1、Chapter FifteenMarket Demand市場需求StructureFrom Individual to Market Demand FunctionsElasticitiesRevenue and own-price elasticity of demandMarginal revenue and price elasticityFrom Individual to Market Demand FunctionsThink of an economy containing n consumers, denoted by i = 1, ,n.Consumer is ordinar

2、y demand function for commodity j isFrom Individual to Market Demand FunctionsWhen all consumers are price-takers, the market demand function for commodity j isIf all consumers are identical then where M = nm.From Individual to Market Demand FunctionsThe market demand curve is the “horizontal sum” o

3、f the individual consumers demand curves.E.g. suppose there are only two consumers; i = A,B.From Individual to Market Demand Functionsp1p12015p1p1”p1p1”From Individual to Market Demand Functionsp1p1p12015p1p1”p1p1”p1From Individual to Market Demand Functionsp1p1p12015p1p1”p1p1”p1p1”From Individual t

4、o Market Demand Functionsp1p1p1201535p1p1”p1p1”p1p1”The “horizontal sum”of the demand curvesof individuals A and B.Elasticities （彈性）Elasticity measures the “sensitivity” of one variable with respect to another.The elasticity of variable X with respect to variable Y isEconomic Applications of Elastic

5、ityEconomists use elasticities to measure the sensitivity ofquantity demanded of commodity i with respect to the price of commodity i (own-price elasticity of demand，需求的自價(jià)格彈性)demand for commodity i with respect to the price of commodity j (cross-price elasticity of demand，需求的交叉價(jià)格彈性). Economic Applic

6、ations of Elasticitydemand for commodity i with respect to income (income elasticity of demand 需求的收入彈性)quantity supplied of commodity i with respect to the price of commodity i (own-price elasticity of supply 供給的自價(jià)格彈性)Economic Applications of Elasticityquantity supplied of commodity i with respect t

7、o the wage rate (elasticity of supply with respect to the price of labor)and many, many others.Own-Price Elasticity of DemandQ: Why not use a demand curves slope to measure the sensitivity of quantity demanded to a change in a commoditys own price?Own-Price Elasticity of DemandX1*5501010slope= - 2sl

8、ope= - 0.2p1p1In which case is the quantity demandedX1* more sensitive to changes to p1?X1*Own-Price Elasticity of Demand5501010slope= - 2slope= - 0.2p1p1X1*X1*In which case is the quantity demandedX1* more sensitive to changes to p1?Own-Price Elasticity of Demand5501010slope= - 2slope= - 0.2p1p110-

9、packsSingle UnitsX1*X1*In which case is the quantity demandedX1* more sensitive to changes to p1?Own-Price Elasticity of Demand5501010slope= - 2slope= - 0.2p1p110-packsSingle UnitsX1*X1*In which case is the quantity demandedX1* more sensitive to changes to p1?It is the same in both cases.Own-Price E

10、lasticity of DemandQ: Why not just use the slope of a demand curve to measure the sensitivity of quantity demanded to a change in a commoditys own price?A: Because the value of sensitivity then depends upon the (arbitrary) units of measurement used for quantity demanded. Own-Price Elasticity of Dema

11、ndis a ratio of percentages and so has nounits of measurement. Hence own-price elasticity of demand is a sensitivity measure that is independent of units of measurement.Point Own-Price ElasticityE.g. Suppose pi = a - bXi. Then Xi = (a-pi)/b andTherefore,Point Own-Price ElasticitypiXi*pi = a - bXi*aa

12、/bPoint Own-Price ElasticitypiXi*pi = a - bXi*aa/bPoint Own-Price ElasticitypiXi*pi = a - bXi*aa/bPoint Own-Price ElasticitypiXi*pi = a - bXi*aa/bPoint Own-Price ElasticitypiXi*api = a - bXi*a/bPoint Own-Price ElasticitypiXi*api = a - bXi*a/ba/2a/2bPoint Own-Price ElasticitypiXi*api = a - bXi*a/ba/2

13、a/2bPoint Own-Price ElasticitypiXi*api = a - bXi*a/ba/2a/2bPoint Own-Price ElasticitypiXi*api = a - bXi*a/ba/2a/2bown-price elastic （有彈性）own-price inelastic （缺乏彈性）Point Own-Price ElasticitypiXi*api = a - bXi*a/ba/2a/2bown-price elasticown-price inelastic(own-price unit elastic)單位彈性Point Own-Price El

14、asticityE.g. ThensoPoint Own-Price ElasticitypiXi*everywhere alongthe demand curve.Revenue and Own-Price Elasticity of DemandIf raising a commoditys price causes little decrease in quantity demanded, then sellers revenues rise.Hence own-price inelastic demand causes sellers revenues to rise as price

15、 rises.If raising a commoditys price causes a large decrease in quantity demanded, then sellers revenues fall.Hence own-price elastic demand causes sellers revenues to fall as price rises.Revenue and Own-Price Elasticity of DemandSellers revenue isRevenue and Own-Price Elasticity of DemandSellers re

16、venue isSoRevenue and Own-Price Elasticity of DemandSellers revenue isSoRevenue and Own-Price Elasticity of DemandSellers revenue isSoRevenue and Own-Price Elasticity of DemandRevenue and Own-Price Elasticity of Demandso ifthenand a change to price does not altersellers revenue.Revenue and Own-Price

17、 Elasticity of Demandbut ifthenand a price increase raises sellersrevenue.Revenue and Own-Price Elasticity of DemandAnd ifthenand a price increase reduces sellersrevenue.Revenue and Own-Price Elasticity of DemandIn summary:Own-price inelastic demand;price rise causes rise in sellers revenue.Own-pric

18、e unit elastic demand;price rise causes no change in sellersrevenue.Own-price elastic demand;price rise causes fall in sellers revenue.Marginal Revenue and Own-Price Elasticity of DemandA sellers marginal revenue is the rate at which revenue changes with the number of units sold by the seller.Margin

19、al Revenue and Own-Price Elasticity of Demandp(q) denotes the sellers inverse demand function; i.e. the price at which the seller can sell q units. ThensoMarginal Revenue and Own-Price Elasticity of DemandandsoMarginal Revenue and Own-Price Elasticity of Demandsays that the rateat which a sellers revenue changeswith the number of units it sellsdepends on the sensitivity of quantitydemanded to price; i.e., upon theof the own-price elasticity of demand.Marginal Revenue and Own-Price Elasticity of DemandIfthenIfthenIfthen Selling onemore