LectureVII

# LectureVII - Lecture VII Expected Utility Maxim I Expected Utility A Under Bernoullis original formulation we assume that utility is a concave

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Lecture VII: Expected Utility Maxim I. Expected Utility A. Under Bernoulli’s original formulation we assume that utility is a concave, increasing function of income. Thus, the value of a bet is less than the expected return on the bet. 1. For example, let the preferences be represented as ( 29 ( 29 ln U ww = Assume that the individual is faced with a bet that pays Table 1. Expected Value of Bet w P[w] ln(w) 75,000 .10 11.225 100,000 .20 11.513 125,000 .40 11.736 150,000 .15 11.918 175,000 .10 12.073 200,000 .05 12.206 ( 29 ( 29 [ ] l n 11.7248 123,599.28 127,500.00 Ew e   = = = 2. Thus, if economic agents act to maximize expected well being and if the utility function is concave and increasing, then the amount that the individual is willing to pay is less than the expected value of the bet. The difference is the risk premium. [ ] ( 29 127,50 0 123,599.2 8 3,900.72 E we p =- = -= B. An axiomatic approach to expected utility. 1. Bernoulli’s original work was not based on tenants or assumptions of consumer behavior. 2. Basis of Axiomatic Proofs: “An axiomatized theory first selects its primitive and represents each one of them by a mathematical object…. Next assumptions on the objects representing the primitive concepts are specified, and consequences are mathematically derived from them. The economic interpretation of theorems so obtained is the last step of the analysis.

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## This note was uploaded on 07/15/2011 for the course AEB 6145 taught by Professor Moss during the Spring '11 term at University of Florida.

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LectureVII - Lecture VII Expected Utility Maxim I Expected Utility A Under Bernoullis original formulation we assume that utility is a concave

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