不确定性下的消费者行为
西南财经大学经济学院
袁正
Structure
或有消费：State contingent consumption (依情形而定的消费）
不确定性商品的预算约束
不确定性下的偏好
不确定性下的选择
Risk aversion
Diversification and risk spreading
不确定性普遍存在
What is uncertain in economic systems?
tomorrow’s prices
future wealth
future availability of commodities
present and future actions of other people.
对不确定性的理性反应
buying insurance (health, life, auto)
资产组合，分散投资
如何描述不确定性
自然的可能状态
“car accident” (a)
“no car accident” (na).
发生事故的概率为 a,
不发生事故的概率为na ; a + na = 1.
不确定性下的预算约束
保费率为.
消费者拥有初始财产m
Accident causes a loss of L.
Cna 表示不发生事故时的消费价值.
Ca 表示发生事故时的消费价值
Without insurance,
Ca = m - L
Cna = m.
不确定性下的预算约束
Cna
Ca
m
The endowment bundle.
不确定性下的预算约束
购买K单位保额的事故保险，.
Cna = m - K.
Ca = m - L - K + K = m - L + (1- )K.
So K = (Ca - m + L)/(1- )
And Cna = m - (Ca - m + L)/(1- )
带禀赋的预算约束
不确定性下的预算约束
Cna
Ca
m
The endowment bundle.
Preferences Under Uncertainty
2 states of nature:
At probability a , consumption is ca
At probability na , consumption is cna
a + na = 1.
Utility is U(ca, cna, a, na).
Preferences Under Uncertainty
Expected utility function:(Von-Neuman-Morgenstern utility function)
Preferences Under Uncertainty
Cna
Ca
EU1
EU2
EU3
Indifference curves EU1 < EU2 < EU3
其边际替代率
For constant EU, dEU = 0.
Preferences Under Uncertainty
Cna
Ca
EU1
EU2
EU3
Indifference curves EU1 < EU2 < EU3
Choice Under Uncertainty
Cna
Ca
m
The endowment bundle.
Affordable plans
Choice Under Uncertainty
Cna
Ca
m
More preferred
Cna
Ca
m
Most preferred affordable plan
Choice Under Uncertainty
Choice Under Uncertainty
Cna
Ca
m
Most preferred affordable plan
MRS = slope of budget constraint; .
风险规避
Think of a lottery（彩票）.
½的概率得90，1/2的概率得0.
假设U(90) = 12, U(0) = 2.
期望效用为：
Preferences Under Uncertainty
彩票的期望货币值为：
U(EM)为期望值的效用
risk-aversion.
Wealth
$0
$90
12
U($45)
U(45) > EU
2
EU=7
$45
Utility
期望值的效用大于期望效用
风险厌恶（凸函数）
Wealth
$0
$90
12
U($45)
U($45) > EU risk-aversion.
2
EU=7
$45
MU declines as wealth
rises.
U”<0.
Utility
风险爱好（凹函数）
Wealth
$0
$90
12
U(45) < EU risk-loving.
2
EU=7
$45
U($45)
Utility
期望值的效用小于期望效用
MU rises as wealth rises.
U”>0.
风险中性
Wealth
$0
$90
12
U($45) = EU risk-neutrality.
2
U($45)= EU=7
$45
Utility
期望值的效用等于期望效用
MU constant as wealth rises.
U”=0.
风险厌恶的度量
不确定性的选择，相当于多少确定性的收入？
确定性等值（CE）：在一个确定的收入水平上，其效用水平等于不确定性条件下的期望效用水平
50%的概率得到100，50%的概率得到36
求期望效用：
该彩票的期望收益为E（L）=*100+*36=68
不确定性，让消费者的收益缩水。
风险升水：表示消费者为了规避风险而愿意付出的最大代价。
竞争性的保险市场
Expected economic profit = 0.
K - aK - (1 - a)0 = ( - a)K = 0.
= a.
保费率应该等于事故发生的概率。
then insurance is fair.
= a.
两种状态下的收入的边际效用必须相等。
买多少保险？
How much fair insurance does a risk-averse consumer buy?
Risk-aversion MU(c) as c .
Hence ，
m - K = m - L + (1- )K.
K= L full-insurance
Uncertainty is Pervasive
What are rational responses to uncertainty?
buying insurance (health, life, auto)
资产组合，分散投资.
不要把鸡蛋放在同一个篮子
?
Diversification (多样化）
Two firms, A and B. 每股$10.
A ：½的概率获利100，1/2的概率获利20.
B： ½的概率获利100，1/2的概率获利20.
You have $100 to invest. How?
分散投资
Buy only firm A’s stock?
$100/10 = 10 shares.
You earn $1000 with prob. 1/2 and $200 with prob. 1/2.
期望获利: $500 + $100 = $600
分散投资
Buy only firm B’s stock?
$100/10 = 10 shares.
You earn $1000 with prob. 1/2 and $200 with prob. 1/2.
Expected earning: $500 + $100 = $600
分散投资
Buy 5 shares in each firm?
You earn $600 for sure.
分散投资可以获得相同的利润，但降低了风险。
