October 21, 2005 12:18masterSheet number 125 Page number 109Risk Aversion109Nevertheless, in the economic literature it is usually assumed thata decision maker’s preferences over wealth changes are induced fromhis preferences with regard to “final wealth levels.” Formally, whenstarting with wealthw, denote bywthe decision maker’s prefer-ences over lotteries in which the prizes are interpreted as “changes”in wealth. By thedoctrine of consequentialismall relationsware de-rived from the same preference relation,, defined over the “finalwealth levels” bypwqiffw+pw+q(wherew+pis the lotterythat awards a prizew+xwith probabilityp(x)). Ifis representedby a vNM utility functionu, this doctrine implies that for allw, thefunctionvw(x)=u(w+x)is a vNM utility function representing thepreferencesw.Invariance to WealthWe say that the preference relationexhibitsinvariance to wealth(in the literature it is often calledconstant absolute risk aversion) if
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absolute risk aversion, VNM utility function