Advanced Microeconomics
Li, Junqing
Professor
Department of Economics , Nankai University Research Center of Fictitious Economics, Nankai University
AME: Choice Under Uncertainty
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
√ ？ √
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Reductio ad absurdum, see Huang cha2-2.3 p27-p29 Department of Economics , Nankai University
Upward probability shift
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Department of Economics , Nankai University
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Department of Economics , Nankai University
FSD doesn’t imply that every possible return of the superior distribution is larger than ever possible return of the inferior one . Although G(x) FSD F(x) implies that the mean of x under G(x) is grater than its mean under F(x), but reverse is not.
Definition（Second-order Stochastic Dominance ）
Suppose F and G have the same mean. Distribution G second-order stochastic dominates distribution F i? lottery G is preferred to F under every concave Bernoulli utility function u(·). That is，for every convave u(·) :
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Department of Economics , Nankai University
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Department of Economics , Nankai University
see Huang cha2: 2.5-2.9 p30-p33
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Department of Economics , Nankai University
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Department of Economics , Nankai University
G(.) F(.)
G(.) F(.)
F(.) is en elementary increase in risk fromG(.)
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G(.) second-order stochastically dominates F(.)
Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
(revenue of insurer) qa=pa+(1-p)0 (expected loss of insurer)
The marginal bene?t of an extra dollar of insurance in the bad state times the probability of loss
The marginal cost of the extra dollar of insurance in the good state.
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
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Department of Economics , Nankai University
an individual's subjective probability that it will rain on a certain date.
~
We define the subjective probability that E occurs by the number p(E) that satisfies
(Sure thing principle)
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Department of Economics , Nankai University
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Department of Economics , Nankai University
The Ellsberg paradox
The
Ellsberg paradox：Ambiguity Averse 300 balls in urn: 100 red balls and 200 are either blue or green. Draw a ball at random Gamble A. You receive $1,000 if the ball is red. Gamble B. You receive $1,000 if the ball is blue. p(R)u(1000) > p(B)u(1000) => p(R) > p(B)
Gamble C. You receive $1,000 if the ball is not red. (Blue or green). Gamble D. You receive $1,000 if the ball is not blue. (red or green) p(-R)u(1000) > p(-B)u(1000 => p(-R) > p(-B)
But, p(R) =1- p(-R) ； p(B)=1- p(-B) And Conflicting with The Sure-Thing Principe)
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Department of Economics , Nankai University
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Department of Economics , Nankai University
u(48) >0.33u(55) +0 .66u(48) ? 0.34u(48) >0.33u(55),
$0
C D
Kahneman and Tversky : Certainty E?ect :people tend to overvalue a sure thing. When we are gain , we are risk-aversion; When we are loss, we are risk-love
A B
Li, Junqing
$48
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$55
Department of Economics , Nankai University
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Department of Economics , Nankai University
买机票:票面250块，如果您有托运行李，请加十块。或者说，票面260块，如
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Department of Economics , Nankai University
Li, Junqing
火腿打标签:25%肥肉，或者75%的瘦肉。 50 Department
果您没托运行李，我们给您10块的折扣。
of Economics , Nankai University
Prospect Theory (1979)
Prospect Theory (1979)
Probability Weighting Function
1 0.9 0.8 Perceived Probability 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Actual Probability
V(x,p;y,q)= π(p)v(x) + π(q)v(y)
The Functiuon Decision weight : π(p) is increasing function;and π(0) = 0 and π(1) = 1. Small probability events are generally overweighted. π(p) > p for small values of p and π(p) < p for high values of p.
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Department of Economics , Nankai University
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Department of Economics , Nankai University
Prospect Theory (1979)
1、“二鸟在林，不如一鸟在手”，在确定的收益和“赌一把”之间， 多数人会选择确定的好处。所谓“见好就收，落袋为安。称之为“确 定效应”。 2、在确定的损失和“赌一把”之间，做一个抉择，多数人会选择“赌 一把”。称之为“反射效应”。 “赔则拖，赢必走” 3、白捡的100元所带来的快乐，难以抵消丢失100元所带来的痛苦。 称之为“损失规避”。 4、很多人都买过彩票，虽然赢钱可能微乎其微，你的钱99.99%的可 能支持福利事业和体育事业了，可还是有人心存侥幸搏小概率事件。 称之为“迷恋小概率事件”。 5、多数人对得失的判断往往根据参照点决定，举例来说，在“其他人 一年挣6万元你年收入7万元”和“其他人年收入为9万元你一年收入8 万”的选择题中，大部分人会选择前者。称之为“参照依赖”。
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Choice Under Uncertainty END
Department of Economics , Nankai University