最新范里安中级微观练习题
中级微观经济学试题
《中级微观经济学》试题一、名词解释需求的交叉价格弹性；产品差别；需求的变动和需求量的变动；边际产品价值吉芬商品；正常利润和经济利润二、选择题1、垄断和垄断竞争之间的主要区别是a 前者依据MR=MC最大化其利润，后者不是b 前者厂商的需求曲线和市场需求曲线是一致的，而后者不是c 前者拥有影响市场的权力d 以上全对2、完全竞争和垄断竞争之间重要相同点是a 长期当中，价格等于平均成本，边际收益等于边际成本b 产品异质的程度c 长期平均成本上使厂商利润最大化的点是相同的d 以上全都不对3、下列哪种情况不正确，a 如果供给减少，需求不变，均衡价格将上升b 如果供给增加，需求减少，均衡价格将下降c 如果需求增加，供给减少，均衡价格将上升d 如果需求减少，供给增加，均衡价格将上升4、无差异曲线的斜率被称为a 边际代替率b 边际技术代替率c 边际转换率d 边际效用5 、对于一个竞争性厂商而言，应使a P=ACb P=MR=ACc P=AR=MCd P=AR=MR6、正常利润是a 经济利润的一部分b 经济成本的一部分c 隐含成本的一部分d b和c两者6. 如果甲商品价格上升引起乙商品的需求曲线向左下方移动，那么a 甲和乙是替代品b 甲和乙是互补品c 甲是正常品，乙上次等品d 甲是次等品，乙是正常品7. 等产量线的斜率被称为a 边际代替率b 边际技术替代率c 边际转换率d 边际产品8. 一个完全竞争厂商发生亏损时，所在行业趋于长期均衡过程中可能发生的情况时a 较高的价格和较少的厂商b 较低的价格和较少的厂商c 较高的价格和较多的厂商d 较低的价格和较多的厂商三、是非题1．如果偏好是传递的，那么商品越多越好。
2．偏好为凸性的消费者认为两组合(1，4)和(9，2)并无差异。
那她至少不会更不喜欢(5，3)。
3．小马的效用函数是max{x,y}，他的偏好是凸的。
4．如果两商品是替代品，那么其中一商品涨价会引起另一商品的需求下降。
范里安_中级微观经济学Ch16
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)
中级微观期末考试题及答案
中级微观期末考试题及答案一、选择题（每题2分，共20分）1. 消费者剩余是指：A. 消费者支付的价格B. 消费者愿意支付的价格与市场价格之间的差额C. 市场价格与生产成本之间的差额D. 生产者剩余答案：B2. 完全竞争市场中，长期均衡下，企业的经济利润为：A. 正B. 零C. 负D. 无法确定答案：B3. 边际成本与平均成本的关系是：A. 边际成本始终低于平均成本B. 边际成本始终高于平均成本C. 边际成本与平均成本没有固定关系D. 边际成本等于平均成本时，平均成本达到最低点答案：D4. 价格弹性的定义是：A. 需求量对价格变化的敏感程度B. 供给量对价格变化的敏感程度C. 需求量对收入变化的敏感程度D. 供给量对收入变化的敏感程度答案：A5. 垄断市场中，垄断者通过：A. 降低价格来增加销量B. 提高价格来增加利润C. 限制产量来提高价格D. 增加产量来降低成本答案：C6. 以下哪项不属于公共品的特点：A. 非排他性B. 非竞争性C. 私人生产D. 政府提供答案：C7. 外部性是指：A. 个人或企业在生产或消费过程中对第三方造成的未被市场机制反映在价格中的成本或收益B. 产品价格与生产成本之间的差额C. 个人或企业在生产或消费过程中产生的所有成本和收益D. 政府对市场的干预答案：A8. 边际效用递减原理指的是：A. 随着消费量的增加，每单位商品带来的效用递增B. 随着消费量的增加，每单位商品带来的效用递减C. 随着消费量的增加，每单位商品带来的效用保持不变D. 随着消费量的减少，每单位商品带来的效用递减答案：B9. 完全信息市场假设是指：A. 市场中的买卖双方对交易信息完全了解B. 市场中的买卖双方对交易信息完全不了解C. 市场中只有卖方了解交易信息D. 市场中只有买方了解交易信息答案：A10. 以下哪项不是市场失灵的原因：A. 外部性B. 公共品C. 信息不对称D. 完全竞争答案：D二、简答题（每题10分，共30分）1. 解释什么是需求弹性，并举例说明如何计算需求弹性。
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(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。
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。
13. 设w=9元/小时，=R 18小时，m=16元，cRc R u =),(求1）??,?,===***L c R2）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%。
中级微观考试题型(范里安版本)
1
q1* 6
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d (q2 )
dq2
17
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q2
1
q2* 24
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p2*
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9
总利润（q1 q2） p1*q1* p2*q2* 1 (q1* q2* )
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264
27
• 证明卡特尔中的厂商存在作弊（独自增加 产量谋取更大利润）的诱惑。
w2, y)
y 4
x*2(w1, w2, y) y.
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w1
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w2
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21
对于生产函数 y k1/ 4L1/ 4 ，有两种可变投入K、L，
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。 写出成本曲线。
q p
q 1
p q
q
p
q1
(
p)
q1
(
p)
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；
当商品不具有弹性需求，即（p） 1时，商品价格上升会导致收益增加；
当商品具有单位弹性需求时，价格的变化与收益无关。
②边际收益和需求价格弹性的关系
由①知，p pq qp
MR
R q
①总收益和需求价格弹性的关系
设厂商总收益为R，价格为p，需求量为q，价格和需求量的 变动分别为p和q.
R pq
R' ( p p)(q q) pq pq qp pq
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。
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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 。
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。
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%。
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 c 16．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1.1%。
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 x 25．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) ba 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, A VC, AFC, MC3）计算minAC 和minA VC 时的AC,A VC,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)=40p 1) 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+p 1) 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)=52.5-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+4y 1) 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ss p Q 40220-=非学生N 的需求函数为NN p Q 20140-=。
已知AC=MC=0，则1）当不能差别定价时，如何定价？sQ =？NQ =？π=？2） 当可以差别定价时，sp =？Np =？sQ =？NQ =？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)=4y 1)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间应满足什么关系？（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)。