Individual DemandOptimal Consumer ChoiceBest Affordable BundleCorner Solutions: Perfect SubstitutesMarginal Rate of Substitution may not be well defined: Perfect ComplementsIncome ChangesIncome Expansion PathSuperior GoodsSuperior and Inferior GoodsIncome and TastesPrice Consumption PathPrice-Consumption PathIndividual Demand CurveFigure 3.7 Demand Curve for Good 1Income and Substitution EffectsThe resulting DemandIncome and Substitution Effects Work in Opposite DirectionsFigure 3.13 Giffen GoodCompensating for Price Changes: “over compensation”Individual DemandIndividual DemandHow Does the Best Affordable How Does the Best Affordable Bundle Change when the Prices or Bundle Change when the Prices or the Income Change the Income ChangeOptimal Consumer ChoiceOptimal Consumer ChoiceAssume consumer’s preferences over Assume consumer’s preferences over bundles of two goods, bundles of two goods, x and y,x and y, can be can be represented by a utility function represented by a utility function U(x,y).U(x,y).The prices of the two goods are The prices of the two goods are Consumer’s income is Consumer’s income is I.I.The optimal bundle will be a solution to the The optimal bundle will be a solution to the following problem: following problem: yxPP , IyPxPyxUyxyxsubject to,max,Best Affordable BundleBest Affordable BundleAssuming convexity and “more-is-better” Assuming convexity and “more-is-better” properties, plus some other technical properties, plus some other technical assumptions, an interior solution will satisfy:assumptions, an interior solution will satisfy:In words: the marginal rate of substitution In words: the marginal rate of substitution between the two goods is equal to the ratio of between the two goods is equal to the ratio of prices and all the income is spent on purchases prices and all the income is spent on purchases of the two goods.of the two goods.IyPxPPPyyxUxyxUyxyx******;/),(/),(Corner Solutions: Perfect Corner Solutions: Perfect SubstitutesSubstitutesIf the goods are perfect If the goods are perfect substitutes, so that the substitutes, so that the marginal rate of marginal rate of substitution is constant no substitution is constant no matter how much of each matter how much of each one of the goods the one of the goods the consumer has, the best consumer has, the best affordable bundle may affordable bundle may contain only one of the contain only one of the goods.goods.xxyyyxPP55 55,yxPPyxyxuMarginal Rate of Marginal Rate of Substitution may not be Substitution may not be well defined: Perfect well defined: Perfect ComplementsComplementsIf the goods are perfect If the goods are perfect complements, so that a complements, so that a consumer uses, say, 5 consumer uses, say, 5 units of good units of good yy for every for every unit of good unit of good x, x, the best the best affordable bundle will affordable bundle will always contain a fixed always contain a fixed proportion of goods proportion of goods independent of the ratio independent of the ratio of prices.of prices.xxyy },5min{, yxyxu Income ChangesIncome ChangesIncome Expansion Path Income Expansion Path traces the traces the changes in the composition of the best changes in the composition of the best affordable bundle as the income changesaffordable bundle as the income changesThe Engel CurveThe Engel Curve is the relationship is the relationship between the income and the amount of a between the income and the amount of a good consumedgood consumedIncome Expansion PathIncome Expansion PathSuperior GoodsSuperior GoodsAs the consumer’s income increases, the quantity demanded increasesSuperior and Inferior Superior and Inferior GoodsGoodsA good is inferior if the quantity demanded falls with the consumer’s incomeIncome and TastesIncome and TastesPrice Consumption PathPrice Consumption PathHolding income and price of the second Holding income and price of the second goodgood fixed, the Price Consumption Path fixed, the Price Consumption Path for good for good oneone is the set of best affordable is the set of best affordable bundles as the price of this good varies.bundles as the price of this good varies.Price-Consumption PathPrice-Consumption PathIndividual Demand CurveIndividual Demand CurveThe individual demand curve is the The individual demand curve is the relationship that shows how much of a relationship that shows how much of a good the consumer wants to purchase good the consumer wants to purchase when the price of this good varies and when the price of this good varies and the rest of the prices and the income are the rest of the prices and the income are held constant.held constant.Figure 3.7 Demand Figure 3.7 Demand Curve for Good 1Curve for Good 1Income and Substitution Income and Substitution EffectsEffectsThe resulting DemandThe resulting DemandIncome and Substitution Income and Substitution Effects Work in Opposite Effects Work in Opposite DirectionsDirectionsFigure 3.13 Giffen GoodFigure 3.13 Giffen GoodCompensating Compensating for Price for Price