Review Class Five
Outlines
 Up to now we have learned a very important
economic model, which is the Two-good model
with endowment .
 Everyone should comprehend the economic
definitions which are your starts and master the
method that you use to analyze the specific
problem.
 Arithmetic tools and geometrical figures will help
you to seek for the answers, but of cause, you
should operate them well.
Outlines
 Two-good model with endowment
 The key sentence: A typical consumer will
satisfy himself as much as possible with limited
resources.
 Start: 1 Def. of budget constraint involving
prices and endowment point (figure and
equation)
2 Def. of preference (indifference curves
and utility function)
So you can begin your march in two ways:
arithmetic and geometric
Outlines
 Finally you will reach your two objectives:
1 Optimal choice (demand) and the
consumption decision the typical
consumer has made.
2 Comparative statics: How the demand
changes in response to….
Endowment point and the relative price
(Warning: it’s uncertain that the typical
consumer will be better or worse off and
the decision the typical consumer will
make. Why?)
Outlines
 Applications of two-good model with
endowment point
 Intertemporal choices (Fisher)
 Insurance market (Stiglitz)
Intertemporal choices
 Recall that when we obtain the optimal
choice facing to the typical consumer, all
we claims is that current consumption is
mostly based on the current income and
relative price facing to the consumer.
 When people decide how much to consume
and how much to save, they consider both
the present and the future.
Intertemporal choices
 The economist Irving Fisher developed
the model with which economists analyze
how rational, forward-looking consumers
make intertemporal choices—that is,
choices involving different periods of time.
 In fact fisher’s model is the application of
two-good model with endowment point.
Intertemporal choices
 The key sentence:
 A typical and forward-looking consumer
will make a consumption decision to
maximize his lifetime utility with the
intertemporal budget constraint.
 How to describe the intertemporal budget
constraint and the preference?
Intertemporal choices





Budget line:
Assumptions:
1 no bequests or debts
2 Two periods
3 Well-operating financial market
Intertemporal choices
Intertemporal choices
 Now if we impose the Def. of preference
and the utility function, we will obtain the
optimal consumption choice geometrically
and arithmetically.
 Further more, we can also find the role of
the consumer.
Intertemporal choices
偏好差异的影响
存款者
借款人
C2
C2
E1
W1
U1
W2
E2
U2
O
C1
O
C1
Intertemporal choices
 How the consumption decision changes
corresponding to the change in
the
endowment point and the
interest rate .
Intertemporal choices
初始禀赋不同的影响
C2
W1
E
W2
O
U
C1
Intertemporal choices
利率变化对预算线的影响
C2
A1
A
A2
利率上升
利率下降
O
B1 B B2
C1
Intertemporal choices
利率上升
C2
A'
A
E'
E
U'
W
O
U
B'
B
C1
Intertemporal choices
 Two special cases:
 1 Borrowing constraint: The inability to borrow
prevents current consumption from exceeding
current income. A constraint on borrowing can
therefore be expressed as

C1 ≤ Y1.
 This additional constraint on the consumer is
called a borrowing constraint or, sometimes, a
liquidity constraint.
Intertemporal choices
Uncertainty
 Preparations:
 1 how to represent an uncertain
consumption facing a typical consumer?
 Let’s think of different outcomes of some
random event as different types of goods.
 2 Different uncertain consumptions will
give the typical consumers different
satisfactions, so we impose the def. of
preference to describe the satisfaction.
Uncertainty
 Expected utility function: The weighted sum of
some function of consumption in each state.
 Def. of positive affine transformation: we say a
function V (u ) is a positive affine transformation
if it can be written in the form that
V (u )  au  b(a  0)
 We can apply the positive affine transformation
to it and get another expected utility function
that represents the same preference.
Uncertainty
 From the expected utility functions to the
indifference curves.
 If we assume
U ' (C1 )  0,U (C2 )  0,U " (C1 )  0,U (C2 )  0
 Then we can conclude that a function of some
indifferent curve satisfies
2
dC2
d C2
 0,
0
2
dC1
dC1
Uncertainty
 Risk aversion VS Risk loving
 Def
 figures
Uncertainty
Stiglitz: how does the Insurance
market operates?
 You’re the risk averser and have a risky asset:
(W1 ,W2 , P)
 You can go into the insurance market and spread
your risk:
(W1  K ,W2  (1   ) K )
 Questions:1 how to fix the premium?

2 what level of insured amount should
you choose?
Stiglitz: how does the Insurance
market operates?
 Feasible set:
1 

C1  C2 
(0  C1  W1 )
 Optimal choice?
 Conclusions?
1 

W1  W2
Applications of two-good model
Summary：
 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。
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。