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1、Chapter FifteenMarket Demand市场需求From Individual to Market Demand FunctionsThink of an economy containing n consumers, denoted by i = 1, ,n.Consumer is ordinary demand function for commodity j isFrom Individual to Market Demand FunctionsWhen all consumers are price-takers, the market demand function
2、for commodity j isIf all consumers are identical then where M = nm.Market demand functionThe market demand curve is the “horizontal sum” of the individual consumers demand curves.Denoted by demand function D=D(P) or inverse demand function P=P(D)p1p1p1201535p1p1”p1p1”p1p1”Elasticities （弹性）Elasticity
3、 measures the “sensitivity” of one variable with respect to another.The elasticity of variable X with respect to variable Y isEconomic Applications of ElasticityEconomists use elasticities to measure the sensitivity ofquantity demanded of commodity i with respect to the price of commodity i (own-pri
4、ce 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 demand，需求的交叉价格弹性). Economic Applications of Elasticitydemand for commodity i with respect to income (income elasticity of demand 需求的收入弹性)quantity supplied of commodity i with r
5、espect to the price of commodity i (own-price elasticity of supply 供给的自价格弹性)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= - 2slope= - 0.2p1p1In wh
6、ich 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-packsSingle UnitsX1
7、*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 Elasticity of Demand
8、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 measurement used for quantity demanded. Own-Price Elasticity of Demandis a ratio of per
9、centages and so has nounits of measurement. Hence own-price elasticity of demand is a sensitivity measure that is independent of units of measurement.Own-Price Elasticity of DemandMeasuring increases in percentage terms keeps the elasticity unit-free或或或或Price elasticity of demandPoint Own-Price Elas
10、ticityE.g. Suppose pi = a - bXi. Then Xi = (a-pi)/b andPoint 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*pi = a - bXi*aa/bPoint Own-Price ElasticitypiXi*api = a - bXi*a/bPoint
11、 Own-Price ElasticitypiXi*api = a - bXi*a/ba/2a/2bPoint Own-Price ElasticitypiXi*api = a - bXi*a/ba/2a/2bPoint Own-Price ElasticitypiXi*api = a - bXi*a/ba/2a/2bPoint Own-Price ElasticitypiXi*api = a - bXi*a/ba/2a/2bown-price elastic （有弹性）有弹性）own-price inelastic （缺乏弹性）缺乏弹性）Point Own-Price Elasticityp
12、iXi*api = a - bXi*a/ba/2a/2bown-price elasticown-price inelastic(own-price unit elastic)单位弹性单位弹性Point Own-Price ElasticityE.g. ThensoPoint Own-Price ElasticitypiXi*everywhere alongthe demand curve.Revenue and Own-Price Elasticity of DemandIf raising a commoditys price causes little decrease in quant
13、ity demanded, then sellers revenues rise.Hence own-price inelastic (缺乏弹性) 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 (富有弹性) demand causes sellers revenues to fall
14、 as price rises.Revenue and Own-Price Elasticity of DemandSellers revenue isRevenue and Own-Price Elasticity of DemandSellers revenue isSoRevenue and Own-Price Elasticity of DemandSellers revenue isSoRevenue and Own-Price Elasticity of DemandSellers revenue isSoRevenue and Own-Price Elasticity of De
15、mandRevenue and Own-Price Elasticity of Demandso ifthenand a change to price does not altersellers revenue.Revenue and Own-Price Elasticity of Demandbut ifthenand a price increase raises sellersrevenue.Revenue and Own-Price Elasticity of DemandAnd ifthenand a price increase reduces sellersrevenue.Re
16、venue and Own-Price Elasticity of DemandIn 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 Elasti
17、city of DemandA 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 Demandp(q) denotes the sellers inverse demand function; i.e. the price at which the seller can sell q units. ThensoMarginal Revenue a
18、nd 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
19、and Own-Price Elasticity of DemandIfthenIfthenIfthen 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 DemandIfthenIfthenIfthenMarginal Revenue and Ow
20、n-Price Elasticity of DemandAn example with linear inverse demand.ThenandMarginal Revenue and Own-Price Elasticity of Demandaa/bpqa/2bMarginal Revenue and Own-Price Elasticity of Demandaa/bpqa/2bq$a/ba/2bR(q)Income Elasticity （收入弹性）Recall that price elasticity of demand isHence income elasticity of
21、demand is Income Elasticity （收入弹性）Normal good: 0Inferior good: 1Necessary good: 01StructureFrom Individual to Market Demand FunctionsElasticitiesRevenue and own-price elasticity of demandMarginal revenue and price elasticity练习消费者对商品 x 和在其它商品上的开支 y（价格为1）的效用函数为 1）市场上有完全同样的消费者100人，写出x的市场需求函数。 2）x该如何定价使销售收入最大？此时价格弹性是多少？
