 cents a mile, or a total of $20.50 per barrel.To produce four widgets, a firm needs 1/10 barrel of oil, 1/2 hour of labor, and the use of one machine. The cost of labor is $10 per hour, and the necessary machine can be rented for $5 per hour. No firm has the capacity to produce more than 100 units of widgets.a)Derive the supply curve for firm1. Derive the supply curve for all theother firms.b)What is the equilibrium price?c)Does any firm earn economic rent (that is, extra economic profit) inthe industry?d)Does firm 1 affect the price of widgets in the industry? If not, whynot?e)Suppose that there is no capacity limit. What will the equilibrium pricebe?f)Will firm 1 affect the price when there is unlimited capacity?16 MONOPOLY1.Show that after a shift in the demand curve, a monopoly’s price mayremain constant but its output may rise.2.When is a monopoly unlikely to be profitable?(Hint: Discuss therelationship between market demand and average cost)3.The inverse demand curve a monopoly faces is p = 100 - Q. The firm’scost curve is C(Q) = 10 + 5Q. What is the profit-maximizing solution?4.How does your answer to Problem 3 change if C(Q) = 100 + 5Q?5.A monopoly’s production function is: y = L1/2K1/2, where L is labor andK is capital. The demand function is p = 100–y. The wage, w, is $1 per hour, and the rental cost of capital, r, is $4.a.Derive the long-run total cost curve equation as a function of y.b.What quantity maximizes this firm’s profit?c.Find the optimal input combination that produces the profit-maximizing quantity. Illustrate with a graph.6. Suppose that a monopolist faces a demand curve of P = 100 - 2Q. Herfirm has costs of C(Q) = 5Q2.a) What is the revenue function for this monopolist?b) What is the marginal revenue function?c) What is the marginal cost function?d) What is the profit-maximizing output for this monopolist?e) What is the maximum profit this firm can make?f) If this monopolist has to pay a permission free of $150 to the stategovernment in order to start the business, will her optimal level of output change? If not, why not?17 FACTOR MARKETS1.A monopsony faces a supply curve: w = 10 + x. What is its marginalexpenditure curve?18 OLIGOPOLY1.What is the duopoly Cournot equilibrium if the market demandfunction is Q = 1000–1000p, and each firm’s marginal cost is $0.28 per unit?2. Consider a duopolistic market with two firms, A and B, facing ademand curve of p = 1 –q A–q B. Assume that initially each firm has access to the same technology with constant returns to scale and that the cost of production is C A = q A/2 for firm A and C B= q B/2 for firm B.a) What is the profit function for each firm?b) Graph the reaction functions for firms.c) What is the equilibrium outputs?d) Assume that the initial output levels of the two firms are given by pointX(3/10, 4/10) and Y(1/10, 2/10). Show in a graph the process of change in the output levels of the two firms and the point at which their output levels converge.3. A duopoly faces a market demand of p= 120–Q. Firm 1 has aconstant marginal cost of MC1 = 20. Firm 2’s constant marginal cost is MC2 = 40. Calculate the output of each firm, market output, and price if there is (a) a collusive equilibrium or (b) a Cournot equilibrium.4. Assume that there are two firms in a market, firm 1 and firm 2. Thetotal demand for the identical product they make is p = 200 – 2(q1 + q2), where q1 is the output of firm 1 and q2 is the output of firm 2. The production costs of firm 1 and firm 2 are C1 = q12and C2 = q22, respectively.a) Assume that firm 2 decides to produce either 20, 40, 60, or 100 units ofoutput. Show the demand curve and the marginal revenue curve facing firm 1 in each of these situations, assuming that the output levels will remain unchanged once they are chosen.b) Define the output that represents the best (the profit-maximizing)response of firm 1 to each of the output levels chosen by firm 2.19 EXCHANGE1.Initially, Michael has 10 candy bars and 5 cookies, and Tony has 5candy bars and 10 cookies. After trading, Michael has 12 candy bars and 3 cookies. In an Edgeworth box, label the initial Allocation A and the new Allocation B. Draw some indifference curves that are consistent with this trade being optimal for both Michael and Tony. 2.In a pure exchange economy with two goods, G and H, the two tradershave Cobb-Douglas utility functions. Amos’s utility is U a =(G a)α(H a)1-α, and Elise’s is U e = (G e)β(H e) 1-β, what are their marginalrates of substitution?3. Continuing with problem 3: between them, Amos and Elise own 100 units of G and 50 units of H . Thus if Amos has G a and H a , Elise has G e =100 – G a and H e = 50 – H a . Solve for their contract curve.4. Arnold and Brigitte are marooned on a deserted island. Arnold has exactly one unit of Xylose and Brigitte has exactly one unit of Yam. Their preferences between these two items are represented by the following two equations:1/32/31/21/2A A AB B B U X Y U X Y =⋅=⋅In these equations, X A and Y A are the consumption of Xylose and Yam by Arnold. Similarly, X B and Y B are the consumption of Xylose and Yam by Brigitte.a) Is the following allocation Pareto-optimal? Explain why or why not.1211,,,2323A AB B X Y andX Y ==== b) If Arnold and Brigitte were to trade between themselves, would they be able to attain this allocation as a competitive equilibrium? What would be the equilibrium price ratio of Xylose to Yam? Would Arnold and Brigitte be able to afford this allocation at the equilibrium prices, given their endowments? If not, what kind of income transfer would be necessary?5. Two people trade two goods that they cannot produce. Suppose that one consumer ’s indifference curves are bowed away from the origin – the usual type of curves – but the other ’s are concave to the origin.In an Edgeworth box, show that a point of tangency between the two consumers’indifference curves is not a Pareto-efficient bundle.(Identify another allocation that Pareto dominates.)6.The demands for two goods depend on the prices of Good 1 and Good2, p1 and p2, Q1 = 15 – 3p1 + p2, Q2 = 6 – 2p2 + p1, but each supply curve depends on only its own price: Q1 = 2 + p1, Q2 = 1 + p2. Solve for the equilibrium: p 1, p2, Q1, and Q2.20 PRODUCTION1. Assume that you have exactly 100 hours of labor to allocate betweenproducing good X and good Y. Your output of goods X and Y depends solely on the hours of labor you spend in the following way:X=and Y=a)If you can sell your output of goods X and Y at the fixed prices P X = 10and P Y= 5, how much of goods X and Y would you produce to maximize your profits?b)Now assume further that you have the following utility function:U=If you can trade a bundle of goods X and Y that you produce in the market at fixed prices of P X = 10 and P Y = 5, what bundle would you produce and what bundle would you consume to maximize your utility?Are you a net demander and a net supplier of the two goods? Draw adiagram to depict what is happening.2. Suppose that the production possibilities frontier for cheeseburgers (C)and milk-shakers (M) is given by C + 2M = 600.a) Graph this function.b) Assuming that people prefer to eat two cheeseburgers with everymilk-shaker, how much of each product will be produced? Indicate this point in your graph.c) Assuming that this fast-food economy is operating efficiently, whatprice ratio (P C/P M) will prevail?21 WELFARE1. Suppose that society used the “opposite”of a Rawlsian welfarefunction: it tried to maximize the well-being of the best-off member of society. Write this welfare function. What allocation maximizes welfare in this society?2. Assume that Bob has a utility function of U = 8X1 + 1X2 – 3X3 and Joanhas a utility function of U = –2X1 + 7X2 + 5X3. Consider the following allocation:a)Is this allocation envy free?b)Is this allocation Pareto-optimal?c)Find a Pareto-optimal allocation, and determine whether it is envyfree.d)Do you think that the allocation in Part c of this problem is desirable?Why or why not?22 EXTERNALITIES1.Suppose that the only way to reduce pollution from paper productionis to reduce output. The government imposes a tax equal to the marginal harm from the pollution on the monopoly producer. Show that the tax may raise welfare.2.Suppose that the inverse demand curve for paper is p = 200–y, theprivate marginal cost (unregulated competitive market supply) is MC p = 80 + Q, and the marginal harm from gunk is MC g = y.a.What is the unregulated competitive equilibrium?b.What is the social optimum? What specific tax (per unit of output orgunk) results in the social optimum?c.What is the unregulated monopoly equilibrium?d.How would you optimally regulate the monopoly? What is theresulting equilibrium?3. A soot-spewing factory that produces steel windows is next to a。

微观经济学：现代观点(范里安著)48题及问题详解

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 。

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。

（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。

（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。

范里安微观经济学现代观点复习参考题

1. Introduction, the research object of microeconomic2. The market demand and budget constraint3. Preference and utility function for a representative consumer4. The optimal choice of a consumer and the relevant comparative analysis5. Slutsky decomposition and Hicks decomposition6. Endowment and the intertemporal choice of a consumer7. Uncertainty and the relevant indices that measure social welfare8. Market equilibrium9. Technology and the framework of producer theory10. Cost function and the industry11. Monopoly and price discrimination12. Oligopoly: Cournot Model and Bertrand Model13. An introduction to Game theory14. General equilibrium theory15. Information economicsLecture 1¡¡Introduction, the research object of microeconomic1. Suppose that there were 25 people who had a reservation price of $500, and the 26 th person had a reservation price of $200. What would the demand curve like?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?3. In the text we assumed that the condominium purchasers came from 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?4. 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?·µ»Ø¶¥²¿Lecture 2¡¡The market demand and budget constraint1. If the price of good 1 doubles and the price of good 2 increases triples, dose the budge line become flatter or steeper?2. What is the definition of a numeraire good?3. 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?·µ»Ø¶¥²¿Lecture 3¡¡Preference and utility function for a representative consumer1. 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?2. Can an indifference curve across itself? For example, would figure3.2 depict a single indifference curve?3. If both pepperoni and anchovies are bads, will the indifference curve have a positive or a negative slope?4. Think of some other goods for which your preference might be concave?5. We claimed in the text that if preference were monotonic, then a diagonal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously?6. Can you explain why taking a monotonic transformation of a utility doesn't change the marginal rate of substitution?·µ»Ø¶¥²¿Lecture 4¡¡The optimal choice of a consumer and the relevant comparative analysis1. If a consumer has a utility function ¦Ì(x1,x2)= x1*(x2^4), what fraction of her income will she spend on good 2?2. If two goods are perfect substitutes, what is the demand function for good 2?3. For what kind of preferences will the consumer be just as well-off facing a quantity tax as an income tax?4. If the preferences are concave will the consumer ever consumer both of the goods together?5. Are all hamburgers and buns complements or substitutes?6. What is the form of the inverse demand function for good 1 in the case of perfect complements?7. True of false? If the demand function is x1=-p1, then the inverse demand function is x=-1/p1.·µ»Ø¶¥²¿Lecture 5¡¡Slutsky decomposition and Hicks decomposition1. 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?2. Suppose that preferences are concave. Is it still the case that the substitution effect is negative?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'?4. In this case described in the preceding question, would the government be paying out more or less than it received in tax revenues?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?·µ»Ø¶¥²¿Lecture 6¡¡Endowment and the intertemporal choice of a consumer1. 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)?2. 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?3. Suppose that by some miracle the number of hours in the day increased from 24 to 30 hours. How would this affect the budget constraint?4. If leisure is an inferior good, what can you say about the slope of the labor supply curve?5. Would the assumption that goods are perfect substitutes be valid in a study of intertemporal food purchases?6. A consumer, who is initially a lender, remains a lender even aftera decline in interest rates. Is this consumer better off or worse off after the change in interest rate? if the consumer becomes a borrower after the change is he better off or worse off?7. 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%?·µ»Ø¶¥²¿Lecture 7¡¡Uncertainty and the relevant indices that measure social welfare1. How can one reach the consumption points to the left of the endowment in figure 12.1?2. The 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?3. What if the payment was $320?4. Draw a utility function that exhibits risk-loving behavior for small gambles and risk-averse behavior for larger gambles?5. Why might a neighborhood group have a harder time self insuring for flood damage versus fire damage?6. 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?7. Suppose that the demand curve is given by D(p)=10-p. What is the gross benefit from consuming 6 units of the good?8. In the above example, if the price changes from 4 to 6, what is the change in consumer's surplus?·µ»Ø¶¥²¿Lecture 8¡¡Market equilibrium1. If the market demand curve is D(p)=100-0.5p, what is the inverse demand curve?2. If D(p)=12-2p, what price will maximize revenue?3. Suppose that the demand curve for a good is given by D(p)=100/p. What price will maximize revenue?4. True or false? In a two good model if one good is an inferior good the other good must be a luxury good.5. What is the effect of a subsidy in a market with a horizontal supply curve? With a vertical supply curve?6. 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?7. Consider the tax treatment of borrowing and lending described in the text. How much revenue does this tax system raise if borrowers and lenders are in the same tax bracket?8. Does such a tax system raise a positive or negative amount of revenue when tl<tb?·µ»Ø¶¥²¿Lecture 9¡¡Technology and the framework of producer theory1. Consider the production function f(x1,x2)=(x1*x2)^2. Dose this exhibit constant, increasing, or decreasing returns to scale?2. Consider the production function f(x1,x2)=4*(x1^(1/2))*(x2^(1/3)). Dose this exhibit constant, increasing, or decreasing return to scale?3. True of false? If the law of diminishing marginal product did not hold. The world's food supply could be grown in a flowerpot.4. In a production process is it possible to have decreasing marginal product in an input and yet increasing returns to scale?5. In the short run, if the price of the fixed factor is increased, what will happen to profits?6. A gardener exclaims: ¡°for only $1 in seeds I've grown over $20 in produce.¡± Besides the fact that most of the produce is in the form of zucchini, what other observations would a cynical economist make about this situation?7. Is maximizing a firm's profits always identical to maximizing the firm's stock market value?8. A profit-maximizing competitive firm that is making positive profits in long-run equilibrium (may/may not) have a technology with constant returns to scale?·µ»Ø¶¥²¿Lecture 10¡¡Cost function and the industry1. Prove that a profit ¨Cmaximizing firm will always minimize costs.2. Suppose that a cost-minimizing firm uses two inputs that are perfect substitutes. If the two inputs are priced the same, what do the conditional factor demands look like for the inputs?3. A firm produces identical outputs at two different plants, if the marginal cost at the first plant exceeds the marginal cost at the second plant, how can the firm reduce costs and maintain the same level of output?4. True or false? In the long run a firm always operates at the minimum level of average costs for the optimally sized plant to produce a given amount of output.5. A firm has a supply function given by S(p)=4p. Its fixed costs are 100. If the price changes from 10 to 20, what is the change in its profits?6. If the long-run cost function is c(y)=y^2+1, what is the ling-run supply curve of the firm?7. What is the major assumption that characterizes a purely competitive market?8. is it ever better for a perfectly competitive firm to produce output even though it is losing money? If so, when?9. If S1(p)=p-10 and S2(p)=p-15, then at what price does the industry supply curve have a kink in it?10. In the short run the demand for cigarettes is totally inelastic. In the long run, suppose that it is perfectly elastic, what is the impact of a cigarette tax on the price that consumers pay in the short run and in the long run?11. True or false? In long ¨Crun industry equilibrium no firm will be losing money.·µ»Ø¶¥²¿Lecture 11¡¡Monopoly and price discrimination1. The monopolist faces a demand curve given by D(p)=100-2p. Its cost function is c(y)=2y. What is its optimal level of output and price?2. The monopolist faces a demand curve given by D(p)=10*(p^(-3)). Its cost function is c(y)=2y. What is its optimal level of output and price?3. If the demand curve facing the monopolist has a constant elasticity of 2, then what will be the monopolist' markup on marginal cost?4. The government is considering subsidizing the marginal costs of the monopolist described in the question above. What level of subsidy should the government choose if it wants the monopolist to produce the socially optimal amount of output?5. Will a monopoly ever provide a Pareto efficient level of output on its own?6. Suppose that a monopolist sells to two groups that have constant elasticity demand curves , with elasticity ¦Å1 and ¦Å2. The marginal cost of production is constant at c.what price is charged to each group?·µ»Ø¶¥²¿Lecture 12¡¡Oligopoly: Cournot Model and Bertrand Model1. We saw that saw that a monopolist never produced where the demand for output was inelastic. Will a monopsonist produce where a factor is inelastically supplied?2. In our example of the minimum wage, what would happen if the labor market was dominated by a monopsonist and the government set a wage that was above the competitive wage?3. In our examination of the upstream and downstream monopolists we derived expressions for the total output produced. What are the appropriate expressions for the equilibrium prices, p and k?4. Consider a cartel in which each firm has identical and constant marginal costs. If the cartel maximizes total industry profits, whatdoes this imply about the division of output between the firms?5. Can the deader ever get a lower profit in a Stackelberg equilibrium than he would get in the Cournot equilibrium?6. Draw a set of reaction curves that result in an unstable equilibrium.7. Do oligopolies produce an efficient level of output?·µ»Ø¶¥²¿Lecture 13¡¡An introduction to Game theory1. Consider the tit-for-tat strategy in the repeated prisoner's dilemma. Suppose that one player makes a mistake and defects when he meant to cooperate. If both players continue to play tit for tat after that, what happens?2. Are dominant strategy equilibria always Nash equilibria? are Nash equilibria always dominant strategy equilibria?3. Suppose your opponent is not playing her Nash equilibrium strategy. Should you play your Nash equilibrium strategy?4. Suppose that player B rather than player A get to move first in the sequential game described in this chapter. Draw the extensive form of the new game. What is the equilibrium for this game? Does player B prefer to move first or second?·µ»Ø¶¥²¿Lecture 14¡¡General equilibrium theory1. In a two-person Nash equilibrium. Each player is making a best response to what? In a dominant strategy equilibrium, each player is making a best response to that?2. Look at the beat responses for row and column in the section on mixed strategies. Do these give rise to best response functions?3. If both players make the same choice in a coordination game, all will be well.4. A contractor says that he intends to ¡°low-ball the bid and make up for it on change orders.¡± What does he mean?5. Is it possible to have a Pareto efficient allocation where someone is worse off than he is at an allocation that is not Pareto efficient?6. True or false? If we know the contract curve, then we know the outcome of any trading.7. Can some individual be made better off if we are at a Pareto efficient allocation?8. If the value of excess demand in 8 out of 10 market is equal to zero. What must be true about the remaining two markets?·µ»Ø¶¥²¿Lecture 15¡¡Information economics1. True or false? An explicit delineation of property rights usually eliminates the problem of externalities.2. True or false? The distributional consequences of the delineation of property rights are eliminated when preferences are quasilinear.3. List some other examples of positive and negative consumption and production externalities.4. Suppose that the government wants to control the use of the commons, what methods exist for achieving the efficient level of use?5. Consider the model of the used-car market. What is the maximum amount of consumer' surplus that is created by trade in the market equilibrium?6. In the same model, how much consumers' surplus would be created by randomly assigning buyers to sellers? Which method gives the lager surplus?7. A worker can produce x units of output at a cost of c(x)=(x^2)/2.He can achieve a utility level of u=0 working elsewhere. What is the optimal wage-labor incentive scheme s(x) for this worker?8. Given the setup of the previous problem, what would the worker be willing to pay to rent the production technology?。

微观经济学：现代观点(范里安著)48题及答案

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 。

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。

（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。

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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 。

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）b a 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。

13. 设w=9元/小时，=R 18小时，m=16元，cR c R u =),(求1）??,?,===***L c R 2）12='w 元，求'*R 和'*L 14．121212(,),2000,1000,u c c c c m m ==⋅== 两期的价格都是p=1，利息率r=10%。

1）求**21,c c ，有无储蓄 2）当%20='r 时，求**21,c c 。

15．一个人只消费粮食，第一期他得到1000斤，第二期得到150斤，第一期的粮食存到第二期将有25%的损耗。

他的效用函数为：1212(,)u c c c c =⋅1）如果粮食不可以拿到市场上交易，最佳消费??,21==**c c 2）如果粮食可以拿到市场上交易，两期的价格都是p=1，利息率r=10%，问最佳消费??,21==**c c16．有一个永久债券（consol ）, 每年支付5万，永久支付，利率为r ，它在市场出售时价格应是多少17．假设你拥有一瓶红酒，第一年价格为15元/瓶，第二年为25元/瓶，第三年为26元/瓶，第四年每瓶价格低于26元，设利息率为5%，你会何时卖掉你的红酒18．课本p173第四题（review questions ）。

19. 一人具有期望效用函数，其对财富的效用为()u c =35,000元，假如发生火灾则损失10,000元，失火的概率为1%，火险的保费率为%。

问他买多少钱的保险（K=），在两种状态下的财富各为多少20．一人具有期望效用函数，其对财富的效用为()u c =10，000元，有人邀请他参加赌博，输赢的概率各为1/2。

问以下情况下他是否同意参加赢时净挣多少时愿意参加（1）赢时净挣10,000，输时丢10,000（2）赢时净挣20,000，输时丢10,00021．某消费者的效用函数为 (,)u x y x y =⨯，x 和y 的价格都是1，他的收入为200。

当x 的价格涨至2元时，计算消费者剩余的变化、补偿变换和等价变换。

22．证明当效用函数为拟线形时，消费者剩余的变化、补偿变换、等价变换都相等。

第二部分生产者理论23. 给定以下生产函数，求证是否边际产量递减，技术替代率递减，规模报酬递增或递减。

（1） 432411x x y = （2）1,)(/121≤+=ρρρρx x y 24．给定生产函数2/122/1121),(x x x x f =，已知21.,w w p ，则 1）当162=x 时，求使利润最大化的*1x 2）当21,x x 都可变时，求使利润最大化的*2*1,x x25．给定生产函数4/122/1121),(x x x x f =， 1,421===w w p ，求使利润最大化的*2*1,x x26. 求条件要素需求和成本函数(1) )2,m in(21x x y =(2) 212x x y +=(3) b a x x y 21⋅=27. 对于生产函数1/41/4y kL =，资本的租赁价格为1元，劳动的工资为1元，固定投入为1000元。

1）写出成本曲线2）计算AC, AVC, AFC, MC3）计算minAC 和minAVC 时的AC,AVC,y,28. 对以下成本函数求供给曲线(1)5308)(23++-=y y y y C (2) 5308)(23++-=y y y y C ，C(0)=0第三部分市场结构理论29．消费者对商品 x 和在其它商品上的开支 y 的效用函数为 y x x y x u +-=221),(1）市场上有完全同样的消费者100人，写出市场需求函数。

2）该如何定价使销售收入最大此时价格弹性是多少30．证明所有消费品的收入弹性的加权平均为1，权重为每个消费品的开支比例。

31, 给定需求和供给函数：D(p)=1000-60p, S(p)=40p1) 求均衡p, q2) 当加数量税 $5时，求新的均衡价格和数量。

3) 消费者和厂商各分担税收的百分比4) 税收带来的额外净损失是多少32. 需求和供给函数分别为：D(p)=40-p, S(p)=10+p1) 求均衡p,q2) 如果对该商品进行配额管理，配额定为20，价格定为厂商所能接受的最低价，问该价格是多少3）假如配给券可以买卖，问配给券的价格是多少33．已知某个行业中有n 个技术相同的企业，每个企业的成本函数为：0)0(1)(2=+=C y y C产品市场需求函数为：D(p)=求长期均衡价格，厂商个数，以及每个厂商的利润。

34．在一个出租车市场上，每辆车每趟活的经营成本（MC ）为5元，每天可以拉20趟活，对出租车的需求函数为 D(p)=1200-20.1）求每趟活的均衡价格、出车次数和出租车个数。

2）需求函数改变为：D(p)=1220-20p, 如果政府给原有的司机每人发一个经营牌照，出租车个数不变，则均衡价格和利润为多少3）设一年出车365天，r=10%，牌照值多少钱出租车所有者们愿出多少钱阻止多发一个牌照35. 给定需求函数p(y)=2000-100y, 成本函数c(y)=1000+4y1) 在垄断的市场下，价格、产量和利润分别为多少2) 如果企业按照竞争市场定价，价格、产量、利润分别为多少36．一个垄断厂商面临学生s 的需求函数为 s s p Q 40220-=非学生N 的需求函数为 N N p Q 20140-=。

已知AC=MC=0，则1）当不能差别定价时，如何定价s Q =N Q =π= 2）当可以差别定价时，s p =N p =s Q =N Q =π=37．某一厂商在要素市场为买方垄断，在产品市场为卖方垄断，求其要素需求。

38. 一个市场的需求函数为：P(Y)=100-2Y, 企业的成本函数为：c(y)=4y1)求完全竞争市场的均衡价格和产量2)当市场上有2个企业时，求Cournot均衡的价格和产量。

3)求Cartel均衡时的价格和产量, 并说明违约动机。

4)求Stackelberg均衡时各个企业的产量和市场价格。

第四部分对策论（博弈论）39. 给定如下支付矩阵Player BL RPlayer A TB(1). 如(T,L)是超优策略，则a-h（2）如(T,L)是纳什策略，则a-h间应满足什么关系（3）如(T,L)和(B,R)都是纳什策略，则a-h间应满足什么关系40. 在足球射门的例子中，混合策略是什么个人的支付（payoff）为多少第五部分一般均衡理论41. 在一个纯粹交换的完全竞争的市场上有两个消费者，A和B，两种商品，X和Y。

交换初始，A拥有3个单位的X，2个Ｙ，B有1个Ｘ和6个Y。

他们的效用函数分别为：U(X A,Y A)=X A Y A, U(X B, Y B)=X B Y B. 求（1）市场竞争均衡的（相对）价格和各人的消费量。

（2）表示帕累托最优分配的契约线的表达式。

42．其它条件相同，如果A的效用函数为 U(X A, Y A)=X A+Y A，求一般均衡价格和契约线。

43．其它条件相同，如果A的效用函数为 U(X A, Y A)=Min（X A,Y A），求一般均衡价格和契约线。

44. 罗宾逊靠捕鱼为生，他的生产函数为F F是鱼的个数，L是工作时间。

他一天有10小时用于工作或者游泳。

他对于鱼和游泳的效用函数为U（F，S）=FS，其中S是游泳时间。

问(1) 最佳捕鱼量是多少，工作多少小时(2) 有一天他自己玩家家，假装成立了一个追求利润最大化的企业来生产鱼，雇佣自己的劳动，然后再用工资从该企业买鱼，该市场被设为竞争型市场。

问(相对)均衡价格是多少此价格下的生产（消费）和工作量是多少45. 罗宾逊每小时可以抓4条鱼（F ），或者摘2个椰子（C ），他一天工作8小时。

礼拜五每小时可以抓1条鱼，或者摘2个椰子，一天也工作8小时。

罗宾逊和礼拜五的效用函数都可以表示为U （F ，C ）=FC 。

(1) 如果两人完全自己自足，各人的消费为多少(2) 如果两人进行贸易，各人的生产和消费为多少，交易价格是什么第六部分公共品、外部性和信息46. 养蜂人的成本函数为：2()/100H C H H =，果园的成本函数为2()/100A C A A H =-。

蜂蜜和苹果各自在完全竞争的市场上出售，蜂蜜的价格是2，苹果的价格是3。

a. 如果养蜂和果园独立经营，各自生产多少b. 如果合并，生产多少c. 社会最优的蜂蜜产量是多少如果两个厂家不合并，那么如何补贴（数量补贴）养蜂人才能使其生产社会最优的产量47. 一条捕龙虾船每月的经营成本为2000元，设x 为船的数量，每月总产量为f(x)=1000(10x-x 2)。

d. 如果自由捕捞,将有多少只船e. 最佳(总利润最大)的船只数量是多少f. 如何对每条船征税使船只数量为最佳48. 一条马路旁住了10户人家, 每户的效用函数都可以表示为: U(x, y) = lnx + y, 其中x 代表路灯的数量, y 代表在其它商品上的开支. 修路灯的成本函数为 c(x)=2x. 求社会最优的路灯数量.。

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