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Unformatted text preview: Microeconomic Theory Econ 101A Fall 2008 GSI: Eva Vivalt Section Notes 10: Expected Utility and Insurance 1 Expected Utility Expected Utility (EU) is a technique developed by Von Neumann and Morgenstern (1944) to deal with situations of quantifiable risk. It requires preferences to exhibit two additional axioms of continuity and independence , which are somewhat controversial. Assume that states of nature can be indexed by an s = 1 , 2 ,...,S , each with a probability of occurring of p 1 ,p 2 ,...,p S , which as probabilities obey p s 0 and S s =1 p s = 1. Let x s be the realization of some random variable, sometimes known as a prospect or lottery, x in state s , which yields utility u ( x s ). The Expected Utility Theorem states that if consumers have rational preferences that exhibit continuity and independence, then agents will behave as if they maximize the expected value of their utility, or just expected utility. E [ u ( x )] = S X s =1 p s u ( x s ) Similarly, firms can be assumed to maximize expected profits E [ ( x )] over various states of the world. The nature of the budget constraint will vary considerably upon the situation considered. The easiest set-up is a 2 state set up with p 1 = p and p 2 = 1- p . Individuals maximize: E [ u ( x )] = pu ( x 1 ) + (1- p ) u ( x 2 ) 1.1 Risk Aversion One way of thinking about risk aversion is to think that people have convex preferences over consumption in either state: they would rather have a moderate consumption in both states rather than low consumption in one state and high consumption in the other, just as people tend to prefer a mixed bundle of goods than a lot of only one good....
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- Fall '08