Rubinstein2005-page127 - October 21, 2005 12:18 master...

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October 21, 2005 12:18 master Sheet number 125 Page number 109 Risk Aversion 109 Nevertheless, in the economic literature it is usually assumed that a decision maker’s preferences over wealth changes are induced from his preferences with regard to “final wealth levels.” Formally, when starting with wealth w , denote by ± w the decision maker’s prefer- ences over lotteries in which the prizes are interpreted as “changes” in wealth. By the doctrine of consequentialism all relations ± w are de- rived from the same preference relation, ± , defined over the “final wealth levels” by p ± w q iff w + p ± w + q (where w + p is the lottery that awards a prize w + x with probability p ( x ) ). If ± is represented by a vNM utility function u , this doctrine implies that for all w , the function v w ( x ) = u ( w + x ) is a vNM utility function representing the preferences ± w . Invariance to Wealth We say that the preference relation ± exhibits invariance to wealth (in the literature it is often called
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.

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