Utility functions Indiff Curves The collection of all indifference curves for a given preference relation is an indifference map An indifference map is equivalent to a utility function; each is the other
Utility Functions & Indiff. Curves The collection of all indifference curves for a given preference relation is an indifference map. An indifference map is equivalent to a utility function; each is the other
Utility Functions There is no unique utility function representation of a preference relation Suppose U(x,, X2 =X,X2 represents a preference relation Again consider the bundles (4, 1), (23)and(2,2)
Utility Functions There is no unique utility function representation of a preference relation. Suppose U(x1 ,x2 ) = x1x2 represents a preference relation. Again consider the bundles (4,1), (2,3) and (2,2)
Utility functions U(x1,X2)=X1X2,S0 U(2,3)=6>U(4,1)=U(2,2)=4; that is,(2,3)x(4,1)~(2,2)
Utility Functions U(x1 ,x2 ) = x1x2 , so U(2,3) = 6 > U(4,1) = U(2,2) = 4; that is, (2,3) (4,1) ~ (2,2). p
Utility functions U(x1,x2)=x1x2國(2,3)x(4,1)~(2,2) Define v=u2
Utility Functions U(x1 ,x2 ) = x1x2 (2,3) (4,1) ~ (2,2). Define V = U2 . p
Utility Functions U(x1,x2)=x1x2國(2,3)x(4,1)~(2,2) Define v=u2 Then V(x,, 2)=Xx2 and V(2,3)=36>V(41)=V(22)=16 so agaIn (23)x(4,1)~(2,2) V preserves the same order as U and so represents the same preferences
Utility Functions U(x1 ,x2 ) = x1x2 (2,3) (4,1) ~ (2,2). Define V = U2 . Then V(x1 ,x2 ) = x1 2x2 2 and V(2,3) = 36 > V(4,1) = V(2,2) = 16 so again (2,3) (4,1) ~ (2,2). V preserves the same order as U and so represents the same preferences. p p