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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’’’. Own-Price Changes Own-Price Changes 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 Own-Price Changes Own-Price Changes Own-Price Changes 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? Own-Price Changes Own-Price Changes Own-Price Changes Own-Price Changes Own-Price Changes What does a p1 price-offer curve look like for a perfect-substitutes utility function? Own-Price Changes Own-Price Changes Usually we ask “Given the price for commodity 1 what is the quantity demanded of commodity 1?” But we could also ask the inverse question “At what price for commodity 1 would a given quantity of commodity 1 be demanded?” Own-Price Changes Own-Price Changes Own-Price Changes Own-Price Changes Own-Price Changes Taking quantity demanded as given and then asking what must be price describes the inverse demand function of a commodity. Own-Price Changes Own-Price Changes Income Changes How does the value of x1*(p1,p2,y) change as y changes, holding both p1 and p2 constant?
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