The Advertising Market in a Product Oligopoly

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1 The Adversg Mare a Produc Olgooly Ahoy Dues chool o Ecoocs ad Maagee Uversy o Aarhus Århus Dear Ocober 003 Absrac A odel s develoed whch roducers a dereaed roduc are coee rces ad orave adversg. The odel also cludes coercal eda whch are led o roducers hrough he adversg are ad o cosuers hrough he eda are. We vesgae how cera are araeers such as eda are dereao or roduc are dereao aec he coeve level adversg chose he are. The odel shows ha less roduc dereao or ore eda dereao leads o a hgher are level o adversg ad he case o sucely hgh eda dereao we observe levels o adversg excess o he socal ou. Acowledges: The edor Davd Geesove a secod edor ad a aoyous reeree ade a sgca uber o coes ha grealy roved hs aer. Ths research was aed a he Uversy o Psburgh whle he docoral rogra he Deare o Ecoocs ad suor hrough he Adrew Mello Predocoral ellowsh s graeully acowledged. I a also graeul o Esher Gal-Or or her advce gudace ad sgh.

2 . Iroduco Ths aer addresses he ollowg quesos: Why do soe roduc ares have ore adversg ha ohers ad wha are roeres cause he are level o adversg o exceed he ece level? To aswer hese quesos we use a odel whch wo or ore roducers a dereaed roduc are coee rces ad adversg. The odel also cludes coercal eda who sell adversg sace o roducers ad broadcas roduc orao he or o adversg essages o cosuers. The odel dcaes ha less dereaed roduc ares ed o have hgher are levels o adversg levels. Also a hghly dereaed eda are corbues o excess adversg. There s ceraly ecooc eres how adversg aecs ares ad are allocaos gve ha U adversers se $43 bllo ¼ % o U GDP o adversg 000. The orace o adversg dusral ecoocs ca be see he rece wave o eda ergers such as ha o Vaco ad CB. Because hs erger bulds such a broad vewersh dusry secalss deered ha he erger's ably o arac adversers was he ey acor brgg hese wo coaes ogeher. O he ecooss who have vesgaed adversg ay have addressed he ossbly ha here exss a socally udesrable excess aou o adversg. Noable exales are Buers 977 Dx & Nora 978 haro 980 Grossa & haro 984 Nchols 985 ad egea 99. oe sudes such as Nelso 974 Grossa & haro 984 ad vo der ehr & ev 998 have vesgaed why cera ares see o have ore adversg ha ohers. These sudes are ued by wo assuos: The sole socal bee o roducers adversg exedure s he oeal ha a adversg essage brgs orh a cusoer o he roduc are; Cosuers choces have o ac o he ye or aou o adversg hey receve. The rese odel dears ro hese assuos or reasos ha are ade clear below. ro he roducer s o o vew he rs o he above assuos should be aare. The roducer s urose adversg s o crease he dead or s roduc Leadg Naoal Adversers Adversg Age 00. ee or exale ''They Have I All Now'' Busess Wee eeber

3 by org cosuers abou he roduc's exsece avalably rce ec. or by ersuadg he ha he roduc bes sus her reereces. However cosuers ge uch o hs adversg hrough coercal eda le ewsaers elevso ad rado whch due o suor by adversg exedures are oe ree o subscrbers. Ths suggess ha here s a large socal bee ro coercal eda servces ad ha ay calculao o socal welare ro adversg exedures should clude such bees. Relaxg he secod assuo by gvg cosuers soe choce adversg exosure has realsc as well as heorecal aeal. ce cosuers ae a choce abou whch edu o subscrbe s he aural o assue ha hey ae hs decso based o her reereces over he ye ad quay o avalable eda servces. or exale oe rado sao devoes 5% o s are o adversg ad a slar rado sao devoes oly 0% o adversg he erhas we would exec he orer sao o have ewer lseers ha he laer sao. Cosequely we should exec ha saos wh ore lseers gh ceers arbus charge a hgher rce or s adversg slos sce wll be heard by ore oeal cusoers. The heorecal aeal o relaxg hs assuo s ha allows oe o edogeze he rce o adversg eablg he odel o accou or ore o he ecooc orces ha deere he roducers' choces o adversg levels. The realsc aeal o hs coes ro evdece ha coercal breas cause ay elevso vewers o swch o aoher chael. ee or exale ddarh & Chaoadhyay 998. The odel reseed hs aer addresses boh o hese os by usg hree yes o ages roducers eda reerred o as saos ad cosuers eracg hrough hree ares. Producers ad cosuers are led by he roduc are roducers ad saos are led by he adversg are ad cosuers ad saos are led by he eda are. I a ae o caure all socal bees o adversg exedures welare calculaos clude saos ros ad he cosuers bee ro lseg. The hree-age odel edogezes he rce o adversg hereby cludg cosuers ably o aec he aou o adversg chose by roducers. There s rece wor ha exaes he choces o adversg wh resec o coercal eda. I deede wor Moa & Polo 00 ad Nlsse & ørgard

4 00 exae odels o roducer s adversg choces wh a eda dusry. Ther wor ocuses o elevso eda bu could be geeralzed o oher broadcas eda such as rado. These aers do o exae welare lcaos o adversg whch s doe he rese aer. Nlsse & ørgard 00 exae elevso sao s veses rogra qualy whch s o doe here. Moa & Polo 00 exae elevso sao ery whch s dscussed here. I a seg slar o he rese aer Dues & Gal-Or 003 exae exclusve adversg coracs ad Gal-Or & Dues 003 vesgae locaoal choce o eda. Oher odels o coercal eda clude Aderso & Coae 000 Masso e. al. 990 Häcer & Nyberg 00 Gabszewcz e. al. 999 ad egea 00 as well as he seal wors o eer 95 Beebe 977 ad ece & Owe 977. The rese aer s dsgushed ro hese by s exlc odelg o dvdual cosuer choce he roduc are. Adversg hs odel aes o a orave role where adversg essages delver roduc rce ad sore locao. Cosuers oly source o roduc orao s ro adversees. Buers 977 Grossa & haro 984 egea 99 ad ahl 994 all rea adversg hs way bu coe o colcg coclusos abou wheher he are rovdes a ece level o adversg. Grossa & haro 984 d ha adversg levels are excessve. Buers 977 ds ha adversg s excessve whe cusoers egage search. O he oher had egea 99 ad ahl 994 rese odels o orave adversg ha show ha he are roduces oo lle adversg as coared o he socal ou. The odel reseed here resolves soe o hs dscreacy by showg ha adversg ca be excessve or uderrovded deedg o characerscs o he eda are. I arcular s show ha adversg levels are excessve whe here s hgh eda are dereao ad are uderrovded by he are whe here s low eda are dereao. There s also dsagreee aog heorecal resuls as o how he degree o roduc dereao aecs he equlbru aou o adversg. The odel o Grossa & haro 984 dcaes ha we should exec ore adversg olgoolsc ares where roducs are ore dereaed. The uo behd hs 3

5 resul s ha as roducs becoe ore dereaed roducers ca charge hgher rces hus rasg he argal bee o adversg. The odel o vo der ehr & ev 998 assues ha adversg s ersuasve o show ha ore adversg occurs wh slar roducs ha wh less dsslar roducs. Ths s due o roducers' eors o brg abou hgher erceved roduc dereces aog cosuers. The resuls o he rese odel are cosse wh hose o vo der ehr & ev 998 wh regard o he relaosh bewee roduc dereao ad equlbru adversg levels. Ths s also cosse wh ercal exales o dusres wh heavly adversed roducs whch exhb lle hyscal dereces. ee cherer & Ross The aer s orgazed as ollows. The ex seco ses u he odel by descrbg he ecooc ages ad her objecves. I eco 3 boh he sac equlbru as well as he ree-ery equlbru are derved ad dscussed. eco 4 coas he welare-axzg oucoe ad coares o he coeve equlbru. The al seco cocludes. Proos o all roosos are coaed he aedx.. The Model There are roducers ad saos servg a se o cosuers who arcae a dereaed roduc are ad a dereaed eda are. 3 We assue ha a cosuer s reerece over roducers s deede o her reereces over saos. Ths deedece allows us o rerese he roduc are ad he eda are searaely o wo dere crcles each wh u crcuerece. The roducers are equally saced aroud oe crcle ad he saos aroud he oher. The sae se o cosuers s uorly dsrbued aroud each crcle. Ay cosuer who ravels soe dsace o a roducer o buy a roduc bears rasorao coss o er u raveled. larly he u rasorao cos he eda are s. These exogeous 3 We have sled he aalyss by cosderg oly oe roduc dusry. I s acowledged ha eda ycally serve ulle dusres lyg releva er-dusry eecs he adversg are. To sly he reseao whle reservg he uo we cosder a sgle roduc dusry here. The ulle roduc dusry case s dscussed searae oes avalable ro he auhor uo reques. 4

6 varables caure he exe o coeo each o he resecve ares. The ey resuls o he odel rely o coarave sacs wh resec o ad. Adversg hs odel aes o he role o orao whereby adversg essages coa orao abou a roduc s exsece locao ad rce. Cosuers who receve o adversg essages are uored abou ay roduc ad do o ae a urchase. Cosuers ow abou a roduc s exsece oly hey receve a adversg essage abou ha roduc. We assue ha cosuers ca cosue a os oe roduc. The oraoal aure o adversg ad s role a dereaed roduc are whch are eloyed here have her oudao he wors o Buers 977 ad Grossa & haro 984. To be sure adversg seldoly aes hs or. or sace adversg oe coas o rce orao. urherore a grea deal o adversg s or roducs whose exsece s wdely ow. Neverheless he odelg aroach we ae here does o resrc us o rce adversg or uow roducs. or exale adversg or a well-ow brad serves o red cosuers abou he roduc s exsece o whch hey ay have eorarly orgoe. 4 Wh hs reder hey are coscous o he brad whle a he sore ad observe s rce. I he odel saos ad roducers ove rs. aos ae rograg choces regardg he sace alloed or adversg. ulaeously roducers ae her adversg ad rcg decsos. A are-clearg rce or adversg s deered ad he adversg bough ad sold. aos broadcas he adversg essages ad lasly cosuers ae her choces he eda are ad roduc are.. Cosuers We sar by exag cosuers reereces ad he exlorg her decsos he roduc ad eda ares. Le be he uber o adversg essages or roduc broadcased by sao ad be he oal uber o adversg essages broadcased by sao. Cosuers receve uly v ro roduc cosuo ad v 4 ee or exale Nelso 974 or a odel o orgeg ad he role o adversg. 5

7 coss. 5 The uly ha a cosuer B receves ro lseg o sao ad urchasg ro ure eda cosuo. Meda cosuo s dshed by adversg essages so ha a cosuer lseg o sao receves uly v gross o ravel ro roducer a a rce s U B [ v d B] + [ v d B] where d B ad d B are he dsaces o roducer ad sao resecvely. We assue ha v > d B ad v > d B or all ossble choces o + + ad cosuers B. The assuo o always served by he saos ad he assuo o receve surlus ro cosuo o ay roduc. v eas ha he ere eda are s v esures ha all cosuers The cosuer s choce he eda are s deede o he roduc are lyg ha cosuer B wll choose sao over sao + ad oly v d + B > v [ d B]. uose a lseer locaed bewee sao ad sao + s dere bewee he wo saos ad deoe her dsace ro sao by ad solvg or y R gves y R + y R. The alyg equaly o +. Ay lseer B locaed bewee saos ad + wll lse o sao ad oly d < B yr. larly dee L y as he dsace ro sao o he lseer bewee 5 Eve hough adversg s uly dshg wh regard o eda choce ca be sad ha rovdes a oraoal bee whch hels cosuers ae her roduc choce. We assue ha a lseer s eda choce does o deed o hs oraoal bee. Relaxg hs assuo would ly ha or each sao cosuers or execaos abou he oeal bee ro lseg over all ossble roduc choces. Cosuers would he cororae hs bee o her eda choce. Igorg hs asec o eda choce ls alcaos o he odel o assve ors o eda le elevso ad rado where subscrbers are arcularly eresed he rograg raher ha he oraoal bees o he adversg. The odel s o as well sued hereore or alcaos o r eda such as ewsaers where he subscrber gh acvely see ou he roduc orao or exale classed ads sales aoucees or ove show es. 6

8 saos ad who s dere bewee he wo saos. Le L deoe he sze o he ere se o lseers o sao he L yl + y or R L whch we reer o as he lseersh o sao. 6 Noe ha uder he assuo ha v s sucely large L. Now we ur o he cosuer s choce he roduc are ad derve roduc deads. Deoe by ϕ 0 he oro o he oulao lseg o sao ha hears he adversg essage or roduc. We assue ha he varables ϕ ad are relaed by ϕ A where A s oe-o-oe ad deoes varous asecs ha aec how eecvely adversg essages reach he lseg audece. Cosequely ϕ A s reerred o as he reach o adversg essages ad deoes he robably ha a cosuer lseg o sao becoes ored o roduc. Asecs ha deere A ay or sace clude sacg bewee essages ad he e o day whch he essage s broadcased. Oe gh exec ha here exs dshg reurs o adversg essages or he ollowg reaso: as he oro o ored cosuers ϕ becoes larger he robably ha a ew adversg essage reaches a uored cosuer becoes saller ad reachg a addoal uored cosuer s hereore argally less lely. Heceorh we ose he ollowg codos o he adversg reach uco: A A A > 0 ad A < 0 or 0. I ac he aalyss ha ollows wll be useul o secy A as he ollowg assuo. Assuo : A [0] We have lcly ade he addoal assuo whou loss o geeraly ha o cosuer ds oal o choose a sao ha s beyod her eares eghbors. or exale cosuer B wll ever choose o lse o sao or sao +. 7 Aoher seccao or A ca be jused by rs observg ha he robably ha a adversg essage reaches a ew cosuer gve ha ϕ o he are currely ored s ϕ A. ce A s he argal crease reach due o a u crease adversg essages ad s equal o hs 7

9 We cosra he choce varable o be bewee 0 ad order o esure ha A rereses a robably value. A useul erreao o he varable s ha rereses he raco o a e aou o broadcas e devoed o adversg essages. A he axu level he sao s ere broadcas day s oly adversg ad or ayoe who s sll lseg o he sao hey are ored abou he adversed roduc wh robably oe. The exogeous araeer s xed he u erval so ha A sases he desred dervave ad cocavy codos dscussed revously. Ths araeer ca be erreed as he roducvy o a adversg essage whch lower values corresod o hgher roducvy sce 0. I s useul o h o adversg worg he ollowg way. A arbrary cosuer hears a adversg essage by roducer o sao wh robably Ths cosuer does o lse o sao assocaed wh l. ϕ. l ad hus does o hear ay adversee We wsh o derve he dead or roduc gve adversg levels. Ths s colcaed by he ac ha here are dere ways each cosuer ca be ored abou roducs. or exale oe cosuer ay hear adversg essages oly ro roducers 5 ad whle aoher cosuer hears adversg essages ro every roducer exce say roducer. Grossa & haro 984 have addressed hs colcao ad we aeal o her dervao o roduc dead. Cosder roducer who sells s roduc a rce. Le ˆ be he equlbru rce whch s chose by he reag roducers. Also le ϕ be he reach o adversg chose by roducer ad le ϕˆ be he equlbru adversg reach chose by he oher roducers. ollowg Grossa ad haro robably we have he ollowg rs order dereal equao: A A. A soluo o whch s A e. However he seccao A aes he aalyss racable whle reservg he desred dervave roeres. urherore he exogeous araeer allows us o ae a coarave sac aalyss wh resec o adversg s roducvy. 8

10 984 we wre he dead sao as D ϕ ϕ D or roduc aog hose cosuers who lse o ˆ ϕ [ ϕˆ ] + ϕˆ ϕˆ [ ] L. To aclae he exoso o he aalyss we voe a large-ubers aroxao 8 whch ers us o assue he ollowg: Assuo : s sucely large so ha ϕ ˆ ϕˆ 0. Uder hs assuo every cosuer s ored o a leas oe roduc. The dead or roducer s roduc aog lseers o sao he becoes D ϕ ˆ ϕ + L. 3 ϕˆ As oe would exec ore adversg by coeg roducers releced by a crease ϕˆ reduces he dead or roduc. More orao abou coeg roducs hels cosuers ae a beer ach wh ore reerred roducs. uarzg a cosuer rs decdes whch sao o lse o ad hs decso deeds o her locao ad o how uch adversg s oered by each sao. Based o he uber o adversg essages she hears o her chose sao she ay ae a decso abou whch roduc o urchase. I she hears o adversg essages she aes o urchase. I she hears oly oe roducer s adversg essage she buys oe u o ha roducer s roduc. Ad ally she hears adversg essages ro ulle roducers she decdes whch roduc o buy based o he roducs locaos ad rces. ϕ. Producers I hs subseco we rs dscuss he cooes o roducers ros ad he derve her sraegc choces o adversg ad rces gve cosuers resose o boh. 8 I absece o hs aroxao uercal ehods ca be used o oba qualavely slar resuls. ee he Joural s edoral webse or urher deals. 9

11 Producers ace a cosa argal cos o roduco c ad xed coss Pros o roducer ca be wre as. Π [ c D a A ϕ ] ϕ 4 where a s he rce o a adversg essage o sao. Producers ae gve. Producers choose he roduc rce ad secy adversg coverage order o axze ros uco as Π ag lseersh The rs order codo wh resec o ˆ + c ϕ ϕˆ ϕ L L as gve. a as ϕ gves roducer s rce reaco L +. 5 I s useul o exae he rcg uco exressed 5 wh ha alo 979. Wh colee orao.e. ϕ ϕˆ or all rcg s cosse wh ha led by alo 979. urherore ca be show ha rce s larger 5 ha he colee orao case. Ths llusraes ha roducers ejoy hgher rces as a resul o colee orao he roduc are Grossa & haro 984. The rs order codo or axzg 4 wh resec o a da ϕ dϕ c + L ˆ ϕˆ ϕ les. 6 Ths s roducer s verse dead or adversg essages o sao ad exhbs he dead roery ϕ a < 0 whch ollows ro he assuos ade o A ad ro he secod order codo Π ϕ 0..3 aos We ow ur o he sao s choce he eda are. Because o he crcular srucure o he eda are each sao has wo eghbors o coee agas or s lseersh. Each sao.... chooses he aou o e devoed o adversg 0

12 Each sao aces o argal cos o adversg ad aes he rce o adversg er lseer as gve so ha sao. Recall ha roducers ae a CL where C s vewed as cosa by he a as gve. Thereore he adversg are each sao yelds a sall degree o are ower owg ha ca coad hgher rces whe has ore lseers. 9 Thus ros are adversg reveue less xed coss. Thereore sao s roble s o choose order o axze Π a or Π C Maxzg 7 wh resec o adversg sace we ca wre sao s reaco uco ers o Noce here ha saos are reacg o he adversg levels o her wo eghborg saos as well as o he uber o saos he eda are. I arcular as he uber o saos grows sao us cu bac o s adversg levels as he coeo or a xed se o lseers becoes gher. 3. Coeve Equlbru Havg ully descrbed he hree yes o ages we ow see a coeve equlbru cossg o roduc rces ˆ ad adversg levels ϕ ˆ ha sasy all o he ages ozao robles. We rs derve he coeve equlbru he sac odel wh ad xed ad he dscuss s coarave sacs roeres. ally we derve he coeve equlbru uder he ree-ery codo where ad ca vary. 9 Gve ha saos ace zero argal cos o adversg hs assuo s ecessary order o gve saos a deable rade-o. I s assued ha saos ossess soe degree o are ower sce each s a roducer s sole source o access o he cosuers s lseg sege.

13 3. ac Equlbru To derve he sac equlbru we use all o he ages rs order codos. eccally characerzg he oal choce o he cosuer are equaos ad 3; o he roducer equaos 5 ad 6; ad o he sao equao 8. I equlbru he saos reaco ucos seced by 8 are sased sulaeously. urherore sce saos are syerc ca be show ha 8 les ˆ or all.... I ollows ro ha lseersh s equally dvded so ha L. As he uber o saos grows or dereao alls he eda are ges crowded ad saos ge squeezed ou o lseers. Cosequely saos us reduce her suly o adversg as hey coee or a saller share o lseers. yery aog roducers les ha each roducer chooses he sae uber o adversg essages ro each sao so ha or all ˆ 9... ad.... Noe ha he equlbru level o adversg deeds crucally o he degree o coeo bewee saos or lseers as easured by /. eccally as coeo aog saos s reduced he argal cos o adversg ers o los lseers decles. As a resul saos suly ore adversg. Usg hs ac syery aog roduc rces ad 5 we ge he syerc equlbru roduc rce: ˆ c. 0 Usg 6 4 ad 8 ca be show ha aˆ ˆ Π Πˆ. 3

14 The sac equlbru characerzed by equaos 9-3 exhbs he execed coarave sacs roeres wh resec o he degree o roduc coeo. As / creases each roducer exracs ore surluses ro cosuers hrough hgher roduc rces. A oro o hs addoal surlus s shared wh saos hrough he adversg are va hgher adversg rces â. O he oher had coarave sacs roeres wh resec o he degree o eda are coeo are less obvous. Recall ha a crease / resuls ore adversg equlbru whch eas ha cosuers are beer ored abou coeg roducs. Ths duces lower roduc rces as releced 0. As a resul roducers exrac less surlus ro cosuers leadg o geerally lower ros boh dusres. Lasly we wa o observe how chages aec equlbru quaes. Recall ha 0 ca be erreed as he roducvy o a adversg essage where lower values o rerese hgher roducvy. 0 Whe he roducvy o adversg roves roducers eed ewer adversg essages o oba her desred reach hereby reducg he dead or adversg essages. ce he suly o adversg essages s xed a / hs yelds a lower adversg rce â. Ths leads o lower sao ros as well as lower adversg coss or roducers. However ore roducve adversg has a adverse eec o roducers reveues. Hgher adversg roducvy aes cosuers ore ored. O he oe had hs lowers roducers reveues. Bu o he oher had hs also reduces her adversg coss. Thus he ac o roducer ros s uclear ad deeds o whch eec he adversg cos eec or he reveue eec doaes. The dscusso cocerg allg has a eresg lcao. I reveue alls ore ha adversg coss he roducers ros wll decrease as a resul o beer 0 or exale suose a clever areg echque s roduced ha ca geerae aeo or hye abou a roduc ad as a resul each adversg essage s ore eecve reachg a larger uber o cosuers. Ths would corresod o a all he value o. 3

15 adversg ehods. I hs case boh saos ad roducers wll have a collecve ceve o avor low adversg roducvy. The above dscusso cocerg he coarave sacs roeres o he sac equlbru s suarzed he ollowg rooso. Prooso ac equlbru levels o adversg ˆ rces ˆ c â ad ros Πˆ Πˆ as ucos o he exogeous araeers ad ad uber o rs ad have he ollowg coarave sacs roeres: ˆ ˆ c â Πˆ - +? - + Πˆ Equlbru wh ree Ery I hs seco we exed he sac equlbru odel o a equlbru wh ree ery by allowg roducers ad saos o eer her resecve dusry as log as here exs osve dusry ros. Assue ha roducers ad saos cosderg ery ace o ery coss ad ha roducers wll eer wheever Πˆ > 0 ad saos wheever Πˆ > 0. Le ˆ ad ˆ be he uber o roducers ad saos resecvely who eer he are. The ˆ ad ˆ us sasy Πˆ ˆ 0 ad ˆ Π ˆ 0 We are arcularly eresed he equlbru uber o adversg essages broadcased o oe sao deoed ˆ ˆ ˆ. / ˆ. I seco 4 we coare he Ths s cosse wh a resul observed Grossa & haro 984. They show ha s ossble or roducers o receve hgher ros as a resul o hgher adversg coss. The exsece o ˆ ad ˆ s led by Prooso ad he ac ha l Πˆ < 0 ad ˆ l Π < 0. 4

16 ree ery equlbru aou ˆ wh he corresodg welare axzg value o adversg. Coarsos are based o hs varable because hs s he uber o adversg essages each cosuer oeally hears. ree ery he eda dusry has a drec eec o ˆ hrough ˆ he uber o saos. However because a sao s ro 3 s deede o he uber o roducers here s a drec eec o ˆ hrough he varable ˆ. As such order o udersad how ˆ s aeced by exogeous araeers ad we rs characerze how ˆ ad ˆ are aeced wh resec o chages hese araeers. By alyg he zero ro codos o equaos ad 3 s vered ha ˆ ad ˆ are boh creasg ad decreasg. Wh regard o roduc are dereao hgher surluses are exraced as creases. A oro o hese surluses accrues drecly o roducers ducg roduc are ery ad drecly o saos va he adversg are whch duces eda are ery. Wh ore saos he eda are each sao us adverse less: d ˆ / d < 0. A corasg resul s obaed whe here s a crease sao dereao. Cosder a argal crease. Ths drecly reduces saos argal cos o adversg ers o los lseers ad saos resod by sellg / ˆ ore us o adversg. Ths s he rs order eec. A secod order eec o ˆ acs hrough sao ex a reduco ˆ. As roducers lower her rces resose o ore cosuer orao saos cao cla as uch surlus hrough he adversg are ad saos ex d ˆ / d < 0. The secod order eec suors he rs order eec ad he oal eec s dˆ d d d ˆ ˆ ˆ dˆ > d I Prooso we suarze he coarave sacs roeres o 0. ˆ ˆ ad ˆ dscussed above as well as boudary roeres ha are used seco 4. 5

17 Prooso I he equlbru wh ree ery ˆ ˆ ad ˆ as ucos o he exogeous dereao araeers coarave sac ad boudary roeres. ad have he ollowg ˆ ˆ ˆ ˆ ˆ ˆ. + + or ay xed > 0 ˆ ˆ 0 0 ad here exss > 0 whch duces he corer soluo: ˆ ˆ. + Par o hs rooso leads o a eresg resul regardg he aggregae level o adversg. I ore dereaed eda ares aggregae adversg s hgher. Bu he rooso reveals ha ore aggregae adversg s rovded by ewer saos. Noe also ha ar o Prooso suggess ha ares or slar roducs we should exec ore adversg er sao. Thereore he dvdual cosuer hears ore adversg whe roducs are close subsues. Casual observao cera roduc ares e.g. he cola are suors such a resul. Ths s coras o Grossa & haro 984 whch cocludes ha here s less adversg whe roducs are slar. Par o he rooso esablshes boudary codos o ˆ wh resec o whch are eeded he welare coarso o seco 4. I says ha or ay gve level o erecly decal saos.e. whe 0 broadcas o adversg ad ha sucely dereaed saos broadcas eough adversg o ully or all cosuers. 4. Welare Aalyss I hs seco we deere he socally oal level o adversg he ree ery odel ad coare o he level obaed he coeve equlbru. We sar by dervg he socal welare W aggregaed all over ages: saos roducers ad cosuers. Dee socal welare o coss o he ollowg cooes: cosuer 6

18 surlus ro roduc cosuo less rasorao coss; cosuer surlus ro eda cosuo less rasorao coss; 3 roducers ros ad saos ros. ocal welare s axzed wh resec o he uber o adversg essages er sao er roducer he uber o roducers ad he uber o saos. Noe ha he socal laer has he ably o choose he roduc rce ad adversg rce a. Bu choce o rce varables s rreleva sce hey serve oly o sh surluses aog he ages raher ha ehace oal welare. Recall ha each erso cosues oe u o he eda good ad uder he large uber aroxao Assuo oe u o he roduc good. Thereore we ca assg he coo gross uly ad cosa argal coss as a xed value K v + v c whch does o eer he socal laer s decso. Hece welare s axzed by zg he su o he rasorao coss boh ares he dsuly ro adversg ad he wo dusres xed coss. I he eda are cosuers ravel o he closes sao. ro alo 979 we ow ha he oal rasorao coss assocaed wh all saos s / 4. The calculao o rasorao coss he roduc are s ore colcaed. We aeal o he dervao o Grossa ad haro 984 who show hs o be Hece oal welare s exressed as T 4. W K A suce codo or he exsece o a eror soluo o he welare-axzg roble s ha / 3. Ths codo guaraees cocavy o he welare exresso 4 ad hece we resrc he welare aalyss o hs rage o. Deoe he ozers o W by ad. I our coarso o he socal ou ad he coeve equlbru we wsh o coare er sao adversg levels. Deoe hs quay by. Wh hs d we rese he releva roeres o rooso. ad he ollowg 7

19 Prooso 3 Assue ha / 3. There exss a eror soluo o he welare axzao roble. A hs socal ou ad are vara o chages ad s creasg. ro he socal laer s ersecve he oal level o adversg s chose o balace he socal cos o aoyace versus he bee o reducg rasorao coss he roduc are va ore orao. The degree o eda dereao hereore does o lay a role he oal level o adversg. larly he oal uber o roducers s chose o balace he cos o ery ad he bee o lower roduc are rasorao coss ad hus does o deed o he level eda dereao as well. or hese reasos he socal laer s choce o vara o chages. saos ad ad hereore s Ths s o he case or he socal laer s choce o he oal uber o. Wh ore saos here s less dsace bewee he ad subsequely cosuers ravel shorer dsaces. The socal bee o ore saos s a reduco eda are rasorao coss. However hs coes a he socal cos o hgher dusry xed coss. adversg rooso. Prooso ad 3 ca be used o coare he coeve equlbru level o ˆ wh he socally oal level whch s gve he ollowg Prooso 4 Assue ha / 3. or ay xed > 0 here exss ~ > 0 wh he ollowg roeres. ˆ ~ ~ ˆ > or > ~ ad ˆ < or < ~. 8

20 ro hs rooso we have he a welare resul: Mare levels o adversg wll ed o be excessve/uderrovded relave o he socally oal level ore/less dverse eda dusres all else equal. More dereao he eda are rases saos ceve o adverse whou chagg he socal laer s ceve. resec o I s ora o ee d ha hs s srcly a coarave resul wh ˆ ad oly. As such s o vald o draw coclusos cocerg he overall ececy o geeral are oucoes sce welare also deeds o he exe o sao ad roducer ery. 5. Cocluso We have reseed a odel o a dereaed roduc olgooly wh a are or orave adversg. I he odel adversg essages are bough by roducers ad sold by eda ages e.g. rado saos ad delvered o a se o cosuers hrough eda broadcasg. The cosruco o he odel wh s cluso o he eda dusry serves o ehasze wo os revously uoed he leraure. rs order o udersad ha whe adversg s chaeled hrough coercal eda eda are srucure ad he decsos ae by eda rs wll aec he equlbru level o adversg. ecod o ully evaluae he degree o whch hs equlbru level coares o ha o he socal bes oe us accou or he socal coss ad bees assocaed wh he coercal eda dusry. The odel descrbed here s used o udersad how are acors deere he aou o adversg chose by olgoolsc coeors ad wheher here exss a excessve aou o adversg. Oe cocluso led by he odel s ha wh less roduc are dereao roducers coee ore ercely va adversg ad hus a hgher are level o adversg. The odel also suggess ha lower equlbru levels o adversg occur whe eda ares are less dereaed because saos coee ore aggressvely or lseers by reducg her adversg levels. The socal laer s rade-o wh regard o adversg levels however s a balace bewee he socal cos o aoyace versus he bee o reducg rasorao coss he roduc are. As a resul he degree o 9

21 dereao does o lay a role he oal level o adversg. Hece equlbru adversg levels wll ed o be excessve whe eda ares are ore dereaed. Oher sudes have reached coradcg coclusos regardg he excessveess o adversg. The resuls o he rese odel ecoass hese sudes by dg codos o are characerscs arcular levels o eda are dereao ha lead eher o excessve adversg as Grossa & haro 984 or Buers 977 or o a uderrovso o adversg as egea 99 or ahl

22 Aedx Proos Proo o Prooso : Exressos ollow drecly ro syery ad equaos 9-3. Noe ha 0 les ha he exresso / ˆ s decreasg. Proo o Prooso : Aly he ree ery codos 0 ˆ ˆ Π ad 0 ˆ ˆ Π o equaos ad 3 ad solve sulaeously wh soe aou o algebra o oba ˆ ad ˆ. The by evaluag ˆ / ˆ he level o adversg s exlcly exressed as / ˆ. A The coarave sacs resuls are deduced by secg hese exressos. Drec subsuo o 0 o A yelds 0 0 ˆ. eg ad subsug o A gves ˆ. Q.E.D. Proo o Prooso 3: Dee he ollowg W W 4 W 3 4

23 whch are seced by he argal dervaves o he welare uco W gve 4. Dee as a soluo o he se o rs order codos gve by he syse 0 A 0 A A4 The s a eror axu o W he he Hessa arx W s egave dee. Ths arx s exressed ad sled as where he slcao resuls ro he ac ha A les. A5 or he above arx s show ha he leadg rcle ors o order have he sg o. The rs order leadg rcle or s see o be egave by seco. The secod order leadg rcle or s exressed [ ] 4 +. A6 Uder he assuo ha 3 / ad he robably cosra ha < A hs exresso s osve. The hrd order leadg rcle or he deera o he above arx s egave uder he sae cosras o ad.

24 3 To rove he coarave sacs roeres o he socal ou rs oe ha he ozers ad are characerzed by A ad A3 ad by A4. ce ad cao be solved exlcly we le ad be deed lcly by A ad A3. By he Ilc uco Theore he dervaves o hese ucos aroud he ou are soluos o he ollowg lear syse: A7 where ad are all evaluaed a. The deera o he le-os arx A7 s he exresso gve A6 whch s osve a he eror equlbru. Thereore 0 / /. The coarave sacs resuls cocerg are obaed by exag he exlc soluo / led by A4. Q.E.D. Proo o Prooso 4 The boudary codos or ˆ ad seced Prooso ly he exsece o soe value ~ such ha he coeve oucoe delvers he oal level o adversg: ~ ~ ˆ. urherore sce ˆ s srcly creasg ad 0 > s cosa he or xed : ~ < > les ˆ < >. Q.E.D.

25 Reereces Aderso. & Coae. 00 Mare Provso o Publc Goods: The Case o Broadcasg eo Uversy o Vrga ad Corell Uversy. Beebe J. 977 Isuoal rucure ad Progra Choce Televso Mares Quarerly Joural o Ecoocs 9:5-37. Buers G. 977 Equlbru Dsrbuo o ales ad Adversg Revew o Ecooc udes 443: Dx A. ad Nora V. 978 Adversg ad Welare The Bell Joural o Ecoocs 9: -7. Dues A. ad Gal-Or E. 003 Negoaos ad Exclusvy Coracs or Adversg Mareg cece : -45. Gabszewcz J. Laussel D. & oac N. 999 TV-Broadcasg Coeo ad Adversg eo CORE. Gal-Or E. ad Dues A. 003 Mu Dereao Coercal Meda Mares Joural o Ecoocs ad Maagee raegy 3: Grossa G. ad haro C. 984 Iorave Adversg wh Dereaed Producs Revew o Ecooc udes 5: Häcer J. & Nyberg. 000 Prce Coeo Adversg ad Meda Mare Cocerao eo Deare o Ecoocs ochol Uversy. Masso R. Mudab R. & Reyolds R. 990 Olgooly Adverser-uored Meda Quarerly Revew o Ecoocs ad Busess 30: 3-6. Moa M. & Polo M. 00 Beyod he ecru Cosra: Cocerao ad Ery he Broadcasg Idusry Rvsa d Polca Ecooca Arl/May. Nelso P. 974 Adversg as Iorao Joural o Polcal Ecooy 8: Nchols L. 985 Adversg ad Ecooc Welare Aerca Ecooc Revew 75: 3-8. Nlsso T. ad ørgard L. 003 The TV Idusry: Adversg & Prograg auscr Uversy o Oslo ad Norwega chool o Ecoocs ad Busess Adsrao. 4

26 alo. 979 Mooolsc Coeo wh Ousde Goods The Bell Joural o Ecoocs 0: cherer. ad Ross D. 990 Idusral Mare rucure ad Ecooc Perorace. Boso: Hougho-Ml. haro C. 980 Adversg ad Welare: Coe The Bell Joural o Ecoocs : ddarh. ad Chaoadhyay A. 998 To Za or No o Za: A udy o he Deeras o Chael wchg Durg Coercals Mareg cece 7: ece M. & Owe B. 977 Televso Prograg Mooolsc Coeo ad Welare Quarerly Joural o Ecoocs 9:03-6. eer P. 95 Progra Paers ad Preereces ad he Worably o Coeo Rado Broadcasg Quarerly Joural o Ecoocs 66:94-3. ahl D. O. 994 Olgoolsc Prcg ad Adversg Joural o Ecooc Theory 64: egea M. 99 Adversg Coeve Mares'' Aerca Ecooc Revew 8: 0-3. egea M. 00 acg Publc Goods Through Adversg worg aer Deare o Ecoocs Vrga Tech. vo der ehr N-H. ad ev K. 998 Persuasve Adversg ad Produc Dereao ouher Ecooc Joural 65: