第十五章市场需要t

ChapterFifteenMarketDemandFromIndividualtoMarketDemandFunctionsThinkofaneconomycontainingnconsumers,denotedbyi=1,…,n.Consumeri’sordinarydemandfunctionforcommodityjis

FromIndividualtoMarketDemandFunctionsWhenallconsumersareprice-takers,themarketdemandfunctionforcommodityjis

FromIndividualtoMarketDemandFunctionsp1p1p1201535p1’p1”p1’p1”p1’p1”The“horizontalsum”

ofthedemandcurves

ofindividualsAandB.ElasticitiesElasticitymeasuresthe“sensitivity”ofonevariablewithrespecttoanother.TheelasticityofvariableXwithrespecttovariableYisOwn-PriceElasticityofDemandQ:Whynotjustusetheslopeofademandcurvetomeasurethesensitivityofquantitydemandedtoachangeinacommodity’sownprice?A:Becausethevalueofsensitivitythendependsuponthe(arbitrary)unitsofmeasurementusedforquantitydemanded.ArcandPointElasticitiesAn“average”own-priceelasticityofdemandforcommodityioveranintervalofvaluesforpiisanarc-elasticity,usuallycomputedbyamid-pointformula.Elasticitycomputedforasinglevalueofpiisapointelasticity.ArcOwn-PriceElasticitypiXi*pi’pi’+hpi’-hWhatisthe“average”own-price

elasticityofdemandforprices

inanintervalcenteredonpi’?ArcOwn-PriceElasticitypiXi*pi’pi’+hpi’-hWhatisthe“average”own-price

elasticityofdemandforprices

inanintervalcenteredonpi’?PointOwn-PriceElasticitypiXi*pi’pi’+hpi’-hWhatistheown-priceelasticity

ofdemandinaverysmallinterval

ofpricescenteredonpi’?Ash®0,PointOwn-PriceElasticitypiXi*pi’Whatistheown-priceelasticity

ofdemandinaverysmallinterval

ofpricescenteredonpi’?istheelasticityatthe

point

PointOwn-PriceElasticityE.g.Supposepi=a-bXi.

ThenXi=(a-pi)/bandTherefore,PointOwn-PriceElasticitypiXi*api=a-bXi*a/ba/2a/2bPointOwn-PriceElasticitypiXi*api=a-bXi*a/ba/2a/2bown-priceelasticown-priceinelastic(own-priceunitelastic)PointOwn-PriceElasticityE.g.ThensoPointOwn-PriceElasticitypiXi*everywherealong

thedemandcurve.RevenueandOwn-PriceElasticityofDemandIfraisingacommodity’spricecauseslittle(alotof)decreaseinquantitydemanded,thensellers’revenuesrise.Henceown-priceinelastic(elastic)demandcausessellers’revenuestorise(drop)aspricerises.RevenueandOwn-PriceElasticityofDemandSellers’revenueisSoRevenueandOwn-PriceElasticityofDemandsoifthenandachangetopricedoesnotalter

sellers’revenue.RevenueandOwn-PriceElasticityofDemandbutifthenandapriceincreaseraisessellers’

revenue.RevenueandOwn-PriceElasticityofDemandAndifthenandapriceincreasereducessellers’

revenue.MarginalRevenueandOwn-PriceElasticityofDemandAseller’smarginalrevenueistherateatwhichrevenuechangeswiththenumberofunitssoldbytheseller.MarginalRevenueandOwn-PriceElasticityofDemandp(q)denotestheseller’sinversedemandfunction;i.e.thepriceatwhichthesellercansellqunits.ThensoMarginalRevenueandOwn-PriceElasticityofDemandandsoMarginalRevenueandOwn-PriceElasticityofDemandIfthenIfthenIfthenMarginalRevenueandOwn-PriceElasticityofDemandAnexamplewithlin