1、中級(jí)微觀經(jīng)濟(jì)學(xué)15Chapter FifteenMarket Demand市場需求市場需求StructureuFrom Individual to Market Demand FunctionsuElasticitiesuRevenue and own-price elasticity of demanduMarginal revenue and price elasticityFrom Individual to Market Demand FunctionsuThink of an economy containing n consumers, denoted by i = 1, ,n.u

2、Consumer is ordinary demand function for commodity j isxp pmjii*(,)12From Individual to Market Demand FunctionsuWhen all consumers are price-takers, the market demand function for commodity j isuIf all consumers are identical then where M = nm.X p pmmxp pmjnjiiin(,)(,).*121121 XppMnxppmjj(,)(,)*1212

3、 From Individual to Market Demand FunctionsuThe market demand curve is the “horizontal sum of the individual consumers demand curves.uE.g. suppose there are only two consumers; i = A,B.From Individual to Market Demand Functionsp1p1xA1*xB1*2015p1p1p1p1From Individual to Market Demand Functionsp1p1xA1

4、*xB1*xxAB11* p12015p1p1p1p1p1From Individual to Market Demand Functionsp1p1xA1*xB1*xxAB11* p12015p1p1p1p1p1p1From Individual to Market Demand Functionsp1p1xA1*xB1*xxAB11* p1201535p1p1p1p1p1p1The “horizontal sumof the demand curvesof individuals A and B.Elasticities 彈性u(píng)Elasticity measures the “sensit

5、ivity of one variable with respect to another.uThe elasticity of variable X with respect to variable Y is x yxy,%. Economic Applications of ElasticityuEconomists use elasticities to measure the sensitivity ofuquantity demanded of commodity i with respect to the price of commodity i (own-price elasti

6、city of demand，需求的自價(jià)錢彈性，需求的自價(jià)錢彈性)udemand for commodity i with respect to the price of commodity j (cross-price elasticity of demand，需求的交，需求的交叉價(jià)錢彈性叉價(jià)錢彈性). Economic Applications of Elasticityldemand for commodity i with respect to income (income elasticity of demand 需求的收入彈需求的收入彈性性)lquantity supplied o

7、f commodity i with respect to the price of commodity i (own-price elasticity of supply 供應(yīng)的自價(jià)錢彈性供應(yīng)的自價(jià)錢彈性)Economic Applications of Elasticitylquantity supplied of commodity i with respect to the wage rate (elasticity of supply with respect to the price of labor)land many, many others.Own-Price Elastic

8、ity of DemanduQ: 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= - 2slope= - 0.2p1p1In which case is the quantity demandedX1* more sensitive to changes to p1?X1*Own-Price Elasticity

9、 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-packsSingle UnitsX1*X1*In which case is the quantity demandedX1* more sensitive to changes to p1?Own-Price Elas

10、ticity 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 Elasticity of DemanduQ: Why not just use the slope of a demand curve to measure the sensitivity of quantity dema

11、nded to a change in a commoditys own price?uA: Because the value of sensitivity then depends upon the (arbitrary) units of measurement used for quantity demanded. Own-Price Elasticity of Demand x pxp1111*,*% is a ratio of percentages and so has nounits of measurement. Hence own-price elasticity of d

12、emand 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 and XpiiiiiipXdXdp*,* .b1dpdXi*i Therefore, Xpiiiiiipapbbpap*,() /. 1Point Own-Price ElasticitypiXi*pi = a - bXi*aa/bPoint Own-Price ElasticitypiXi*pi =

13、a - bXi* Xpiiiipap*, aa/bPoint Own-Price ElasticitypiXi*pi = a - bXi* Xpiiiipap*, p 00 aa/bPoint Own-Price ElasticitypiXi*pi = a - bXi* Xpiiiipap*, p 00 0aa/bPoint Own-Price ElasticitypiXi*api = a - bXi*a/b Xpiiiipap*, paaaa 2221 / 0Point Own-Price ElasticitypiXi*api = a - bXi*a/b Xpiiiipap*, paaaa

14、2221 / 1 0a/2a/2bPoint Own-Price ElasticitypiXi*api = a - bXi*a/b Xpiiiipap*, paaaa 1 0a/2a/2bPoint Own-Price ElasticitypiXi*api = a - bXi*a/b Xpiiiipap*, paaaa 1 0a/2a/2b Point Own-Price ElasticitypiXi*api = a - bXi*a/b Xpiiiipap*, 1 0a/2a/2b own-price elastic 有彈性有彈性own-price inelastic 缺乏彈性缺乏彈性Poin

15、t Own-Price ElasticitypiXi*api = a - bXi*a/b Xpiiiipap*, 1 0a/2a/2b own-price elasticown-price inelastic(own-price unit elastic)單位彈性單位彈性Point Own-Price Elasticity XpiiiiiipXdXdp*,* dXdpapiiia* 1 Xpiiaiaiaiaiipkpkapappa*,. 1Xkpiia*. E.g. ThensoPoint Own-Price ElasticitypiXi*Xkpkpkpiiaii* 22 2everywhe

16、re alongthe demand curve.Revenue and Own-Price Elasticity of DemanduIf raising a commoditys price causes little decrease in quantity demanded, then sellers revenues rise.uHence own-price inelastic demand causes sellers revenues to rise as price rises.uIf raising a commoditys price causes a large dec

17、rease in quantity demanded, then sellers revenues fall.uHence own-price elastic demand causes sellers revenues to fall as price rises.Revenue and Own-Price Elasticity of DemandR ppXp( )( ).* Sellers revenue isRevenue and Own-Price Elasticity of DemandR ppXp( )( ).* Sellers revenue isSodRdpXppdXdp *(

18、 )Revenue and Own-Price Elasticity of DemandR ppXp( )( ).* Sellers revenue isSo dpdX)p(Xp1)p(X*dRdpXppdXdp *( )Revenue and Own-Price Elasticity of DemandR ppXp( )( ).* Sellers revenue isSo Xp*( ).1 dpdX)p(Xp1)p(X*dRdpXppdXdp *( )Revenue and Own-Price Elasticity of Demand dRdpXp *( ) 1 Revenue and Ow

19、n-Price Elasticity of Demand dRdpXp *( ) 1 so if 1thendRdp 0and a change to price does not altersellers revenue.Revenue and Own-Price Elasticity of Demand dRdpXp *( ) 1 but if 10 thendRdp 0and a price increase raises sellersrevenue.Revenue and Own-Price Elasticity of Demand dRdpXp *( ) 1 And if 1the

20、ndRdp 0and a price increase reduces sellersrevenue.Revenue and Own-Price Elasticity of DemandIn summary: 10 Own-price inelastic demand;price rise causes rise in sellers revenue. Own-price unit elastic demand;price rise causes no change in sellersrevenue. 1 Own-price elastic demand;price rise causes

21、fall in sellers revenue. 1Marginal Revenue and Own-Price Elasticity of DemanduA sellers marginal revenue is the rate at which revenue changes with the number of units sold by the seller.MR qdR qdq( )( ). Marginal Revenue and Own-Price Elasticity of Demandp(q) denotes the sellers inverse demand funct

22、ion; i.e. the price at which the seller can sell q units. ThenMR qdR qdqdp qdqqp q( )( )( )( ) R qp qq( )( ) so p qqp qdp qdq( )( )( ).1Marginal Revenue and Own-Price Elasticity of DemandMR qp qqp qdp qdq( )( )( )( ). 1 dqdppqandsoMR qp q( )( ). 11 Marginal Revenue and Own-Price Elasticity of Demand

23、MR qp q( )( ) 11 says 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 Demand 11)q(p)q(MRIf 1thenMR q( ). 0If 10 thenMR q( ). 0If 1thenMR q( ). 0 Selling onemore unit raises the sellers revenue. Sel