the ecomonics of informationWord格式.docx

the ecomonics of informationWord格式.docx

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*Inthemarket,bothsellersandbuyerswillsearchtheprices.Butinthispresentation,mostoftimeIonlyillustratedthesearchbehaviorofbuyers,sincetheconditionofsellersisparalleltotheanalysisforbuyers.

Thebenefitsofsearch

Becauseofthepricedispersion,thebuyerscanfindlowerpriceandsavemoneythroughsearching.

Then,atanytime,therewillbeafrequencydistributionoftheaskingprices.

AskingpricesP1,P2,…,Pnarei.i.d

F（p）:

thecdfofaskingprices;

f（p）thepdfofaskingprices.

Thecdfofminimumpriceswithnsearchesis

Thepdfofminimumpriceswithnsearchesis

Theexpectedminimumpriceswithnsearchesis

E（n）isadecreasingfunctionofn,and

Therefore,asnincreases,theminimumpricedecreasesatadecreasingrate.

NOW,takingtwospecificexamplestoillustrate:

（1）Ifthedistributionofaskingpricesisauniformdistributionbetween0to1（becauseofitsalgebraicsimplicity）

Theexpectedminimumpriceswithnsearches

Thevarianceoftheminimumpriceis

Notethatasthenumberofsearches（n）increases,theaverageminimumpriceanditsvariancebothdecreaseatadecreasingrate.

Furthermore,Thepaperintroducesaconcept--expectedsavingsfromanadditionalunitofsearch,whicharegivenbytheproductofthequantitypurchased（q）andtheabsolutevalueoftheexpectedreductionofminimumpriceswitheachadditionalsearch:

Whensearchamountnisfixed,themorepricedispersioninthemarket,theexpectedsavingfromwillbelarger.Thesavingswillalsoobviouslybegreater,thegreatertheexpenditureonthecommodity.

（2）Ifthedistributionofaskingpricesisanormaldistribution.

Notethatasthenumberofsearches（n）increases,theaverageminimumpriceanditsvariancebothdecrease.

Thecostofsearch

Indeed,searchwillhelpbuyersincreaseexpectedsavings.However,thereisasearchbehaviour,thereisasearchcost.

a）Thecostofsearchisproportionaltothenumberofsellersfromwhichthebuyerinquiresaboutthegood’sprice.

b）Themaincostistime,sohighincomebuyersfacehighersearchcosts

c）Attheoptimumlevelofsearch:

（expectedmarginalreturn）=（costofsearch）

d）Foruniquegoods（therearefewbuyersorsellersinthemarket）,thecostofsearchismuchhighersincethecostofsearchmustbedevidedbythefractionofpotentialbuyersinthepopulationwhichisbeingsearched.（Ifthereisonlyonepotentialsellerin100sellers,thecostofsearchisincreasedby100times.）

Theretwomethodstodecreasesearchcostsbyidentifyingpotentialbuyersandsellers

（1）“Specializedtraders”centralizetrading.Theyprovideameetingplaceforpotentialbuyersandsellers.

（2）Advertising（classifieds）—aobviousmodernmethodtoidentifyingbuyersandsellers.Buyersandsellersarelisted,reducingsearch,butthecostofplacingtheadvertisementmustalsobeconsidered.

Dealermarket

Fordealer:

howthedemandcurvefacingadealerisdetermined

Onceasellerchoosesapricep,allbuyersforwhomthispistheminimumpricewillbuyfromthisseller.Iftherearersellersquotethesamepricep,thenumberofpossiblebuyersisNb,andthedistributionofaskingpricesisuniform,thentheexpectednumberofbuyersforthesellerisgivenby:

where

（1）For

and

ifn>

2

Asthepricefalls,thenumberofbuyersincreasesatanincreasingrate.

（2）Let

Then,

if

thenumberofbuyersincreaseswithincreasedsearch.

Forbuyer:

howtodeciedesearch（amountandtime）

（1）Forauniquepurchase（likehouseselling）,itstransactiononlyhasoneperiod.Theequationdefiningoptimimsearchis

thecostofsearch=theexpectedmarginalreturn（?

）

（2）Ifpurchasesarerepetitive,thetransactionwillcontinueseveralperiods.Thereisaneffectofsearchonthevolumeofgoodspurchased.Now,weconsideratwoperiodsphurchase.

Lettheexpectedminimumpricebep1=E（n1）inperiod1andlettheexpectedminimumpriceinperiod2,withrameasureofthecorrelationbetweensellers’successiveaskingprices,be

Ifthecostofsearchisλperunit,totalexpendituresforafixedquantityofpurchases（Q）perunitofperiodare,neglectinginterest,

TEisatminimun,when

（1）Ifr=1,whichmeansthecorrealtionofaskingpricesofdealersinsuccessivetimeperiodsisperfect,thenp2=p1,n2=0,n2isdeterminedby

.Theinitialsearchistheonlyonethatneedbeundertaken.Theexpectedsavingsofthesearchwillbethepresentvalueofthediscountedfuturesavingsonfuturespurchasesovertheplanninghorizonofthebuyer.

（2）Ifr=0,whichmeansthatpricesareuncorrelatedacrosstimeperiods,thenthesearchdoneineachperiodwillbeindependentofpreviousexperiencesandn1=n2.

（3）If0<

r<

1,takeE（n）=e-nforexample,wecanknowTEisminimumwhen

Ifthecorrelationofsuccessivepriceispositive,customersearchwillbelargerintheinitialperiodthaninsubsquentperiods.

Theauthorsfindsthatthecorrelationofsuccessiveaskingpricesofsellersusuallypositive.Andapositivecorrelationjustifiesthewidelyheldviewthatinexperiencedbuyerspayhigherpricesinamarketthandoexperiencedbuyers.Theinexperiencedbuyershavenoaccumulatedknowledgeofaskingprices,andevenwithpaywithanoptimumamountofsearchtheywillpayhigherpricesonaverage.

Advertiseing

Forbuyers,advertisngcanhelpthemtoreducesearchcostbyidentifyingsellers.

Model:

Supposeagivenadvertisementofsizeawillinformcpercentofthepontentialbuyersinagivenperiod,soc=g（a）.Acertainfractionb,ofpotentialcustomerwillbebornanddie（departureorforgettingtheseller）inastablepopulation.

Inthefirstperiod

∙Totalnumberofpotentialcustomers:

N

∙Theprobabilityofbeinginformed:

c

Thenumberofpotentialcustomersbeinginformedshouldbe:

cN

Inthesecondperiod

∙Thenumberofthesepotentialcustomerswhohavebeinformedinfirstperiod:

cN（1-b）

∙Thenumberofnewpotentialcustomerswhoarebeinformedinthisperiod:

cbN

∙Thenumberofpotentialcustomerswhowerenotinformedinthefirstperiodbutareinformedinthesecondperiod:

c[（1-b）N-cN（1-b）]

Thetotalnumberofcustomerswhohaveinformedbythisperiod:

cN[1+（1-b）（1-c）]

Inthekthperiod

Totalnumberofpotentialcustomersbeinginformed:

Askgoeslarge,thisapproaches

Let

λistheprobabilitythatanyonesellerwillinformanybuyer（anyonebuyerwillidentifyanyseller）

Iftherearersellers,theprobabilitythatacustomerwillidentifymsellersis

Hence,ifrsellersadvertise,theaveragenumberofsellersacustomerwillidentifyisrλwithvariancerλ（1-λ）.

Andthevalueoftheinformationtobuyersisapproximately:

where

istheexpectedsavingsbecauseofsearchingmtimes.

Forsellers,what’stheirdecisionforadvertising?

Monopoly

Firstweconsideramonopolisticsituation.Inthiscase,thevalueofsearchinthefaceofpricedispersionisabsent.

Amonopolistwilladvertise（andpricetheproduct）soastomaximizehisprofits

ProfitFunction:

p=f（q）isthedemandcurveoftheindividualbuyer,paisadvertisingexpenditure,

isproductioncostsotherthanadvertising.

Theconditionsformaximizeprofit:

Fromequation

（1）,weobtain

（1）

Themarginalcost=marginalrevenue

（2）

istheelasticityofabuyer’sdemandcurve

Inaddition,combiningequation

（1）and

（2）weobtain

themarginalrevenuefromadvertisingexpenditure=theabsolutevalueoftheelasticityofdemand

CompetitiveMarket

Assumptions:

Therearerfirmsandallfirmsareidentical.

Allbuyershaveidenticalldemandcurvesandengageinaequalamountsofsearch.

Undercompetition,theamountofadvertisingbyanyonefirm（seller）canbedeterminedasfollow:

1.Findingthefractionofpotentialbuyerswhowillcanvasstheselleri

Foronetimesearch（s=1）:

Theamountofsellersthateachbuyeronaveragewillknow

sellers

Forbuyerswhoknowselleri:

∙Thepercentofbuyerswhowillcanvassselleri:

∙Thepercentofbuyerswhowillnotcanvassselleri:

Forssearches（s=s）:

Theamountofsellersthateachbuyerinaveragewillknow:

∙Thepercentofbuyerswhowillcanvasssell