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1、Chapter Fifteen,Market Demand,Structure,From Individual to Market Demand FunctionsElasticitiesRevenue and own-price elasticity of demandMarginal revenue and price elasticity,From Individual to Market Demand Functions,Think of an economy containing n consumers,denoted by i=1,n.Consumer is ordinary de
2、mand function for commodity j is,From Individual to Market Demand Functions,When 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 Functions,The market demand curve is the“horizontal sum”of the
3、 individual consumers demand curves.E.g.suppose there are only two consumers;i=A,B.,From Individual to Market Demand Functions,p1,p1,20,15,p1,p1”,p1,p1”,From Individual to Market Demand Functions,p1,p1,p1,20,15,p1,p1”,p1,p1”,p1,From Individual to Market Demand Functions,p1,p1,p1,20,15,p1,p1”,p1,p1”,
4、p1,p1”,From Individual to Market Demand Functions,p1,p1,p1,20,15,35,p1,p1”,p1,p1”,p1,p1”,The“horizontal sum”of the demand curvesof individuals A and B.,Elasticities（弹性）,Elasticity measures the“sensitivity”of one variable with respect to another.The elasticity of variable X with respect to variable Y
5、 is,Economic Applications of Elasticity,Economists use elasticities to measure the sensitivity ofquantity demanded of commodity i with respect to the price of commodity i(own-price elasticity of demand，需求的自价格弹性)demand for commodity i with respect to the price of commodity j(cross-price elasticity of
6、 demand，需求的交叉价格弹性).,Economic Applications of Elasticity,demand for commodity i with respect to income(income elasticity of demand 需求的收入弹性)quantity supplied of commodity i with respect to the price of commodity i(own-price elasticity of supply 供给的自价格弹性),Economic Applications of Elasticity,quantity su
7、pplied of commodity i with respect to the wage rate(elasticity of supply with respect to the price of labor)and many,many others.,Own-Price Elasticity of Demand,Q:Why not use a demand curves slope to measure the sensitivity of quantity demanded to a change in a commoditys own price?,Own-Price Elasti
8、city of Demand,X1*,5,50,10,10,slope=-2,slope=-0.2,p1,p1,In which case is the quantity demandedX1*more sensitive to changes to p1?,X1*,Own-Price Elasticity of Demand,5,50,10,10,slope=-2,slope=-0.2,p1,p1,X1*,X1*,In which case is the quantity demandedX1*more sensitive to changes to p1?,Own-Price Elasti
9、city of Demand,5,50,10,10,slope=-2,slope=-0.2,p1,p1,10-packs,Single Units,X1*,X1*,In which case is the quantity demandedX1*more sensitive to changes to p1?,Own-Price Elasticity of Demand,5,50,10,10,slope=-2,slope=-0.2,p1,p1,10-packs,Single Units,X1*,X1*,In which case is the quantity demandedX1*more
10、sensitive to changes to p1?It is the same in both cases.,Own-Price Elasticity of Demand,Q: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 mea
11、surement used for quantity demanded.,Own-Price Elasticity of Demand,is 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 Elasticity,E.g.Suppose pi=a-bXi.Then Xi=(a-pi)/b
12、and,Therefore,Point Own-Price Elasticity,pi,Xi*,pi=a-bXi*,a,a/b,Point Own-Price Elasticity,pi,Xi*,pi=a-bXi*,a,a/b,Point Own-Price Elasticity,pi,Xi*,pi=a-bXi*,a,a/b,Point Own-Price Elasticity,pi,Xi*,pi=a-bXi*,a,a/b,Point Own-Price Elasticity,pi,Xi*,a,pi=a-bXi*,a/b,Point Own-Price Elasticity,pi,Xi*,a,
13、pi=a-bXi*,a/b,a/2,a/2b,Point Own-Price Elasticity,pi,Xi*,a,pi=a-bXi*,a/b,a/2,a/2b,Point Own-Price Elasticity,pi,Xi*,a,pi=a-bXi*,a/b,a/2,a/2b,Point Own-Price Elasticity,pi,Xi*,a,pi=a-bXi*,a/b,a/2,a/2b,own-price elastic（有弹性）,own-price inelastic（缺乏弹性）,Point Own-Price Elasticity,pi,Xi*,a,pi=a-bXi*,a/b,a
14、/2,a/2b,own-price elastic,own-price inelastic,(own-price unit elastic)单位弹性,Point Own-Price Elasticity,E.g.,Then,so,Point Own-Price Elasticity,pi,Xi*,everywhere alongthe demand curve.,Revenue and Own-Price Elasticity of Demand,If raising a commoditys price causes little decrease in quantity demanded,
15、then sellers revenues rise.Hence own-price inelastic demand causes sellers revenues to rise as price 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
16、Own-Price Elasticity of Demand,Sellers revenue is,Revenue and Own-Price Elasticity of Demand,Sellers revenue is,So,Revenue and Own-Price Elasticity of Demand,Sellers revenue is,So,Revenue and Own-Price Elasticity of Demand,Sellers revenue is,So,Revenue and Own-Price Elasticity of Demand,Revenue and
17、Own-Price Elasticity of Demand,so if,then,and a change to price does not altersellers revenue.,Revenue and Own-Price Elasticity of Demand,but if,then,and a price increase raises sellersrevenue.,Revenue and Own-Price Elasticity of Demand,And if,then,and a price increase reduces sellersrevenue.,Revenu
18、e and Own-Price Elasticity of Demand,In summary:,Own-price inelastic demand;price rise causes rise in sellers revenue.,Own-price 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 Elast
19、icity of Demand,A sellers marginal revenue is the rate at which revenue changes with the number of units sold by the seller.,Marginal Revenue and Own-Price Elasticity of Demand,p(q)denotes the sellers inverse demand function;i.e.the price at which the seller can sell q units.Then,so,Marginal Revenue
20、 and Own-Price Elasticity of Demand,and,so,Marginal Revenue and Own-Price Elasticity of Demand,says that the rate,at 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 Re
21、venue and Own-Price Elasticity of Demand,If,then,If,then,If,then,Selling onemore unit raises the sellers revenue.,Selling onemore unit reduces the sellers revenue.,Selling onemore unit does not change the sellersrevenue.,Marginal Revenue and Own-Price Elasticity of Demand,If,then,If,then,If,then,Mar
22、ginal Revenue and Own-Price Elasticity of Demand,An example with linear inverse demand.,Then,and,Marginal Revenue and Own-Price Elasticity of Demand,a,a/b,p,q,a/2b,Marginal Revenue and Own-Price Elasticity of Demand,a,a/b,p,q,a/2b,q,$,a/b,a/2b,R(q),Income Elasticity,Normal good:0Inferior good:1Necessary good:01,A Special Property,Weighted average of income elasticities of all goods is one with the weights being expenditure shares of the goods.In the case of 2 goods,
