Chapter Six Demand Properties of Demand Functions uComparative 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 uHow does x1*(p1,p2,y) change as p1 changes, holding p2 and y constant? uSuppose 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 uThe curve containing all the utility- maximizing bundles traced out as p1 changes, with p2 and y constant, is the p1- price offer curve. uThe plot of the x1-coordinate of the p1- price offer curve against p1 is the ordinary demand curve for commodity 1. Own-Price Changes uWhat does a p1 price-offer curve look like for Cobb-Douglas preferences? Own-Price Changes uWhat does a p1 price-offer curve look like for Cobb-Douglas preferences? uTake 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 uWhat does a p1 price-offer curve look like for a perfect-complements utility function? Own-Price Changes uWhat 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 uWhat 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 Fixed p2 and y. Own-Price Changes x2 x1 p1 x1* Fixed p2 and y. p1 p1 = p1 = p2 p2 = p1 Fixed p2 and y. Own-Price Changes x2 x1 p1 x1* Fixed p2 and y. p1 p1 p2 = p1 Fixed p2 and y. Own-Price Changes x2 x1 p1 x1* Fixed p2 and y. p1 p2 = p1 p1 p1 price offer curve Ordinary demand curve for commodity 1 Own-Price Changes uUsually we ask “Given