Chapter 7Market Demand CurvesSlide 3Slide 4Slide 5Slide 6Shifts in the Market Demand CurveShifts in Market DemandSlide 9Slide 10GeneralizationsSlide 12ElasticityPrice Elasticity of DemandDistinguishing Values of eQ,PPrice Elasticity and Total ExpenditureSlide 17Slide 18Slide 19Income Elasticity of DemandCross-Price Elasticity of DemandRelationships Among ElasticitiesSlide 23Slide 24Slutsky Equation in ElasticitiesSlide 26Slide 27Slide 28HomogeneitySlide 30Cobb-Douglas ElasticitiesSlide 32Slide 33Slide 34Linear DemandSlide 36Slide 37Slide 38Slide 39Constant Elasticity FunctionsSlide 41Important Points to Note:Slide 43Slide 44Slide 45Chapter 7MARKET DEMAND AND ELASTICITYCopyright ©2002 by South-Western, a division of Thomson Learning. All rights reserved.MICROECONOMIC THEORYBASIC PRINCIPLES AND EXTENSIONSEIGHTH EDITIONWALTER NICHOLSONMarket Demand Curves•Assume that there are only two goods (X and Y) and two individuals (1 and 2)–The first person’s demand for X isX1 = dX1(PX,PY,I1)–The second person’s demand for X isX2 = dX2(PX,PY,I2)Market Demand Curves•Features of these demand curves:–Both individuals are assumed to face the same prices–Each buyer is assumed to be a price taker•must accept the prices prevailing in the market–Each person’s demand depends on his or her own incomeMarket Demand Curves•The total demand for X is the sum of the amounts demanded by the two buyers–The demand function will depend on PX, PY, I1, and I2total X = X1 + X2total X = dX1(PX,PY,I1) + dX2(PX,PY,I2)total X = DX(PX,PY,I1,I2)Market Demand Curves•To construct the market demand curve, PX is allowed to vary while PY, I1, and I2 are held constant•If each individual’s demand for X is downward sloping, the market demand curve will also be downward slopingMarket Demand CurvesX XXPXPXPXdX1dX2X1*X2*PX*To derive the market demand curve, we sum thequantities demanded at every priceIndividual 1’sdemand curveIndividual 2’sdemand curveMarket demandcurveX*DXX1* + X2* = X*Shifts in the MarketDemand Curve•The market demand summarizes the ceteris paribus relationship between X and PX–Changes in PX result in movements along the curve (change in quantity demanded)–Changes in other determinants of the demand for X cause the demand curve to shift to a new position (change in demand)Shifts in Market Demand•Suppose that individual 1’s demand for oranges is given byX1 = 10 – 2PX + 0.1I1 + 0.5PY and individual 2’s demand isX2 = 17 – PX + 0.05I2 + 0.5PY•The market demand curve isX = X1 + X2 = 27 – 3PX + 0.1I1 + 0.05I2 + PYShifts in Market Demand•To graph the demand curve, we must assume values for PY, I1, and I2•If PY = 4, I1 = 40, and I2 = 20, the market demand curve becomesX = 27 – 3PX + 4 + 1 + 4 = 36 – 3PXShifts in Market Demand•If PY rises to 6, the market demand curve shifts outward toX = 27 – 3PX + 4 + 1 + 6 = 38 – 3PX–Note that X and Y are substitutes•If I1 fell to 30 while I2 rose to 30, the market demand would shift inward toX = 27 – 3PX + 3 + 1.5 + 4 = 35.5 – 3PX–Note that X is a normal good for both buyersGeneralizations•Suppose that there are n goods (Xi, i = 1,n) with prices Pi, i = 1,n.•Assume that there are m individuals in the economy•The j th’s demand for the i th good will depend on all prices and on IjXij = dij(P1,…,Pn, Ij)Generalizations•The market demand function for Xi is the sum of each individual’s demand for that good),...,,,...,(mnmjiijiPPDXX II111•The market demand function depends on the prices of all goods and the incomes and preferences of all buyersElasticity•Suppose that a particular variable (B) depends on another variable (A)B = f(A…)•We define the elasticity of B with respect to A asBAABAABBABeAB// in change % in change %,–The elasticity shows how B responds (ceteris paribus) to a 1 percent change in APrice Elasticity of Demand•The most important elasticity is the price elasticity of demand–measures the change in quantity demanded caused by a change in the price of the goodQPPQPPQQPQePQ// in change % in change %,•eQ,P will generally be negative–except in cases of Giffen’s paradoxDistinguishing Values of eQ,PValue of eQ,P at a PointClassification of Elasticity at This PointeQ,P < -1ElasticeQ,P = -1Unit ElasticeQ,P > -1InelasticPrice Elasticity and Total Expenditure•Total expenditure on any good is equal tototal expenditure = PQ•Using elasticity, we can determine how total expenditure changes when the price of a good changesPrice Elasticity and Total Expenditure•Differentiating total expenditure with respect to P yieldsPQPQPPQ•Dividing both sides by Q, we getPQeQPPQQPPQ,/11Price Elasticity and Total Expenditure•Note that the sign of PQ/ P depends on whether eQ,P is greater or less than -1–If eQ,P > -1, demand is inelastic and price and total expenditures move in the same direction–If eQ,P < -1, demand is elastic and price and total expenditures move in opposite directionsPQeQPPQQPPQ,/11Price Elasticity and Total ExpenditureResponses of PQDemand Price Increase Price DecreaseElastic Falls RisesUnit Elastic No Change No ChangeInelastic Rises FallsIncome Elasticity of Demand•The income elasticity of demand (eQ,I) measures the relationship between income changes and quantity changesQQQeQIIII in change % in change %,•Normal goods  eQ,I > 0–Luxury goods  eQ,I > 1•Inferior goods  eQ,I < 0Cross-Price Elasticity of Demand•The cross-price elasticity of demand (eQ,P’) measures the relationship between changes in the price of one good and and quantity changes in anotherQP'P'QP'QePQ in change % in change %',•Gross substitutes  eQ,P’ > 0•Gross complements  eQ,P’ < 0Relationships Among Elasticities•Suppose that there are only two goods (X and Y) so that the budget constraint is given byPXX + PYY = I•The individual’s demand functions areX = dX(PX,PY,I)Y = dY(PX,PY,I)Relationships Among Elasticities•Differentiation of the budget constraint with respect to I yields1IIYPXPYX •Multiplying each item by 11YYYPXXXPYXIIIIIIRelationships Among Elasticities•Since (PX · X)/I is the proportion of income spent on X and (PY · Y)/I is the proportion of income spent on Y,sXeX,I + sYeY,I = 1•For every good that has an income