第一讲经济理论的基础Nicholson. Chapter 1pp.1-20决策行为的模型化经济学通常被定学通常被定义为“在一个稀缺性的在一个稀缺性的环境之下的理性境之下的理性选择行行为研究研究”，但是从我，但是从我们的的课本内容来看，往往并不能看到本内容来看，往往并不能看到这一一点，点，经济学在其中似乎只能被定学在其中似乎只能被定义为“在在一个一个变化的化的环境中境中对于市于市场交易和市交易和市场行行为的研究的研究”。近一个世近一个世纪以来，以来，经济学的研究方法学的研究方法虽然然已已经取得了很大的取得了很大的进步，但是步，但是结论似乎并似乎并没有多大的没有多大的变化。化。但在另一方面，个人主但在另一方面，个人主义方法方法论在其他社在其他社会科学会科学领域的推广域的推广应用却用却给我我们带来了很来了很大的收大的收获。而。而这些推广些推广应用的基石正是用的基石正是经济学的基本学的基本逻辑：“理性人理性人”在自利本性在自利本性下的下的选择。我我们在在课堂中学堂中学习的主要是的主要是经济学的分析学的分析方法。掌握了方法。掌握了这套方法和套方法和逻辑，日后我，日后我们可以运用它分析任何可以运用它分析任何选择行行为。因此，。因此，经济学的适用性学的适用性远远超出了超出了经济学本身的学本身的领域。或者域。或者说，经济学的研究学的研究领域已域已经不再不再是是传统上上认识的范畴了。的范畴了。e. g. the study of the implications of choice in a setting of scarcity. Political wheeling and dealing is seen as a form of complex exchange. The criminal justice system is seen as a method of pricing illegal activities. Politicians, status seekers, altruists and criminals are all seen as rational decision makers pursuing well-defined goals in a setting of scarcity.The purpose of the Micro sequence it to provide you with a core set of tools (ideas, intuitions, mathematical models, and aptitude for interpreting the world in economic terms) that will allow you to approach economic problems with greater sophistication than you have now. ( I will often use nontraditional examples as a means of seeing whether you can see how to apply traditional economic tools to non-market decision making.)经济学分析的基本逻辑经济学学总是假定人是假定人们在做出某种在做出某种选择行行为，特特别是，我是，我们往往往往总是假定他是假定他们在把什么在把什么东西力西力图最大化（最最大化（最优化）。因此，几乎化）。因此，几乎所有的决策所有的决策选择都可以被模型化都可以被模型化为一个最一个最大化的大化的问题。A. 在任一决策行在任一决策行为中，你有中，你有选择的的权利，利，这些些选择就可以就可以对应于最于最优化化问题中的中的变量（量（variables）。）。B. 你当然想做出最你当然想做出最优的的选择（optimal choice）。）。这就意味着你就意味着你试图为你的你的变量量选择一个一个值，从而使其最大化某种函数，从而使其最大化某种函数（function）目）目标函数。函数。C. 你的你的选择或或许会随着某些情况的会随着某些情况的变化而化而变化，你必化，你必须依依赖于某些情况做出决定，于某些情况做出决定，而而这是在你的能力之外的事情，你无法改是在你的能力之外的事情，你无法改变，比如你只能根据天气来决定穿什么衣，比如你只能根据天气来决定穿什么衣服。所以我服。所以我们必必须要特要特别列明一些情况做列明一些情况做为选择的条件，的条件，这些条件就是最些条件就是最优化化问题的参数（的参数（parameter）。）。(包包络定理定理)D. 一旦你建构了一个特定情况下的模型，一旦你建构了一个特定情况下的模型，你就可以估你就可以估计出个人（理性主体）到底会出个人（理性主体）到底会做出什么做出什么样的的选择决策。决策。在最在最优化化问题中，中，这就意味着我就意味着我们找到了找到了参数函数中参数函数中变量的最量的最优值。E. 一旦特定的一旦特定的环境境发生了改生了改变，即参数，即参数变化了，那么化了，那么变量的最量的最优值也会跟着改也会跟着改变，这就是比就是比较静静态（comparative statics），），比如需求的改比如需求的改变（不同于需求量的改（不同于需求量的改变）。）。F. Ceteris Paribus means “other things the same”Economic models attempt to explain simple relationshipsfocus on the effects of only a few forces at a timeother variables are assumed to be unchanged during the period of study人不能两次跳人不能两次跳进同一条河中同一条河中人不能一次跳人不能一次跳进同一条河中同一条河中如果所有的事情都在如果所有的事情都在变化，就会陷于不可化，就会陷于不可知知论的泥潭，世界就无法的泥潭，世界就无法认识了。了。经济模型模型试图从从纷繁复繁复杂的的经济世界中，世界中，抽抽丝剥剥茧，找到其所关心的主要，找到其所关心的主要变量之量之间是在存在着内在关系，因此，一次只能研是在存在着内在关系，因此，一次只能研究一种或几种究一种或几种变量的相互关系，且此量的相互关系，且此时其其他他变量保持不量保持不变。G. 经济命命题的的“可可证伪性性” （falsification）是命）是命题科学性的关科学性的关键所在所在（Karl Popper）。）。There are two general methods used to verify economic models:direct approachestablishes the validity of the models assumptionsindirect approachshows that the model correctly predicts real-world eventsSuggested ReadingsNagel, Ernest. “Assumptions in Economic Theory.” American Economic Review (May 1963): 211219.Caldwell, Bruce J. “Clarifying Popper.” Journal of Economic Literature (March 1991): 133.Harrod, Roy F. “Scope and Method in Economics.” Economic Journal 48 (1938): 383412.第二讲征税与补贴的影响参考书目：pp.270.微观经济学平狄克、鲁宾费尔德关于税收的两种常关于税收的两种常见的的误解：解：1、征税、征税1￥并不是商品价格上￥并不是商品价格上涨1￥；￥；2、政府提高消、政府提高消费税税1￥并不是消￥并不是消费者者购买商品商品时多付出多付出1￥。￥。一、无一、无论是征税是征税还是是补贴，都一定是在需，都一定是在需求者与供求者与供给者之者之间进行分担（分行分担（分摊）的，）的，而且，而且，这种分种分摊效效应与征税或者与征税或者补贴直接直接面面对的的对象到底是哪一方无关。象到底是哪一方无关。二、二、这种分担的效种分担的效应取决于供求曲取决于供求曲线的形的形状，尤其是它状，尤其是它们两者之两者之间的相的相对弹性的大性的大小。小。The Impact of a Tax or SubsidyThe burden of a tax (or the benefit of a subsidy) falls partly on the consumer and partly on the producer.We will consider a specific tax （从量税）which is a tax of a certain amount of money per unit sold.DSBDABuyers lose A + B, andsellers lose D + C, and the government earns A + D in revenue. The deadweightloss is B + C.CIncidence of a SpecificTaxQuantityPriceP0Q0Q1PSPbtPb is the price (includingthe tax) paid by buyers.PS is the price sellers receive,net of the tax. The burdenof the tax is split evenly.P Pb b - P - PS S = tax = taxIncidence of a Specific TaxFour conditions that must be satisfied after the tax is in place:1) Quantity sold and Pd must be on the demand line: QD = QD(Pd)2) Quantity sold and PS must be on the supply line: QS = QS(PS)Incidence of a Specific TaxFour conditions that must be satisfied after the tax is in place:3) QD = QS 4) Pd - PS = taxImpact of a Tax Dependson Elasticities of Supply and DemandQuantityQuantityPricePriceSDSDQ0P0P0Q0Q1PbPStQ1PbPStBurden on BuyerBurden on Seller想一想税收与想一想税收与补贴的份的份额到底与什么因素到底与什么因素相关？相关？是什么使消是什么使消费者或者生者或者生产者能者能够更多地将更多地将税税赋转嫁嫁给对方，而把方，而把补贴攫取攫取过来，占来，占为己有？己有？如果将税如果将税赋换成成补贴也是一也是一样的。的。Pass-through fraction（转嫁因子嫁因子）ES/(ES - Ed)表明以高价形式表明以高价形式转嫁嫁给消消费者的税收份者的税收份额For example, when demand is perfectly inelastic (Ed = 0), the pass-through fraction is 1, and all the tax is borne by the consumer.当当Ed=0，转嫁因子嫁因子1 1，所有税，所有税赋由消由消费者承者承担；担；当当Ed=，转嫁因子嫁因子0 0，所有税，所有税赋由生由生产者者承担。承担。The Impact of a Tax or SubsidyThe Effects of a Tax or SubsidyA subsidy can be analyzed in much the same way as a tax.It can be treated as a negative tax. （补贴等于降价等于降价）The sellers price exceeds the buyers price.注意：税注意：税赋使均衡价格并没有上升使均衡价格并没有上升T，而只，而只是其是其3/5。第三讲最优值的数学处理方法Nicholson. Chapter2pp.52-55Constrained MaximizationSuppose we want to choose x1 and x2 to maximizey = f(x1, x2)subject to the linear constraintc - b1x1 - b2x2 = 0We can set up the LagrangianL = f(x1, x2) + (c - b1x1 - b2x2)经常可以表达为：经常可以表达为：Max y = f(x1, x2) s.t. c - b1x1 - b2x2 = 0Constrained MaximizationThe first-order conditions aref1 - b1 = 0f2 - b2 = 0c - b1x1 - b2x2 = 0To ensure we have a maximum, we must use the “second” total differentiald 2y = f11dx12 + 2f12dx1dx2 + f22dx22Constrained MaximizationOnly the values of x1 and x2 that satisfy the constraint can be considered valid alternatives to the critical pointThus, we must calculate the total differential of the constraint-b1 dx1 - b2 dx2 = 0dx2 = -(b1/b2)dx1These are the allowable relative changes in x1 and x2Constrained MaximizationBecause the first-order conditions imply that f1/f2 = b1/b2, we can substitute and getdx2 = -(f1/f2) dx1Sinced 2y = f11dx12 + 2f12dx1dx2 + f22dx22 we can substitute for dx2 and getd 2y = f11dx12 - 2f12(f1/f2)dx12 + f22(f12/f22)dx12Constrained MaximizationCombining terms and rearrangingd 2y = f11 f22 - 2f12f1f2 + f22f12 dx12/ f22Therefore, for d 2y 0, it must be true thatf11 f22 - 2f12f1f2 + f22f12 0This equation characterizes a set of functions termed quasi-concave functionsany two points within the set can be joined by a line contained completely in the set关于quasi-concave functions的详细讨论可以参看蒋中一的数理经济学的基本方法一书P506的相关内容。二阶条件的另一表示方法Bordered Hessian determinant加边海塞行列式f11 f22 - 2f12f1f2 + f22f12 0二阶条件表明MRS递减，无差异曲线凸向原点，原函数为拟凹函数。N个未知数的最值问题对于最大化的目标而言，要求对于最大化的目标而言，要求d2y必须为负定的，必须为负定的，即所有即所有the leading principal minors of Hb（加（加边主子式），必须遵循边主子式），必须遵循 。而对于最小值的目标而言，则要求而对于最小值的目标而言，则要求d2y必须为正必须为正定的，即所有定的，即所有the leading principal minors of Hb （加边主子式）都为负。（加边主子式）都为负。蒋中一蒋中一P.502清晰、权威。清晰、权威。pp.60 E2.3请认真阅读蒋书中的请认真阅读蒋书中的P499504的相关内容。的相关内容。其中之所以与我们教材中关于最大值判定的符其中之所以与我们教材中关于最大值判定的符号相反是因为那里的切记！号相反是因为那里的切记！pp.61e.g.效用的最大化一阶条件二阶条件Economic ProfitsTotal costs for the firm are given bytotal costs = C = wl + vkTotal revenue for the firm is given bytotal revenue = pq = pf(k,l)Economic profits () are equal to = total revenue - total cost = pq - wl - vk = pf(k,l) - wl - vkEconomic ProfitsEconomic profits are a function of the amount of capital and labor employedwe could examine how a firm would choose k and l to maximize profit“derived demand” theory of labor and capital inputs for now, we will assume that the firm has already chosen its output level (q0) and wants to minimize its costsCost-Minimizing Input ChoicesTo minimize the cost of producing a given level of output, a firm should choose a point on the isoquant at which the RTS is equal to the ratio w/vit should equate the rate at which k can be traded for l in the productive process to the rate at which they can be traded in the marketplaceCost-Minimizing Input ChoicesMathematically, we seek to minimize total costs given q = f(k,l) = q0Setting up the Lagrangian:L = wl + vk + q0 - f(k,l)First order conditions areL/l = w - (f/l) = 0L/k = v - (f/k) = 0L/ = q0 - f(k,l) = 0Cost-Minimizing Input ChoicesDividing the first two conditions we getThe cost-minimizing firm should equate the RTS for the two inputs to the ratio of their pricesCost-Minimizing Input ChoicesCross-multiplying, we getFor costs to be minimized, the marginal productivity per dollar spent should be the same for all inputsCost-Minimizing Input ChoicesNote that this equations inverse is also of interestThe Lagrangian multiplier shows how much in extra costs would be incurred by increasing the output constraint slightlyq0Given output q0, we wish to find the least costly point on the isoquantC1C2C3Costs are represented by parallel lines with a slope of -w/vCost-Minimizing Input Choicesl per periodk per periodC1 C2 U(B)UtilityUtility rankings are ordinal in naturethey record the relative desirability of commodity bundlesBecause utility measures are not unique, it makes no sense to consider how much more utility is gained from A than from BIt is also impossible to compare utilities between peopleUtilityUtility is affected by the consumption of physical commodities, psychological attitudes, peer group pressures, personal experiences, and the general cultural environmentEconomists generally devote attention to quantifiable options while holding constant the other things that affect utilityceteris paribus assumptionUtilityAssume that an individual must choose among consumption goods x1, x2, xnThe individuals rankings can be shown by a utility function of the form:utility = U(x1, x2, xn; other things)this function is unique up to an order-preserving transformationEconomic GoodsIn the utility function, the xs are assumed to be “goods”more is preferred to lessQuantity of xQuantity of yx*y*Preferred to x*, y*?Worsethanx*, y*Indifference CurvesAn indifference curve shows a set of consumption bundles among which the individual is indifferentQuantity of xQuantity of yx1y1y2x2U1Combinations (x1, y1) and (x2, y2)provide the same level of utilityMarginal Rate of SubstitutionThe negative of the slope of the indifference curve at any point is called the marginal rate of substitution (MRS)Quantity of xQuantity of yx1y1y2x2U1Marginal Rate of SubstitutionMRS changes as x and y changereflects the individuals willingness to trade y for xQuantity of xQuantity of yx1y1y2x2U1At (x1, y1), the indifference curve is steeper.The person would be willing to give up morey to gain additional units of xAt (x2, y2), the indifference curveis flatter. The person would bewilling to give up less y to gainadditional units of xIndifference Curve MapEach point must have an indifference curve through itQuantity of xQuantity of yU1 U2 /, undefined if y/x = /, and MRS = 0 if y/x 0. The most common cases of homogeneous functions are k = 0 and k = 1. If f is homogeneous of degree zero, doubling all of its arguments leaves f unchanged in value. If f is homogeneous of degree 1, doubling all its arguments will double the value of f. We shall encounter functions homogeneous of degree 1 in Part IV.Homogeneous FunctionA function, f(X1, X2, . . . , Xn), is homogeneous of degree k iff(mX1, mX2, . . . , mXn ) = mkf(X1, X2, . . . , Xn ).Stigler, G. “The Development of Utility Theory.” Journal of Political Economy 59, pts. 12 (August/October 1950): 307327, 373396.第五讲效用与生产函数的几种常见形式Nicholson. pp.80-83.& Chap.11,12几个常用的希腊字母deltaepsilonsigmarhopp.81Examples of Utility FunctionsCobb-Douglas Utilityutility = U(x,y) = xy where and are positive constantsThe relative sizes of and indicate the relative importance of the goodsExamples of Utility FunctionsPerfect Substitutesutility = U(x,y) = x + yQuantity of xQuantity of yU1U2U3The indifference curves will be linear.The MRS will be constant along the indifference curve.Examples of Utility FunctionsPerfect Complementsutility = U(x,y) = min (x, y)Quantity of xQuantity of yThe indifference curves will be L-shaped. Only by choosing more of the two goods together can utility be increased. U1U2U3Examples of Utility FunctionsCES Utility (Constant elasticity of substitution)The elasticity of substitution (The elasticity of substitution ( ) is equal ) is equal to 1/(1 - to 1/(1 - ) ) Perfect substitutes Perfect substitutes = = Fixed proportions Fixed proportions = 0 = 0所所谓的替代的替代弹性性为无差异曲无差异曲线的曲的曲率，即率，即过曲曲线上两点切上两点切线的正向的正向夹角与角与这两点之两点之间弧弧长的比的比值。Examples of Utility FunctionsCES Utility (Constant elasticity of substitution)utility = U(x,y) = x/ + y/ when 0 andutility = U(x,y) = ln x + ln y when = 0Perfect substitutes Perfect substitutes = = = 1 = 1Cobb-Douglas Cobb-Douglas = 1 = 1 = 0 = 0Perfect complements Perfect complements = 0 = 0 = - = - pp.281The Linear Production FunctionSuppose that the production function isq = f(k,l) = ak + blThis production function exhibits constant returns to scalef(tk,tl) = atk + btl = t(ak + bl) = tf(k,l)All isoquants are straight linesRTS is constant = The Linear Production Functionl per periodk per periodq1q2q3Capital and labor are perfect substitutesRTS is constant as k/l changesslope = -b/a = Fixed ProportionsSuppose that the production function isq = min (ak,bl) a,b 0Capital and labor must always be used in a fixed ratiothe firm will always operate along a ray where k/l is constantBecause k/l is constant, = 0Fixed Proportionsl per periodk per periodq1q2q3No substitution between labor and capital is possible = 0k/l is fixed at b/aq3/bq3/aCobb-Douglas Production FunctionSuppose that the production function isq = f(k,l) = Akalb A,a,b 0This production function can exhibit any returns to scalef(tk,tl) = A(tk)a(tl)b = Ata+b kalb = ta+bf(k,l)if a + b = 1 constant returns to scaleif a + b 1 increasing returns to scaleif a + b 0 1 1 increasing returns to scale increasing returns to scale 1 0the entire income effect is negativeif x is an inferior good, then x/I 0the entire income effect is positiveA Slutsky DecompositionWe can demonstrate the decomposition of a price effect using the Cobb-Douglas example studied earlierThe Marshallian demand function for good x was（pp.135 EX 5.4）A Slutsky DecompositionThe Hicksian (compensated) demand function for good x wasThe overall effect of a price change on the demand for x isA Slutsky DecompositionThis total effect is the sum of the two effects that Slutsky identifiedThe substitution effect is found by differentiating the compensated demand functionA Slutsky DecompositionWe can substitute in for the indirect utility function (V)A Slutsky DecompositionCalculation of the income effect is easierInterestingly, the substitution and income effects are exactly the same sizeMarshallian Demand ElasticitiesMost of the commonly used demand elasticities are derived from the Marshallian demand function x(px,py,I)Price elasticity of demand (ex,px)Marshallian Demand ElasticitiesIncome elasticity of demand (ex,I)Cross-price elasticity of demand (ex,py)Price Elasticity of DemandThe own price elasticity of demand is always negativethe only exception is Giffens paradoxThe size of the elasticity is importantif ex,px -1, demand is inelasticif ex,px = -1, demand is unit elasticPrice Elasticity and Total SpendingTotal spending on x is equal tototal spending =pxxUsing elasticity, we can determine how total spending changes when the price of x changesPrice Elasticity and Total SpendingThe sign of this derivative depends on whether ex,px is greater or less than -1if ex,px -1, demand is inelastic and price and total spending move in the same directionif ex,px -1, demand is elastic and price and total spending move in opposite directionsCompensated Price ElasticitiesIt is also useful to define elasticities based on the compensated demand functionCompensated Price ElasticitiesIf the compensated demand function isxc = xc(px,py,U) we can calculatecompensated own price elasticity of demand (exc,px)compensated cross-price elasticity of demand (exc,py)Compensated Price ElasticitiesThe compensated own price elasticity of demand (exc,px) isThe compensated cross-price elasticity of demand (exc,py) isCompensated Price ElasticitiesThe relationship between Marshallian and compensated price elasticities can be shown using the Slutsky equationIf sx = pxx/I, thenCompensated Price ElasticitiesThe Slutsky equation shows that the compensated and uncompensated price elasticities will be similar ifthe share of income devoted to x is smallthe income elasticity of x is smallThis provides a further rationale for basing consumer surplus estimates on Marshallian demand curves.也就是说，消费者剩余的边界代表了希克斯需求曲线（补偿需求曲线）（P141）HomogeneityDemand functions are homogeneous of degree zero in all prices and incomeEulers theorem for homogenous functions shows that（P181）Eulers Theorem A mathematical theorem: if f(X1, . . . , Xn) is homogeneous of degree k, thenf1X1 f2X2 . . . fnX n =kf(X1, . . . , X n ).HomogeneityDividing by x, we getAny proportional change in all prices and income will leave the quantity of x demanded unchanged第八讲寡头垄断模型Nicholson. Chap. 19. 20垄断市场的均衡完全完全竞争市争市场中的均衡：需求量与供中的均衡：需求量与供给量相等；量相等；垄断市断市场的均衡：的均衡：边际收益等于收益等于边际成成本。本。无无论如何，当一个市如何，当一个市场均衡均衡时，厂商所做，厂商所做的就是它的就是它们所能做的最好的，并且它所能做的最好的，并且它们没没有理由改有理由改变它它们的价格与的价格与产量。量。寡头垄断的决策寡寡头垄断的市断的市场中，一个厂商的定价和定中，一个厂商的定价和定产部分要基于部分要基于对它的它的竞争者的行争者的行为的策略的策略性考性考虑。与此同。与此同时，竞争者的决策也取决争者的决策也取决于于该厂商的决策。厂商的决策。各厂商考各厂商考虑到它的到它的竞争者，并假争者，并假设它的它的竞争者也会同争者也会同样做。做。纳什均衡：在什均衡：在给定它的定它的竞争者的行争者的行为以后，以后，各厂商采取它能采取的最好的行各厂商采取它能采取的最好的行为。Cournot ModelOne of the first researchers to develop a model of markets containing few firms was the French economist Augustin Cournot, who presented a formal analysis of duopoly behavior in 1838. The Cournot ModelDuopolyTwo firms competing with each otherHomogenous goodThe output of the other firm is assumed to be fixedThe Cournot ModelIn our notation Cournot assumed that each firm recognizes that its own decisions about qi affect price but that its own output decisions do not affect those of any other firm. 自己的自己的产量会影响市量会影响市场价格价格自己的自己的产量不会影响量不会影响别人，反人，反过来，来，别人人的的产量却会影响自己。量却会影响自己。Cournot ModelEach firm recognizes that its own decisions about qi affect priceP/qi 0However, each firm believes that its decisions do not affect those of any other firmqj /qi = 0 for all j iMC150MR1(75)D1(75)12.5If Firm 1 thinks Firm 2 will produce 75 units, its demand curve is shifted to the left by this amount. Firm 1s Output DecisionQ1P1What is the output of Firm 1if Firm 2 produces 100 units?D1(0)MR1(0)If Firm 1 thinks Firm 2 will produce nothing, its demandcurve, D1(0), is the market demand curve.D1(50)MR1(50)25If Firm 1 thinks Firm 2 will produce 50 units, its demand curve is shifted to the left by this amount. Cournot ModelThe Reaction CurveA firms profit-maximizing output is a decreasing schedule of the expected output of Firm 2.将厂商的产量与它认为另一个厂商将生产的产量联系起来的函数Q2*（Q1）或者Q1*（Q2）。Firm 2s ReactionCurve Q*2(Q2)Firm 2s reaction curve shows how much itwill produce as a function of how much it thinks Firm 1 will produce. Reaction Curves and Cournot EquilibriumQ2Q1255075100255075100Firm 1s ReactionCurve Q*1(Q2)xxxxFirm 1s reaction curve shows how much itwill produce as a function of how much it thinks Firm 2 will produce. The xs correspond to the previous model.In Cournot equilibrium, eachfirm correctly assumes howmuch its competitors willproduce and therebymaximize its own profits.CournotEquilibriumCournot ModelQuestions1) If the firms are not producing at the Cournot equilibrium, will they adjust until the Cournot equilibrium is reached?2) When is it rational to assume that its competitors output is fixed?Cournot ModelThe first-order conditions for a profit maximization areThe firm maximizes profit where MRi = MCithe firm assumes that changes in qi affect its total revenue only through their direct effect on market priceCournot ModelEach firms output will exceed the cartel output（Cartel时厂商做厂商做为一个一个整体整体进行行产量量选择）the firm-specific marginal revenue is larger than the market-marginal revenueEach firms output will fall short of the competitive outputqi P/qi MCIs this a contradiction to the competitive rule that P = MC?Hint: What happens to the opportunity cost of producing an exhaustible resource?Price of an Exhaustible ResourceP = MCMC = extraction cost + user costUser cost = P - marginal extraction costPrice of an Exhaustible ResourceHow would a monopolist choose their rate of production?They will produce so that marginal revenue revenue less marginal cost rises at exactly the rate of interest, or(MRt+1 - c) = (1 + R)(MRt - c)Price of an Exhaustible ResourceThe monopolist is more conservationist than a competitive industry.They start out charging a higher price and deplete the resources more slowly.Price of an Exhaustible ResourceResource Production by a MonopolistHow Depletable AreDepletable Resources?Crude oil.4 to .5Natural gas.4 to .5Uranium.1 to .2Copper.2 to .3Bauxite.05 to .2Nickel.1 to .2Iron Ore.1 to .2Gold.05 to .1ResourceUser Cost/Competitive PriceThe market structure and changes in market demand have had a very dramatic impact on resource prices over the past few decades.QuestionWhy would oil and natural gas have such a high user cost ratio compared to the other resources?How Depletable AreDepletable Resources?How Are Interest Rates Determined?The interest rate is the price that borrowers pay lenders to use their funds.Determined by supply and demand for loanable funds.SHouseholds supply funds toconsume more in the future;the higher the interest rate, themore they supply.Supply and Demand for Loanable FundsQuantity ofLoanable FundsRInterestRateDTR*Q*DT = DH + DF andequilibrium interestrate is R*.DHDFDH and DF, the quantity demanded for loanable funds by households (H)and firms, respectively, varies inverselywith the interest rate.Changes In The EquilibriumSDTR*Q*During a recession interestrates fall due to adecrease in the demand for loanable funds.DTQ1R1Quantity ofLoanable FundsRInterestRateChanges In The EquilibriumSDTR*Q*When the federal government runs largebudget deficits the demand for loanablefunds increase.Q2R2DTQuantity ofLoanable FundsRInterestRateChanges In The EquilibriumSDTR*Q*When the FederalReserve increasesthe money supply, thesupply of loanablefunds increases.SR1Q1Quantity ofLoanable FundsRInterestRateA Variety of Interest Rates1) Treasury Bill Rate2) Treasury Bond Rate3) Discount RateHow Are Interest Rates Determined?A Variety of Interest Rates4) Commercial Paper Rate 5) Prime Rate6) Corporate Bond RateHow Are Interest Rates Determined?第十讲信息经济学Nicholson. Chap.8PP.197信息经济学概述 信息经济学起源于20世纪40年代，发展于5060年代，到70年代基本发展成熟。在创建初期，研究重点多种多样，有的学者侧重于基础理论研究，有的学者则侧重于应用研究，也正是这两种研究的互相补充和互相促进，才奠定了信息经济学的理论基础。进入70年代以后，信息经济学的发展基本上达到了成熟，其标志是有大量信息经济的论著问世。如：美国霍罗威茨的信息经济学，英国威尔金森的信息经济学-计算成本和收益的标准，日本曾田米二的情报经济学等。 信息经济学的研究从一开始就有两条主线。一是以弗里兹马克卢普(Fritz Machlup)和马克尤里波拉特(Mac Uri Porat)为创始人的宏观信息经济学。宏观信息经济学又称情报经济学、信息工业经济学。以研究信息产业和信息经济为主,是研究信息这一特殊商品的价值生产、流通和利用以及经济效益的一门新兴学科。是在信息技术不断发展的基础上发展建立起来的,是经济学的重要领域。二是以斯蒂格勒和阿罗为最早研究者的西方信息经济学、微观信息经济学。微观信息经济学又被称为理论信息经济学是从微观的角度入手,研究信息的成本和价格,并提出用不完全信息理论来修正传统的市场模型中信息完全和确知的假设。重点考察运用信息提高市场经济效率的种种机制。因为主要研究在非对称信息情况下,当事人之间如何制定合同、契约、及对当事人行为的规范问题,故又称契约理论或机制设计理论。信息经济学简介信息很重要（虽然经济学对它的正式研究起步较晚）信息是有成本的！1信息的性质信息与其他的经济品不同，甚至对于它的定义都很困难。信息的数量也很难定义。信息的形式的特殊性，使其难以使用我们以往研究其他物品的价格数量的方式对它进行描述和研究。但是，研究信息的经济学家更关心信息的环境这是特定决策问题的决定性因素（information set），以及这个环境将如何受到个人行为的影响而改变。这样，就产生了大量的特定环境下的模型，它们之间缺乏共同性。信息的性质另外，信息的研究还涉及到信息本身的一些特殊性。信息具有公共产品的特性。即非竞争性和非排他性。这就意味着以市场机制来配置信息资源常常会无效率。且标准的供求模型理解这些行为具有局限性。信息的基本悖论：信息的价值必须通过揭露信息才能传达给另一方，但是这种揭露又使得信息失去了价值。信息不对称的市场不对称信息解释了我们社会中许多制度性按排。不对称信息导致市场失灵保险及保险引发的问题，激励机制问题。在完全竞争的市场上，由于存在着大量的买方和卖方，所以我们每个人都不能影响市场的价格只能是价格的接受者。这时，市场价格可以作为一个充足的决定指标。每个人所能决定的只是数量。只要接受市场价格，我们就可以找到自己交易的另外一方，而且，我们不用关心商品的品质，因为完全竞争市场给我们提供的产品是同质的。作为商品的购买者，我们很容易地观察到我们所预期的东西。但是，这些条件是十分苛刻的，只有价格可以吸收、包含和反映所有必要信息的时候，我们才能把价格机制当作惟一的沟通工具。让我们来考察某些价格机制对沟通所需要的必要信息不充足的情况我们将非常接近完全竞争市场模型的情况作为考察的起点。市场可以处理某些具有不确定性的问题（签订意外声明合同），但是很多这样的问题还是不能处理的。在许多情况下，我们是不愿意签订意外声明合同的。因为列明所有的可能的意外情况几乎是不可能的。这时，组织的解决办法就是在潜在的交易双方实现纵向整合（纵向一体化）：一方吞并另一方。这种办法也是价格机制和生产调节不能吸纳全部相关不确定性因素的一个解决方案。市场中存在着有用信息，但是信息的分布是不均匀的，这种情况我们称为信息不对称。信息的基本悖论：信息的价值必须通过揭露信息才能传达给另一方，但是这种揭露又使得信息失去了价值。特别地，在信息不对称的情况下，产生了很多有趣的问题。原因在于信息不对称会造成投机行为。2隐藏信息隐藏信息又叫逆向选择，隐藏行为又叫道德风险。这里，我们以对保险问题的分析来举例说明。首先，隐藏信息。所谓健康保险产品只是对那些相对于平均风险率而言的高风险人群具有吸引力，而很少有健康风险低于平均风险率的人会买健康保险。逆向选择的定义逆向选择：当不同质量的产品在交易双方交易时没有充分的信息来确定产品的真实质量，从而不同质量的产品以单一的价格出售时，逆向选择就出现了。结果，市场上就有太多的低质量产品。Adverse Selection: When buyers and sellers have asymmetric information about market transactions, trades actually completed may be biased to favor the actor with better information.这样的行为就叫做逆向选择。这样的行为会导致一个结果就是保险公司停止其业务。逆向选择是信息不对称的一个基本类型。它是一个隐藏信息的问题。潜在交易的一方比另一方获得了关于交易相关多样性的更多信息，用经济学的术语来说就是一个事前信息问题。对于保险公司而言，问题是怎样确定潜在客户的真正风险。虽然公司能够获得一些信息，但是他们自身比保险公司更清楚这些信息，且他们没有动机去诚实地反映这些信息。逆向选择现象的出现是因为一方拥有与潜在交易相关的私人信息，而这些私人信息基本上不能被另一方觉察。正是这种私人信息的不易觉察性构成了信息问题的实质，并把风险转嫁给了交易的另一方。血液捐献的例子旧车市场的例子对于隐藏信息的问题有很多种解决方法，尽管这往往只是部分解决方法。因为问题的实质是某些信息不容易被察觉，我们就要试图增加这些隐藏信息的可察觉性。质量不确定性和“lemon market”由于买主对市场中二手车的平均质量的预期的影响作用，使得在市场中交易的车，低质量车的数量要高于高质量车的数量。最终，只有低质量车可以售出了。（价格太低以至于高质量车无法进入市场出售）。由于信息不对称，低质量商品把高质量商品逐出市场。比如，在健康保险的例子中，我们可以要求进行体检，在旧车市场的例子中要求汽车也进行检查。但是这些都是只能揭示表面问题，并不能从根本上解决逆向选择问题。总之，隐藏信息、隐藏行为或者只是一种怀疑，会阻止这两种类型的交易。3隐藏行为隐藏行为又叫道德风险，是在市场和组织这两种情况下都能够发生的一种信息不对称行为。但是，它不是一个事前信息问题，而是一种事后信息现象。也就是说，它是指交易各方可能采取的行动发生在他们同意进行这项交易之后。如果这些行动对于交易的另一方是不易觉察的，并且如果这些行动会损害交易的另一方的利益，那么，这些隐藏行为就会阻碍这项交易的完成。更为严重的是，对这种隐藏行为可能性的预期也会阻碍这项交易的完成。比如，保险公司普遍面临的 “骗保”的问题就是一个很好的例子。投保行为的动机，以及是由不可抗力还是其他原因，甚至是投保人自己故意引起的灾害，对保险公司来说，调查落实这些细节几乎是不可能的。这就是道德风险。通常有两种途径解决这个问题：一种战略是增加行为的可察觉性，另一种是考虑分担风险的安排。隐藏信息和隐藏行为的联系与区别：共同点：它们都是不易觉察性问题的结果。任何时候，如果交易各方都能观察到他们所需要的所有信息来准备和进行这场交易，则与这两个概念毫无关系。它们都是信息分布是不均匀的。交易的一方拥有私人信息，而这对于交易的另一方是不易觉察的。这些私人信息是有价值的。它会影响交易的条款。因为这些信息是私人的，所以它的所有者能够决定是揭露它还是不揭露它。不同点：隐藏信息是一个事前的概念，指私人信息存在于各方达成一个交易之前；而隐藏行为是一个事后的概念，指私人信息发展于交易执行的过程中。此外，它还表示了一个私人信息的特殊类型，即关于交易中某一方的不易察觉的行为。进一步说，这种行为是有价值的。4信息的价值从经济学的角度研究信息，就是要研究信息的稀缺性，以及这种稀缺性的价值。因为，在现实世界中，信息、特别是有价值的信息，并不是人人都掌握的。比如，你作为一个公司的市场经理，开发了一种新产品，现在必须决定是否将它推向市场。如果这种产品成功了，你将获利，假设获利为8单位。如果失败了，你会受损，假设受损为2单位。你估算出成功的概率为0.3，失败的概率为0.7。你会做出什么决策呢？成功失败推出82不推出00自然情境行动如果你是一个风险中立者，你可以算出它的期望价值为：0.380.7（2）1这个结果是盈利的，所以你会决定推出新产品。另外，我们可以使用一种叫做“决策树”的形式，帮助决策分析。决策树一般含有两种类型的节点：一种节点处在个人能够进行选择的位置，图中用方块表示；另一种节点处在自然随机选择的位置，图中用圆圈表示。逆向思维，也就是从右往左看，我们能够计算出每一个节点的期望价值。CBA28推出不推出成功失败0.30.7A点的期望价值为：0.380.7（2）1B点的期望值是0。因此，在节点C你就可以选择A而不选择B。节点C的期望值也是1。这就是这个人与自然博弈的期望值。现在假设还需要确定在推出这个新产品之前，是否需要进一步进行产品的市场测试以进一步保证市场推出的成功。但是，市场测试仍然存在着不确定因素，并不能完全保证市场推出的成功。成功失败推出0.80.2不推出0.10.9新产品的实际情况市场测试的情况节点A的期望值是：0.880.2（2）6在节点C你会选择A，节点C的期望值也是6。节点B的期望值是：0.180.9（2）1在节点D你决定不推出新产品，节点D的期望值是0。为了得到节点E的期望值，我们需要市场测试成功的概率P。新产品成功的概率等于：P0.8（1P）0.1这个表达式一定等于0.3，这是已知的新产品成功的概率。这样，我们可以得到P2/7所以，节点E的期望值是：2/7612/7通过比较节点E、F的期望值可以计算出由市场测试得到的信息的价值。我们知道节点F的期望值为1，所以市市场测试所得到的信息的价所得到的信息的价值是是：12/71=5/7如果市场测试的成本低于这个数值，你就应该对新产品进行市场测试。F无市场测试市场测试E测试成功的概率P测试失败的概率1PCD00AB2828成功成功失败失败推出推出不推出不推出第十一讲 Expected Utility & Risk Aversion（N.chap.8 P.197）ProbabilityThe probability of a repetitive event happening is the relative frequency with which it will occurprobability of obtaining a head on the fair-flip of a coin is 0.5If a lottery offers n distinct prizes and the probabilities of winning the prizes are i (i=1,n) then （一个重复事件各种可能性的和是1）Expected ValueFor a lottery (X) with prizes x1,x2,xn and the probabilities of winning 1,2,n, the expected value of the lottery isThe expected value is a weighted sum of the outcomes （各种支付的加权平均）the weights are the respective probabilitiesExpected ValueSuppose that Smith and Jones decide to flip a coinheads (x1) Jones will pay Smith $1tails (x2) Smith will pay Jones $1From Smiths point of view,Expected ValueGames which have an expected value of zero (or cost their expected values) are called actuarially fair gamesa common observation is that people often refuse to participate in actuarially fair gamesFair GamesPeople are generally unwilling to play fair gamesThere may be a few exceptionswhen very small amounts of money are at stakewhen there is utility derived from the actual play of the gamewe will assume that this is not the caseSt. Petersburg ParadoxA convincing example is the “St. Petersburg paradox,” which was first investigated rigorously by the mathematician Daniel Bernoulli in the eighteenth century.A coin is flipped until a head appearsIf a head appears on the nth flip, the player is paid $2nx1 = $2, x2 = $4, x3 = $8,xn = $2nThe probability of getting of getting a head on the ith trial is ()i1=, 2= , n= 1/2nSt. Petersburg ParadoxThe expected value of the St. Petersburg paradox game is infiniteBecause no player would pay a lot to play this game, it is not worth its infinite expected valueExpected UtilityIndividuals do not care directly about the dollar values of the prizesthey care about the utility that the dollars provideIf we assume diminishing marginal utility of wealth, the St. Petersburg game may converge to a finite expected utility valuethis would measure how much the game is worth to the individualExpected UtilityExpected utility can be calculated in the same manner as expected valueBecause utility may rise less rapidly than the dollar value of the prizes, it is possible that expected utility will be less than the monetary expected valueThe von Neumann-Morgenstern TheoremSuppose that there are n possible prizes that an individual might win (x1,xn) arranged in ascending order of desirabilityx1 = least preferred prize U(x1) = 0xn = most preferred prize U(xn) = 1The von Neumann-Morgenstern TheoremThe point of the von Neumann-Morgenstern theorem is to show that there is a reasonable way to assign specific utility numbers to the other prizes available这样，我们就可以给各种收益以一个特定的效用值。事实上，VM就是将Xi的效用定义为一个个体认为的等价于Xi的一个游戏的期望效用。The von Neumann-Morgenstern TheoremThe von Neumann-Morgenstern method is to define the utility of xi as the expected utility of the gamble that the individual considers equally desirable to xiU(xi) = i U(xn) + (1 - i) U(x1)The von Neumann-Morgenstern TheoremSince U(xn) = 1 and U(x1) = 0U(xi) = i 1 + (1 - i) 0 = iThe utility number attached to any other prize is simply the probability of winning itNote that this choice of utility numbers is arbitraryThe von Neumann-Morgenstern Theorem个人总是对于一个有风险的游戏和一个确定的收益之间是无差异的，前提是只要提供给他足够高的可能得到最好收益的概率；这样， i越高，对于xi 的欲望就越大。而xi越好，就必须给予个人更大的机会赢得xn，才能使他参加游戏。事实上，概率i就代表了个人对于xi 的欲望程度。The von Neumann-Morgenstern TheoremU(xi) = i 1 + (1 - i) 0 = i通过把特定的效用赋予最好与最坏的结果，我们就可以将效用数值赋予到任何的收益水平去，它就是等于个人认为等价于当前收益的一个游戏中的获得最好结果的概率。Expected Utility MaximizationA rational individual will choose among gambles based on their expected utilities (the expected values of the von Neumann-Morgenstern utility index)Expected Utility MaximizationConsider two gambles:first gamble offers x2 with probability q and x3 with probability (1-q)expected utility (1) = q U(x2) + (1-q) U(x3)second gamble offers x5 with probability t and x6 with probability (1-t)expected utility (2) = t U(x5) + (1-t) U(x6)Expected Utility MaximizationSubstituting the utility index numbers givesexpected utility (1) = q 2 + (1-q) 3 expected utility (2) = t 5 + (1-t) 6 The individual will prefer gamble 1 to gamble 2 if and only ifq 2 + (1-q) 3 t 5 + (1-t) 6 Expected Utility MaximizationIf individuals obey the von Neumann-Morgenstern axioms of behavior in uncertain situations, they will act as if they choose the option that maximizes the expected value of their von Neumann-Morgenstern utility index.Risk AversionTwo lotteries may have the same expected value but differ in their riskinessflip a coin for $1 versus $1,000Risk refers to the variability of the outcomes of some uncertain activityWhen faced with two gambles with the same expected value, individuals will usually choose the one with lower risk.Risk AversionIn general, we assume that the marginal utility of wealth falls as wealth gets largera flip of a coin for $1,000 promises a small gain in utility if you win, but a large loss in utility if you losea flip of a coin for $1 is inconsequential as the gain in utility from a win is not much different as the drop in utility from a lossRisk AversionUtility (U)Wealth (W)U(W)U(W) is a von Neumann-Morgensternutility index that reflects how the individualfeels about each value of wealthThe curve is concave to reflect theassumption that marginal utilitydiminishes as wealth increasesRisk AversionUtility (U)Wealth (W)U(W)Suppose that W* is the individuals currentlevel of incomeW*U(W*) is the individualscurrent level of utility U(W*)Risk AversionSuppose that the person is offered two fair gambles:a 50-50 chance of winning or losing $hUh(W*) = U(W* + h) + U(W* - h)a 50-50 chance of winning or losing $2hU2h(W*) = U(W* + 2h) + U(W* - 2h)Risk AversionUtility (U)Wealth (W)U(W)W*U(W*)The expected value of gamble 1 is Uh(W*)Uh(W*)W* + hW* - hRisk AversionUtility (U)Wealth (W)U(W)W*U(W*)W* + 2hW* - 2hThe expected value of gamble 2 is U2h(W*)U2h(W*)Risk AversionUtility (U)Wealth (W)U(W)W*U(W*)W* + 2hW* - 2hU(W*) Uh(W*) U2h(W*)U2h(W*)Uh(W*)W* - hW* + hRisk AversionThe person will prefer current wealth to that wealth combined with a fair gambleThe person will also prefer a small gamble over a large oneRisk Aversion and InsuranceThe person might be willing to pay some amount to avoid participating in a gambleThis helps to explain why some individuals purchase insurance想一想风险中立者与风险爱好者的财富效用曲线应该是什么样子？Risk Aversion and insuranceUtility (U)Wealth (W)U(W)W*U(W*)Uh(W*)W* - hW* + hThe individual will bewilling to pay up toW* - W ” to avoidparticipating in thegamble W ” provides the same utility asparticipating in gamble 1W ”Risk Aversion and InsuranceAn individual who always refuses fair bets is said to be risk aversewill exhibit diminishing marginal utility of incomewill be willing to pay to avoid taking fair betsWillingness to Pay for InsuranceConsider a person with a current wealth of $100,000 who faces a 25% chance of losing his automobile worth $20,000Suppose also that the persons von Neumann-Morgenstern utility index isU(W) = ln (W)Willingness to Pay for InsuranceThe persons expected utility will beE(U) = 0.75U(100,000) + 0.25U(80,000)E(U) = 0.75 ln(100,000) + 0.25 ln(80,000)E(U) = 11.45714In this situation, a fair insurance premium would be $5,000 (25% of $20,000)E(U) = U(100,000 - 5000)=ln（95000）=11.46163（此人愿意购买这个保险）Willingness to Pay for InsuranceThe individual will likely be willing to pay more than $5,000 to avoid the gamble. How much will he pay?E(U) = U(100,000 - x) = ln(100,000 - x) = 11.45714100,000 - x = e11.45714x = 5,426The maximum premium is $5,426Measuring Risk AversionThe most commonly used risk aversion measure was developed by Pratt（J.W Pratt 1960s）For risk averse individuals, U”(W) 0r(W) will be positive for risk averse individualsr(W) is not affected by which von Neumann-Morganstern ordering is used即线性变换不影响风险类型U”(W) 0风险爱好者U”(W) = 0风险中立者EU(W)U E(W) 风险爱好者EU(W)=U E(W) 风险中立者（将参与任何具有正的期望值的博弈活动）Measuring Risk AversionThe Pratt measure of risk aversion is proportional to the amount an individual will pay to avoid a fair gambleMeasuring Risk AversionLet h be the winnings from a fair betE(h) = 0Let p be the size of the insurance premium that would make the individual exactly indifferent between taking the fair bet h and paying p with certainty to avoid the gambleEU(W + h) = U(W - p)Measuring Risk AversionWe now need to expand both sides of the equation using Taylors seriesBecause p is a fixed amount, we can use a simple linear approximation to the right-hand sideU(W - p) = U(W) - pU(W) + higher order termsMeasuring Risk AversionFor the left-hand side, we need to use a quadratic approximation to allow for the variability of the gamble (h)EU(W + h) = EU(W) - hU(W) + h2/2 U”(W)+ higher order termsEU(W + h) = U(W) - E(h)U(W) + E(h2)/2 U”(W)+ higher order termsMeasuring Risk AversionRemembering that E(h)=0, dropping the higher order terms, and substituting k for E(h2)/2, we get上式表明，风险厌恶者为了避免公平博弈所愿意支付的费用大致与The Pratt measure of risk aversion 成比例。因为在现实世界中，支付的保险费用是可观察的，所以它常常被用来当作评估个人的风险厌恶系数，或者比较个人之间的风险厌恶程度。因此，可以通过市场信息获取一点个人对于风险的态度，量化一个人对于风险厌恶的程度。Risk Aversion and WealthIt is not necessarily true that risk aversion declines as wealth increasesdiminishing marginal utility would make potential losses less serious for high-wealth individualshowever, diminishing marginal utility also makes the gains from winning gambles less attractivethe net result depends on the shape of the utility functionRisk Aversion and WealthIf utility is quadratic in wealthU(W) = a + bW + cW 2 where b 0 and c 0Pratts risk aversion measure isRisk aversion decreases as wealth increasesRisk Aversion and WealthIf utility is exponentialU(W) = -e-AW = -exp (-AW) where A is a positive constantPratts risk aversion measure isRisk aversion is constant as wealth increasesRelative Risk AversionIt seems unlikely that the willingness to pay to avoid a gamble is independent of wealthA more appealing assumption may be that the willingness to pay is inversely proportional to wealthRelative Risk AversionThis relative risk aversion formula isRelative Risk AversionThe power utility functionU(W) = WR/Rfor R 1, 0 exhibits diminishing absolute relative risk aversion but constant relative risk aversionAn Example: Buying Insurance (I)Suppose there is a bad event (e.g. a fire)with a probability p of occurring.If this bad event occurs, you will lose ddollars.If your current wealth is w, what is yourexpected utility?An Example: Buying Insurance (II)Now suppose someone is selling insurance against this event happening.How much insurance should you buy?This depends on the price of the insurance!How Insurance Works$1 of insurance costs q (q p? Then insurers make aprofit.u(yb)u(yg)yb ygHow did we get the last step?Expensive Insurance (II)Since , yb yg you are not fully insuring against risk. So x p? Not very realistic, as then insurers are losing money.u(yb) ygStrange.Cheap Insurance (II)Here you are actually over-insuring. You want your house to burn down!Since q p buying insurance is like taking a bet with a positive expected payoff.The insurance companys loss is your gain.So after you fully insure, you happily take (some of) this bet on top of the insurance.The State-Preference ApproachThe approach taken in this chapter up to this point is different from the approach taken in other chaptershas not used the basic model of utility-maximization subject to a budget constraintThere is a need to develop new techniques to incorporate the standard choice-theoretic frameworkStates of the WorldOutcomes of any random event can be categorized into a number of states of the world“good times” or “bad times”Contingent commodities are goods delivered only if a particular state of the world occurs“$1 in good times” or “$1 in bad times”States of the WorldIt is conceivable that an individual could purchase a contingent commoditybuy a promise that someone will pay you $1 if tomorrow turns out to be good timesthis good will probably cost less than $1 Utility AnalysisAssume that there are two contingent goodswealth in good times (Wg) and wealth in bad times (Wb)individual believes the probability that good times will occur is Utility AnalysisThe expected utility associated with these two contingent goods isV(Wg,Wb) = U(Wg) + (1 - )U(Wb)This is the value that the individual wants to maximize given his initial wealth (W)Prices of Contingent CommoditiesAssume that the person can buy $1 of wealth in good times for pg and $1 of wealth in bad times for pbHis budget constraint isW = pgWg + pbWbThe price ratio pg /pb shows how this person can trade dollars of wealth in good times for dollars in bad timesFair Markets for Contingent GoodsIf markets for contingent wealth claims are well-developed and there is general agreement about , prices for these goods will be actuarially fairpg = and pb = (1- )The price ratio will reflect the odds in favor of good timesRisk AversionIf contingent claims markets are fair, a utility-maximizing individual will opt for a situation in which Wg = Wbhe will arrange matters so that the wealth obtained is the same no matter what state occursRisk AversionMaximization of utility subject to a budget constraint requires thatIf markets for contingent claims are fairSince the market for contingentclaims is actuarially fair, theslope of the budget constraint = -1Risk Aversioncertainty lineWgWbWg*Wb*U1The individual maximizes utility on thecertainty line where Wg = WbIf the market for contingentclaims is not fair, the slope ofthe budget line -1Risk Aversioncertainty lineWgWbU1In this case, utility maximization may not occur on the certainty lineInsurance in the State-Preference ModelAgain, consider a person with wealth of $100,000 who faces a 25% chance of losing his automobile worth $20,000wealth with no theft (Wg) = $100,000 and probability of no theft = 0.75wealth with a theft (Wb) = $80,000 and probability of a theft = 0.25Insurance in the State-Preference ModelIf we assume logarithmic utility, thenE(U) = 0.75U(Wg) + 0.25U(Wb)E(U) = 0.75 ln Wg + 0.25 ln WbE(U) = 0.75 ln (100,000) + 0.25 ln (80,000)E(U) = 11.45714Insurance in the State-Preference ModelThe budget constraint is written in terms of the prices of the contingent commoditiespgWg* + pbWb* = pgWg + pbWbAssuming that these prices equal the probabilities of these two states0.75(100,000) + 0.25(80,000) = 95,000The expected value of wealth = $95,000Insurance in the State-Preference ModelThe individual will move to the certainty line and receive an expected utility of E(U) = ln 95,000 = 11.46163to be able to do so, the individual must be able to transfer $5,000 in extra wealth in good times into $15,000 of extra wealth in bad timesa fair insurance contract will allow thisthe wealth changes promised by insurance (dWb/dWg) = 15,000/-5,000 = -3A Policy with a DeductibleSuppose that the insurance policy costs $4,900, but requires the person to incur the first $1,000 of the lossWg = 100,000 - 4,900 = 95,100Wb = 80,000 - 4,900 + 19,000 = 94,100E(U) = 0.75 ln 95,100 + 0.25 ln 94,100E(U) = 11.46004The policy still provides higher utility than doing nothingRisk Aversion and Risk PremiumsConsider two people, each of whom starts with an initial wealth of W*Each seeks to maximize an expected utility function of the formThis utility function exhibits constant relative risk aversionRisk Aversion and Risk PremiumsThe parameter R determines both the degree of risk aversion and the degree of curvature of indifference curves implied by the functiona very risk averse individual will have a large negative value for R U2A person with more tolerance for risk will have flatter indifference curves such as U2U1A very risk averse person will have sharply curvedindifference curves such as U1Risk Aversion and Risk Premiumscertainty lineWgWbW*W*U2U1Suppose that individuals are faced with losing h dollars in bad timesRisk Aversion and Risk Premiumscertainty lineWgWbW*W*The difference between W1 and W2 shows the effect of risk aversion on thewillingness to accept riskW* - hW2W1Important Points to Note:In uncertain situations, individuals are concerned with the expected utility associated with various outcomesif they obey the von Neumann-Morgenstern axioms, they will make choices in a way that maximizes expected utilityImportant Points to Note:If we assume that individuals exhibit a diminishing marginal utility of wealth, they will also be risk aversethey will refuse to take bets that are actuarially fairImportant Points to Note:Risk averse individuals will wish to insure themselves completely against uncertain events if insurance premiums are actuarially fairthey may be willing to pay actuarially unfair premiums to avoid taking risksImportant Points to Note:Decisions under uncertainty can be analyzed in a choice-theoretic framework by using the state-preference approach among contingent commoditiesif preferences are state independent and prices are actuarially fair, individuals will prefer allocations along the “certainty line”will receive the same level of wealth regardless of which state occurs第十二讲博弈论博弈论简介在每个博弈中，至少有两个参与者。他们的决策相互依存，相互作用。任何参与者的决策都是受到其他参与者的决策的影响的，任何参与者在制订自己的决策时都要考虑其他参与者的决策的。我们假定每个参与者都是理性的决策者，他们所有的行为都只是为了自己的利益。而且，他们也认为其他参与者也是理性的。博弈有多种类型，它有两个重要的特征：相关参与者的人数；博弈阶段数。根据这两个特征，我们区分不同的博弈类型。两个参与者N个参与者（N2）一个阶段协调博弈拍卖M个阶段（M2） 进入博弈重复剔除囚徒困境协调博弈我们从两个参与者的博弈开始。在这个博弈中，博弈的双方只博弈一次，只有一个阶段。它的主要问题是参与者怎样才能协调他们的行为，因此，我们叫它协调博弈。协调博弈介绍了同步博弈和继起博弈的区别。为了得到各自最好的结果，参与者不得不协调他们的决策。假设菲利浦公司和索尼公司要决定一项新的电子技术的标准化，比如说视频和光盘结合的技术，我们称它叫视频光盘技术。这两家公司都在为实现这一突破而努力。有两种可供选择的体系类型。如果他们选择了同样的体系，我们假设这时消费者从菲利浦公司购买的价格是A，而从索尼公司购买的价格是B，反过来，如果他们选择了不同的体系，则价格分别是C和D。我们说A和B的价格一定高于C和D。原因很简单，如果他们选择了不同类型的技术体系，那么新产品的价格竞争不仅仅在于消费者要选择不同的品牌，还在于消费者要选择不同的技术体系，这时的价格竞争更加激烈，自然更低。换句话说，他们选择了同样类型的技术体系时，每个企业利润更多。与DISC技术相比，VI技术对他们双方都有更高的盈利。VI技术对他们的吸引力是DISC的两倍。下面的图可以代表这个例子的博弈特点。图中的数字表示参与者双方的获利，第一个数字始终指行参与者的获利，第二个数字始终指列参与者的获利。获利指在博弈的最后使参与者的报酬。那么，最后到底是什么结果呢？这取决于博弈的方式。VIDISCVI4,4-2,-2DISC-2,-22,2索尼公司菲利浦公司如果博弈双方必须同时做出选择，没有任何关于另一方偏好的信息，那么他们将无法做出任何的预计。这种情况的原因是参与者彼此不清楚彼此会怎样假设另一方的做法。如果菲利浦能够预计索尼会选择DISC，那么它就会被诱惑也选择DISC。如果一个参与者被允许在另一方行动之后再采取行动，我们就可以预言两个公司会选择同样的技术。这是因为，对第二个参与者来说，跟随第一个参与者的行动永远是最有利的选择。假设菲利浦必须先采取行动，那么索尼一定会观察它的行动并采取同样的行动。我们也可以把这个博弈用博弈树的形式表示出来。这里的博弈树与前面的决策树所不同的是，在博弈树中有两个参与者，而决策树中只有一个。在博弈树节点的最后，有两个数字，前一个代表先采取行动一方的盈利。ABCVIDISCVIVIDISCDISC（4,4）（2,2）（-2,-2）（-2,-2）菲利浦索尼索尼菲利浦先采取行动。它会采取什么行动呢？假设所需的信息没有问题，负责制订决策的菲利浦的经理会查看博弈树。他会发现索尼会在节点B选择VI，在节点C选择DISC。也就是说，他会发现无论他选择了什么，索尼都会做出和他同样的选择。在这个博弈中，有一点非常重要，那就是其中一个参与者被允许可以先采取行动。在继起博弈里，参与者双方协调彼此的选择是很容易的。而在同步博弈里要观察参与者双方是如何协调选择则是根本不可能的。什么时候的博弈是同时博弈？真的需要参与者双方在同一时间做出选择吗？当然不需要。参与者双方可以在不同的时间做出选择。关键是当一方选择的时候不知道另一方做出了什么选择或者将会做出什么选择。信息不足使同时博弈和继起博弈区分开来。在这个博弈中，菲利浦在他们做出选择之后把他们的选择告诉索尼，这是菲利浦的利益所在。对于索尼来说，他们没有理由不相信从菲利浦得到的这一信息。所以用继起博弈来描述现实中的这种博弈比用同时博弈更加合适。继起可以用矩阵列表表示，也可以用博弈树表示。下图与前面的图非常相似，除了环绕索尼两个节点的椭圆。这个椭圆代表索尼的信息设置。它指明一个事实：当索尼要知道决策的时候，它是不能区分这两个节点的情况的。因为信息不足，这种博弈是不能预测的。ABCVIDISCVIVIDISCDISC（4,4）（2,2）（-2,-2）（-2,-2）菲利浦索尼索尼协调博弈是一种非常简单的博弈。如果只有两个参与者，那么只要这两个参与者之间进行沟通，就可以得到最好的解决方案。如果参与者的数量增多，那么就有必要制订一个规则。当然，如果是反复出现同样情形的博弈，行为人也会努力寻求一定规范的制订。这里有一个例子，汽车应该在公路的哪一边行驶。在一个国家如果只有两个汽车所有者，那么政府就没有必要制订一个规则，这两个汽车所有者之间会很容易达成一致。如果汽车所有者的数量很大，那么他们彼此之间要达成一致就会很困难，并且成本很高。在这种情况下，政府就应该出面制订一个规则，建立一个秩序。乐队演奏的例子。这一节举例说明了博弈论的两个特点，这在组织经济学的研究中是至关重要的。第一个特点是同时博弈和继起博弈是相区别的。在继起博弈中，第一个参与者的行动能够为第二个参与者观察到，协调是很容易实现的。第二个参与者决策的基础是获得了第一个参与者的信息。相反地，同时博弈的信息是不足的，因此它也是不能预测的。第二个特点是两个参与者或者少量参与者是如何通过相互调节实现协调的。但是因为参与者的决策是互相依赖的，这种协调机制会因为参与者的增加而崩溃。这时它就必须由其它协调机制所代替。进入博弈这就是两阶段博弈。进入博弈是指垄断者和潜在进入者之间的继起博弈。首先假定垄断者限制产出和维持垄断高价。这正给了潜在进入者进入该行业的机会。我们先从一阶段来分析这种情况，然后再从两阶段博弈来分析。假设有两家移动电讯公司，一家叫移动公司，一家叫联通公司，移动公司已经先存在于这个市场，联通公司是否应该进入呢？因为是一阶段博弈，假设我们让联通公司先采取行动。它知道移动公司收取了一个相对较高的价格。它也知道在它进入市场之后，如果移动公司保持这一价格，它能够获取可观的利润。但是，如果它在其进入以后降低了自己的价格，则它不一定有利润。联通公司会怎样做呢？假设联通公司非常清楚移动公司在每一种情境下的获利情况，我们可以用下面这个博弈树来说明其面临的选择。联通公司移动公司移动公司进入不进入高价低价低价高价（4,6）（1,2）（0,16）（0,7）联通公司的决策依赖于移动公司在它进入该市场以后所从选择的价格水平。所以它会尽力预测移动公司地它进入市场之后的动作。当其不进入时，移动公司一定选择高价，获得较高的利润。当其选择进入的时候，如果移移动公司是一个理性的参与者（公司是一个理性的参与者（绝对利益利益还是相是相对利益）利益），而且如果联通公司知道它是一个理性的参与者，那么，它能够预测移动公司在它进入以后依然选择高价，于是它就选择进入这个行业。这说明了一个解决继起博弈问题的一个重要法则，就是前瞻后溯法则。通过前瞻后溯，联通公司可以做出预测进入该市场获利。那么，移动公司有没有办法可以阻止联通的进入呢？假设移动在联通制订决策之前威胁在其进入以后选择低价。如果联通相信了它的威胁，它就不会进入。因为选择低价会使联通亏损。但是联通很可能不相信移动的威胁，毕竟，一旦进入已经成为事实了，低价不是移动的利益所在。所以，我们说，移动公司的威胁不是一个可置信威胁。但是，在现实中，可能会出现这样的情况。在联通进入之前，移动已经拥有一个相对庞大的运营网络。如果联通选择进入，移动可以降低价格，虽然其固定成本很高，但是其可变成本很低，可以吸引更多的新客户。所以，一旦进入已经成为事实了，移动实行低价实际上会实现更好的利润。下图就是这种情况的一个修正。联通公司移动公司移动公司进入不进入高价低价低价高价（4,2）（1,4）（0,10）（0,6）在这种新的情况下，移动公司的威胁是一个可置信威胁。如果移动公司只是拥有一个小网络会发生什么？而如果拥有一个大网络又会发生什么？如果移动先在建立小网络还是大网络之间做出选择，它会怎样选择？这就是一个两阶段继起博弈。下面的决策树就是一个结合了前面两个图的博弈树的大博弈树。移动小网络大网络联通联通进入进入不进入不进入移动移动移动移动高价高价高价高价低价低价低价低价（4,6）（0,16）（0,7）（4,2）（1,4）（0,10）（0,6）（1,2）AGFEDCB移动究竟会怎样选择？联通针对移动的网络选择会怎样选择？移动又会给予怎样的反应？回答这些问题可以使用前瞻后溯法则。在节点D和E，移动会选择高价政策。所以，在节点B联通会选择进入。在节点F移动会选择低价政策，而在G选择高价政策，联通知道这一信息，所以在节点C联通会决定不进入。现在，移动知道了这一信息：如果它选择小网络，那么联通就会决定进入，这样它的获利是6；如果它选择大网络，那么联通就不会进入，这样它的获利是10。所以，为了阻止联通的进入，移动决定建立大网络。这个例子的关键在于，通过建立大网络，移动可以在其他竞争者进入市场时降低价格。用博弈论的语言来说就是：承承诺是一是一个一方参与者可以个一方参与者可以预先改先改变其收益的其收益的过程，程，这样它就可以从它自身的利益出它就可以从它自身的利益出发给其他其他参与者一个威参与者一个威胁。在这个例子中，移动通过建立大网建立大网络改改变了它的利益了它的利益，这样在联通进入市场之后，它就可以从它自身的利益出发，用低价策略来威胁对方。因此，这种承诺使得移动的威胁成为可置信威胁。在继起博弈里你要预测你的竞争对手的反应。这一点你可以通过使用前瞻后溯法则分析博弈树的办法进行，即使博弈包括多个阶段。威胁可以通过承诺成为可置信威胁。通过承诺行为，一方参与者可以让另一方参与者知道实践践这一威一威胁是它的利益所在是它的利益所在。为了使其更加有效，承诺必须可以被另一方观察到察到并且必须是可置信的。拍卖一个阶段，两个参与者的博弈。一个典型的例子就是拍卖。拍卖的形式有很多种，其中重要的是公开式拍卖和标单密封式拍卖。前者指所有的投标者都能看到投标价格的拍卖方式，后者指只有拍卖商能看到投标者投标价格的方式。我们再一次看到信息的可信息的可观察性察性起了关键的作用。比如在对于一块土地的拍卖，注意在整个竞标过程中，你会获得关于这块土地对其他竞标者的最大价值的信息。在竞标开始以后你可以通过观察哪些竞标者仍在参与竞标，哪些退出了，以此来获得关于这块土地对其他竞标者的最大价值的信息。竞标的过程迫使竞标者表现出他们的偏好。但是，从拍卖商的角度来看，这种“渐升式拍卖”并不是完全最优的拍卖方式。为了抓住这一点，设想你是所有竞标者中坚持到最后的两位中之一。这两位中的一位拥有这块土地的最高价值。可是这时候另一位竞标者是要比你先一步退出竞争的，一旦价格超过了这块土地所能为他创造的最大价值他就会马上退出。但是这一价格还远远低于它为你所创造的最大价值。这对拍卖商而言是不利的。拍卖商抵御这种风险的策略还是很多的。其中最有趣的一种就是使用“荷兰式拍卖”代替这种渐升式拍卖，荷兰式拍卖也叫渐降式拍卖。拍卖人是从一个很高的价格开始拍卖的，在拍卖人眼中这一价格远远高于所有竞标者的最高私人价值。只要有人喊出“我要”，拍卖立即停止。这时，每个竞标者并不知道其他人会有怎样的报价。在这种拍卖方式中，拍卖商至少获得了来自拥有最高使用价值的竞标者和拥有第二高使用价值的竞标者之间的差价的一部分。但是，对于拍卖商来说仍然存在着风险：在渐升式拍卖中，拍卖人是从一个较低的价格开始拍卖的，而在这里，这个最低价是不存在的。为了建立一个最低价格，拍卖人可以把拍卖活动从一个一阶段博弈变成两阶段博弈。在第一阶段使用渐升式拍卖，获胜者获得一定的报酬，但是还不能最后得到标的。随后进入第二阶段的拍卖，使用荷兰式拍卖。通常第一阶段的竞标获胜者只是为了获得第一阶段的报酬，而并无意于真正获得标的物。这种公开式拍卖的特点：这种博弈是有私人信息的。这些私人价值中的绝大部分在博弈开始的时候就成为公开的信息了。在渐升式拍卖中，获胜者的信息也是唯一能够最终被公开的。这种博弈的设计决定了参与者公开他们的私人信息的动机。通过增加第二阶段的荷兰式拍卖，拍卖商试图诱惑潜在的购买者在第一阶段的最终价格之上公开他们的私人信息。这里的私人信息是有价的拍卖商为了把这种设计付诸实施准备支付给第一阶段的胜出者一个价格。一阶段标单密封式拍卖中，所有的竞标者必须在同一时间把他们的竞价密封在一个信封里。与公开拍卖方式的区别就是在拍卖过程中你无法获得其他人的私人信息。竞标者只有一次机会，在其他参与者的私人信息不确定的条件下，把自己的报价密封于一个信封之内。如果你是最高价值的战略竞标者，你报价的原则就是只要高出第二高价值的战略竞标者的报价就可以了。你必须考虑第二高价值的战略竞标者可能的报价是多少。在许多竞标者激烈竞争的情况下，最终的胜出者往往是估计最乐观的人。不过，这既是好消息又是坏消息。好消息是因为你得到了最后标的，坏消息是你可能最乐观地估计了竞争对手，而实际上没有那么乐观。在博弈论里这种现象被称为“赢家的诅咒”。它是指赢家中标并不是因为他的价值是最高的，而是因为他做了过于乐观的估计。公开拍卖与标单密封式拍卖之间的主要的区别在于其他参与者的私人信息不确定性。拍卖方式的设计很大程度上决定了拍卖的结果。拍卖的结果还取决于竞标者的人数、拍卖标的的数目以及其他的一些规则。囚徒困境经典的博弈论模型。我们先从两个游戏人来说明它的基本结构，然后再进一步讨论有两个或者多个参与者的重复博弈囚徒困境，目的是为了说明单次博弈和重复剔除博弈之间的区别。单次博弈囚徒困境不坦白坦白不坦白3，3 6，1坦白1，6 5，5AB对于任何一方来说，他们面临着这样的选择，即不论对方做出什么选择，自己的最佳选择是坦白。以博弈论的语言来说，双方都有一个占优策略：无论其他参与者采取什么策略，某参与者有惟一的最优策略。想一想，囚徒困境与协调博弈之间的区别是什么？合作背叛合作R，RN，T背叛T，NP，P行列R合作的报酬。N守信的收益。T背叛的诱惑。P互相背叛的惩罚。如果在每一个参与者可能得到的四种结果中存在某种关系，那么上图所表示的博弈就是一个囚徒困境。这种关系是：NPRT。当NP时，它表示如果列参与者背叛他的诺言，那么行参与者最好的选择也是选择背叛。当PR时，它表示互相背叛的收益低于互相合作的收益。当RT时，它表示如果一个参与者坚守诺言，那么另一个参与者最好背叛诺言（由于背叛的诱惑）。囚徒困境的基本问题是：对于每一个参与者来说占优策略都是背叛诺言，而其实互相合作的话他们的收益才是最大的。实际上像囚徒困境这样的情况有很多。OPEC的例子。美苏军备竞赛的例子。合作背叛合作3，30，5背叛5，01，1多个参与者的重复剔除囚徒困境假设那两个自私、理性的参与者进行了多次囚徒困境博弈，这就是重复剔除囚徒困境。在其中，每一个参与者都必须在每一轮博弈中在合作与背叛之间进行选择。在选择的过程中每个参与者都可以参考其他参与者在上一轮中所做的选择。在重复博弈中策略被定义为一套规则，用来详细说明自博弈论产生以来至今所有的可能被采取的行动。为了说明重复剔除囚徒困境策略的概念，下面我们给出几个例子。一报还一报策略（针锋相对策略）你在第一轮对局中选择了合作，那么你在以后的每一轮对局中都要跟随上一轮其他参与者的选择。终极报复策略你在第一轮对局中选择了合作，无论其他参与者在哪一轮选择了背叛，你以后的每一轮对局中都选择背叛。总是选择D策略无论其他参与者选择什么，你总是选择背叛。总是选择C策略无论其他参与者选择什么，你总是选择合作。随机策略你对合作还是背叛的选择是随机的，可以通过扔硬币来决定。一报还一报附加策略你在第一轮选择了合作，那么在下面的对局中，如果其他参与者在前一轮中选择了合作，则你选择合作的概率是1，你选择背叛的概率是；如果其他参与者在前一轮中选择了背叛，则你也选择背叛。两轮之后一报还一报策略你在前两轮对局中选择了合作；如果其他参与者在前两轮中都选择了背叛，那么在下一轮对局中你选择背叛，而不是继续选择合作。奇数策略在第一轮对局和以后所有的奇数轮对局中你都选择合作，而在偶数对局中选择背叛。Axelrod 在1984年对重复剔除博弈囚徒困境进行了调查研究。在世界的绝大多数情况下永久的互相合作比轮番的互相剥削要好。在重复剔除博弈囚徒困境中可以表示为0.5（NT）R合作背叛合作3，30，5背叛5，01，1根据他的实验结果显示，竞赛最终获胜的都是一报还一报策略。其有很多特征可以解释它的成功。1、一报还一报策略是善良的。其意味着不首先背叛。2、一报还一报是宽容的。这意味着如果其他参与者只背叛了一次，那么也只是惩罚他一次，重新开始合作，既往不咎。这一点完全不象终极报复策略。3、一报还一报还是现时现报的。如果其他参与者选择了背叛，一报还一报会马上对它进行惩罚。由于这些原因，要想战胜一报还一报的策略是很困难的。Axelrod的实验结果很好地说明了两个自私、理性的参与者是如何在重复剔除博弈中成功实现合作的，即使他们没有彼此许诺（他们根本不信任彼此会坚守承诺）。这包含了组织成员合作方式的一个重要结果。在重复剔除博弈中，参与在重复剔除博弈中，参与者可以投者可以投资建立自己的信誉，建立自己的信誉，值得依得依赖的的信誉和信誉和坚持合作的信誉有助于持合作的信誉有助于实现合作，合作，即使是在囚徒困境中的不利情况下。即使是在囚徒困境中的不利情况下。在重复博弈之中，都有一个持续的学习过程，在此过程中，博弈的参与者学习他们能够从别人那里期待的行为类型，并建立起一组共同遵循的行为规范。正是在这些共同建立起来的规范的基础上，一个为每个参与者规定了冲突状态下的行为的社会惯例或制度被建立起来。 刚才的发言，如刚才的发言，如有不当之处请多指有不当之处请多指正。谢谢大家！正。谢谢大家！475