1Individual DemandHow Does the Best Affordable Bundle Change when the Prices or the Income Change Optimal Consumer Choice• Assume consumer’s preferences over bundles of two goods, x and y, can be represented by a utility function U(x,y).• The prices of the two goods are • Consumer’s income is I.• The optimal bundle will be a solution to the following problem: yxPP ,()IyPxPyxUyxyx≤+subject to,max,Best Affordable Bundle• Assuming convexity and “more-is-better” properties, plus some other technical assumptions, an interior solution will satisfy:• In words: the marginal rate of substitution between the two goods is equal to the ratio of prices and all the income is spent on purchases of the two goods.IyPxPPPyyxUxyxUyxyx=+=∂∂∂∂******;/),(/),(Corner Solutions: Perfect Substitutes• If the goods are perfect substitutes, so that the marginal rate of substitution is constant no matter how much of each one of the goods the consumer has, the best affordable bundle may contain only one of the goods.xxyyyxPP55()55,<+=yxPPyxyxuMarginal Rate of Substitution may not be well defined: Perfect Complements• If the goods are perfect complements, so that a consumer uses, say, 5 units of good y for every unit of good x, the best affordable bundle will always contain a fixed proportion of goods independent of the ratio of prices.xxyy()},5min{,yxyxu=Income Changes• Income Expansion Path traces the changes in the composition of the best affordable bundle as the income changes• The Engel Curve is the relationship between the income and the amount of a good consumed2Income Expansion PathSuperior GoodsAs the consumer’s income increases, the quantity demanded increasesSuperior and Inferior GoodsA good is inferior if the quantity demanded falls with the consumer’s incomeIncome and TastesPrice Consumption Path• Holding income and price of the second good fixed, the Price Consumption Path for good one is the set of best affordable bundles as the price of this good varies.Price-Consumption Path3Individual Demand Curve• The individual demand curve is the relationship that shows how much of a good the consumer wants to purchase when the price of this good varies and the rest of the prices and the income are held constant.Figure 3.7 Demand Curve for Good 1Income and Substitution EffectsThe resulting DemandIncome and Substitution Effects Work in Opposite DirectionsFigure 3.13 Giffen Good4Compensating for Price