The Case of Perfect-Complements Utility Function What does a p, price-offer curve look like for a perfect-complements utility function? U(X1,X2)=min(x1, X2) Then the ordinary demand functions for commodities 1 and 2 are
The Case of Perfect-Complements Utility Function What does a p1 price-offer curve look like for a perfect-complements utility function? U(x ,x ) minx ,x . 1 2 = 1 2 Then the ordinary demand functions for commodities 1 and 2 are
The Case of perfect-Complements Utility Function X1(p1,p2,y)=x2(p1,p2,y) y p1+p2
The Case of Perfect-Complements Utility Function x p p y x p p y y p p 1 1 2 2 1 2 1 2 * * ( , , ) = ( , , ) = . +
Own-Price Changes X1(p1,p2,y)=X2(P1,p2,y)= y p1+p2 With p2 and y fixed higher p, causes smaller x,*and x2 Asp1→>0,X1=X2→ AsP1→>∞,X1=X2->0
Own-Price Changes x p p y x p p y y p p 1 1 2 2 1 2 1 2 * * ( , , ) = ( , , ) = . + With p2 and y fixed, higher p1 causes smaller x1 * and x2 *. p x x y p 1 1 2 2 → 0, = → . * * As p1 → , x1 = x2 → 0. * * As
p Own-Price Changes Ordinary demand curve Fixed p2 and y. p1" for commodity 1 X2 s yep p p1+p2 X2 p y p1+p2 y X p2 y X p1+p2
p1 x1 * Ordinary demand curve for commodity 1 is Fixed p2 and y. x y p p 2 1 2 * = + x y p p 1 1 2 * = + x y p p 1 1 2 * = . + Own-Price Changes x1 x2 p1 ’ p1 ’’ p1 ’’’ y p2 y/p2
The Case of Perfect-Substitutes Utility function U(X1,x2)=X1+X2 Then the ordinary demand functions for commodities 1 and 2 are
The Case of Perfect-Substitutes Utility Function U(x ,x ) x x . 1 2 = 1 + 2 Then the ordinary demand functions for commodities 1 and 2 are