Chapter Six,Demand,Properties of Demand Functions,Comparative statics analysis of ordinary demand functions - the study of how ordinary demands x1*(p1,p2,y) and x2*(p1,p2,y) change as prices p1, p2 and income y change.,Own-Price Changes,How does x1*(p1,p2,y) change as p1 changes, holding p2 and y constant? Suppose only p1 increases, from p1 to p1 and then to p1.,x1,x2,p1 = p1,Fixed p2 and y.,p1x1 + p2x2 = y,Own-Price Changes,Own-Price Changes,x1,x2,p1= p1,p1 = p1,Fixed p2 and y.,p1x1 + p2x2 = y,Own-Price Changes,x1,x2,p1= p1,p1= p1,Fixed p2 and y.,p1 = p1,p1x1 + p2x2 = y,p1 = p1,Own-Price Changes,Fixed p2 and y.,x1*(p1),Own-Price Changes,p1 = p1,Fixed p2 and y.,x1*(p1),p1,x1*(p1),p1,x1*,Own-Price Changes,Fixed p2 and y.,p1 = p1,x1*(p1),p1,x1*(p1),p1,p1 = p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),p1,x1*(p1),p1,p1 = p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),p1,p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),p1,p1,p1 = p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),p1,p1,p1 = p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),x1*(p1),p1,p1,p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),x1*(p1),p1,p1,p1,x1*,Own-Price Changes,Ordinary demand curve for commodity 1,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),x1*(p1),p1,p1,p1,x1*,Own-Price Changes,Ordinary demand curve for commodity 1,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),x1*(p1),p1,p1,p1,x1*,Own-Price Changes,Ordinary demand curve for commodity 1,p1 price offer curve,Fixed p2 and y.,Own-Price Changes,The curve containing all the utility-maximizing bundles traced out as p1 changes, with p2 and y constant, is the p1- price offer curve. The plot of the x1-coordinate of the p1- price offer curve against p1 is the ordinary demand curve for commodity 1.,Own-Price Changes,What does a p1 price-offer curve look like for Cobb-Douglas preferences?,Own-Price Changes,What does a p1 price-offer curve look like for Cobb-Douglas preferences? Take Then the ordinary demand functions for commodities 1 and 2 are,Own-Price Changes,and,Notice that x2* does not vary with p1 so the p1 price offer curve is,Own-Price Changes,and,Notice that x2* does not vary with p1 so the p1 price offer curve is flat,Own-Price Changes,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,Own-Price Changes,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.,x1*(p1),x1*(p1),x1*(p1),Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*,Own-Price Changes,Ordinary demand curve for commodity 1 is,Fixed p2 and y.,Own-Price Changes,What does a p1 price-offer curve look like for a perfect-complements utility function?,Own-Price Changes,What does a p1 price-offer curve look like for a perfect-complements utility function?,Then the ordinary demand functions for commodities 1 and 2 are,Own-Price Changes,Own-Price Changes,With p2 and y fixed, higher p1 causes smaller x1* and x2*.,Own-Price Changes,With p2 and y fixed, higher p1 causes smaller x1* and x2*.,As,Own-Price Changes,With p2 and y fixed, higher p1 causes smaller x1* and x2*.,As,As,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,x1*,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,p1 = p1,y/p2,p1,x1*,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,p1,p1 = p1,y/p2,p1,x1*,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,p1,p1,p1 = p1,y/p2,p1,x1*,Ordinary demand curve for commodity 1 is,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,p1,p1,y/p2,Own-Price Changes,What does a p1 price-offer curve look like for a perfect-substitutes utility function?,Then the ordinary demand functions for commodities 1 and 2 are,Own-Price Changes,and,Fixed p2 and y.,Own-Price Changes,x2,x1,Fixed p2 and y.,p1 = p1 p2,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1 = p1 p2,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1 = p1 = p2,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1 = p1 = p2,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1 = p1 = p2,