主讲教师：周飞跃 讲师
微观经济分析
Intermediate Microeconomics
产品市场：产品市场：
企业出售企业出售
家庭购买家庭购买
企业企业
生产出售物品与劳务生产出售物品与劳务
雇佣并使用生产要素雇佣并使用生产要素
家庭家庭
购买并消费物品与劳务购买并消费物品与劳务
拥有并出售生产要素拥有并出售生产要素
生产要素市场：生产要素市场：
家庭出售家庭出售
企业购买企业购买
生产什么生产什么
怎样生产怎样生产
为谁生产为谁生产
收益收益 支出支出
物品与劳务出售物品与劳务出售 物品与劳务购买物品与劳务购买
生产投入生产投入
劳动、土劳动、土
地和资本地和资本生产投入生产投入
工资、租金与利润工资、租金与利润 收入收入
物品与劳务的流向物品与劳务的流向
货币的流向货币的流向
微观经济学的两个主要原则
最大化：效用最大化、利润最大化
均衡：
经济学的局限性：
Ch 3: 消费者理论
北京信息科技北京信息科技
大学工商分院大学工商分院
微观经济分析微观经济分析
Intermediate Intermediate
Micro-Micro-
economicseconomics
byby
Zhou Fei YueZhou Fei Yue
• 在任何有关消费者选择的模型里，存在四大构造区域在任何有关消费者选择的模型里，存在四大构造区域
–– 消费集消费集XX ：代表一切备择物或整个消费计划的集合。：代表一切备择物或整个消费计划的集合。
假设假设 消费集消费集XX的性质（消费集的最低条件）是：的性质（消费集的最低条件）是：
第一节第一节 Preference Preference
–– 可行集可行集BB：代表一切的可选择的消费计划：代表一切的可选择的消费计划————是现实中在是现实中在
给定的环境里消费者可获得的消费备选物。则给定的环境里消费者可获得的消费备选物。则
–– 偏好关系：对消费者感知选择环境的能力，以及消费者对偏好关系：对消费者感知选择环境的能力，以及消费者对
不同选择对象的好恶信息等限制。不同选择对象的好恶信息等限制。
–– 行为假设：消费者用于作出最终选择并确认选择中的最终行为假设：消费者用于作出最终选择并确认选择中的最终
目标的指导原理目标的指导原理————消费者寻求认定与选择一个可以获得消费者寻求认定与选择一个可以获得
的备择物，后者依照其个人的喜好确定，属于最受偏爱的的备择物，后者依照其个人的喜好确定，属于最受偏爱的
选择。选择。
Rationality in EconomicsRationality in Economics
• Behavioral Postulate:
A decision maker always chooses its most A decision maker always chooses its most preferred preferred
alternativealternative from its set of from its set of available alternativesavailable alternatives..
• So to model choice we must define
Preferences over alternativesPreferences over alternatives
Available alternativesAvailable alternatives
NotationsNotations
• 消费束消费束 为为 一组商品一组商品: : x={xx={x11, …, x, …, xnn}}
• Vector of prices: Vector of prices: p=p={{pp11, …, p, …, pnn}},, where each price where each price
is non-negative (is non-negative (ppi i 0, for all 0, for all ii))
• yy is the lump sum money income is the lump sum money income
Properties of the Consumption Set, X
消费集
Consumption set, X, represent the set of all Consumption set, X, represent the set of all
alternatives, or complete consumption plans, that the alternatives, or complete consumption plans, that the
consumer can conceive—whether some of them will consumer can conceive—whether some of them will
be achievable in practice or not. Sometimes, be achievable in practice or not. Sometimes,
consumption set is also called consumption set is also called choice setchoice set..
消费束
Let x=(xLet x=(x11, x, x22,…x,…xnn) be a vector containing different ) be a vector containing different
quantities of each of the n commodities, x is called a quantities of each of the n commodities, x is called a
consumption bundleconsumption bundle or or consumption planconsumption plan..
Properties of the Consumption Set, X
Assumption :
消费集的最低条件消费集的最低条件
1. 1. XXRRnn++
2. X is closed 2. X is closed
3. X is convex. 3. X is convex.
4. 0 4. 0 .
Properties of the Consumption Set, X
可行集可行集
All those consumption plans that are both conceivable All those consumption plans that are both conceivable
and more important, realistically obtainable given the and more important, realistically obtainable given the
consumer circumstances.
Feasible set is that subset of the consumption set that Feasible set is that subset of the consumption set that
remains after we have accounted for any constraints remains after we have accounted for any constraints
on the consumer’s access to commodities due to the on the consumer’s access to commodities due to the
practical, institutional, or economic realities of the practical, institutional, or economic realities of the
.
Properties of the Consumption Set, X
偏好关系
A preference relation typically specifies the limits, if A preference relation typically specifies the limits, if
any, on the consumer’s ability to perceive in any, on the consumer’s ability to perceive in
situations involving choice, the form of consistence or situations involving choice, the form of consistence or
inconsistency in the consumer’s choice, and the inconsistency in the consumer’s choice, and the
information about the consumer’s taste for the information about the consumer’s taste for the
different objects of choice. different objects of choice.
行为假设
The consumer seeks to identify and select an The consumer seeks to identify and select an
available alternative that is most preferred in the available alternative that is most preferred in the
light of his personal of his personal taste.
Preference RelationsPreference Relations
1. 1. ComparingComparing two different consumption bundles, x and y: two different consumption bundles, x and y:
–– strict preference: x is more preferred than is preference: x is more preferred than is y.
–– weak preference: x is as at least as preferred as is preference: x is as at least as preferred as is y.
–– indifference: x is exactly as preferred as is : x is exactly as preferred as is y.
2. 2. 严格偏好关系严格偏好关系,,弱偏好关系，无差异关系弱偏好关系，无差异关系 are all preference are all preference
.
3. Particularly, they are ordinal relations; . they state only 3. Particularly, they are ordinal relations; . they state only
the order in which bundles are order in which bundles are preferred.
Preference RelationsPreference Relations
• denotes strict preference so x denotes strict preference so x y means that y means that
bundle x is strictly preferred to bundle x is strictly preferred to bundle y.
• ~~ denotes indifference; x denotes indifference; x ~~ y means x and y are y means x and y are
equally preferred.
• denotes weak preference; denotes weak preference;
x y means x is preferred at least as much as is y. x y means x is preferred at least as much as is y. ~
~
Standard PropertiesStandard Properties
• Axiom 1: Axiom 1: 完备性完备性..
For all For all xx11 and and xx22 in in XX, either , either xx11 xx22 or or x x22 x x11
bundles can always be compared, bundles can always be compared,
–– either either xx is preferred to is preferred to yy
–– or or yy is preferred to is preferred to xx
–– or both.
•• Reflexivity: Any bundle Reflexivity: Any bundle xx is always at least as good as itself. is always at least as good as itself.
~ ~
Standard PropertiesStandard Properties
• Axiom 2: Axiom 2: 传递性传递性
For any three elements, For any three elements, xx1 1 ,, xx22 and and xx33 in in XX, if , if xx11 xx22 and and
xx22 x x3 3 , then , then xx11 x x3 3 ..
(consistent(consistent，，otherwise there is no best element)otherwise there is no best element).
• Definition: Definition:
Preference Relation Preference Relation:TThe binary relation on the consumption he binary relation on the consumption
set X is called preference relation if it satisfies Axioms 1 and X is called preference relation if it satisfies Axioms 1 and 2.
Strict Preference RelationStrict Preference Relation: : xx11 xx22 iff iff xx11 xx22 andand xx22 xx11
Indifference RelationIndifference Relation: : xx11 ~~ xx22 iff iff xx11 xx22 andand xx22 xx11
~~
~
~
~ ~
~ ~
Standard PropertiesStandard Properties
•• Definition: Definition:
let let xx00 be any point in the consumption set, relative to any such be any point in the consumption set, relative to any such
point, we can define the following subsets of point, we can define the following subsets of XX::
1. (1. (xx00 )){{xx||xxXX, , x x xx0 0 }, }, called the “called the “at least as good asat least as good as” set” set. .
2. ( 2. (xx00 )){{xx||xxXX, , x x xx0 0 }, }, called the “called the “no better thanno better than” set” set. .
3. ( 3. (xx00 )){{xx||xxXX, , x x xx0 0 }, }, called the “called the “worse thanworse than” set” set. .
4. 4. ((xx00 )){{xx||xxXX, , x x xx0 0 }, }, called the “called the “preferred topreferred to” set” set. .
5. 5. ~~ ( (xx00 )){{xx||xxXX, , x x ~~ xx0 0 }, }, called the “called the “indifferenceindifference” set” set. .
~~
~ ~
Standard PropertiesStandard Properties
•• Axiom 3: Axiom 3: 连续性连续性
For all For all xx in the consumption set, the in the consumption set, the “at least as good as” “at least as good as” and and “no better “no better
than” than” are closed closed sets.
(namely, (namely, the “the “worse thanworse than” set and “” set and “preferred topreferred to” set are open sets” set are open sets))
•• Axiom 4Axiom 4´: ´: 局部非饱和性局部非饱和性
For all For all xx00RRnn++ and for all and for all >0, there exists some x >0, there exists some x BB ((xx00)) nn RR
nn
++ , ,
such that x such that x x x00 ..
•• Axiom 4Axiom 4´: ´: 严格单调性严格单调性
For all For all xx00 ,, xx1 1 RRnn++ , if , if xx0 0 xx11 then then xx00 xx11 , while if , while if xx00 >>>> xx11 , then , then xx00 xx11.. ~
Standard PropertiesStandard Properties
• Axiom 5Axiom 5´: ´: 凸性凸性
If If xx1 1 xx00 , then , then t t xx1 1 ++(1(1-t -t ) ) xx00 xx00 ,, for all t for all t [0,1][0,1]
((if x and y are as least as good as z, then for all if x and y are as least as good as z, then for all 00tt11, tx+, tx+(1-t)(1-t)y y
is as least as good as as least as good as z.))
• Axiom 5Axiom 5: : 严格凸性严格凸性
If If xx1 1 xx00 , and , and xx1 1 xx00 then then t t xx1 1 ++(1(1-t -t ) ) xx00 xx00 ,, for all t for all t (0,1)(0,1)
(( if xif xy and x and y are as least as good as z, then for all y and x and y are as least as good as z, then for all 0<t<10<t<1, tx+, tx+
(1-t)(1-t)y is strictly preferred to z.)y is strictly preferred to z.)
~~
~
Well-Behaved PreferencesWell-Behaved Preferences
• A preference relation is “A preference relation is “well-behavedwell-behaved” if it is” if it is
– rational: rational: completecomplete and and transitivetransitive
– strictly monotonicstrictly monotonic
– continuouscontinuous
– strictly convexstrictly convex
专题1：基数效用理论
Topic 1: Cardinal Utility
基数效用理论 (边际效用理论)
11、、基数效用分析法：总效用和边际效用基数效用分析法：总效用和边际效用
22、边际效用递减法则、边际效用递减法则((戈森第一法则戈森第一法则):):
效用函数凹向原点，即两阶微分小于效用函数凹向原点，即两阶微分小于00
33、边际效用均等法则，又名戈森第二法则。、边际效用均等法则，又名戈森第二法则。
基数效用理论 (边际效用理论)
• 目标函数：Max U=U(x, y)
• 约束条件： pxx+pyy=m
• 拉格朗日乘数法：L=U+λ(m-pxx-pyy)
基数效用理论 (边际效用理论)
边际效用理论三大奠基者边际效用理论三大奠基者：：
门格尔、瓦尔拉、杰文斯门格尔、瓦尔拉、杰文斯
边际效用学派又分为三个流派边际效用学派又分为三个流派：：
奥地利学派〔维也纳学派〕奥地利学派〔维也纳学派〕 ：：
门格尔、维色、庞巴维克门格尔、维色、庞巴维克
数理学派〔罗桑学派〕数理学派〔罗桑学派〕 ：：
杰文斯、瓦尔拉、帕累托杰文斯、瓦尔拉、帕累托
美国学派美国学派：：
克拉克克拉克
基数效用理论 (边际效用理论)
实际上边际效用理论的奠基者和直接先驱者是实际上边际效用理论的奠基者和直接先驱者是
德国的戈森，其在德国的戈森，其在18541854年就提出了两个定律，年就提出了两个定律，
即戈森一、二定律，但未被重视。即戈森一、二定律，但未被重视。
1919世纪末世纪末7070年代，杰文斯、门格尔和瓦尔拉斯年代，杰文斯、门格尔和瓦尔拉斯
几乎同时提出边际效用理论，他们的理论和戈几乎同时提出边际效用理论，他们的理论和戈
森并无直接渊源。森并无直接渊源。
基数效用理论 (边际效用理论)
马歇尔（马歇尔（18421842－－19241924））
• 英国，酷爱数学。中学毕业后，就读于牛津大学。英国，酷爱数学。中学毕业后，就读于牛津大学。
18611861年，放弃了牛津大学的奖学金，进入剑桥大学年，放弃了牛津大学的奖学金，进入剑桥大学
转学数学。转学数学。18651865年毕业留校，转修物理，兼教数学，年毕业留校，转修物理，兼教数学，
并开始涉及经济、政治和社会问题。并开始涉及经济、政治和社会问题。
• 《经济学原理》的发表，使马歇尔声明显赫，其门《经济学原理》的发表，使马歇尔声明显赫，其门
徒亦倍受青睐。因马歇尔及其门徒先后在剑桥大学徒亦倍受青睐。因马歇尔及其门徒先后在剑桥大学
任教，被称为新古典学派，又名任教，被称为新古典学派，又名“ “ 剑桥学派剑桥学派””，。，。
门徒中较著名的有庀古、罗宾逊和凯恩斯。《经济门徒中较著名的有庀古、罗宾逊和凯恩斯。《经济
学原理》与斯密的《国富论》和李嘉图的《政治经学原理》与斯密的《国富论》和李嘉图的《政治经
济学及赋税原理》齐名。济学及赋税原理》齐名。
专题 2：序数效用理论
Topic 2: Ordinal Utility
序数效用理论
• 序数效用理论由意大利的帕累托提出。
• 帕累托是罗桑学派的创建人之一，接替瓦
尔拉斯在罗桑大学任教。先追随边际效用
学派。后提出序数效用理论和无差异曲线
偏好公理
H1:H1:反身性反身性(reflexivity)(reflexivity)：：
X X ≥≥ XX
H2:H2:完全性完全性(completeness)(completeness)：：
X X ≥ ≥ Y or Y Y or Y ≥ ≥ XX
H3:H3:传递性传递性(transitivity)(transitivity)：：
X X ≥ ≥ Y and Y Y and Y ≥ ≥ Z, X Z, X ≥ ≥ ZZ
H4:H4:连续性连续性(continuity)(continuity)：：
A≡{ X: X A≡{ X: X ≥ ≥ XX00 } } ，，B≡{ X: X B≡{ X: X ≤ ≤ XX00 } }为闭集为闭集。。
H5:强单调性,又名一致性（consistency）
X=(A1, B1) Y=(A2, B1),
如果A1>A2, => X ＞ Y ，
意味着:
与A点等效用的点的集合必定在区2和4。
• 2 1
•
• A
•
• 3 4
H6:凸性(convexity)
如X ≥ Z，Y ≥ Z，对任意 λ∈(0,1),
有λX＋（1－λ）Y ＞ Z.
实际上满足上述公理的函数，
U (λX＋（1－λ）Y )> U (Z),
定义为严格准凹函数
公理6 保证了无差异曲线凸向原点。
H7:局部非饱和性：给定消费集中的任意X，
对于任意e>0，总存在Y，满足：
abs(X-Y)<e，使得Y≥X
• 德布勒1959证明，如上述公理成立，存在
连续的效用函数U，满足：
X ≥ Y U(X) ≥ U(Y)，
但效用函数不唯一
专题3：无差异曲线
Topic 3: Indifference curves
无差异曲线相关性质无差异曲线相关性质
性质性质11：不同的无差异线代表不同效用：不同的无差异线代表不同效用
性质性质22：无差异曲线不能相交：无差异曲线不能相交
性质性质33：无差异曲线凸向原点：无差异曲线凸向原点。。
两条无差异曲线不可能相交两条无差异曲线不可能相交
Y
X
I1
I2
a
c
b
边际替代率 Marginal rate of substitution (Marginal rate of substitution (MRSMRS))
为了保持效用不变，增加一单位商品而必须放弃
的另一种商品的数量称为边际替代率，以MRS
表示:
MRSxy=-dy/dx =MUx/MUy
Marginal rate of substitution (Marginal rate of substitution (MRSMRS))
边际替代率 Marginal rate of substitution (Marginal rate of substitution (MRSMRS))
为了保持效用不变，增加一单位商品而必须放弃
的另一种商品的数量称为边际替代率，以MRS
表示:
MRSxy=-dy/dx =MUx/MUy
U=C dU=0
MUxdx+ MUydy=0
MRSxy=d y/dx = -MUx/MUy
Marginal rate of substitution (Marginal rate of substitution (MRSMRS))
Marginal rate of substitution (Marginal rate of substitution (MRSMRS))
a
b
Y
X
26
6 7
DY = 4
DX = 1
MRS = 4
Marginal rate of substitution (Marginal rate of substitution (MRSMRS))
a
b
Y
X
26
6 7
c
d
DY = 4
DX = 1
DY = 1
DX = 1
MRS = 1
MRS = 4
13 14
9
问题：
为什么边际替代率递减？
问题：
为什么边际替代率递减？
无差异曲线凸向原点，本身就意味着边际替代率
递减法则成立。边际替代率递减不是根据边际
效用递减法则得到的。
CHAPTER ONE
CONSUMER THEORY
Topic 2: Utility FunctionsTopic 2: Utility Functions
The Utility FunctionThe Utility Function
•• Definition:Definition: Existence of utility function Existence of utility function
A real-valued A real-valued uu: : RRnn++ R R is calledis called a utility function a utility function representing representing
the preference relation , if the preference relation , if
for all for all xx00 , , xx11 RRnn++ , u , u((xx00)) uu((xx11) ) xx0 0 xx11
•• Notes:Notes:
–– Mathematically, the question is one of existence of a continuous Mathematically, the question is one of existence of a continuous
UF representing a preference representing a preference relation.
–– It can be showed that any binary relation that is complete, It can be showed that any binary relation that is complete,
transitive and continuous can be represented by a continuous realtransitive and continuous can be represented by a continuous real
-valued UF.-valued UF.
–– The representation does not depend on convexity and The representation does not depend on convexity and
.
~
~
The Utility FunctionThe Utility Function
•• Theorem :Theorem :
If the binary relation is complete, transitive, continuous and If the binary relation is complete, transitive, continuous and
strictly monotonic, then there existsstrictly monotonic, then there exists a continuous real-valued a continuous real-valued
functionfunction uu: : RRnn++ R , R , whichwhich represents .represents .
Proof: Debreu (1954), or JR:pp14-16 Proof: Debreu (1954), or JR:pp14-16
•• Notes: Notes:
–– Naturally enough,Naturally enough, any additional structure we imposed on the preferences any additional structure we imposed on the preferences
will be reflected as additional structure on the UF that representing be reflected as additional structure on the UF that representing them.
–– By the same token, whenever we assume the UF to have properties beyond By the same token, whenever we assume the UF to have properties beyond
utility, we will in effect be invoking set of additional assumptions on the utility, we will in effect be invoking set of additional assumptions on the
underlying preferences preferences relations.
~
~
The Utility FunctionThe Utility Function
•• Theorem : Theorem : Invariance of the UF to positive monotonic Invariance of the UF to positive monotonic
transformationtransformation
Let be a preference relation on Let be a preference relation on RRnn++ and suppose and suppose uu((xx)) is is a a
utility function thatutility function that represents it. Then represents it. Then vv((xx)) also represents also represents iffiff
vv((xx)) = = f f ((uu((xx)))) for every for every xx, where , where ff: : RR RR is strictly increasing is strictly increasing
on the set of values taken on by on the set of values taken on by uu. .
•• Theorem :Theorem : Properties of preferences and UF Properties of preferences and UF
Let be represented by Let be represented by uu: : RRnn++ R R then:then:
1. 1. uu((xx)) is strictly increasing is strictly increasing iffiff is strictly monotonic. is strictly monotonic.
2. 2. uu((xx)) is quasi-concave is quasi-concave iffiff is convex. is convex.
3. 3. uu((xx)) is strictly quasi-concave is strictly quasi-concave iffiff is strictly convex. is strictly convex.
~
~
~
~
~
~
The Utility FunctionThe Utility Function
•• Assumption :Assumption :
If the binary relation is complete, transitive, continuous, If the binary relation is complete, transitive, continuous,
strictly monotonic , and strictly monotonic , and strictly strictly convexconvex on on RRnn++ , , it can be it can be
represented by a represented by a real-valued function that isreal-valued function that is continuous, continuous,
strictly increasing and strictly quasi-concavestrictly increasing and strictly quasi-concave on on RRnn++
~
Topic 3: Topic 3: Indifference Curve
Indifference CurvesIndifference Curves
• Take a reference bundle x’. The set of all bundles Take a reference bundle x’. The set of all bundles
equally preferred to x’ is the equally preferred to x’ is the indifference curve indifference curve
containing x’containing x’; the set of all bundles y ; the set of all bundles y ~~ x’. x’.
• Since an indifference “curve” is not always a Since an indifference “curve” is not always a
curve a better name might be an indifference curve a better name might be an indifference
“set”.“set”.
Indifference CurvesIndifference Curves
x2
x1
x”
x”’
x’ ~ x” ~ x”’x’
Indifference CurvesIndifference Curves
x2
x1
z x y
x
y
z
Indifference CurvesIndifference Curves
x2
x1
I(x’)
x
I(x)
WP(x), the set of bundles weakly
preferred to x, also called upper
contour set.
Strictly Convex PreferencesStrictly Convex Preferences
x2
y2
x1 y1
x
y
z =(tx1+(1-t)y1, tx2+(1-t)y2)
is preferred to x and y for
all 0 < t < 1.
Indifference Curve
Utility is an Utility is an ordinalordinal (. ordering) concept. (. ordering) concept.
Therefore there exist not one but an infinity of Therefore there exist not one but an infinity of
function representing the same preferencesfunction representing the same preferences.
An indifference curve contains equally preferred An indifference curve contains equally preferred
.
Equal preference Equal preference same utility level. same utility level.
Therefore, all bundles in an indifference curve Therefore, all bundles in an indifference curve
have the same utility the same utility level.
Indifference Curve
The following are equivalentThe following are equivalent
. Preferences are (strictly) convexPreferences are (strictly) convex
. Indifferences curves are (strictly) convexIndifferences curves are (strictly) convex
. Utility functions are (strictly) quasi-concaveUtility functions are (strictly) quasi-concave
Note: concave Note: concave quasi-concave, but the quasi-concave, but the
converse is not always is not always true.
Marginal Utilities and MRSMarginal Utilities and MRS
•• Marginal means “incremental”.Marginal means “incremental”.
•• The marginal utility of commodity The marginal utility of commodity ii is the rate-of-change of is the rate-of-change of
total utility as the quantity of commodity total utility as the quantity of commodity ii consumed changes; consumed changes;
.
•• The general equation for an indifference curve isThe general equation for an indifference curve is
U(U(xx11,,xx22) = ) = kk, a constant. Totally differentiating this identity , a constant. Totally differentiating this identity
givesgives
Marginal Rate of SubstitutionMarginal Rate of Substitution
rearranged is
This is the Marginal Rate of Substitution.
Marginal Rate of SubstitutionMarginal Rate of Substitution
x2
x1
x’
MRS at x’ is the absolute value
of slope of the indifference
curve at x’
MRS & ConvexityMRS & Convexity
Good 2
Good 1
MRS always decreases with x1
if and only if preferences are
strictly convex and IC are
decreasing.
Marginal rate of substitution (Marginal rate of substitution (MRSMRS))
a
b
Y
X
26
6 7
DY = 4
DX = 1
MRS = 4
Marginal rate of substitution (Marginal rate of substitution (MRSMRS))
a
b
Y
X
26
6 7
c
d
DY = 4
DX = 1
DY = 1
DX = 1
MRS = 1
MRS = 4
13 14
9
The end
