2. From preferences to utility Desirability: preference is desirable if is monotone: x,yEX, and v>>x.thenyx ify2x, then y>x, it's strongly monotone is local non-satiation: WxeX, and e >0 there is a y, that ly-xc, andyrx proposition: 9 is strong monotone, then it's monotone is monotone, it's local non-satiation2.From preferences to utility • Desirability: preference is desirable if – is monotone: – is local non-satiation: there is a • proposition3: is strong monotone, then it’s monotone; is monotone, it’s local non-satiation. % % x y y x y x , ,and , then X if , then , it's strongly monotone y x y x  %  x X,and >0  y y x ,that y-x ,and   % %