2. From preferences to utility If x-y,Va20, ax-ay then are homothetic Proposition: The are homothetic if and only if it's utility function is HD1 fx~y,v=(0,…0),anda∈,(x+ae)~(y+ae1) then are quasi-linear of commodity 1(it's called standard commodity) Proposition: are quasi-linear if and only if it's utility function is Gorman form l(x)=x1+y(x2,…xn)2.From preferences to utility • If , then are homothetic. • Proposition4: The are homothetic if and only if it’s utility function is HD1. • If then are quasi-linear of commodity 1(it’s called standard commodity) • Proposition5: are quasi-linear if and only if it’s utility function is Gorman form x y x y , 0,      % % 1 1 1 x y e x e y e , (1,0, 0),and ,( ) ( )  =  + +    % 1 2 ( ) ( , ) n u x x x x = + %