Econ171-Spring2010-04-ExpUtil1-handout

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Economics 171 ecisions Under Uncertainty Decisions Under Uncertainty 3. Expected Utility Preferences inter 2010 Winter 2010 Herb Newhouse 1 eadings Readings • Machina Reader – Handout 3: p. 15 – 16. • Lindley – Ch. 4 • Additional References: – Kreps (1990), A Course in Microeconomic Theory , Princeton University Press: Ch 3 – 3.2. – Machina (1987), “Choice under Uncertainty: Problems olved and Unsolved”, Economic Perspectives: p. 121 Solved and Unsolved , Economic Perspectives: p. 121 132 • http://econ.ucsd.edu/~mmachina/papers/Machina_Problems_Pa per.pdf 2 utline Outline he axioms of expected utility theory The axioms of expected utility theory. • Expected utility preferences over objective tteries lotteries. • The triangle diagram. 3 bjective Lotteries Objective Lotteries he big assumption we’re making for this The big assumption we re making for this topic is that probabilities are objective. robabilities are given/known ahead of time – Probabilities are given/known ahead of time. • Like casino games – roulette, craps, blackjack. given probability distribution ( ..., for A given probability distribution ( p 1 , p 2 , . . . , p n ) for our states of nature ( θ 1 , θ 2 , . . . , θ n ). p (\$100) = 0.1, p (\$50) = 0.5, p (-\$100)=0.4 p (2 S , 1 B ) = 0.25, p (2 S , 2 B ) = 0.4, p(3 S , 1 B ) = 0.35 p (new drug) = 0.3, p (no discovery) = 0.7 » These last two are probably subjective probabilities. 4

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robability Mixtures Probability Mixtures onsider probability distributions and s well as q  Consider probability distributions as well as the mixture 1- where 0 1. pq   1 The support of this new distribution is the union of the supports of and . q   pp 2 If is some member of this union, x then the probability given by to is , where 0 if is not in the support of . x p x q x p xx p    pp pp 5       Ex: Lottery : 10 0.3, 0 0.1, 5 0.6 ottery : 10 6 10 0 4 p p p p      Lottery : .6, 0.4 2 1 qp 12 Consider the mixture : 33 3 0 10 1 10 p p    
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