厦门大学研究生《高级微观经济学(I)》课程复习资料

期末复习指南第二部分：厂商理论一、叙述题1．厂商利润最大化条件的意义及应用边界；厂商成本最小化条件的意义及应用边界（新加）（1）写出利润最大化的形式化描述。

（2）利润最大化的一阶条件和意义（三个）。

（3）应用边界：生产函数不能微分；某些投入要素可能取0值；可能不存在利润最大化生产技术。

（4）写出成本最小化的形式化描述。

（5）成本最小化的一阶条件和意义。

2．分析生产集的性质（1）非空的；（2）闭凸；（3）没有免费的午餐；（4）不生产是可能的；（5）自由处置；（6）不可逆性；（7）规模报酬；（8）可加性。

3．阐述欧拉方程和克拉克分配定理的理论意义和现实意义。

（1）欧拉方程：),(212211x x kf f x f x =+经济意义：投入要素x 1和x 2与其边际产品的乘积之和等于k 倍的产出量。

（2）克拉克定理：),(212211x x f f x f x =+经济意义：总产出可按投入要素的边际产品完全分配。

（3）现实意义：每种投入按其边际产出将全部产品耗尽 按这种理论分析，则最大化长期利润等于0（长期每种生产要素都可以调整）。

4．证明利润函数是价格的凸函数。

令价格分别为p p p ''',,时的产出为y y y ''',,，其中p p p '-+='')1(t ty p y p y p p y p p '''-+''='''-+=''''='')1(])1([)(t t t t πpy y p ≤''（因为y 是价格p 下的利润最大化产出，其他产出的利润都小于py ）同理，y p y p ''≤'''，代入（*）得到：)()1()()1()(p p y p py p '-+=''-+≤''πππt t t t5．给出要素需求函数、条件要素需求函数、成本函数及利润函数形式化描述，并解释经济意义。

一、某个消费者的间接效用函数为αα-=12121),,(p p y y p p v ，其中10<<α。

求：（1） 该消费者的直接效用函数；（2） 该消费者的支出函数；二、利用效用函数11321212(,)u x x x x=，预算约束1122m p x p x =+，计算(,)mx p m ，(,)v p m 和(,)hx p u消费者的效用最大化问题为：11321212max :(,)u x x x x =1122..:s t p x p x m +=拉格朗日函数为：1132121122(,)()L x x x m p x p x λλ=+-+一阶条件为：113212112x x p λ-= 213212213x x p λ-= 1122p x p x m +=联立以上三式求解得到：113(,)5m x p m p =，222(,)5mx p m p = 将需求函数代入效用函数即得出间接效用函数为：111152323612123232(,)555m m m v p m p p p p ⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫== ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭由(,(,))v p e p u u =得：32655125(,)532p p e p u u ⎛⎫⎛⎫= ⎪ ⎪⎝⎭⎝⎭根据谢泼德引理，(,)(,)i ie p u h p u p ∂=∂，可以得到希克斯需求函数为： 226551251(,)32p p h p u u -⎛⎫⎛⎫= ⎪ ⎪⎝⎭⎝⎭336551252(,)32p p h p u u -⎛⎫⎛⎫= ⎪ ⎪⎝⎭⎝⎭（1）消费者i 面临如下最小化支出问题：0xmin px (p,)e u = ..s t 0(x)u u ≤当 00u ≠ 且 00u >时，由效用函数严格递增可得 00x (x)1u u u u ⎛⎫≤⇔≤⎪⎝⎭厦门大学研究生《高级微观经济学(I)》课程试卷＿＿＿＿学院＿＿＿＿系＿＿＿＿年级＿＿＿＿专业主考教师：＿＿＿＿试卷类型：（A 卷）∴ 原问题转化为： 000x min p (p,1)u u e u⋅=⋅ ..s t 0x 1u u ⎛⎫≤ ⎪⎝⎭这表明，0(p,)(p,1)e u u e =⋅；显然，当00u =时，该式子亦成立。

硕士博士高级微观经济学复习重点高微考试重点第一章消费者理论消费者选择公理：完备性。

传递性。

连续性。

局部非饱和性。

严格单调。

凸性。

严格凸性定理1.1——效用函数存在性证明P13定理1.4——消费者一阶条件充分性效用函数简单计算定理1.6——间接效用函数的性质。

证明（尤其是罗伊恒等式）定理1.7——支出函数的性质。

证明（尤其是谢泼德引理）定理1.8——间接效用函数和支出函数的关系定理1.9——马歇尔需求函数和希克斯需求函数的关系定理1.10——齐次性和预算平衡性定理1.11——斯勒茨基方程第二章消费者理论的若干专题定理2.3——直接效用和间接效用的对偶定理2.5——预算平衡性和对称性意味着齐次性定义2.1——显示偏好若公理（概念。

知道）不确定性下选择公理1-6完备性。

传递性。

连续性。

单调性。

替代性。

简化公理定理2.8 VNM效用函数正放射变换的唯一性定义2.4 风险厌恶、风险中性和风险偏好（知道）定义2.5 确定性等价和风险溢价（知道）第三章厂商理论定义3.3——全局的规模报酬定理3.4——位似生产函数的成本与条件要素需求（第2点）定理3.7——利润函数的性质（4）关于（p，w）是凸的第四章局部均衡补偿变化（或叫收入变差，CV）和等价变差的计算（等价变化，EV，这个书上没有。

见PPT）第五章一般均衡定理5.2——总超额需求函数的特性定理5.3——总超额需求与瓦尔拉斯均衡（瓦尔拉斯一般均衡存在性的条件，知道）定理5.7 第一福利定理定理5.8 第二福利定理第六章一般均衡定义7.2——严格占优策略定义7.7——纯策略纳什均衡。

微观经济学重点复习资料整理微观经济学是研究个体经济行为和市场调节机制的学科，包括供求关系、消费者决策、厂商行为、市场竞争、市场失灵等内容，是经济学的重要分支之一。

在学习微观经济学时，需要掌握一些重点知识点和方法，下面将对这些内容进行整理和复习。

一、供求关系供需关系是市场经济的基础，它是指在某种物品的市场上，供给量与需求量之间形成一种关系，同时，随着需求与供给条件的变化，这种关系也在不断变化。

在学习供求关系时，需要掌握以下内容：•供求图形的解释：供求图形通常由供给曲线和需求曲线组成，通过交点分析供需关系。

•外部影响因素的分析：外部影响因素包括产量、技术、商品替代、人口增长和财富等因素，这些因素的变化会对供需关系产生影响。

•市场平衡与价格调整：当供需关系达到平衡时，市场价格也就确定了。

二、消费者决策消费者决策是指人们在有限的收入和需求之间做出选择的过程。

在学习消费者决策时，需要掌握以下内容：•边际效用分析：边际效用是指每增加一单位消费所带来的总效用的变化量，通过边际效用的分析，可以找出最优的消费量。

•预算约束条件的分析：消费者在购买商品时，通常需要考虑价格和收入之间的相互关系，这就需要运用预算线来分析。

•消费选择的影响因素：消费选择的影响因素包括价格、收入、品味等，了解这些因素可以更好地理解和分析消费者决策。

三、厂商行为厂商行为是指生产商为了获得最大化利润而采取的决策。

在学习厂商行为时，需要掌握以下内容：•利润的最大化：利润最大化是厂商决策的核心，了解成本、生产函数、市场价格等因素，可以帮助厂商做出最优的决策。

•市场型态的分析：市场型态包括完全竞争、垄断、垄断竞争、寡头垄断等，不同的市场型态对厂商行为会产生不同的影响。

•市场失灵的分析：市场失灵是指市场机制不能有效地引导资源分配和生产行为，了解市场失灵的原因和影响，有助于减少市场失灵的损失。

四、市场竞争市场竞争是市场经济的重要特征之一，它可以促进资源的优化配置和生产效率的提高。

第一篇导论―要想真正掌握经济学的基本原理，最好的办法就是去阅读三位伟大的经济学家的著作——亚当·斯密、卡尔·马克思和梅纳德·凯恩斯。

亚当.斯密：英国经济学家“经济学之父”《国民财富的性质和原因的研究》(1776年)简称《国富论》标志着现代经济学的诞生―经济人‖、―看不见的手‖卡尔.马克思：19世纪德国经济学家。

从对资本主义批判的角度开创了与资产阶级相对立的经济学体系——马克思主义经济学1867年《资本论》第一卷发表约翰·梅纳德·凯恩斯John Maynard Keynes：宏观经济学的创始者20世纪英国经济学家1936年发表《就业、利息和货币通论》引起了经济学的革命。

一度被誉为资本主义的―救星‖、―战后繁荣之父‖等美称。

突破：第一，突破了传统的就业均衡理论，建立了一种以存在失业为特点的经济均衡理论；第二，把国民收入作为宏观经济学研究的中心问题；第三，用总供给与总需求的均衡来分析国民收入的决定；第四，建立了以总需求为核心的宏观经济学体系；第五，对实物经济和货币进行分析的货币理论；第六，批判了―萨伊法则‖，反对放任自流的经济政策，明确提出国家直接干预经济的主张。

第一章汽车与经济学一、什么是经济学? 它要解决的基本问题是什么？研究我们社会中的个人、厂商、政府和其他组织如何进行选择，以及这些选择如何决定社会资源的使用方式。

在稀缺性的前提下，经济学要解决的基本问题是：1、生产什么，生产多少？2、如何生产？3、为谁生产？（如何分配）4、谁作出经济决策，依据什么程序？决策可以由市场来做出（市场经济制度）决策可以由计划来做出（计划经济制度）决策可以由市场和计划共同来做出（混合经济制度）二、混合经济中的市场与政府经济学家认为私人决策是有效率的，但同时相信政府的某些干预也是合意的。

在一个经济的公共部门和私人部门之间找到恰当的平衡，是经济分析的一个中心问题。

一般来说，市场可以解决好前两个基本的经济问题，在每个人追求个人利益最大化的同时也就实现了效率最高和资源的最优配置。

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Final ExamAdvanced Microeconomics I2014SpringDuration:210minutes•You are going to answer6questions.Each is worth25marks.The total is150marks.•Questions in Part One and Part Four are mandatory;questions in Part Two and Part Three are optional.Please circle below the question numbers you choose in Part Two and Part Three.–Part One:Uncertainty(Mandatory:1question)–Part Two:Producer Theory(Optional:choose1out of2questions)I choose12–Part Three:Partial Equilibrium(Optional:choose2out of3ques-tions)I choose123–Part Four:General Equilibrium(Mandatory:2questions)Name:Major:Student Number:Part One:Question1(mandatory)Suppose you and I consider the following game:we both put$50on the table,thenflip a coin.If it comes up heads,I get everything on the table;and if it comes up tails,you get everything on the table.Suppose we both have$150available for consumption this week and both of us are risk averse with the same Bernoulli utility function u(x)=ln x,where x is the weekly consumption.(a)(2marks)Draw a curve showing the relationship between your weekly consumption x andutility u.(b)(2marks)Clearly label the expected value of the gamble E(x)and the expected utilityEU from playing the gamble,assuming the coin is fair,i.e,the coin comes up with heads half the time and tails the other half.(c)(2marks)Will you agree to play the gamble?Explain why or why not.(d)(4marks)Suppose you know the coin is ingδfor the probability of tails comingup,write down an inequality to show that if the coin is sufficiently unfair you will play the gamble.(e)(6marks)Consider both of us in a context of an Edgeworth Box,and suppose that the coinis fair.Draw the Edgeworth Box with consumption x H under”heads”on the horizontal and consumption x T under”tails”on the vertical axis.Illustrate our endowment point E before the gamble and outcome bundle A if we do the gamble.Show the four indifference curves,two for you and two for me,going through point E and A.Explain why it is NOT efficient for us to play the gamble.(f)(2marks)Suppose that I know the coin is unfair and that it comes up tails with aprobability ofδ<0.5.How would the slope of my indifference curve at point E differ from what you draw in the previous question?(g)(3marks)Suppose that I know that the coin is unfair and it comes up tails with aprobability ofδ<0.5.You still believe the coin is fair.To make you accept the gamble,I sweetened the terms for you:if the coin comes up heads,I agree to give you k out of my winnings.Draw a new Edgeworth Box with the endowment bundle E,the outcome bundleA in the previous gamble and the new outcome bundleB in the new gamble.Indicate kin the diagram.(h)(4marks)Write down an equation ofδand k to show the condition under which takingthe gamble is Pareto efficient.Part Two:Question1(optional)Consider a constant-returns to scale Cobb-Douglas technology using two inputsf(K,L)=AKαL1−αwhere0<α<1.(a)(8marks)Derive the cost function.(b)(3marks)Show that long-run average and long-run marginal cost are constant and equal.(c)(4marks)Fix input K at K and derive the short-run cost function.(d)(7marks)Show that for every level of K,short-run average cost and long-run averagecost are equal at the minimum level of short-run average cost.(e)(3marks)Illustrate your results in the cost-output plane.Part Two:Question2(optional)The market for commodity q is perfectly competitive.All potentialfirms have the identicalshort run cost functionc(w,k,q)=w2q2k+9kwhere w is the wage rate and k is the short runfixed level of capital.Now let the wage rate be determined by the aggregate output level of q,denoted as Q,according to the equation w(Q)=0.1Q.The market demand for q isQ d(p)=1600−p(a)(8marks)What is the long run supply curve for q?(b)(9marks)What is the long run competitive equilibrium price of q,total market outputQ,and wage rate?(c)(8marks)What can you say about the number offirms,and the aggregate amount ofcapital in the long run for this market?Part Three:Question1(optional)Consider a market of differentiated product duopoly where twofirms(1and2)sell the same physical good.Eachfirm i∈{1,2}chooses both the product price p i∈R and retail location x i∈[0,1].Suppose in thefirst stage,bothfirms choose locations x i’s on[0,1].Eachfirm observes the other’s location choice.In the second stage,the twofirms set prices p1and p2 simultaneously.The marginal cost of producing one unit of the good is the same for both firms:c>0.Each consumer is indexed by his/her location y on[0,1].And suppose the consumer population is uniformly distributed on[0,1].A location-y consumer’s utility from buying a unit of good at location x i and price p i is10−t(y−x i)2−p i,where p i is the price of the good,|y−x i|is the consumer’s distance from the retail location,t∈(0,1)is some parameter,and t(y−x i)2 the“transportation cost.”(a)(10marks)Let usfirst investigate the second-stage price competition,fixing thefirms’locations x1=a and x2=1−b(without loss of generality,suppose a+b≤1,i.e.x1≤x2).(1)(5marks)Derive the demand function for thefirms:D1(p1,p2)and D2(p1,p2).(Hint:your answer should be two demand functions of(p1,p2)with parameters a,b and t).(2)(5marks)Given the locations(a,b),eachfirm i maximizes its profitπi(a,b)=(p i−c)D i(p1,p2).Derive the Nash equilibrium prices:p∗1(a,b)and p∗2(a,b).(Hint:youranswer should be functions of a,b with parameters c and t).(b)(10marks)Now let us consider thefirst-stage location competition given the price com-petition derived in part(a).(1)(5marks)Show that while choosing their locations in thefirst stage,firms have anincentive to differentiate maximally,i.e.dπ1(a,b)da <0anddπ2(a,b)db<0(2)(5marks)In the outcome of the entire game(both location and price choices),whatis the equilibrium price markup,i.e.difference between price and marginal cost?(c)(5marks)Suppose a social planner chooses the twofirms’locations to maximize the sumof consumer and producer surplus;and then thefirms compete on prices as in part(a)of the question.What locations would the social planner choose?Part Three:Question2(optional)w12r12x2+F,where w represents All coffee shops in a town have cost function C(w,r,x)=3500per unit labour cost,r represents per unit capital service cost,x represents the number of cups of coffee served and F representsfixed costs.(a)(4marks)Suppose w=25and r=9,find the long-run equilibrium price of a cup of coffeeas a function of F.(b)(2marks)The government is considering to impose a recurring weekly license fee.Beforethe introduction of the license fee,a coffee shop’s weeklyfixed cost is$144.The license fee is$81.Show the impact of the license fee on the long-run equilibrium coffee price. (c)(5marks)Suppose that tastes for coffee x and a composite good y can be characterizedby the utility function u(x,y)=15x12+y for all100,000coffee consumers in the town.Assume that all consumers have a budget of$100for x and y and p y=1.Derive the individual consumer’s demand function for coffee.To evaluate the license fee’s impact on consumers’welfare,will different measures of welfare change,compensating variation, equivalent variation and consumer surplus,give different numbers?Explain why.(d)(2marks)How many cups of coffee are sold in the town before and after the impositionof the license fee?(e)(4marks)How many coffee shops are active in long-run equilibrium before and after theimposition of the license fee?(f)(8marks)What is the deadweight loss associated with the license fee?Part Three:Question 3(optional)There are N firms in a market.Each firm has the same cost function c (q i )=k +cq i where c >0,k >0.The market demand is p =a −bQ ,where Q = i q i .(a)(9marks)Suppose entry by new firms is effectively blocked and existing firms competein their choice of quantity.Calculate the equilibrium market price,each firms output and total dead weight loss incurred by the entry barrier.(b)(8marks)Suppose existing firms compete in their choice of price and new entry is stillimpossible.Solve the same problems as (a).(c)(8marks)Suppose free entry and exit is available and that firms compete in their choiceof quantity,what will be the long-run equilibrium number of firms in the market?Part Four:Question1(mandatory)Consider a pure exchange economy with two consumers,i=1,2,and two commodities, l=1,2.The utility functions of the consumers areu1(x1)=x11×x21,u2(x2)=x12+x22.The endowment of consumer1isω1=(7,2)and that of consumer2isω2=(3,2).(a)(6marks)Find the set of Pareto-efficient allocations of this economy.(b)(6marks)Find the core of this economy.(c)(4marks)Find the Walrasian equilibrium and the equilibrium allocation.(d)(2marks)Is consumer1better offat this equilibrium than at the endowment?Whatabout consumer2?(e)(3marks)Do the marginal rates of substitution of the two consumers equal at this equi-librium?Explain why or why not.(f)(4marks)Find an allocation that is in the core of this economy,but not in the core of its2-fold replica.Part Four:Question2(mandatory)Consider an island with two winemakers and two consumers.(a)(10marks)Suppose grapes are freely available on the island.Firm1is entirely ownedby consumer1.It produces red wine(in barrels)with labour input via the production function R=2l.Firm2is entirely owned by consumer2and produces white wine(in barrels)with labour input via the production function W=3l.Each consumer owns and supplies10units of labour,i.e,aggregate labour supply is inelastic.Consumer1’s utility function is u1(R,W)=R0.4W0.6and consumer2’s utility function is u2(R,W)= 10+0.5ln R+0.5ln W.Define and calculate the general equilibrium of this economy.(You can normalize the price of per unit labour to1)(b)(15marks)Suppose there are international markets for red wine and white wine and thewinemakers on the small island are price takers.Vineries on the island produce30tons of grapes per year and it is impossible to ship grapes from elsewhere to the island.The labour requirements for producing one barrel of red wine and white wine are the same asin question(a).In addition,12ton of grapes are needed for one barrel of red wine and35ton of grapes are needed for one barrel of white wine.Write down the unit cost function for red wine and white wine.Suppose the international prices for red wine and white wine are p R=p W=1per barrel.Find the wage rate w l∗,grape price w g∗,red wine output R∗and white wine output W∗in general equilibrium.。