第十五章市场需要英文

1、Chapter FifteenMarket DemandFrom Individual to Market Demand FunctionsuThink of an economy containing n consumers, denoted by i = 1, ,n.uConsumer is ordinary demand function for commodity j isxp pmjii*(,)12From Individual to Market Demand FunctionsuWhen all consumers are price-takers, the market dem

2、and function for commodity j isX ppmmxppmjnjiiin(,)(,).*121121 From Individual to Market Demand Functionsp1p1xA1*xB1*xxAB11* p1201535p1p1”p1p1”p1p1”The “horizontal sum”of the demand curvesof individuals A and B.ElasticitiesuElasticity measures the “sensitivity” of one variable with respect to anothe

3、r.uThe elasticity of variable X with respect to variable Y is x yxy,%. Own-Price Elasticity of DemanduQ: 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?uA: Because the value of sensitivity then depends upon the (arbi

4、trary) units of measurement used for quantity demanded. Arc and Point ElasticitiesuAn “average” own-price elasticity of demand for commodity i over an interval of values for pi is an arc-elasticity, usually computed by a mid-point formula.uElasticity computed for a single value of pi is a point elas

5、ticity. Arc Own-Price ElasticitypiXi*pipi+hpi-hWhat is the “average” own-priceelasticity of demand for pricesin an interval centered on pi?XiXi X piiiiXp*,*% Arc Own-Price ElasticitypiXi*pipi+hpi-hWhat is the “average” own-priceelasticity of demand for pricesin an interval centered on pi? X piiiiXp*

6、,*% % phpii 1002%()() /* XXXXXiiiii 1002XiXiPoint Own-Price ElasticitypiXi*pipi+hpi-hWhat is the own-price elasticityof demand in a very small intervalof prices centered on pi?XiXiAs h 0, Point Own-Price ElasticitypiXi*piWhat is the own-price elasticityof demand in a very small intervalof prices cen

7、tered on pi?Xi XpiiiiiipXdXdp*,* is the elasticity at the point (,).XpiiPoint Own-Price ElasticityE.g. Suppose pi = a - bXi. Then Xi = (a-pi)/b and XpiiiiiipXdXdp*,* .b1dpdXi*i Therefore, Xpiiiiiipapbbpap*,() /. 1Point Own-Price ElasticitypiXi*api = a - bXi*a/b Xpiiiipap*, paaaa 1 0a/2a/2b Point Own

8、-Price ElasticitypiXi*api = a - bXi*a/b Xpiiiipap*, 1 0a/2a/2b own-price elasticown-price inelastic(own-price unit elastic)Point Own-Price Elasticity XpiiiiiipXdXdp*,* dXdpapiiia* 1 Xpiiaiaiaiaiipkpkapappa*,. 1Xkpiia*. E.g. ThensoPoint Own-Price ElasticitypiXi*Xkpkpkpiiaii* 22 2everywhere alongthe d

9、emand curve.Revenue and Own-Price Elasticity of DemanduIf raising a commoditys price causes little (a lot of ) decrease in quantity demanded, then sellers revenues rise.uHence own-price inelastic (elastic) demand causes sellers revenues to rise (drop) as price rises.Revenue and Own-Price Elasticity

10、of DemandR ppXp( )( ).* Sellers revenue isSo Xp*( ).1 dpdX)p(Xp1)p(X*dRdpXppdXdp *( )Revenue and Own-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

11、increase raises sellersrevenue.Revenue and Own-Price Elasticity of Demand dRdpXp *( ) 1 And if 1thendRdp 0and a price increase reduces sellersrevenue.Marginal Revenue and Own-Price Elasticity of DemanduA sellers marginal revenue is the rate at which revenue changes with the number of units sold by t

12、he seller.MR qdR qdq( )( ). Marginal 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. ThenMR qdR qdqdp qdqqp q( )( )( )( ) R qp qq( )( ) so p qqp qdp qdq( )( )( ).1Marginal Revenue and Own-Price Elasticit

13、y of DemandMR qp qqp qdp qdq( )( )( )( ). 1 dqdppqandsoMR qp q( )( ). 11 Marginal Revenue and Own-Price Elasticity of Demand 11)q(p)q(MRIf 1thenMR q( ). 0If 10 thenMR q( ). 0If 1thenMR q( ). 0Marginal Revenue and Own-Price Elasticity of DemandAn example with linear inverse demand.p qabq( ). ThenR qp q qabq q( )( )() andMR qabq(). 2Marginal Revenue and Own-Price Elasticity of Demandp qabq( ) MR qabq()