2. From preferences to utility Definition: u: X> is a utility function of preference % if x%yeu(x)2u(y),x,yEX Can we always find a utility function of % Maybe If X is finite, there always exist utility function Proposition: only rational% can be represented by a utility function(Nc not S C) Lexicographic preference: rational but no utility function exist2.From preferences to utility • Definition: is a utility function of preference , if • Can we always find a utility function of ? – Maybe – If X is finite, there always exist utility function. • Proposition1: only rational can be represented by a utility function. (N.C not S.C) • Lexicographic preference: rational but no utility function exist. u :X→  % x y u x u y x y %     ( ) ( ), , X % %