the ecomonics of information.docx
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theecomonicsofinformation
TheEconomicsofInformation[1]
[1]StiglerGJ.Theeconomicsofinformation[J].Thejournalofpoliticaleconomy,1961:
213-225.
Ineconomics,theinformationknownbyactorsisgenerallytakentobegivenandisoftenassumedtobeperfect.Thispaperaddsadimensiontoinformation-relatedproblemsbyconsideringthesearchforinformation.Thepaperattemptstoanalyzesystematicallyoneimportantproblemofinformation---theascertainmentofmarketprice.
Thenatureofsearch:
Evenforhomogenousgoods,theaskingpricesofsellersarenotequal.
Theexistenceofthesepricedifferencesistermedpricedispersion.
Thepaperemphasizesthefactthatdispersionofaskingpricesalwaysexistsinthemarket.
Pricedispersionderivesfromtwosources:
∙Consumersbeingunawareofallofthepricesatwhichagoodisavailable(marketignorance)
∙Additionalservicesprovidedbyseller(customerservice,varietyofstock)
Inamarket,eachsellerhasitsownpriceforagood.Eachbuyer,unlessamarketiscompletelycentralized,willnotknowalloftheaskingpriceswhichvarioussellersquoteatanygiventimebecausepriceschangefrequently.Therefore,eachbuyerdoesnotknowtheminimumpriceforwhichhecanpurchaseagood.Asaresult,abuyerengagesinsearch.Forbuyers,searchisdefinedasaprocessofsurveyinganumberofsellerstodeterminethelowestprice.
*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)
Thecdfofminimumpriceswithnsearchesis
Thepdfofminimumpriceswithnsearchesis
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)If0Ifthecorrelationofsuccessivepriceispositive,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:
Forbuyerswhoknowselleri:
∙Thepercentofbuyerswhowillcanvasssell