C, then A ? 6.1.1 Preferences Over Lotteries We begin by building up a theory of rational preferences over lotteries. Lecture Notes 1 Microeconomic Theory Guoqiang TIAN Department of Economics Texas A&M University College Station, Texas 77843 (gtian@tamu.edu) August, 2002/Revised: January 2018 Expected Utility Expected Utility Theory is the workhorse model of choice under risk Unfortunately, it is another model which has something unobservable The utility of every possible outcome of a lottery So we have to –gure out how to test it We have already gone through this process for the model of ™standard™(i.e. Slightly longer version than the published one. Expected Utility Theory – Crucial Features • Utility (“degree of liking”) is defined by (revealed) preferences – i.e. U(A) > U(B) iff A is preferred to (chosen over) B – Contradicted by preference reversals • Preferences are well ordered – i.e. For example, the studies described in Kahneman and Tversky 3 (1979) report frequency distributions of the choices among lotteries by groups of individu-als. 2 Expected Utility We start by considering the expected utility model, which dates back to Daniel Bernoulli in the 18th century and was formally developed by John von Neumann and Oscar Morgenstern (1944) in their book Theory of Games and Economic Be-havior. transitive: If A ? Remarkably, they viewed the development of the expected utility model However, according to expected utility theory, the probabilistic insurance is better than the regular insurance. Expected Utility Theory This is an alternative to “the classical expected utility model, decision makers are assumed to be stonemen”. Studies that investigate the empirical validity of expected utility theory predominantly use a random choice setting. The higher a consumer’s total utility, the greater that consumer’s level of satisfaction. De nition:Full insurance is d = 1. Total Utility. His expected utility from buying d dollars of insurance is EU(d) = (1 p)u(w qd) + pu w qd (1 d): Under what conditions will he insure, and for how much of the loss? EXPECTED UTILITY THEORY Prepared for the Handbook of Economic Methodology (J.Davis, W.Hands, and U.Maki, eds. In other words, if one would like to pay yto insure a probability pof losing x, then one should de nitely be willing to pay a lower price ryto reduce the probability of losing xfrom pto (1 r)p, 0
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