Own-Price Changes What does a p, price-offer curve look like for Cobb-Douglas preferences? Take U(X1, X2) X1X 2 .Then the ordinary demand functions for commodities 1 and 2 are
Own-Price Changes uWhat does a p1 price-offer curve look like for Cobb-Douglas preferences? U x x x x a b ( , ) . 1 2 1 2 uThen the ordinary demand functions for commodities 1 and 2 are Take
Own-Price Changes a X1(p1,p2,y)= a+b pl and X y 2(P1P2, y) a+b p2 Notice that x, does not vary with p, so the p1 price offer curve is flat and the ordinary demand curve for commodity 1 is a rectangular hyperbola
Own-Price Changes x p p y a a b y p 1 1 2 1 * ( , , ) x p p y b a b y p 2 1 2 2 * ( , , ) . and Notice that x2 * does not vary with p1 so the p1 price offer curve is flat and the ordinary demand curve for commodity 1 is a rectangular hyperbola
Own-Price Changes Fixed p2 and y X2 X by (a+b)p2 ay X (a+b)p1
x1 *(p1 ’’’) x1 *(p1 ’) x1 *(p1 ’’) x2 x1 Own-Price Changes Fixed p2 and y. x by a b p 2 2 * ( ) x ay a b p 1 1 * ( )
p1 Own-Price Changes Ordinary demand curve Fixed p2 and y for commodity 1 X2 s ay x1 (a+ b)pl X by (a+b)p2 X1 ay X (a+b)p1
x1 *(p1 ’’’) x1 *(p1 ’) x1 *(p1 ’’) x2 x1 p1 x1 * Own-Price Changes Ordinary demand curve for commodity 1 is Fixed p2 and y. x by a b p 2 2 * ( ) x ay a b p 1 1 * ( ) x ay a b p 1 1 * ( )
Own-Price Changes 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
Own-Price Changes uWhat 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