高级微观经济学 Part 2_Consumption Theory I
厦门大学 高级微观经济学2 consumer theory 1 update.2015.10.26
Recap
Notations
Preference
Utility
UMP
EMP
Welfare
Set the stage
• Individual consumer: n = 1, ..., N • Commodity: l = 1, ..., L • Consumption bundle: • x = (x1 , ..., xL ), xl ≥ 0 for ∀l = 1, ..., L • consumptions bundles x1 , x2 , ... n n • or for consumer n, xn = (x1 , ..., xL ) • Consumption/choice set: X ⊆ • closed • convex • 0∈X
• ⇒ x2 ∼ x1 and x3 ∼ x1 then tx2 + (1 − t)x3 x1 • Indifference curves convex to the origin - diminishing marginal
rate of substitution
8 / 40
Recap
Notations
Recap
Notations
Preference
Utility
UMP
EMP
Welfare
Consumer’s problem (intermediate micro)
• Utility function: U (x1 , x2 )
- indifference curves • Budget constraint: p1 x1 + p2 x2 = w - budget line • Utility maximization: maxx1 ,x2 U (x1 , x2 ) subject to p1 x1 + p2 x2 = w - tangency condition ∗ (p , p , w), x∗ (p , p , w) get demand functions: x1 1 2 2 1 2 • Comparative static analysis
高级微观经济学 Part 1_Production Theory II
D 2(p ) 0 Dy S (p ) Dy L (p )
y(p)
yL(p) yS(p)
p*
p
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Supply function
y2 y(p)
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5.Profit function
• Proposition10: (p) is homogenous of degree 1. • Proposition11: (p) is convex.
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(p) max {py : y Y }
– When it is one production:
(p) ( p, w) max p f (x) - wx
x
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2. Isoprofit curve
• The profit : ( p, w) p f (x) w x • We then got the
isoprpfit curve .
q
p f ( x) w x =
slope w / p q f ( x) /p
• Then
f (x ) w/p
• Proposition6:demand for factor i is:
(.) xi ( p, w ) wi
or
微观3--消费理论
人们愿为边际效用高的钻石支付高价格，为边际效 用低的水支付低价格。―物以稀为贵‖的道理正在于 ―稀‖的物品边际效用高。
2.3.2 边际效用均等原理
从效用角度理解的―公平交易‖ 若： MU为商品的边际效用 MUm为货币的边际效用(设为常数) P为商品的价格 则，消费者所得到消费品的效用正好等 于其所失去的货币的效用，即 MU = MUm×P
MUm = MU ，或 P = MU P MU
m
注意：
MU = MUm×P 的含义：商品的 价格与其所能提供的边际效用成 正比。
“效用”所涉之伦理学意义。
1.2 两种效用理论 1.2.1 基数效用论 (cardinal utility)
效用论源于功利主义思潮，一问世便 以 “基数效用” 为标志, 自1700’s末至 1930’s, 长期主导着关于效用的思维。
基数效用论者于注重“效用”的客观属 性, 认为“效用”大小可用基数来表示, 可以计量，并加总求和。
The Law of Diminishing Marginal Utility 2.2.1 含义 在一定时间范围内，在对其他商品的消 费保持不变的前提下，随着对某商品消 费量的不断增加，消费者从连续增加的 每一消费单位中所获得的效用增量(即 边际效用)递减。
边际效用递减规律示意图
TU
70 60 50 40 30 20 10
Law of Equal Marginal Utility 定义：消费者同时选购若干种商品时， 若其对每一种商品的最后一单位货币
《高级宏观经济学》教学大纲(硕士研究生)-RonaldoCarpio
《高级宏观经济学》教学大纲（硕士研究生） - RonaldoCarpio《高级微观经济分析》教学大纲(博士研究生)课程代码:(按本专业或方向培养方案填写)课程名称:(按本专业或方向培养方案填写)英文名称:Advanced Microeconomic Analysis课程性质:(按本专业或方向培养方案填写)学分学时:3学分，48学时授课对象:金融学院一年级博士研究生课程简介:Based on Microeconomics I (for master students), the course will discuss thecontemporary development in microeconomics. This course is also designed to develop andextend the students’ analytical and reading skills in modern microeconomics. A student who haspassed the course should be able to read typical articles in the mainline journals, understand theanalytical derivations and arguments commonly used in the literature, and know how to solve themore widely used models.先修课程:Microeconomics for master students选用教材:1、 Mas-Colell, A., M. D. Whinston, and J. Green, Microeconomic Theory. (MWG)2、 Jehle, Geoffrey A. and Philip J. Reny, Advanced Microeconomic Theory. (JR)考核方式与成绩评定:Final Exam %; Midterm Exam %; Class Participation % 主讲教师:Carpio Ronaldo、颜建晔所属院系:金融学院联系方式:******************、*******************答疑时间及地点:求索楼123,Wednesday 13:30-14:30 (Carpio)，Tuesday 15:00-17:00(颜)第一章:Consumer Theory教学目标和要求:Understand the consumer’s problem and consumer demand.教学时数:6学时教学方式:讲授准备知识:calculus教学内容:Preferences, Utility, and Consumer’s Problem第一节:Consumer’s Problem第二节:Indirect Utility, Demand作业与思考题:JR Ch 1.6参考资料:JR Ch 1, Appendix A1, A21第二章: Topics in Consumer Theory教学目标和要求:Understand duality, integrability, and uncertainty.教学时数:6 学时教学方式:讲授准备知识:statistics教学内容:Duality, Integrability, and Uncertainty 第一节:Duality of Consumer’s Problem第二节:Revealed Preferences & Uncertainty 作业与思考题:JR Ch 2.5 参考资料:JR Ch 2第三章: Theory of the Firm教学目标和要求:Understand the firm’s profit maximization problem.教学时数:6 学时教学方式:讲授准备知识:Chapter 1,2教学内容:Production, Cost, Profit Maximization 第一节:Production Functions & Cost第二节:Duality in Production, Competitive Firms 作业与思考题:JR Ch 3.6参考资料:JR Ch 3第四章: Partial Equilibrium教学目标和要求:Understand partial equilibrium markets. 教学时数:3学时教学方式:讲授准备知识:Chapter 3教学内容:Perfect & Imperfect Competition, Welfare 第一节:Competition 第二节:Equilibrium & Welfare作业与思考题:JR Ch 4.4参考资料:JR Ch 4第五章: Walras’/competitive equilibrium2教学目标和要求:competitive market economies from a Walrasian (general) equilibrium perspective.Let students understand “why the competitive market/equilibrium may work or fail?”教学时数:6学时方式:讲授教学准备知识:consumer theory, production theory教学内容:第一节:Walrasian economy and mathematical language of microeconomics 第二节:competitive equilibria of pure exchange and with production 作业与思考题:JR5.5, exercises of MWG Ch15, 18, 教师自编习题集参考资料:MWG Mathematical Appendix, Ch15, 18; JR5.4第六章: Social choice function/theory and social welfare: normative aspect of microeconomics教学目标和要求:When we judge some situation, such as a market equilibrium, as “good”or “bad”, or “better” or “worse” than another, we necessarily make at least implicit appeal to some underlying ethical standard. Welfare economics helps to inform the debate on social issues by forcingus to confront the ethical premises underlying our arguments as well as helping us to seetheir logical implications.Let students have a systematic framework for thinking about normative and social welfare topics.教学时数:3学时教学方式:讲授准备知识:Walrasian equilibrium教学内容:第一节:social choice, comparability, and some possibilities第二节:Rawlsian, Utiliterian, and flexible forms作业与思考题:JR6.5, exercises of MWG Ch21, 22, 教师自编习题集参考资料:MWG Ch21.A, Ch21.E, Ch22.C; JR Ch6第七章: Strategic Behavior and Asymmetric Information教学目标和要求:A central feature of contemporary microeconomicsafter Walrasian economy is the multi-agent interaction which represents the potential for the presence of strategicinterdependence. Let students grasp classic models of imperfect competition under symmetric and asymmetric information.3教学时数:3学时教学方式:讲授准备知识:perfect competition教学内容:第一节:monopoly and oligopoly under symmetric information第二节:oligopoly under asymmetric information作业与思考题:教师自编习题集参考资料:MWG Ch12; JR Ch4第八章: Theory of Incentives教学目标和要求:The strategic opportunities that arise in the presence of asymmetricinformation typically lead to inefficient market outcomes, a form of market failure. Underasymmetric information, the first welfare theorem no longer holds generally. Thus, the main themeto be explored is to stimulate different agents’ optimal/efficient behaviors in differentinformational settings to achieve the “second-best” market outcomes.教学时数:9学时教学方式:讲授准备知识:Strategic Behavior and Asymmetric Information教学内容:第一节:Adverse selection第二节:Moral hazard*第三节:Task separation/integration,第三节:Career concern作业与思考题:exercises of MWG Ch13, 14, 教师自编习题集参考资料:JR Ch8; MWG Ch13, 14第九章前沿研究讲座:待定邀请校外老师(待定)给学生们讲演最新研究，引导学生讨论;在学生掌握现代微观经济学基本模型之后能够接触到前沿研究。
高级微观经济学消费理论
高级微观经济学课本：参考书：1)Andreu Mas-Colell，Michael D. Whinston andJerry R. Green，1995，Microeconomic Theory，Oxford University Press；中译本：《微观经济理论》，经济科学出版社2)David Kreps，1992，3)Hal Varian，Microeconomic Analysis，中译本，4)Eugene Silberberg and Wing Sun，2000，TheStructure of Economics: a Mathematical Analysis,3rd edition, McGraw-Hill Higher Education第一章：消费理论（关于消费者的行为研究理论。
其研究方法有两种，其一是古典需求理论或者说偏好理论；其二是显示偏好理论）1.基本概念2.偏好关系和效用函数3.消费者的优化问题4.间接效用函数和支出最小化5.需求的特征一、 基本概念1、选择集（消费集合）X定义：所有可能的（能实现的和不能实现的）消费（选择）方案x 的集合。
消费方案x ：商品：1) 商品数量无限可分：R x i ∈，商品数量是连续的。
2) 商品数量非负： +∈R x i3) 商品种类为：n消费方案（选择方案，消费束）：()1,...,n n x x X +=∈=x特征：1、 非空集(X ≠Φ,否则没有研究意义)2、 X 闭集（连续性）3、 凸集4、 包含原点：X0∈（消费者可以选择不消费，这也是选择集合的下限）2x (12,x x =x n+2、可行集B（可选择的消费束）：制度约束、经济约束等限制之后仍保留下来的消费集合。
x23、偏好关系（指在同一消费集中，两个消费束哪个更受消费者偏好。
）4、行为假设The consumer seeks to identify and select an available alternative that is most preferred in the light of his personal tastes.在各种能够实现的消费方案中，消费者选择他最偏好的消费方案。
高级微观经济学讲义 (1)
5.Relationship
• Hicks demand and expenditure function:
h(p, u ) p e(p, u )
2 – D p h(p, u ) D p e(p, u ) is s.n.s.d.
• Hicks and Walras demand:
3.Utility maximization
• Consumer’s problem (UMP):
max u ( x)
x0
s.t.
x B(p.w)
• The solutions x(p.w) are called Walras’ Demand Correspondence, or function if it’s single point.
3.Utility maximization
• Properties of x(p.w)
– HD0 – Satisfied Walras’ Law – If % are concave, x(p.w) are concave too, if % are strictly concave, x(p.w) is single point.
– % is local non-satiation: x X, and >0 there is a y, that y-x ,and y x
• proposition3: % is strong monotone, then it’s monotone; % is monotone, it’s local non-satiation.
2.From preferences to utility
• Convexity: x upper contour sets are convex.
高级微观经济学 Part 2_Consumption Theory I
• Proposition4: if X is concave, then is
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4.Demand function
• For any p and w are strictly positive, the
corresponding demand set x(p,w) are nonempty, if x(p,w) is single point, we call it the Walrasian( Marshallian) demand function. • x(p,w) is homogenous of degree zero and satisfied Walras’ law. That is px=w for all
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• Slutsky matrix (substitution matrix)
• Substitution effects • is n.s.d • Giffen good is necessary inferior good.
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petive budget
• Consumption set X and it’s price
with
the wealth w>0. • Definition: Walras (competive) budget set
WA and demand law
x2 x2 x2
x1
x1
x1
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《高级微观经济学》课件
考试安排
课程结束后将进行一次期末考试，考察学生对微观经济学理论和实践的理解和运用能力。
结语
通过学习高级微观经济学，您将拥有深入洞察经济问题的能力，成为经济学 的专家，并能运用所学知识解决实际经济问题。
研究消费者的偏好和选择行为，分析消费者 的需求曲线和边际效用。
市场结构和竞争
了解不同市场结构的特点，包括完全竞争、 垄断、寡头垄断和垄断竞争。
学习方法
1
课堂学习
通过听课和参与讨论，加深对微观经济学的理解和思考。
2
案例分析
通过分析实际经济问题和案例，将理论知识应用到实际情境中。
3
小组讨论
与同学一起合作讨论，分享思考和观点，促进深度学习和交流。
《高级微观经济学》 课件
让我们一起探索高级微观经济学的奥秘吧！本课程将帮助您深入了解微观经 济学的核心概念和分析方法，让您成为经济学的专家。
课程简介
通过本课程，您将了解微观经济学的基本原理和理论框架，掌握市场经济中个体和企业的行为分析方法， 以及了解市场失灵和政府干预等相关问题。
教材介绍
我们将使用《高级微观经济学》教材，该教材包含了丰富的案例研究和实际 问题分析，帮助学生将理论知识应用到实际经济问题中。
课程目标
本课程的目标是帮助学生深入理解微观经济学的核心概念，掌握经济学的思维方式和分析工具，以及培 养学生独立思考和问题解决的能力。
主要内容
供求关系分析
通过供求关系曲线的分析，了解市场价格和 数量的决定因素。
生产者行为分析
研究生产者的成本和利润最大化行为，分析 生产者的供给曲线和边际成本。
消费者行为分析
neoclassical consumer theory微观经济学
neoclassical consumer theory微观经济学neoclassical consumer theory 即新古典消费者理论，是新古典经济学的一部分。
新古典经济学是对应于早期的新古典派经济学（Neoclassical Economics），对应于始于20世纪70年代的新古典派经济学第二代（New Classical Economics），对20世纪80年代以后发展起来的一个新流派即新兴古典经济学（New Classical Economics），以及20世纪末开始的第四次综合。
新古典消费者理论研究的是消费者行为。
消费者行为研究的三个步骤为：消费者偏好-预算约束-结合前面二者确定消费者选择。
消费者偏好的基本假设包括偏好的完全性、可传递性，以及“多总比少好”。
无差异曲线的特征为向下倾斜、其右上和左下分别表示偏好于和不偏好于、每条无差异曲线绝不相交、边际替代率（无差异曲线的斜率）递减（无差异曲线是凸的）。
2019复旦大学管理学院 高级微观经济学课件
max
x1;x2
(x1
+
x2)1=
subject to: p1x1 + p2x2 I; x1; x2 0
To solve this problem, …rst write down the Lagrangian. Because
the utility function is strictly increasing, the budget contraint will hold
@L @x1
= (x1 + x2)(1= )
1x1
1
p1 = 0
@L @x2
= (x1 + x2)(1= )
1x2
1
p2 = 0
@L
=I @
p1x1
p2x2 = 0
2
1.1.1 Marshallian demands By the …rst two equations, we can get
x1 = x2
with equality. Assuming the interior solution, the Kuhn-Tucker
conditions coincide with the ordinary …rst-order condition, therefore,
L(x1; x2; ) = (x1 + x2)1= + (I p1x1 p2x2) By the …rst-order conditions:
a contradiction. Hence, the consumer optimization problem has a unique solution.
高级微观经济学(上海财经大学 陶佶)note02
Let x1 , x2 and x3 be any three consumption bundles in X .
Axiom 2.1 - Complete. Either x1 \ x2 or x2 \ x1 .
上海财大经济学院
2
作者：陶佶
2005 年秋季
高等微观经济学 I
Axiom 2.2 - Reflexive. For all x in X , x \ x . Axiom 2.3 - Transitive. If x1 \ x2 and x2 \ x3 , then x1 \ x3 .
Let X be a consumption set, a collection of all alternatives or complete consumption plans. The consumption set is also called as the choice set. Let xi ∈ be the number of units of ith
good, and x = ( x1, x2 , , xn ) be a vector containing different quantities of n commodities,
called as a consumption bundle or a consumption plan.
Properties of the Consumption Set, X : The minimal requirements are
Terminology 1. Let x0 be any points in the consumption set X . Relative to any such point,
高级微观经济学L2
see the figure
11
从偏好到效用
效用函数（Utility Functions）
对消费集 X 中的任意两个消费束x和y，如果存在一 个实值函数(real value) u : X ，使得
x y u x u y 则称函数 u . 为代表偏好关系 的一个效用函数。
14
从偏好到效用
常见的效用函数 完全替代： u x1 , x2 a1 x1 a2 x2
无差异曲线是一条斜率为负的直线 边际替代率为常数
完全互补（里昂惕夫效用函数）： u x1 , x2 min a1 x1 , a2 x2
无差异曲线呈现L型 无差异曲线的顶点位于直线 边际替代率为零或负无穷
the figure
8
从偏好到效用
定理2.1：设
系，则有
是定义在消费集 X 上的偏好关
严格单调性单调性 单调性局部非饱和性 弱单调性、传递性和局部非饱和性单调性
9
从偏好到效用
公理性假设之四：凸性（convexity）
定义2.9：设 x, y, z X, 0 1 。若 x y, y z 时，
u x max L x x p , w T s . t . p x w, x 0
19
效用最大化
效用最大化模型（UMP） u x max x
s.t. x B p , w
定理2.6（解的唯一性）：若p 0 ，效用函数u x 是
一阶微分条件只对内点解有效，若考虑角点解，需 运用库恩—塔克定理来求解
微观经济学课件第二章消费者理论
p2x2
w
s2]
0
L 2s 0 s
L 1
[ x1
s
2 1
]
0
L s1
2 1s1
0
L 2
[ x2
s
2 2
]
0
L s2
22s2
0
效用极大化
Kuhn-Tucker condition (参见第一章式(1-26))：
(I) u1**p10; u2**p2 0 (II) [u1**p1]x1* 0; [u2**p2]x2* 0 (III)*[p1x1*p2x2*w]0
t 0, u1(x1(tp1,tp2;tw), x2 (tp1,tp2;tw)) (tp1,tp2;tw) (tp1) 0 u2 (x1(tp1, tp2;tw), x2 (tp1, tp2;tw)) (tp1, tp2;tw) (tp2 ) 0
(tp1) x1(tp1,tp2;tw) (tp2) x2(tp1,tp2;tw) tw u1(x1( p1, p2; w), x2 ( p1, p2; w)) (tp1,tp2;tw) (tp1) 0 u2 (x1( p1, p2; w), x2 ( p1, p2; w)) (tp1,tp2;tw) (tp2 ) 0 p1 x1( p1, p2; w) p2 x2 ( p1, p2; w) w
李四对 x 的选择没有矛盾：〝曾经有一次 x 与 y 可供选择时，李四有选择 x，则 以后只要 x 与 y 可供选择而 y 有被选取，则 x 也要被同时选取〞(亦即 x c({x, y}) ，则若 y c2 ({x, y, z}) x c2 ({x, y, z}) )。
但是李四对 y 的选择却有矛盾：〝曾有一次 x 与 y 可供选择时，李四有选 y，但 下一次 x 与 y 可供选择时，李四选了 x 却没有同时也选取 y〞(亦即 y c2 ({ x, y, z}) ，但是 x c2 ({ x, y}) 时， y c2 ({x, y}) )。
微观经济学1_2
OGood1
DiscreteGoods（离散商品） x1:adiscretegoodthatisonlyavailableinintegeramounts. Supposethatx2ismoneytobespentonothergoods.
Good2
OGood1
TheMarginalRateofSubstitution Marginalrateofsubstitution(MRS，边际替代 率):slopeofanindifferencecurve. ----measurestherateatwhichtheconsumerisjustwillingtosubstitut eonegoodfortheother.
中级微观经济学
参考书： HalR.Varian.IntermediateMicroeconomics,AModernApproach .W.W.Norton&Company,Inc.
来源：网络转载
1BUDGETCONSTRAINT
Consumertheory----howconsumersbuytheirgoods? Economistsassume:consumerschoosethebestbundleofgoodsthey canafford. Twoaspects: ----Consumerschoosethemostpreferredgoods. ----Theyarelimitedbyeconomiccondition. TheBudgetConstraint Consumptionbundles:（消费束，商品组 合）:alistofnumbersofgoodsandservices. X=(x1,x2,…,xn,) Inthecaseoftwogoods:good1andgood2:X=(x1,x2) Pricesofgoods:(p1,p2), Theamountofmoneytheconsumerhastospend:m. Theconsump1exr1’+sapf2fxo2r≤damb.leconsumptionbundles,(x1,x2)satisfying ----Thebudgetsetoftheconsumer.
厦门大学 高级微观经济学2 consumer theory 2 update.2015.11.08
∂Ls ∂l ∂lh ∂l(w, p, Y ) =− =− − (T − l) ∂w ∂w ∂w ∂Y Derive the individual labour supply curve: it could be backward bending when labour supply or wage is very high.
MUx MUl + µl MUx MUl = ⇒ > p w p w
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More on duality
Endowment
Over-time Consumption
Revealed preference
Aggregation
Solutions
• Labour market participation decision • Reservation wage wR - willingness to work (supply labour)
• Labour supply conditional on participation (wR < w) • Marshallian demand for leisure l(w, p, Y ) = l(w, p, I + wT ) • Labour supply function Ls = T − l(w, p, Y ) = T − l(w, p, I + wT )
different ps • Any function of (p, u) with the properties of an expenditure function - taking zero with minimum u, continuous in u, strictly increasing and unbounded above in u, increasing in p, homogeneous of degree 1 in p and concave in p - is an expenditure function. From an expenditure function:
厦门大学 高级微观经济学2 consumer theory 3 update.2015.11.18
Some concepts
Lottery
Preference axioms
Uncerntainty - Motivation
EU function
Risk preference
Application
Introducing uncertainty: would you like to pay $200 to play the following game? A coin is flipped
distribution satisfies (1) f (x) ≥ 0 for ∀x; (2)
+∞ −∞
f (x)dx
=
1.
Notice that the probability of a single point x is zero; but it is
positive for a range. The related "cumulative density function" is
F(x) =
x −∞
f
(x)dx.
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Motivation
Some concepts
Lottery
Preference axioms
EU function
Risk preference
Basic concepts in probability theory,continue
Application
• Simple lottery
• Set of outcomes A = {a1, ..., aN} - a finite set (extension to infinite
sets)
• A simple lottery on A is L = (p1 ◦ a1, ..., pN ◦ aN) with
高级微观经济理论 第2章 消费者最优选择和需求分析
© All Copyrights Reserved by Liu Jianghui, SHNU
19/51
2.2.2 支出函数及其性质
支出函数的定义 支出函数的性质
© All Copyrights Reserved by Liu Jianghui, SHNU
20/51
10
A、支出函数的定义
将支出最小化问题的解代如其目标函数而得到的函数即为 支出函数，记为e(p,u):
n 性质1： v ( p, m) 在 R + + × R n 上是连续的[1]；
性质2： v ( p, m) 是关于 ( p, m) 的零次齐次函数； 性质3： v ( p, m) 是关于m的严格递减函数； 性质4： v( p, m) 是关于p的严格递增函数 性质5： v ( p, m) 对价格 是拟凸 对价格p是拟凸 性质6： v ( p, m) 满足罗伊恒等式（Roy’s identity）
v ( p , m ) = m ax u ( x*)
n x∈ R +
( 2 .2 )
s .t : p ⋅ x ≤d by Liu Jianghui, SHNU
7/51
B、间接效用函数的性质
如果直接效用函数在上是连续且严格递增的，那么间接效用函数就一定 具有以下几个性质：
{ {
} }
但： 1 x > m , p 2 x > m ，这显然不可能 p 因此：
v ( p t , m ) = max u( x )满足x属于B t ≤ max u( x )满足 x属于B1 U B 2 , 因为B1 U B 2 ⊃ B t ≤ a因为v ( p1 , m ) ≤ a和v ( p 2 , m ) ≤ a
[微观经济学课件].(ppt)第三章 消费理论(消费者行为理论)
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生理、安全、社会、受尊重和自我实现的欲望需求。欲望遵
循的规律：欲望强度递减规律；
� 享受递减规律。
� 2.效用（ utility )__指欲望的满足感或程度，是指个人从消费 某种商品中所得到的满足。
�
效用的度量单位是尤特尔（util），一个尤特尔即为一个
效用单位。
� 二、总效用与边际效用
� 1. 总效用（TU）__消费一定数量的商品所得到的总的满 足程度。
�
ＭＵ＿边际效用
� Ｐ＿商品价格
� Ｑ＿商品购买量
� Ｍ＿货币总量或收入
第三章第二节 序数效用理论
第二节 序数效用理论（无差异曲线分析）
� 一、无差异曲线 � 是现代西方经济学家进行微观经济分析常用的工具。 � 1． 无差异曲线的假设条件 � 消费者在一定的嗜好、一定的技术条件和一定的资源
第三章第二节 序数效用理论
1．无差异曲线的特征
� 设无差异曲线为S：Y = f（X）
�
X—x商品；
�
Y—y商品。
� （1）无差异曲线是dY一条向右下方倾斜的曲线， � 且 斜率 为负。即 ＜dX０，说明在同效用条件下，
� 增加一商品（X商品）的消费，则要减少另一商 品（Y商品）的消费，亦即两种商品不能同时增 加或减少。
� 三、消费者均衡 � 它是研究在收入一定的条件下，消费者如何购
买各种商品，其目标是实现效用最大化。
� 消费者均衡理论认为：消费者的货币收入是固 定的，市场上各种商品的价格是已知的，则要使效 用最大化，消费者一定要使其购买的商品的边际效 用与他所付出的价格成比例，即使每单位货币所获 得的效用都相等。
第三章消费理论
第三章 消费理论（消费者行为理论）
《微观经济学microeconomics》英文版
Expenditure Minimization Problem
The problem:
Minx0 px
s.t. u(x) u
The first order condition:
u( x* ) / xl u( x* ) / xk
pl pk
u( x) u
The solution: Hicksian demand function h(p,u)
ECON501 Lecture Note 3
Consumer Theory 2 ( Textbook Chapter 3 )
Structure
Utility Maximization Problem Utility maximization Walrasian demand function Indirect utility function
of demand Preference (Chapter 3) The basic properties of preference Existence of utility function
The Budget set
Commodities The physical constraints and the consumption set
Convexity of Walrasian budget set: proof
Consumer’s Choice
The consumer’s problem: to choose a consumption bundle x from the Walrasian budget set.
Walrasian Demand Function x( p, w)
Intuition: Figure 2.F.1
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• Slutsky matrix (substitution matrix)
• Substitution effects • is n.s.d • Giffen good is necessary inferior good.
5.WA and demand law
• Walrasian demand function x(p,w) satisfied
WA if for any
See the fig
we have:
.
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• Changing in price will change wealth too. But
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• Choice construct: a choice under certain
budget: – Budget set: and , is a budget family, represented a limited list of all possible choice under certain system, nature, technology and other social environments that the decision-maker must take. – Choice rule: , maybe contain more than one elements.
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• Defay “rational preference rationalization • Propersition3: if satisfied WA and contain all subsets of X that is ternary and less than ternary. – Example: X={x,y,z}, B ={{x,y},{y,z},{x,z}}, C({x,y})={x},C({y,z})={y},C({x,z})={z},(B , C(.)) satisfied WARP, but there is no rationalization preference relation over it.
lecture5 for Chu Kechen Honors College
• Weak Axiom of Revealed Preference (WARP
or WA) : if for certain and for and must • Revealed Preference “ ”: ,
, then
how can we tell the demand changing by price changing from wealth changing? • Given a changing from , and people will not get worse that is here wealth changing (compensation ) was called “Slutsky wealth compensation” and “(Slutsky) compensated price changing”.
lecture5
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• Proposition5: x(p,w) satisfied WA if and only
if:
,
and when
• Prop.5 indicates,
, or that’s called “demand law ”, or “compensation demand law ”.
WA and demand law
x2 x2 x2
x1
x1
x1
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WA and demand law
x2
x2
x1
x1
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Consumption set
x2
x2
3 2 1
x1
x1
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Consumption set
Leisure
24
Leisure
24
8
x1
x1
lecture5
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1.Preference
• An (acceptable) alternatives set (or a consumption
set
) – A (weak) preference relation“ ”: a binary relationship on X, for any , means” x is at least as good as y”. – A strict preference “ ”:
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Consumption set
rice Rice of Hangzhou
4
4
bread
Bread of Shanghai
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expansion path
x2
x1
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petive budget
• Consumption set X and it’s price
with
the wealth w>0. • Definition: Walras (competive) budget set
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2.The rule of choice
• We can only observe what a man choice under
a certain constrain. • Is the man’s preference rational when we observed several choice of him? • Or if his preference was rational, what rules will his choice take?
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• Price effects:
– Supply curve: – Price effects:
– Giffen good:
See the fig.
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• Cournot Aggregation: if Walrasian demand
– An indifference relation “ ”:
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• Definition: preference on X is rational if:
– It’s complete: – It’s reflexive: – It’s transitive:
• Proposition4: if X is concave, then is
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4.Demand function
• For any p and w are strictly positive, the
corresponding demand set x(p,w) are nonempty, if x(p,w) is single point, we call it the Walrasian( Marshallian) demand function. • x(p,w) is homogenous of degree zero and satisfied Walras’ law. That is px=w for all
Wealth effects
x2
x2
x2
x1
x1 luxury goods
x1
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Supply curve:
x2
x1
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Giffen good
x2
x1
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• Wealth effects:
– Commodity l is normal goods if – Commodity l is inferior goods if – The demand is normal if
See the fig
Advanced Microeconomics