mid-exam review class. consumer theory a typical consumer will satisfy himself as much as possible...
TRANSCRIPT
Mid-exam review class
Consumer theory
A typical consumer will satisfy himself as much as possible with limited resources.
First I should use proper tools to describe the “limited resources” and “satisfaction”
Budget Set
Two important definitions: The budget set consists of all bundles
that are affordable at the given prices and income.
The budget line consists of all bundles that just exhaust the consumer’s income.
You should describe the above two definitions in arithmetical and geometrical ways!
Preference
Def.1 Consumption set is the set which consists of all consumption bundles, or say, consumption plans which the typical consumer desires, regardless whether they are feasible or not.
Def.2 If the binary relation defined on the consumption set satisfies Axiom 1,2 and 3, then this binary relation is said to be the Preference relation.
Preference
Axiom 1 Completeness: x is w.p. to y or y is w.p. to x for any pair of x and y.
Axiom 2 Reflexivity: x is w.p. to x for any bundle x.
Axiom 3 Transitivity: If x is w.p. to y and y is w.p. to z, then x is w.p. to z.
Strict preference relation andindifference relation
Def.3 If the binary relation defined on the consumption set satisfies
and
then we say ,which is called the strict preference relation.
Def.4 If the binary relation defined on the consumption set satisfies
andthen we say ,which is called the
indifference relation,
21 .pxwx12 .. pxwnx
21 xx
21 .pxwx12 .pxwx
21 ~ xx
Indifference curves
Def. 5 An indifference curve is a set of consumption bundles with the same desire level of a representative consumer.
Now we can conclude that for a specific preference, there’s a unique shape of indifference curves corresponding to it.
We can use a cluster of IC to describe a specific preference.
Well-behaved preference
Def.6 A given preference is called well-behaved preference if it satisfies Axiom 1,2,3,4 and 5.
Axiom 4monotonic (meaning more is better)
Axiom 5convex (meaning average are preferred to extremes).
Utility function
Utility function is a way to describe preference.
Def. 7 A mapping u: is called the utility function which stands for the preference relat
ion if the mapping satisfies u ( x ) ≥ u ( y ) if and only if
bundle x is w.p. to bundle y.
RR 2
Positive Monotonic transformation
Lemma: Ordinal utility holds that the size of the utility difference between any two consumption bundles doesn’t matter.
So what we care is only the ordinal represented by the amount of utility function.
Positive Monotonic transformation of the utility function represents the same preference as the original utility function.
Positive Monotonic transformation
For a given preference, there’s at least one utility function to describe it.
2 A utility function
0x2
x1
Take a slice at given utility level Project down to get contours
U(x1,x2)U(x1,x2)
The indifference curve
The indifference curve
Demand
Three factors of demand: price, income and preference Now we can obtain the demand function,
and carry out the comparative statics.
Demand function
Key point: Lagrangian method Two properties: 1)
2)
j
i
j
i
p
p
MU
MU
j
j
i
i
p
MU
p
MU
Demand function
Warning: the two arithmetical properties only hold for the tangency case.
In order to obtain the demand, we can also use the geometrical tools.
Find the highest IC in the budget set! Interior solution: Tangency case and kinky case Boundary solution: Some examples
Comparative statics(1)
How does the demand of one good change corresponding to the change in income with the prices constant?
Def. income offer curve and Engle curve
For different types of goods For different types of preferences (H.M)
Comparative statics(1)
Def. normal goods(p97) and inferior goods(p98)
Def. luxury goods and necessary goods(p101)
To make the def. more clearly, we can impose the def. of income elasticity of demand.
Comparative statics(1)
Arithmetical form:
Geometrical meaning: The ratio of the slope of the ray and the slope of
the tangent line of some point on the Engle curve.
dQdIQI
IdIQdQ
Comparative statics(1)
Strict def.
Normal goods: Inferior goods:
Luxury goods: Necessary goods:
001
1,0
Comparative statics(2)
How does the demand of one good change corresponding to the change in its price with the income and price of the other good constant?
Def. price offer curve and personal demand curve
For different types of goods For different types of preferences (H.M)
Comparative statics(2)
Ordinary goods Giffen goods Substitutes Complements
Distinguish the ordinary and Giffen goods in the figures of price offer curve and demand curve
01
1 p
Q
01
1 p
Q
01
2 p
Q
01
2 p
Q
画四种曲线的思路 总原则：直观切入，代数辅助。 1 、为了有好的引导，应先求出两种商品的
需求函数； 2 、根据定义和函数形式开始直观作图； 3 、对比函数形式，检验图像的正确性； 4 、最后要检查曲线（尤其是价格提供曲线
和需求曲线）的起点、终点和渐近线。
注意： 原点一般来说都会在收入提供曲线和恩格
尔曲线上面 在分析价格提供曲线和个人需求曲线时，
我们要尤其注意起点、终点和渐近线。而起点和终点分别是价格趋向于无穷大和零的情形。对此李杰老师认为这两个极限点可取可不取；而我认为对于两个极限情形我们都取空心点，毕竟极限情形是无法达到的。
Deeper sight
Two problems about price and income we should think about seriously:
We have known How the demand of one good changes corresponding to the change in its price with the income and price of the other good constant, but do you know the mechanism that forms the ordinary good or Giffen good? (Ch 8)
Do you know the source of income? (Ch 9)
Chapter 8
Slutsky and Hicks decomposition: The common ground: the process of the c
hange in demand corresponding to the change in the relative price can be decomposed into substitution effect and income effect.
Chapter 8
Def. of substitution effect : the difference between the new optimal choice and the original optimal choice with the real income unchanged and the relative price adjusted.
Def. of income effect : the difference between the final optimal choice and the optimal choice with the real income unchanged and the relative price adjusted.
Chapter 8
Slutsky and Hicks decomposition: The differentia: the def. of “unchanged real in
come” Slutsky: After the change in the relative price, the typical
consumer is still able to buy the original optimal consumption bundle. (Keep the purchasing power constant before and after the change in the relative price.)
Chapter 8
Hicks: After the change in the relative price, the
typical consumer is still able to reach the same level of satisfaction as the original optimal consumption bundle. (Keep the utility constant before and after the change in the relative price.)
Figures.
Slutsky decomposition
Hicks decomposition
Y
X
E E'
G
U1 U2
替代效应
收入效应
希克斯分解
O
Chapter 8
Warning : Subs. Effect is non-positive, while the sign of th
e income effect isn’t unique, depending on the type of the good.
Can we compare the subs. Effects? Giffen goods must be the inferior goods, but not
vice versa. The law of demand. Some examples.
Chapter 8
Chapter 8
Chapter 8
Chapter 8
Chapter 9
To explain the source of “income”, we impose a def. of “endowment”, which means the initial holding of different goods.
Budget constraint:
We can see the endowment is always on the budget line, independent of the relative price.
Chapter 9
Chapter 9
Figure: Gross demand, net demand or net supply
Now in the equilibrium, we should find the optimal choice (gross demand) and make it clear that the decision the typical consumer makes (net demand or net supply).
Figure 1
X
Y
W
B
用
A
W'
W"
A'
B'
A"
B"
E'
E"
E
U'
U" U
O
Figure 2
X
Y
E
U
W
A
B YW
XW
X
Y
W' X'W
Y'W O
初始禀赋改变Ⅱ
Chapter 9
Comparative statics:
Income(1 and 2) figure
Price :figure
Chapter 9
How to obtain the price offer curve? Endowment point must be on the price
offer curve, and the line through w and a, which is another point on the price offer curve is the budget line corresponding to a.
The area which the price offer curve must be in.
X
Y
提供曲线
W
U
B
A
l1
l2
效用增加
效用增加
此处效用最小
O
Chapter 9
From personal gross demand curve to net demand or supply curve (Def.) (figure)
Two examples: (figures) Impose a quantity tax on the consumption
of good 1 Analysis of the labor supply curve (from
the price offer curve to the labor supply curve)
X
PX
A
B
PX
X X
个人总需求曲线 个人净需求曲线 个人净供给曲线
WX
P
O O O
PX
R
劳动供给曲线的推导
E2
W
E3
A3
A2
L2 L1
I
L
A1
W0
W1
W2
W0
W1
W2
W
O
O
Applications of two-good modelSummary ：
在分析具体背景之后，要找准应该把那些因素抽象为两种商品。这个是分析问题的突破口。
确定主旨句：这个经济主体要在一定的约束条件下追求自身利益的最大化。
接下来就做翻译工作，刻画好“约束”和“自身利益”，正如前面所述，这就是你们分析的出发点。
展开相应的几何分析或代数推导，建议两者联合运用。
最后得到我们想要的“最优选择”，有需要还要进行比较静态分析。
Outlines
Applications of two-good model with endowment point
Intertemporal choices (Fisher) Insurance market (Stiglitz)
Intertemporal choices
The key sentence: A typical and forward-looking consumer wi
ll make a consumption decision to maximize his lifetime utility with the intertemporal budget constraint.
How to describe the intertemporal budget constraint and the preference?
Stiglitz: how does the Insurance market operates?
You’re the risk averser and have a risky asset:
You can go into the insurance market and spread your risk:
Questions:1 how to fix the premium? 2 what level of insured amount shoul
d you choose?
),,( 21 PWW
))1(,( 21 KWKW
Chapter 14
Here we have discussed the two-good model, and we have learned how to use this model to solve the optimal problem facing a typical agent.
But why does a typical consumer come into a market, or say, take part in the transaction?
Because a consumer will earn the transaction benefits from it.
Chapter 14
The transaction benefits a typical consumer will earn in the market is considered as consumer’s surplus.
Def. of (net) consumer’s surplus: a buyer’s willingness to pay minus the amount the buyer actually pays.
Figures Arithmetical way （这是定积分的运用，一
定会考核的内容）
Chapter 14
Chapter 14Change in the price
Chapter 14Producer’s surplus
Def. of producer’s surplus: the amount a seller is paid for a good minus the seller’s variable cost.
Figures Arithmetical way
Chapter 14Producer’s surplus
Chapter 14Market surplus
Market (total) surplus=Consumer’s surplus + Producer’s surplus
Market surplus can reflect the transaction benefits earned by the consumer and the producer.
Why will the transaction happen? The answer is transaction benefits.
Chapter 14Market surplus
P
Q
P
市场剩余
S
S
O Q
D
D
E
Chapter 15Outlines
Horizontal summation------- Competitive equilibrium
Two important elasticity: Income elasticity of demand Price elasticity of demand
Taxes
Chapter 15Horizontal summation
The market is made up of many agents, so in order to obtain the market demand or supply we can use the method of Horizontal summation.
Method: You should draw the rough figure and find the kinky point, and then you can calculate the functional form with some different domains. At last you should make “price” the independent variable.
( 这是一定要考核的内容）
Chapter 15Horizontal summation
Chapter 15Competitive equilibrium
In the perfectly competitive market, we can reach the competitive equilibrium, which is the intersection of market supply and demand curve.
Key points of Chapter 1
Welfare economics: the study of how the allocation of
resources affects economic well-being
Two very important definitions about the welfare economics:
Key points of Chapter 1
A Pareto improvement is a change to make some people better off without hurting anybody else.
An economic situation is Pareto efficient if there is no way to make any person better off without hurting anybody else.
Pareto efficiency or Pareto optimal : if there is already no way to make any more
Pareto improvement.
Key points of Chapter 1
Competitive market Monopoly Shortage
Chapter 15 Price elasticity of demand
Def. of Elasticity: a measure of the responsiveness of quantity demanded or quantity supplied to one of its determinants
Def. of Price elasticity of demand: a measure of how much the quantity demanded of a good responds to a change in the price of that good, computed as the percentage change in quantity demanded divided by the percentage change in price.
Chapter 15 Price elasticity of demand
Arithmetical form:
Geometrical meaning: the slope of the ray over the slope of the tangent line of one point on the demand curve.
Warning: Price elastic is usually negative. Price or income elasticity is the point elasticity.
dQdP
QP
PdPQdQ
P
Chapter 15Application of price elastic:
Analysis of revenue Suppose the producer is a monopoly, and
then he can control the price or quantity in order to affect the revenue. (Can he control the price and quantity at the same time?)
1 He controls the price 2 He controls the quantity
Chapter 15Application of price elastic:
Analysis of revenue 1
2
)1)(( PPQdP
dR
)1
1)(()(P
QPQMRdQ
dR
Taxes
Here we only consider the quantity tax Two important conclusions: In the case of quantity tax the values of P
p and Pr, and the relation Pp=Pr+T are independent of tax objects.
The steeper the curve is, the more tax burden, and vice versa.
Deadweight loss
考试注意 七道大题，里面会有小题，所以要抓紧时间。 中英文答题皆可。不会在语言上扣分。 请大家答题时千万不要长篇大论，在开头就明确表明自己观点。图形要清晰（很关键），代数推导会帮你省墨水的。一句话：“少说废话。”
你们千万不要用套模型的观念去做题，一定要根据具体的问题展开。如果你碰到难以攻克的地方，请你思考定义。定势思维会很吃亏的！