1、1,第一讲 经济理论的基础,Nicholson. Chapter 1 pp.1-20,2,决策行为的模型化,经济学通常被定义为“在一个稀缺性的环境之下的理性选择行为研究”，但是从我们的课本内容来看，往往并不能看到这一点，经济学在其中似乎只能被定义为“在一个变化的环境中对于市场交易和市场行为的研究”。 近一个世纪以来，经济学的研究方法虽然已经取得了很大的进步，但是结论似乎并没有多大的变化。,3,但在另一方面，个人主义方法论在其他社会科学领域的推广应用却给我们带来了很大的收获。而这些推广应用的基石正是经济学的基本逻辑：“理性人”在自利本性下的选择。 我们在课堂中学习的主要是经济学的分析方法。掌握了
2、这套方法和逻辑，日后我们可以运用它分析任何选择行为。因此，经济学的适用性远远超出了经济学本身的领域。或者说，经济学的研究领域已经不再是传统上认识的范畴了。,4,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.
3、 Politicians, status seekers, altruists and criminals are all seen as rational decision makers pursuing well-defined goals in a setting of scarcity.,5,The purpose of the Micro sequence it to provide you with a core set of tools (ideas, intuitions, mathematical models, and aptitude for interpreting t
4、he 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.),6,经济学分析的基本逻辑,经济学总
5、是假定人们在做出某种选择行为，特别是，我们往往总是假定他们在把什么东西力图最大化（最优化）。因此，几乎所有的决策选择都可以被模型化为一个最大化的问题。 A. 在任一决策行为中，你有选择的权利，这些选择就可以对应于最优化问题中的变量（variables）。,7,B. 你当然想做出最优的选择（optimal choice）。这就意味着你试图为你的变量选择一个值，从而使其最大化某种函数（function）目标函数。 C. 你的选择或许会随着某些情况的变化而变化，你必须依赖于某些情况做出决定，而这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服。所以我们必须要特别列明一些情况做为
6、选择的条件，这些条件就是最优化问题的参数（parameter）。(包络定理),8,D. 一旦你建构了一个特定情况下的模型，你就可以估计出个人（理性主体）到底会做出什么样的选择决策。 在最优化问题中，这就意味着我们找到了参数函数中变量的最优值。 E. 一旦特定的环境发生了改变，即参数变化了，那么变量的最优值也会跟着改变，这就是比较静态（comparative statics），比如需求的改变（不同于需求量的改变）。,9,F. Ceteris Paribus means “other things the same” Economic models attempt to explain simpl
7、e relationships focus on the effects of only a few forces at a time other variables are assumed to be unchanged during the period of study,10,人不能两次跳进同一条河中 人不能一次跳进同一条河中 如果所有的事情都在变化，就会陷于不可知论的泥潭，世界就无法认识了。 经济模型试图从纷繁复杂的经济世界中，抽丝剥茧，找到其所关心的主要变量之间是在存在着内在关系，因此，一次只能研究一种或几种变量的相互关系，且此时其他变量保持不变。,11,G. 经济命题的“可证伪性”
8、 （falsification）是命题科学性的关键所在（Karl Popper）。 There are two general methods used to verify economic models: direct approach establishes the validity of the models assumptions indirect approach shows that the model correctly predicts real-world events,12,Suggested Readings,Nagel, Ernest. “Assumptions in
9、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.,13,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,14,关于税收的两种常见的误解： 1、征
10、税1￥并不是商品价格上涨1￥； 2、政府提高消费税1￥并不是消费者购买商品时多付出1￥。 一、无论是征税还是补贴，都一定是在需求者与供给者之间进行分担（分摊）的，而且，这种分摊效应与征税或者补贴直接面对的对象到底是哪一方无关。 二、这种分担的效应取决于供求曲线的形状，尤其是它们两者之间的相对弹性的大小。,15,The Impact of a Tax or Subsidy,The burden of a tax (or the benefit of a subsidy) falls partly on the consumer and partly on the producer. We wil
11、l consider a specific tax （从量税）which is a tax of a certain amount of money per unit sold.,16,Incidence of a SpecificTax,Quantity,Price,Pb - PS = tax,17,Incidence of a Specific Tax,Four conditions that must be satisfied after the tax is in place:1) Quantity sold and Pd must be on the demand line: QD
12、= QD(Pd)2) Quantity sold and PS must be on the supply line: QS = QS(PS),18,Incidence of a Specific Tax,Four conditions that must be satisfied after the tax is in place:3) QD = QS 4) Pd - PS = tax,19,Impact of a Tax Depends on Elasticities of Supply and Demand,Quantity,Quantity,Price,Price,Burden on
13、Buyer,Burden on Seller,20,想一想税收与补贴的份额到底与什么因素相关？ 是什么使消费者或者生产者能够更多地将税赋转嫁给对方，而把补贴攫取过来，占为己有？,21,如果将税赋换成补贴也是一样的。,22,Pass-through fraction（转嫁因子） ES/(ES - Ed) 表明以高价形式转嫁给消费者的税收份额 For example, when demand is perfectly inelastic (Ed = 0), the pass-through fraction is 1, and all the tax is borne by the consume
14、r. 当Ed=0，转嫁因子1，所有税赋由消费者承担； 当Ed=，转嫁因子0，所有税赋由生产者承担。,The Impact of a Tax or Subsidy,23,The Effects of a Tax or Subsidy,A 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） The sellers price exceeds the buyers price.,24,25,26,注意：税赋使均衡价格并没有上升T，而只是其3/5。,27
15、,第三讲最优值的数学处理方法,Nicholson. Chapter2 pp.52-55,28,Constrained Maximization,Suppose we want to choose x1 and x2 to maximize y = f(x1, x2) subject to the linear constraint c - b1x1 - b2x2 = 0 We can set up the Lagrangian L = f(x1, x2) + (c - b1x1 - b2x2),29,经常可以表达为： Max y = f(x1, x2)s.t. c - b1x1 - b2x2
16、= 0,30,Constrained Maximization,The first-order conditions are f1 - b1 = 0 f2 - b2 = 0 c - b1x1 - b2x2 = 0 To ensure we have a maximum, we must use the “second” total differential d 2y = f11dx12 + 2f12dx1dx2 + f22dx22,31,Constrained Maximization,Only the values of x1 and x2 that satisfy the constrai
17、nt can be considered valid alternatives to the critical point Thus, we must calculate the total differential of the constraint -b1 dx1 - b2 dx2 = 0 dx2 = -(b1/b2)dx1 These are the allowable relative changes in x1 and x2,32,Constrained Maximization,Because the first-order conditions imply that f1/f2
18、= b1/b2, we can substitute and get dx2 = -(f1/f2) dx1 Since d 2y = f11dx12 + 2f12dx1dx2 + f22dx22we can substitute for dx2 and get d 2y = f11dx12 - 2f12(f1/f2)dx12 + f22(f12/f22)dx12,33,Constrained Maximization,Combining terms and rearranging d 2y = f11 f22 - 2f12f1f2 + f22f12 dx12/ f22 Therefore, f
19、or d 2y 0, it must be true that f11 f22 - 2f12f1f2 + f22f12 0 This equation characterizes a set of functions termed quasi-concave functions any two points within the set can be joined by a line contained completely in the set,34,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。,35,二阶条件的另一
20、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。,36,N个未知数的最值问题,37,对于最大化的目标而言，要求d2y必须为负定的，即所有the leading principal minors of Hb（加边主子式），必须遵循 。 而对于最小值的目标而言，则要求d2y必须为正定的，即所有the leading principal minors of Hb （加边主子式）都为负。蒋中一P.502 清晰、权威。,pp.60 E2.3,38,请
21、认真阅读蒋书中的P499504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号相反是因为那里的 切记！,39,pp.61e.g.,40,效用的最大化,一阶条件,41,二阶条件,42,Economic Profits,Total costs for the firm are given by total costs = C = wl + vk Total revenue for the firm is given by total revenue = pq = pf(k,l) Economic profits () are equal to = total revenue - total
22、cost = pq - wl - vk = pf(k,l) - wl - vk,43,Economic Profits,Economic profits are a function of the amount of capital and labor employed we 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 al
23、ready chosen its output level (q0) and wants to minimize its costs,44,Cost-Minimizing Input Choices,To 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/v it should equate the rate at which k can be traded fo
24、r l in the productive process to the rate at which they can be traded in the marketplace,45,Cost-Minimizing Input Choices,Mathematically, we seek to minimize total costs given q = f(k,l) = q0 Setting up the Lagrangian: L = wl + vk + q0 - f(k,l) First order conditions are L/l = w - (f/l) = 0 L/k = v
25、- (f/k) = 0 L/ = q0 - f(k,l) = 0,46,Cost-Minimizing Input Choices,Dividing the first two conditions we get,The cost-minimizing firm should equate the RTS for the two inputs to the ratio of their prices,47,Cost-Minimizing Input Choices,Cross-multiplying, we get,For costs to be minimized, the marginal
26、 productivity per dollar spent should be the same for all inputs,48,Cost-Minimizing Input Choices,Note that this equations inverse is also of interest,The Lagrangian multiplier shows how much in extra costs would be incurred by increasing the output constraint slightly,49,Costs are represented by pa
27、rallel lines with a slope of -w/v,Cost-Minimizing Input Choices,l per period,k per period,C1 C2 C3,50,C1,C2,C3,q0,The minimum cost of producing q0 is C2,Cost-Minimizing Input Choices,l per period,k per period,51,第四讲 偏好与效用,Nicholson. Chapter 3 pp.65-90,52,Axioms of Rational Choice,Completeness if A a
28、nd B are any two situations, an individual can always specify exactly one of these possibilities: A is preferred to B B is preferred to A A and B are equally attractive,53,Axioms of Rational Choice,Transitivity if A is preferred to B, and B is preferred to C, then A is preferred to C assumes that th
29、e individuals choices are internally consistent,54,Axioms of Rational Choice,Continuity if A is preferred to B, then situations suitably “close to” A must also be preferred to B used to analyze individuals responses to relatively small changes in income and prices,55,Utility,Given these assumptions,
30、 it is possible to show that people are able to rank in order all possible situations from least desirable to most Economists call this ranking utility if A is preferred to B, then the utility assigned to A exceeds the utility assigned to B U(A) U(B),56,Utility,Utility rankings are ordinal in nature
31、 they record the relative desirability of commodity bundles Because utility measures are not unique, it makes no sense to consider how much more utility is gained from A than from B It is also impossible to compare utilities between people,57,Utility,Utility is affected by the consumption of physica
32、l commodities, psychological attitudes, peer group pressures, personal experiences, and the general cultural environment Economists generally devote attention to quantifiable options while holding constant the other things that affect utility ceteris paribus assumption,58,Utility,Assume that an indi
33、vidual must choose among consumption goods x1, x2, xn The 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 transformation,59,Economic Goods,In the utility function, the xs are assumed to be “g
34、oods” more is preferred to less,Quantity of x,Quantity of y,x*,y*,60,Indifference Curves,An indifference curve shows a set of consumption bundles among which the individual is indifferent,Quantity of x,Quantity of y,x1,y1,y2,x2,U1,Combinations (x1, y1) and (x2, y2) provide the same level of utility,
35、61,Marginal Rate of Substitution,The negative of the slope of the indifference curve at any point is called the marginal rate of substitution (MRS),Quantity of x,Quantity of y,x1,y1,y2,x2,U1,62,Marginal Rate of Substitution,MRS changes as x and y change reflects the individuals willingness to trade
36、y for x,Quantity of x,Quantity of y,x1,y1,y2,x2,U1,63,Indifference Curve Map,Each point must have an indifference curve through it,Quantity of x,Quantity of y,U1 U2 U3,64,Transitivity,Can any two of an individuals indifference curves intersect?,Quantity of x,Quantity of y,U1,U2,A,B,C,The individual
37、is indifferent between A and C. The individual is indifferent between B and C. Transitivity suggests that the individual should be indifferent between A and B,But B is preferred to A because B contains more x and y than A,65,Convexity,A set of points is convex if any two points can be joined by a st
38、raight line that is contained completely within the set,Quantity of x,Quantity of y,U1,The assumption of a diminishing MRS is equivalent to the assumption that all combinations of x and y which are preferred to x* and y* form a convex set,x*,y*,66,Convexity,If the indifference curve is convex, then
39、the combination (x1 + x2)/2, (y1 + y2)/2 will be preferred to either (x1,y1) or (x2,y2),Quantity of x,Quantity of y,U1,x2,y1,y2,x1,This implies that “well-balanced” bundles are preferred to bundles that are heavily weighted toward one commodity,(x1 + x2)/2,(y1 + y2)/2,67,Utility and the MRS,Suppose
40、an individuals preferences for hamburgers (y) and soft drinks (x) can be represented by,Solving for y, we get y = 100/x,Solving for MRS = -dy/dx: MRS = -dy/dx = 100/x2,68,Utility and the MRS,MRS = -dy/dx = 100/x2 Note that as x rises, MRS falls when x = 5, MRS = 4 when x = 20, MRS = 0.25,69,Marginal
41、 Utility,Suppose that an individual has a utility function of the form utility = U(x,y) The total differential of U is,Along any indifference curve, utility is constant (dU = 0),70,Deriving the MRS,Therefore, we get:,MRS is the ratio of the marginal utility of x to the marginal utility of y,71,Dimin
42、ishing Marginal Utility and the MRS,Intuitively, it seems that the assumption of decreasing marginal utility is related to the concept of a diminishing MRS diminishing MRS requires that the utility function be quasi-concave this is independent of how utility is measured diminishing marginal utility
43、depends on how utility is measured Thus, these two concepts are different,72,Convexity of Indifference Curves,Suppose that the utility function is,We can simplify the algebra by taking the logarithm of this function U*(x,y) = lnU(x,y) = 0.5 ln x + 0.5 ln y,73,Convexity of Indifference Curves,Thus,74
44、,Convexity of Indifference Curves,If the utility function is U(x,y) = x + xy + y There is no advantage to transforming this utility function, so,75,Convexity of Indifference Curves,Suppose that the utility function is,For this example, it is easier to use the transformation U*(x,y) = U(x,y)2 = x2 +
45、y2,76,Convexity of Indifference Curves,Thus,77,Homothetic Preferences,If the MRS depends only on the ratio of the amounts of the two goods, not on the quantities of the goods, the utility function is homothetic（pp.84/277） Perfect substitutes MRS is the same at every point Perfect complements MRS = i
46、f y/x /, undefined if y/x = /, and MRS = 0 if y/x /,78,对于Homothetic function的理解,Pp.84/277. Homothetic 函数的特征就是每一条无差异曲线都有相同的形状。曲线的斜率只与Y/X的比率有关，无论其与原点的距离有多远。这样，我们研究消费者的行为，即便是在不同的效用水平上，也不用担心其会有不同的偏好！保证了偏好保持不变。,79,The importance of homothetic functions is that in such a situation, one indifference curve
47、is much like another. Slopes of the curves depend only on the ratio Y/X, not on how far the curve is from the origin. Indifference curves for higher utility are simple copies of those for lower utility. Hence, we can study the behavior of an individual who has homothetic preferences by looking only
48、at one indifference curve or at a few nearby curves without fearing that our results would change dramatically at very different levels of utility.,80,homogeneity（pp.116）,More generally, a function f (X1, X2, . . . , Xn) is said to be homogeneous of degree k if f (tX1, tX2 . . . , tXn) = t kf (X1, X
49、2, . . . , Xn) for any t0. 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.,81,Homogeneous Function,A function, f(X1, X2, . . . , Xn), is homogeneous of degree k if f(mX1, mX2, . . . , mXn ) = mkf(X1, X2, . . . , Xn ).,
