THE ANALYSIS OF MERGERS THAT INVOLVE MULTI-SIDED PLATFORM BUSINESSES

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1 Davd S. Evan and Mchael D. Noel A moe ecent veon of th atcle ha been accepted fo publcaton n: Jounal of Competton Law and Economc, 2008 THE ANALYSIS OF MERGERS THAT INVOLVE MULTI-SIDED PLATFORM USINESSES Davd S. Evan * Mchael D. Noel Apl 2008 * Unvety College London and Unvety of Chcago, and LECG, LLC. [email protected]. Unvety of Calfona at San Dego, [email protected]. Th pape an extenve evon of a pape that pevouly cculated unde the ttle Analyzng Maket Powe and Maket Defnton n Mult-Sded Platfom Maket. We would lke to thank Howad Chang, Kten Edwad, Ande Hagu, Alon Oldale, Mchael Salnge, Rchad Schmalenee, and Vanea Yanhua Zhang fo valuable comment and Mutaza Akhte, E udo, Mana Danlevky and Nee Naf fo exceptonal eeach atance. 1

2 Davd S. Evan and Mchael D. Noel ASTRACT A mult-ded platfom (MSP) eve a an ntemeday fo two o moe goup of cutome who ae lnked by ndect netwok effect. Recent eeach ha found that MSP ae gnfcant n many ndute and that ome tandad economc eult uch a the Lene Index do not apply to them, n mateal way, wthout ome gnfcant modfcaton to take lnkage between the multple de nto account. Th atcle extend eveal key tool ued fo the analy of mege to tuaton n whch one o moe of the upple ae MSP. It how that the applcaton of tadtonal tool to mege nvolvng MSP eult n bae the decton of whch depend on the patcula tool beng ued and othe condton. It alo extend thee tool to the analy of the mege of MSP. The technque ae llutated wth an applcaton to an acquton nvolvng the mult-ded onlne advetng nduty. 2

3 Davd S. Evan and Mchael D. Noel I. INTRODUCTION Th atcle peent an empcal famewok fo examnng maket defnton and unlateal effect n mege n whch one o moe of the bunee that may be condeed fo the hypothetcal maket ae mult-ded platfom (MSP). MSP povde good o evce to eveal dtnct goup of cutome who need each othe n ome way and who ely on the platfom to ntemedate tanacton between them (Evan (2003a, b), Rochet and Tole (2003, 2006)). 1 They typcally educe tanacton cot and theeby pemt value-ceatng exchange to take place that othewe would not occu (Evan and Schmalenee (2007a, b)). In patcula, they facltate the ealzaton of ndect netwok extenalte, and extenalte n ue, between the membe of dtnct cutome goup (Rochet and Tole (2003)). Many old ndute ae baed on MSP, angng fom vllage matchmake that date fom ancent tme to advetng-uppoted newpape ntoduced n the 17 th centuy to payment cad ntoduced n the md 20 th centuy. Howeve, an nceang numbe of gnfcant moden bunee ae MSP a a eult of technologcal change that have datcally loweed the cot and nceaed the beneft of connectng dvee cutome goup on a ngle platfom. Thee nclude mot ntenet-baed bunee uch a eay, Facebook, and Google. Thee bunee ae ceatng new poduct and evce uch a ocal netwokng platfom and ae duptng extng ndute uch a advetng-uppoted meda (Evan and Schmalenee (2007b)). The tandad tool of anttut and mege analy, whch wee developed baed on the economc of ngle-ded bunee, do not necealy apply n way that ae mateal to the analy of competton that nvolve mult-ded bunee. Each de of the MSP' bune nfluence and contan t tatege on the othe de. Anttut analy that focue on one de of the bune n olaton fom the 1 Many mult-ded platfom have two pmay de uch a advetng and eade, and much of the economc lteatue ha focued on the cae of two-ded platfom (2SP). 3

4 Davd S. Evan and Mchael D. Noel othe de ncoect a a matte of economc, and can lead to the wong anwe when ndect netwok effect ae gnfcant and ae elevant fo aeng the pactce at ue (Evan (2003a), Wght (2004)). Th atcle how how the tandad tool ued fo analyzng maket defnton and unlateal effect fo mege need to be modfed when the pate ae MSP. Whle we cauton agant n elyng too heavly on mechancal maket defnton exece a a geneal matte, a long a pacttone and cout ue thee technque, they hould be done coectly when MSP ae nvolved. The analy of maket defnton and powe fo mege ha obvou extenon to othe aea of anttut. We peent an empcal famewok that can be ued to handle tuaton n whch one o moe MSP may be the ubect of the mege analy. Secton II povde an nfomal dcuon of the analy of maket defnton, maket powe, and unlateal effect fo tuaton that nvolve MSP and how that analy dffe fom that fo tuaton that only nvolve ngle-ded fm. Secton III then peent ou fomal analy fo the pecal cae of two-ded maket. Secton IV conde a ee of example and mulaton to hghlght the beneft of puung the coect analy. Secton V apple the analy to an example baed on Google acquton of DoubleClck. Secton Eo! Refeence ouce not found. peent bef concluon. II. ANALYSIS OF MARKETS WITH MULTI-SIDED PLATFORMS Conde poft maxmzaton fo a platfom that eve cutome goup A and. Suppoe the platfom ha aleady etablhed pce fo both goup and condeng changng them. 2 If t ae the pce fo membe of goup A, fewe A' wll on. If nothng ele changed, the elatonhp between pce and the numbe of A would depend on the pce elatcty of demand fo A. Snce, howeve, membe of goup value the platfom moe f thee ae moe A, fewe wll 2 To keep matte mple we conde the cae whee each de chaged a membehp fee a n Amtong and Wght (2007). MSP geneally nvolve platfom on whch nteacton take place and cutome face an acce fee and a uage fee although they may chooe to make ome of thoe fee zeo. 4

5 Davd S. Evan and Mchael D. Noel on the platfom at the cuent pce fo. That dop-off depend on the ndect netwok extenalty whch meaued by the value that place on A. ut wth fewe on the platfom, A alo value the platfom le leadng to a futhe dop n the demand. Thee a feedback loop between the two de. Once th taken nto account the effect of an nceae n pce on one de a deceae n demand on the ft de becaue of the dect effect of the pce elatcty of demand and on both de a a eult of the ndect effect fom the extenalte. The change n evenue fom a change n the pce fo A theefoe depend on the pce elatcty of demand fo A and the ndect netwok effect between the two de. Cot necealy go down o long a magnal cot ae potve nce the numbe of cutome ha dopped on both de. A alway the cae wth poft maxmzaton, the pce nceae poftable f evenue do not declne moe than cot declne. The platfom would lke to fnd the pce fo each de that maxmze t poft by takng thee condeaton nto account. A Rochet and Tole (2003) obeve, one can thnk of thee a detemnng the abolute and elatve level of pce. Thee key eult hold fo two-ded platfom baed only on the aumpton that thee ae two dtnct cutome goup, thee ae potve extenalte between membe of thoe goup, and a two-ded platfom povde a good o evce that facltate exchange of value between the two cutome goup n the face of thee extenalte: Each optmal pce depend on the pce elatcte of demand fo both de; the natue and ntenty of the ndect netwok effect between each de; and the magnal cot that eult fom changng output of each de. An nceae n magnal cot on one de doe not necealy eult n an nceae n pce on that de elatve to the pce of the othe de. The pce ato between two de depend only on the ato of elatcte (not nvee elatcte), and not on magnal cot. The poft-maxmzng pce fo one de may be below the magnal cot of upply fo that de o even negatve. A common tuaton analyzed by 5

6 Davd S. Evan and Mchael D. Noel Amtong (2006) when the platfom n effect buy A who ae valued by. The elatonhp between pce and cot complex, and the mple fomula that have been deved fo ngle-ded maket do not apply. Seveal eult that ae elevant fo the analy of maket defnton and unlateal effect follow mmedately fom thee eult. Sgnfcantly fo ou pupoe, the wdely ued Lene Index p c p 1 = η (1) whee η the uual own-pce elatcty of demand, doe not accuately ummaze the poft-maxmzng equlbum fo MSP when appled to a patcula de. Th condton doe not conde the lnkage between the two de and a a eult doe not eflect the poft-maxmzng equlbum condton fo a two-ded platfom. Fo the pecal cae condeed by Rochet and Tole (2003) the two-ded veon of the Lene Index p p A + p c 1 = A A η +η + p (2) Mege analye tool uch a the Ctcal Lo and Dveon Rato that ae baed on the one-ded Lene Index ae theefoe not coect when appled to mult-ded bunee. 3 Moeove, mege mulaton model ae mpecfed when they fal to conde the mult-ded natue of the bune. 4 Standad model, when appled to one de of a two-ded nduty, fal to conde the feedback effect between the two de n othe wod that the demand by de A depend on the numbe of cutome on de and one mut conde the demand by de A and multaneouly to popely account fo all the feedback effect. 3 We deve the two-ded Lene Index fo ou model below. 4 See Weden, Gegoy J & Foeb, Luke M (1994); ake, J., and T. enahan (1985); Feldman, R. (1994); and Nevo, A. (2000). 6

7 Davd S. Evan and Mchael D. Noel A futhe mplcaton that the SSNIP tet fo defnng a elevant maket doe not apply wthout gnfcant modfcaton when any of poduct nvolved n the analy ae poduced by an MSP. Conde the cae of a mege between two ymmetc MSP that eve the ame cutome goup A and. To defne the maket an analyt poceed by tatng wth the mege of the poduct that eve demand fo, ay, de A becaue that the focu of the competton concen. 5 The et of poduct expanded untl a hypothetcal monopolt ove that et of poduct could ae pce by, ay, 5 pecent o moe on each of thoe poduct. That et of poduct then defne the maket fo analy. Howeve, by gnong de the analyt fal to conde that the hypothetcal pce nceae educe the numbe of de A cutome avalable to de, whch theeby educe the pce that de cutome wll pay, and futhemoe educe the numbe of de cutome avalable to de A, whch n tun educe the pce that de A cutome wll pay. The lnk between de A and educe the poftablty of any pce nceae. Theefoe, the maket would be dawn too naowly and etmate of maket concentaton too hgh, becaue the tandad appoach fal to conde the tempeng effect on pce comng fom the othe de. Howeve, we wll alo how that the ue of common one-ded calbaton technque to obtan elatcty etmate whch could not othewe be dectly etmated can caue a evee ba ntead, wth the maket dawn too boadly. So the oveall ba wll depend on the natue of the MSP and the etmaton technque ued. The mtake though moe pofound. The pupoe of maket defnton, n pat, to help focu the economc analy on a elevant but fnte et of poduct and compettve elatonhp fo analy. Fo ndute n whch the mult-ded effect ae uffcently tong, maket defnton that exclude one de of an MSP eult n the falue to conde mult-ded tatege and maket lnkage. Falue to conde thoe mult-ded elatonhp can eult n Type I and Type II eo: falng to 5 Fo a dcuon of the SSNIP tet ee US Depatment of Jutce Mege Gudelne avalable at In patcula ee Secton 1 on Maket Defnton, Meauement and Concentaton. 7

8 Davd S. Evan and Mchael D. Noel ecognze pactce that may be hamful becaue of the two-ded elatonhp and condemnng pactce that ae nnocuou n a two-ded context. The emande of th pape povde the toolkt fo conductng mege and unlateal effect analye fo MSP. III. CRITICAL LOSS ANALYSIS FOR MULTI-SIDED PLATFORMS Economt have developed a numbe of technque to ae maket defnton and the compettve conequence of a mege followng emnal contbuton by Faell and Shapo (1990), Wllg (1991), and Weden and Foeb (1994). Th wok and ubequent contbuton buld on the fundamental nght that one can nfe own-pce elatcte of demand fom pce-cot magn (the Lene Index) and ue thee etmated elatcte to conduct a vaety of mple analye. Gven enough data, one can alo evaluate the effect of a mege by etmatng a demand ytem unde ome aumpton (uch a dffeentated-maket etand) about tategc nteacton (ee Ivald and Veboven (2005)). Th ecton ue one of the moe popula pamonou technque Ctcal Lo Analy to how how thee technque can be extended and modfed fo mege nvolvng MSP. We begn wth a bef ovevew of one-ded Ctcal Lo Analy and then ntoduce the two-ded vaant. A. One-Sded Ctcal Lo Ctcal Lo Analy wa ntoduced by Ha and Smon (1989) a a uefendly mplementaton of the SSNIP tet. 6 It a mple calculaton ntended to povde a ft look at potental maket ze. It compae Ctcal Lo (CL) the pecentage lo n quantty of a hypothetcal monopolt poduct that would be exactly enough to make an X % pce nceae n the pce of all t poduct unpoftable to Actual Lo (AL) the pedcted pecentage lo n quantty that 6 See Ha and Smon (1989), O en and Wckelgen (2003) and Katz & Shapo (2003). See Ha and Velanovk (2003) fo dcuon of the ue of ctcal lo analy n anttut poceedng. 8

9 Davd S. Evan and Mchael D. Noel the monopolt would uffe f t dd nceae pce on all t poduct by X %. Wth ymmetc one-ded fm, the well-known fomula ae gven by CL = X /( X + M ) OWN CROSS OWN and AL = X ( ε ε ), whee M the pecentage makup, and ε and CROSS ε ae the own and co pce elatcte epectvely. A elevant maket found when Actual Lo equal Ctcal Lo fo a hypothetcal monopolt of the gven et of poduct n the popoed anttut maket. If Actual Lo exceed Ctcal Lo, the elevant maket expanded to nclude moe ubttute. Othewe, t contacted. Ctcal Lo Analy ha alo been ued to etmate potental unlateal pce effect fom popoed mege. In th context, one nque whethe the mege of the pate would lead the meged fm to ae pce by X% o moe. If the tet how that Actual Lo exceed Ctcal Lo, the meged entty would not fnd an X % pce nceae n all t poduct poftable. Othewe, t would fnd t poftable. Ued n th way, t povde a ft look at the potental fo unlateal pce effect, although moe ophtcated mulaton technque that take nto account the ntcace of the nduty and bunee nvolved would deally be ued to confm th ntal fndng. The one-ded calculaton ae tval, and the technque ha won gnfcant appeal both becaue of t mplcty and becaue of t eay meauement of nput. 7. Two-Sded Ctcal Lo We now how the one-ded fomula gven above ae analytcally wong wheneve they ae appled to maket nvolvng MSP. The eaon that when an MSP nceae the pce to cutome on one de of t bune, t eult not only n a lo of cutome on that de but alo n a lo of cutome on the othe de of the maket. Th n tun caue a hft n the elatve and abolute ze of all platfom n 7 One could alo calculate and compae poft total dectly aco hypothetcal and eal wold. The um of fm poft befoe π = 2Mpq, and the ont poft afte π = 2pq(M+X)(1+X(ε OWN ε CROSS )). We, howeve, mantan the Ctcal Lo fomulaton thoughout the pape becaue of t appeal, t tanpaency (ove black box poft compaon), and t tangble metc namely, how many ale a fm can affod to loe when t ae pce. 9

10 Davd S. Evan and Mchael D. Noel the maket, gvng e to futhe mplcaton. The decton of the ba fom ung one-ded fomula depend upon the analytcal method beng ued and the natue of the dffeence between the MSP, but can be non-tval a a geneal ule. Fo ou expoton of the bae fom the ue of one-ded fomula when MSP ae nvolved, we conde the cae of two ymmetc platfom evng two dtnct cutome goup. Symmety mple that each elatcty and ndect netwok extenalty ae the ame aco the two platfom. Whle le commonly encounteed n pactce, the ymmetc model bet convey the key nght n the analy. We peent the moe complex equaton fo the cae of aymmetc platfom (whch alo nclude the cae of platfom that do not have all de n common) and the cae of MSP wth N>2 n detal n Appendx 1.A. Thee ae two oppote bae that can occu Etmaton a and Lene a dependng on the etmaton technque. In the ymmetc cae, the decton of each ba unambguou. Etmaton a. Suppoe the analyt etmate a demand ytem fo one of the poduct offeed by two-ded platfom ung data and followng the technque that gve an unbaed etmate of the hot-un own-pce elatcty of demand. Hee we defne hot-un to epeent the length of tme t take fo cutome who expeence a pce nceae dectly to epond, but befoe any feedback effect commence. (The feedback effect, we know, wll caue addtonal ndect epone ove tme a elatve and abolute platfom ze change. 8 ) Snce the analyt etmate doe not account fo feedback effect, the full mpact of the pce nceae on demand undeetmated. A a eult, anttut maket necealy wll be defned too naowly, and mege analy wll ovetate the nceae n maket powe of megng pate and ovetate the pedcted unlateal pce effect of the tanacton. Lene a. An oppote ba can occu when the analyt ue obeved makup to calbate the own elatcty of demand baed on the one-ded Lene 8 In pactce, mot lkely the analyt wll etmate ome unknown mx of a hot-un and long-un elatcty (.e. once all feedback effect have been woked out), nce ndect netwok effect fom platfom ze change ae not popely accounted fo. The decton of ba the ame. 10

11 Davd S. Evan and Mchael D. Noel Index. Th ba ovetate the tue hot-un own-pce elatcty of demand. In fact, t yeld an elatcty etmate that even lage than the tue long-un own-pce elatcty of demand. We defne long-un to be a long a neceay fo all meanngful feedback effect to be woked out, fom the conequent change n platfom ze. 9 In th cae, the eultng maket defnton would be too boad and pedcted unlateal effect of a tanacton would be too mall. The tuaton moe complex wth aymmetc platfom. When the tet conde equal pce change (e.g. X = 5%) aco all of the hypothetcal monopolt poduct, the bae ae gned a above. Howeve, f the aymmety gnfcant and f the analyt conde dffeental pce change aco poduct, the decton of the oveall ba depend on the analytcal method and alo the elatve and abolute ze of the pce nceae() condeed. Dffeental pce change ae moe lkely to be a condeaton n the analy of unlateal effect, whee anttut concen may cente aound patcula poduct, than n maket defnton analye whee the pce nceae deemed gnfcant ae geneally taken to be unfom (e.g. 5% o 10%), a uggeted by the DOJ/FTC mege gudelne. Thee addtonal complcaton become petnent n ou analy of the Google-DoubleClck mege n Secton V, below. We now etun to the ymmetc cae. Call the platfom fm 1 and fm 2, and the two goup of cutome A and. Note that platfom ymmety mple P P = 1 P2 = fo = A,, but even wth ymmetc platfom we ae not aumng ymmety aco the two de, A P P. The de ae typcally qute dffeent n pactce. Alo, defne total quantty aco platfom on de a Q Q + 1 Q2 =. Imagne that a hypothetcal monopolt of both two-ded platfom nceaed pce to the conume on de by P and to conume on de by P, whee. Smla to the one-ded cae, the gan on nfamagnal ale due to the pce nceae on de would be: 9 Ou defnton of hot and long ae defned to be the peod n whch the dect pce epone and meanngful ndect pce effect take place, epectvely. They do not elate to calenda tme and ae dffeent fom the concept of hot- and long-un (+/- one o two yea) geneally ued by anttut pacttone. 11

12 Davd S. Evan and Mchael D. Noel P ( Q + Q ) (3) Howeve, unlke the one-ded cae, the magnal lo due to the pce nceae on de now cont of two component: ) ( P C ) Q ( P C Q (4) the lo on de and the lo on de due to the pce nceae on. 10 Hee, magnal cot ae denoted by C and C, and Q epeent the lo n total quantty on de ove the tme peod that elevant fo the mege evew (typcally one o two yea). Summng up and equatng the gan to the loe, we get the Two-Sded Ctcal Lo Fomula n epone to change n the pce on de A and of X A % and X % epectvely: = A, Q R ( X + M )( ) + R X = 0 (5) Q whee R = Q P, the evenue eaned fom de. Ctcal Lo the et of pecentage quantty educton on de A, Q A / Q A, and de, would leave the hypothetcal monopolt poft unchanged. 11 Q / Q, that The Actual Lo to the hypothetcal MSP monopolt depend on eveal facto. A wth one-ded fm, Actual Lo depend on the (hot-un) own-pce and co-pce elatcte of demand. Hghe own pce elatcte tend to nceae Actual Lo nce a pce nceae at a gven platfom eult n elatvely moe cutome wtchng away fom that platfom. On the othe hand, hghe (hot-un) co pce elatcte between the monopolt platfom tend to deceae Actual 10 The mege gudelne tate that when detemnng the elevant anttut maket the tem of ale of all othe poduct [outde the popoed anttut maket] ae held contant. In geneal, we would expect a hypothetcal monopolt to adut pce on de a well a on de A. Th and ubequent fomula account fo both cae. 11 A pecal cae when the two de ae ted togethe n a fxed popoton, e.g. a tanacton maket lke cedt cad evce, whee a tanacton take place between a cutome on de A (a cad holde) and a cutome on de (a mechant). Th the cae condeed by Rochet and Tole (2003) and Emch and Thompon (2006) among othe. Suppoe the popoed anttut maket the tanacton, whch by defnton nclude both de. Gven A A Q = Q = Q and X = X = 5%, equaton (8) collape to: A Q / Q = X /( X + M ) whee A A A A M = ( P + P C C ) /( P + P )). Th the famla one-ded Ctcal Lo fomula whee the poduct A the tanacton wth a compote pce of p + p. 12

13 Davd S. Evan and Mchael D. Noel Lo becaue elatvely moe of the cutome that wtched away fom one platfom can be ecaptued wth the monopolt othe platfom. Unlke one-ded fm, Actual Lo alo depend on the tength of the ndect netwok extenalte that cutome goup povde to one anothe. Recall that an MSP only ucceful becaue t able to bng two dtnct cutome goup togethe n gnfcant numbe. When an MSP nceae t pce on de fo platfom, thee the uual contacton n demand on de, a wth one-ded fm. ut now becaue thee ae fewe de cutome, the platfom le valuable to de cutome. Th caue a contacton on de a well. The feedback effect take ove, caung anothe contacton of de, then de agan, and o on. The tonge the extenalty aco goup, the geate the demand contacton wll be afte a pce nceae and the geate the Actual Lo, all ele equal. The exact Actual Lo fomula depend on the pecfc demand fom choen. We conde, a an example, an oelatc demand functon adapted to nclude the pecal featue of MSP. 12 Let q = α q δ q + θ wheeθ = µ β p + γ p (6),, whee q = ln( Q ) the log quantty demanded by de cutome at platfom, p = ln( P ) log pce to de on platfom, and paamete α, β, and δ ae non-negatve. 13 Snce each platfom offeng a competng evce to the othe platfom on each de of t bune, γ non-negatve a well. Gven the loglog fom, the β and γ ae the uual hot-un own and co pce elatcte fo de cutome epectvely. Recall that we defne hot-un to nclude the tme needed fo the dect epone of cutome mpacted by the pce nceae but too hot to nclude any of the ndect netwok feedback effect that follow. The ndect netwok extenalte (the magnal value one de put on the peence of the othe at a platfom) ae captued by α, the wthn-platfom co-de extenalty, and δ, the 12 The bae decbed hee ae not excluve to the patcula demand functon choen. 13 Fo expotonal pupoe, we take the ndect netwok effect to be potve aco the two de n the man text, though th need not hold n geneal. 13

14 Davd S. Evan and Mchael D. Noel co-platfom co-de extenalty. 14 The α, fo example, the pecentage change n quantty demanded by de at platfom n epone to a one pecent change n the quantty of platfom de cutome. We aume α > δ, β > γ, and α + δ <1 to enue tablty of the ytem. 15 Solvng fo the educed fom equaton of the pce), and takng the total devatve of each q (a a functon only of q, we deve the fomula fo Actual Lo to de cutome afte pce nceae to de A and de of X A % and X % epectvely: L ( γ β ) X + ( α δ )( γ β ) X = (7) 1 ( α δ )( α δ ) L the pecentage Actual Lo on de at each platfom and at both platfom collectvely, L = A q = A ln Q = all feedback effect have been woked out. Q A / Q A (nce platfom ae ymmetc), once We ee the two-ded Actual Lo fomula fo de a genealzaton of the one-ded fomula. When all co-de extenalte ae zeo, o that each goup demand do not depend on the numbe of cutome on the othe de at ethe platfom, the fomula fo L A and L concde wth the one-ded countepat. When two-ded extenalte ae peent, howeve, t necealy the cae wth ymmetc platfom that the coect two-ded fomula gve lage Actual Lo etmate than the one-ded veon, gven othewe unbaed etmate of the hot-un pce elatcte. Thee ae two eaon fo the Etmaton a hee. Ft, an nceae n pce on de A alone caue not only a educton n demand on de A but alo a educton n demand on de, nce the goup value a platfom le when thee 14 The ame fomula apply whethe fm mult-home o ngle-home. Whle t doe not change the tuctue of the demand ytem, t would be expected to mpact etmate of the paamete. 15 The ft condton enue demand on the othe de of both platfom doe not nceae afte a pce nceae and demand contacton at both platfom on the ft de. The econd enue demand doe not nceae on both de afte a pce nceae on one de by both platfom. The thd pevent explodng demand followng a pce nceae on one de by one platfom. 14

15 Davd S. Evan and Mchael D. Noel ae fewe A. So, unlke the one-ded cae, thee ae loe on both de (L A < 0 and L < 0). Second, and mpotantly, thee a multple effect n two-ded ndute that magnfe the mmedate lo on de A and on de ove tme. A dcued above, when de A contact afte t pce nceae, the platfom le valuable to t cutome and the de contact. ut fewe deceae the value of the platfom to the A cutome and now the A de contact futhe. oth de contact n tun, and Actual Loe ae lage than they would be n a one-ded wold whee abolute and elatve platfom ze doe not matte. The multple effect can be een n the denomnato of the two-ded Actual Lo fomula. The denomnato necealy le than one, o the two-ded Actual Lo fomula necealy yeld lage etmate of lo than the one-ded fomula, fo a gven et of paamete. The baed one-ded veon oveetmate the hypothetcal monopolt ablty to ae pce. To calculate whethe a gven pce nceae o nceae ae lkely to be poftable, one mply compae Ctcal Lo and Actual Lo, by ubttutng the value of L nto Q / Q n the Ctcal Lo equaton (5). If the left hand de of (5) negatve, the pce nceae() wll not be poftable. If potve, the pce nceae() wll be poftable. In mege analye, the tet would be pefomed ung ut the et of poduct o evce that the newly meged fm would contol. The meged entty de facto the hypothetcal monopolt and aumpton about poble cot effcence potmege ae ealy woked nto the analy. In maket defnton exece th tet epeated many tme, each tme expandng o contactng the popoed anttut maket, untl a maket found whee Ctcal Lo would equal Actual Lo fo a hypothetcal monopolt of all the poduct n that maket. Gven a maket defnton, the maket hae of the n fm ae calculated and then ued a poxe fo maket powe. 15

16 Davd S. Evan and Mchael D. Noel Whle peentng thee coected fomula, we contnue to cauton that thee ae many eaon to be way of mechancal maket defnton exece uch a the SSNIP tet and thee concen do not go away when MSP ae nvolved. Some may even be exacebated by the peence. Fo example, hould one nclude both de of the bune of an MSP n the maket defnton o ut one de? The anwe can be dffcult and depend on the tuaton at hand. The mege gudelne, n dcung the SSNIP tet, efe to addng o emovng ubttute poduct. The dffculty that the de of a gven MSP epeent hghly complementay poduct, and pcng decon on both de ctcally affect the MSP poftablty. Yet the SSNIP tet lent on handlng complementay poduct 16. We beleve f the two de ae vey hghly complementay and cloely lnked fo example, f the MSP facltate tanacton between the goup that occu n fxed popoton and MSP n an nduty all tend to eve the ame two de, then t can be eaonable to nclude both de n the maket defnton and the tanacton a the poduct. Howeve, n othe ndute MSP may all cate to the ame de A cutome but cate to vey dffeent knd of de cutome. If the anttut concen centeed aound the de A bune, ncludng both de of all MSP that hae the A de n the maket defnton would open a Pandoa box of unelated type that make no ene unde a ngle coheent maket defnton. Then the maket may need to be defned on the ba of de A only, but wth the ctcal undetandng that the de ae an mpotant contant on behavo and the fomula peented hee mut be ued to account fo t nfluence. A econd ue wth the SSNIP tet that we would expect a hypothetcal monopolt of eveal platfom to eoptmze pce aco de and aco platfom ut a we would expect a hypothetcal monopolt to eoptmze aco poduct n a one-ded wold. The DOJ/FTC mege gudelne ugget that the pce nceae deemed gnfcant fo maket defnton pupoe wll geneally be unfom 16 Weman (200) alo note that the peence of complementay good, f gnoed by the analyt, can lead to an oveetmaton of equlbum makup and of maket powe. 16

17 Davd S. Evan and Mchael D. Noel aco all poduct wthn the defnton (e.g. 5%), and the tem of ale of all othe poduct [outde the popoed anttut maket] ae held contant (.e. 0% pce nceae). In the cae of MSP, one could ntead magne pce nceae that dffe aco de o platfom, o conde a knd of 5% quantty-weghted aveage pce nceae aco de, allowng the hypothetcal platfom monopolt to eoptmze elatve pce. Settlng thee ue, whch ae alo concen wth one-ded SSNIP tet, le beyond the cope of ou pape. Ou goal hee mply to how that the one-ded Ctcal Lo fomula fo conductng the SSNIP tet ae wong when appled to twoded maket, and alo to povde a ueable famewok fo how to conduct a SSNIP tet when MSP ae nvolved. Whethe to nclude one o both de, and how to chooe X A and X, wll depend on the tuaton. The equaton we peent whch allow fo dffeental X handle all thee tuaton. A an altenatve to the SSNIP tet, one could ntead pefom a full-cale mulaton allowng full elatve and abolute eoptmzaton of pce by the hypothetcal monopolt, and uch an exece helpful n an advanced analy. Howeve, the Ctcal Lo mplementaton eman a mple and ueful ft pa, n pte of t dawback, and t mpotant, f one whe to apply t to MSP, to ue the coect fomula. Wth the SSNIP tet, a n any etmaton, t geneally pefeable to etmate all the paamete of the demand ytem wheneve elable data ext. 17 In pactce, data avalablty often uch that at leat ome paamete mut be calbated wth lmted nfomaton. Theoetcal etcton, lke the Lene Index 17 Thee ae eveal empcal pape that etmate two-ded demand ytem n patcula ndute n ode to etablh the extence of ndect netwok effect. Although geneally not n the context of mege o maket defnton analy, thee hghlght the mpotance and challenge of pope demand dentfcaton n a two-ded context. Fo example, ee Ryman (2004) etablhng a lnk between eade and advete n the yellow page maket, Ryman (2007) fo cadholde and mechant n the payment cad nduty, Agente and Fltucch (2005) fo eade and advete n the Italan magazne nduty wth an etmaton of maket powe, Wght (2004) and Kae and Wght (2006) fo lnkng eade and advete n the Geman magazne nduty and Dubo, Henandez-Peez, and Ivald (2007) lnkng eade and autho n the academc publhng nduty. Agente and Ivald (2005) ecap anttut cae nvolvng maket defnton n (two-ded) meda ndute. Ung lmted data fo the Fench magazne maket, they nclude an etmaton of ubcbe demand elatcte ung the pce of advetng a an ntument, uggetng a two-ded lnkage. Elatcty etmate dffe wth and wthout the ntument. 17

18 Davd S. Evan and Mchael D. Noel that elate makup and elatcte, can be ued to calbate paamete that othewe may be dffcult o mpoble to etmate. Othe theoetcal etcton, uch a the Slutky Symmety ule that elate co-pce elatcte, can be ued to enue logcal contency aco cetan paamete. The elatonhp between makup and elatcte epecally mpotant hee becaue makup appea n the Ctcal Lo fomula and the elatcte appea n the Actual Lo fomula. Th elatonhp hould be content wth economc theoy. 18 In calbaton exece, t now common pactce to ue the (one-ded) Lene Index to etmate the own pce elatcty fom the obeved makup when the latte cannot be etmated fom data, pehap becaue data ae lackng o the analyt ha nuffcent tme. Th tun out to be a poblem n two-ded ettng. The one-ded Lene Index ncoect fo MSP and elyng on t gnfcantly oveetmate the tue hot-un own pce elatcty of demand and ovetate Actual Lo. It well known n the one-ded cae that the pecentage makup equal the nvee of the own pce elatcty at the poft maxmzng output. In the two-ded cae, we can deve the ft ode condton fo poft maxmzaton. Each platfom chooe pce on each de to maxmze: max Π = q ( p)*( p c ) A u (8) p, p = A, The two ft ode condton mplfy to: R M ε + R M ε = R (9) fo = {A,}, whee: ε ( α Aδ + α δ A) γ + (1 α Aα δ Aδ ) β = (1 ( α δ )( α δ ))(1 ( α + δ )( α + δ )) A A A A 18 Some autho degad the Lene Index a too mple and unealtc fo applcaton n pecfc eal-wold anttut cae (ee Scheffman and Smon (2003) and Ha (2003)). We agee wth Katz and Shapo (2003) that thee hould be a peumpton of the theoetcal makup-elatcty elatonhp pendng evdence to the contay. It poble, howeve, to etmate both makup and elatcte ndependently of one anothe dectly fom the data and detep thee ue. 18

19 Davd S. Evan and Mchael D. Noel ε ( α Aδ + α δ A)( α γ + β δ ) + (1 α Aα δ Aδ )( α β + δ γ ) = (1 ( α δ )( α δ ))(1 ( α + δ )( α + δ )) A A A A We call ε and ε the long-un own-pce elatcty and the long-un co-de pce elatcty, n abolute value, once all feedback effect have been woked out. The ubcpt on the ε ndcate thee ae elatcte wth epect to change n the pce of the de good by fm only. The ft ode condton do not epoduce the one-ded Lene Index fomula. They do not even unquely dentfy the value of the own pce elatcte fom the makup, but athe only contan the elatonhp between the own and co pce elatcte and the ndect netwok extenalte. Ung the one-ded Lene Index to calbate own pce elatcte when MSP ae nvolved ceate a Lene a. To ee the Lene a mot ealy, magne fo a moment ymmety aco de α A = α and δ A = δ. The makup equaton fo de then mplfe to S M = ( ε + ε ) 1. Now note that the long-un own pce elatcty, ε, necealy lage than β (the uual hot-un own pce elatcty), due to the ndect netwok effect. The long-un co-de pce elatcty, ε, whch zeo n a tuly one-ded nduty, geate than zeo n abolute value hee. 19 Conequently, fo a gven et of elatcty etmate, equlbum makup ae lowe than the one-ded Lene Index would mply. The convee that fo a gven et of makup obeved n the data, the tue hot-un own-pce elatcte of demand ae lowe than the one-ded Lene Index would ugget. The eaon that the ndect netwok extenalte penalze pce nceae moe, o the hot-un own pce elatcty mut be epecally low n ode to uppot makup at a gven level. 19 Recall th the long un change n quantty on de at platfom due to a change n the pce of de at platfom, once all feedback effect have been woked out. Thee no dect effect of de pce on de demand, but thee an ndect effect of de pce on de demand fo two-ded platfom, va change n de demand. 19

20 Davd S. Evan and Mchael D. Noel The ba tong nce ε > 0, the one-ded etmate even lage than the tue long-un own-pce elatcty, and th eult n a ba n the oppote decton. Maket defnton wll be et too lage, o the expected pce nceae fom a mege wll be aumed too mall. The compaatve tatc of the two-ded makup equaton gve nght nto the poblem. A wth the one-ded calculaton, a hghe hot-un own elatcty β (whch nceaed both ε and ε ) lowe makup. ut unlke the one-ded cae, a hghe hot-un co pce elatcty of demand γ alo eult n lowe makup (agan nceang ε and ε ). The eaon that a hghe co pce elatcty caue a hghe popoton of the de A cutome who wtch afte a de A pce nceae to buy fom platfom athe than buy nothng ntead. Snce platfom ae two-ded, the elatve value of fm platfom to the de cutome fall when moe A move to, caung a demand contacton on the de a well. The feedback effect begn, and platfom contact futhe. Geate ndect netwok extenalte alo wok to deceae makup. Ft, by ang pce a platfom tgge the maket hnkng feedback effect caung t demand to epeatedly contact on each de. It eaet to ee th by notng (1 α)/β when δ = 0 n the ymmetc cae. A geate co-de own-platfom M = extenalty α penalze pce nceae moe and act to lowe equlbum makup. Second, and upngly, a hghe co-de co-platfom extenalty δ alo act to lowe makup. To ee th, note that M = (1 (α + δ))/β a γ β n the lmt n the ymmetc cae. The paamete α and δ now appea a a um, athe than a dffeence (a they dd n the Actual Lo fomula). Only platfom changng pce, not the hypothetcal monopolt of both poduct. A hghe δ mean that n epone to the hnkng of de A at platfom afte t ae p A, moe de cutome wtch to platfom athe than to nothng at all. Th make moe attactve to de A, then moe attactve to de, then de A and o on. Thu, hghe 20

21 Davd S. Evan and Mchael D. Noel value of both α and δ penalze pce nceae moe and lead to lowe makup n equlbum. Oveall, fo a gven et of hot-un own-pce and co-pce elatcte, two-ded peue lowe equlbum makup below that whch the one-ded Lene Index would pedct. One-ded etmate of hot-un own-pce elatcty deved fom makup ovetate the tue elatcty and undetate the poftablty of potental pce effect. We now tun to a demontaton of the potental Etmaton and Lene ae fom ung one-ded fomula n tuaton nvolvng ymmetc MSP. IV. COMPARISON OF ONE AND TWO-SIDED CRITICAL LOSS: SOME SIMULATIONS Aume that two platfom each eve de A and, and a an example, aume a elevant anttut maket popoed that would nclude the poduct on de A of thee two platfom. The tet would be the ame f we wee condeng a mege between the two platfom and wanted to know f a gven pce nceae on de A would be poftable fo the meged entty. 20 We mantan the aumpton of ymmetc platfom (though not necealy ymmetc de). L fo It ueful to eaange the Ctcal Lo equaton (5), ubttutng n L A and Q A / Q A and Q / Q, to get: A + A X M A X + M ω L + ( 1 ω) L = 1 (10) A X X whch hold when Ctcal Lo equal Actual Lo exactly. It clea that the equaton eally a weghted um of the ato of Actual Lo to Ctcal Lo on each de, whee the weght gven by ω = R A R A X A X + R A X 20 If the maket wee popoed to nclude both de A and, we would et X A =X =5% and the ame qualtatve eult tll hold. 21

22 Davd S. Evan and Mchael D. Noel We efe to the left hand de of th equaton, n abolute value, a the Actual- Ctcal Lo Rato (ACR). If the ACR geate than 1, Actual Lo exceed Ctcal Lo, and the pce nceae would not be poftable. The elevant maket would be expanded. If ACR le than 1, the pce nceae moe than poftable and the elevant maket contacted. The ACR epeent a meaue of the cloene of the Actual and Ctcal Lo. 21 Note that f the nduty wee tuly one-ded, o that L = 0 afte a pce nceae on de A, th equaton educe to the ato of Actual Lo to Ctcal Lo that would be applcable wth one-ded fm. Ft, aume that the hot-un own-pce elatcte ae well etmated and the analyt doe not depend on the (one-ded) Lene Index. We ee the one-ded calculaton ae baed towad a lowe ACR, and the ba gow a the ndect netwok extenalte become moe mpotant. Fgue 1 plot the ACR agant the own-pce elatcty β fo eveal dffeent value of the co-de own-platfom extenalty α. Recall the paamete α epeent the hot un pecentage change n a platfom de A bune due to a 1% change n demand on t de bune, and vce vea. The fgue nclude both the ACR calculated ung the one-ded fomula (whch aume α and δ ae both zeo), and alo ung the coect two-ded fomula fo MSP. Othe paamete ae held contant, and the pce nceae to de taken to be 5%. 22 Ft, and a we would expect, the ACR nceae a the hot-un own-pce elatcty nceae n both calculaton fo a gven α. Thee an ndect effect of hghe β though makup that nceae Ctcal Lo, but the dect effect of β that nceae Actual Lo domnate, and the ACR e wth β. The calculated effect of the own-platfom co-de extenalty α on the ACR, howeve, depend on the calculaton beng ued. In the two-ded calculaton, a hghe α aocated wth tonge feedback effect, whch eult n geate Actual Lo and geate ACR followng a pce nceae, all ele equal. In contat, the ACR 21 The devaton aume X A 0 and X 0. When X = 0, the econd tem educe to A A ( R M / R X ) L. 22 The aumpton of 5% often ued but abtay. 22

23 Davd S. Evan and Mchael D. Noel fall unde the one-ded calculaton. Th becaue the Actual Lo calculated wth the one-ded fomula ( ( β γ ) X ) ndependent of α, but the Ctcal Lo A A A geate nce obeved equlbum makup ae lowe wth hghe α. The gap between the ACR unde the two calculaton gow wth hghe α, and wth hghe β. Fgue 2 plot the ctcal beta unde each calculaton agant the co-de own-platfom extenalty α. The ctcal beta the value of the own pce elatcty, condtonal on the othe paamete, that would caue Actual Lo to exactly equal Ctcal Lo. The aea between the one and two-ded ctcal β the egon of eo: the combnaton of α and β fo whch a contacton of the popoed anttut maket would be called fo unde the one-ded calculaton when an expanon of the popoed maket hould be called ntead. In mege analye, thee would be the combnaton of α and β fo whch the analyt would conclude fom the one-ded calculaton that the hypothetcal monopolt n a maket defnton analy o the meged entty n the unlateal effect analy would gnfcantly nceae pce when n fact t could not. The fgue how that a the ndect netwok effect become tonge, the egon of eo gow wde. The coepondng fgue fo the ctcal gamma, wth β held fxed (not hown), yeld the ame concluon. 23

24 Davd S. Evan and Mchael D. Noel Actual/Ctcal Rato alpha= eta One-Sded Calculaton Two_Sded Calculaton (Alpha = {0,0.2,0.4,0.6,0.8}, Gamma = 1, Delta = 0) Fgue 1. Actual/Ctcal Lo Rato, One- and Two-Sded Calculaton Ctcal eta One-Sded Ctcal eta Regon of Eo Two-Sded Ctcal eta Alpha (Gamma = 1, Delta = 0) Fgue 2. Regon of Eo, One- and Two-Sded Calculaton 24

25 Davd S. Evan and Mchael D. Noel In thee example, t aumed that the hot-un elatcte ae popely etmated; only the fomula ued dffe. Howeve, f the analyt ele on the oneded Lene Index to etmate the own pce elatcty of demand, and then ue the uual one-ded fomula, the ba goe n the othe decton. The analyt wll oveetmate the hot-un and long-un own pce elatcte of the MSP and wll oveetmate Actual Lo. The one-ded Ctcal Lo calculaton unchanged (becaue t baed on obeved makup) and o the ACR wll be eoneouly hgh. In othe wod, poftable pce nceae wll not be expected fo even elatvely low value of the tue hot-un own-pce elatcty β. The ctcal beta and the egon of eo ae plotted n Fgue 3, and th tme the ctcal beta ae lowe unde the oneded calculaton than unde the two-ded one. In the egon of eo, the analyt who ele on the one-ded calculaton would ecommend an expanon of the anttut maket when a contacton hould be called fo, o would conclude that megng platfom could not poftably ae pce afte the mege when n fact they could. Ctcal eta Two-Sded Ctcal eta One-Sded Ctcal eta Regon of Eo Alpha (Gamma = 1, Delta = 0) Fgue 3. Regon of Eo, Mmeaued β n One-Sded Calculaton 25

26 Davd S. Evan and Mchael D. Noel The aymmetc platfom cae, gven by fomula et out n Appendx 1.A, moe nvolved. When platfom ae aymmetc but the pce nceae condeed on any de ae equal aco platfom, the bae move n the ame decton a n the ymmetc cae. Howeve, when platfom ae aymmetc and pce nceae condeed ae alo allowed to dffe aco poduct, the decton of the ba alo depend on the degee of aymmety and the patcula mx of pce nceae. The eaon dffeental pce nceae ae mpotant becaue they eult n a hft n the elatve ze of the platfom and geneate feedback effect. If the platfom aymmetc enough, the mpact of cetan pce nceae wll be ovetated, and othe undetated. 23 A an example, conde a popoed mege whee the platfom dffe gnfcantly n ntal poftablty. A pce nceae at the low-magn platfom wll be benefcal fo the hypothetcal monopolt f netwok effect ae tong and dong o convnce enough cutome to wtch to t hgh-magn platfom. One-ded calculaton do not account fo th poblty, and a a eult, undetate the poftablty of th pce nceae. If we conde a pce change at only the hghmagn platfom, we can get an oppote ba. The poftablty of the pce nceae would be ovetated by a one-ded calculaton a long a the gan fom expanon of the low-magn platfom cannot compenate fo the contacton of demand at the hgh-magn platfom. Thu, when aymmetc platfom and aymmetc pce change ae condeed, the decton of the bae depend on the pecfc queton beng aked a well a the method ued. 23 Aco all fou potental pce change of a gven equal amount, the aveage ba fom thoe pce change collectvely goe n the ame decton a that n the ymmetc cae, whch n tun depend on the analytcal method ued. Howeve, n the aymmetc cae thee vaaton n the ze of thee bae and wth uffcently aymmetc fm, ome may have the evee gn. ecaue dffeental pce change act a weght n Actual Lo (equaton A.4), the oveall ba can go n the oppote decton of the ymmetc cae f the evee-gned bae ae uffcently hghly weghted. 26

27 Davd S. Evan and Mchael D. Noel V. ANALYSIS OF UNILATERAL EFFECTS: AN APPLICATION TO GOOGLE S ACQUISITION OF DOULECLICK Google a povde of onlne advetng evce fo web publhe and advete n addton to opeatng a each-engne that ell advetng pace. DoubleClck pncpally a povde of eve-baed oftwae tool and evce fo managng onlne advetng fo web publhe and advete. Google ageed to puchae DoubleClck fo $3.1 bllon and ought cleaance fom eveal competton authote aound the wold. The mege wa cleaed by the Fedeal Tade Common, the Euopean Common, and othe competton authote afte lengthy nvetgaton. Th ecton ue data on magn fo Google and DoubleClck along wth othe aumpton on the compettve elatonhp to how how the technque ued above can be employed to etmate the unlateal effect fom a mege of MSP. The data and calculaton ae llutatve. We take no poton on whethe the mege hould o hould not have been cleaed by the competton authote; thee authote had acce to moe elable data than what ae ued hee and addeed fulle ange of ue n the aement. 24 pupoe only to how how the tool developed n the pevou ecton can be ued n pactce. Ou Web publhe make pace avalable on the web page fo advetement. The ad nventoy coepond oughly to the numbe of people that wll vew each pace ove ome gven tme peod. 25 Advete ae on the othe de of the maket. They buy advetng nventoy to each conume. Lke all elle and buye, publhe and advete eque way to dentfy optmal tadng oppotunte and to etablh tanacton pce. Th ntemedaton occu dectly though blateal exchange between publhe and advete and ndectly though multlateal exchange between publhe and advete ung advetng 24 The autho wee conultant to Mcooft and authoed ubmon to the competton authote that aeed the poble compettve effect of the acquton baed on nfomaton that wa publcly avalable. 25 Advete value the demogaphc and othe chaactetc of vewe n addton to the hee numbe. Thu vew by hgh-ncome edent of oton ae moe valuable to the local MW deale than vew by low-ncome edent o hgh-ncome edent of Topeka. 27

28 Davd S. Evan and Mchael D. Noel netwok. Lage publhe ue moe dect method whle malle publhe ue moe ndect method. Th ecton concentate on lage web publhe, whch account fo the pepondeance of advetng evenue and lage advete, whch account fo the pepondeance of onlne pendng. 26 A gnfcant pat of the advetng nventoy bought and old by thee lage advete and publhe nvolve blateal exchange. Lage publhe ethe have dect ale foce o he thd-paty ale ep to ell the ad nventoy. Lkewe, lage advete have puchang agent o, moe often, ue meda buye at the advetng agency to puchae ad nventoy. Advetng nventoy old th way ad to be eeved. Lage publhe often ell the pemum ad pace th way. Lage publhe often alo ely on othe ntemedae to ell ad nventoy ndectly that they have not eeved fo advete dectly. Thee ntemedae ae called advetng netwok. Publhe may ue ad netwok becaue they ae moe effcent than a dect ale foce fo ome, o all, of the ad nventoy; o becaue they have exce nventoy that they have not old dectly, pehap becaue of pke n vewe. Advete ue ad netwok becaue t anothe way to each vewe. Advetng nventoy old ndectly cot le on aveage than advetng nventoy old dectly becaue the pace le deable than the dectly old pace. Advete and publhe eque management, epotng, and technology oluton uch a thoe offeed by DoubleClck and aquantve. Thee tend to be eve-baed oftwae that can help manage advetng nventoy and campagn that may nvolve mllon of ad mpeon (that, vew of an ad by an ndvdual) a day. Thee eve-baed oftwae tool ae hghly ophtcated mon-ctcal applcaton 26 A lage publhe efe to one whch uffcently lage to ue tand-alone tool to eve the dectly old ad and any emnant ad old though non-ntegated and/o ntegated ad netwok. Th nclude at leat the top 500 publhe, and account fo the maoty of advetng evenue. Smalle publhe do not fnd t economcally effcent to he dect ale foce. They uually ely on an ad netwok to ell the ad nventoy. 28

29 Davd S. Evan and Mchael D. Noel Lage publhe uually ue a publhe tool uch a DoubleClck Dat fo Publhe (DFP). 27,28 Th tool typcally hoted on a web eve mantaned by the povde. The publhe hadcode lnk to the publhe tool to fll the ad pace fo whch t want to ue the management, epotng, and evng capablte of the publhe tool. It alo typcally ntegate the publhe tool nto many othe apect of the webte technology and bune pactce. Publhe wll typcally only ue one publhe tool (.e., they ngle-home on tool). Suvey of lage webte how that DFP ued by omewhat moe than half of thee webte. Lage te ae moe lkely than malle te to have DFP. DFP ha about 63 pecent hae baed on page vew. 29 Lage advete and advetng agence often have an advete tool uch a DoubleClck Dat fo Advete (DFA). 30 Lage advete typcally manage advetng on hunded of webte and aco numeou poduct ung many method of onlne advetng. Th tool help them manage thee vaou campagn. Advete uually ue one advete tool although advetng agence may ue eveal. Howeve, ngle-homng doe appea to be the nom. DFA hold oughly a 26 pecent hae of non-each advete tool. 31 Google the leadng ntegated ad platfom. A few povde offe moe o le complete oluton fo advete and publhe. Google AdSene/AdWod platfom one of thee. Publhe can hadcode ad pace to Google AdSene 32, whch take cae of eveythng ellng the nventoy, managng the ad pace, evng ad to the vewe, and endng the publhe a poton of the poceed afte takng a common. 33 Advete, 27 See 28 A handful of mega-lage publhe uch a MSN have the own popetay tool but mot othe ue a thdpaty tool. 29 The uvey conducted by LECG how that AdSene ued on 50% of all webte ampled. DoubleClck ued on 63% of all webte ampled. A econd uvey conducted by Keytone Stategy fo Amecan vewe how that AdSene ued on 45% of uveyed te whle DoubleClck ued on 61%. 30 See 31 Th baed on aquantve etmate of hae fo telf and DoubleClck n advete tool (among povde that ell thoe a tandalone non-ntegated poduct), aduted fo thoe advete tool that ae old on an ntegated ba (wth the ad), by povde uch a AdSene. 32 See 33 In the onlne advetng Taffc Acquton Cot (TAC) efe to what an advetng platfom pay fo taffc. Google pay TAC to publhe n etun fo contbutng the advetng nventoy to the Google 29

30 Davd S. Evan and Mchael D. Noel lkewe, can buy pace fom the Google Content Netwok 34 though AdWod 35 (whch bundle Google each-baed and contextual-baed advetng poduct). Yahoo! and Mcooft offe mla all-ncluve oluton. Thee oluton have all eulted fom leveagng the technologe developed fo each-baed advetng epecally the keywod bddng aucton to the buyng and ellng of publhe ad nventoy. Some othe ad netwok ae alo ntegated to lee degee; they may offe publhe evng technologe o that publhe can hadcode ad netwok nto patcula pace. Many lage publhe ue an ntegated platfom fo contextual ad and an unntegated platfom (baed on a patcula publhe tool) fo non-contextual ad; the unntegated platfom ued to acce multple tandalone ad netwok, a well a ad old dectly. Etmate ugget that Google account fo 51 pecent of the ad evenue though the ndect channel and 27 pecent oveall. The unntegated ad netwok account fo an etmated 45 pecent of ad evenue though the ndect channel and 25 pecent of web publhe ad pendng oveall. 36 Followng the acquton, Google contol an nput nto the unntegated channel fo ellng ad dectly and ndectly. It would theefoe be expected to coodnate the pce of DFP, and though DFP, the oveall pce of dtbuton though the dect ale and though the ad netwok. 37 The queton we conde whethe the combned entty wll have the ncentve to alte pce gnfcantly and, moe mpotantly fo ou pupoe, how the eult dffe between the one-ded and two-ded calculaton. Incopoatng two-ded effect mpotant fo analyzng th queton becaue change n the pce of the nput alte the advete demand fo pace a well a the publhe demand fo ellng though a patcula method. Table 1 epot the data and ouce we have eled on. Google and DoubleClck appea to ean oughly 75 pecent go magn baed on publcly Content Netwok. The publhe eceve TAC. In th cae 1-TAC the pecent common pad by the publhe to Google fo ellng t ad nventoy. If Google pay the publhe 80% of the evenue that Google eceve fom the advete the publhe ha pad a common of 20% to Google. 34 See 35 See 36 Souce: Keytone Stategy. 37 We focu on pce effect a tadtonal n th ot of analy. Google could engage n a vaety of othe tatege pot-acquton that could nvolve the exece of acqued maket powe but that do not necealy nvolve nceang pce. 30

31 Davd S. Evan and Mchael D. Noel avalable data. Ad nventoy ell on aveage, wth geat dpeon, fo about $2 pe thouand mpeon (that, vew by ue) baed on etmate epoted to u by nduty obeve. Google ell on a cot pe clck ba but obtan the equvalent of appoxmately 40 pe thouand mpeon baed on the evdence we have een. 38 Publhe typcally pay 40 pe thouand mpeon on aveage to the tandalone ad netwok and 5 pe thouand mpeon to the publhe tool povde. DFP DFA AdSene Souce Unt pce (cpm) Dcuon wth publhe. The evenue pad to Google by advete etmated at aound $2 CPM of whch publhe keep appoxmately 80%. Pecentage go magn 75% 75% 75% DoubleClck go magn accodng to t 2004 Fom 10K wa 74%. Accodng to Google 2006 Fom 10K t cot of eanng evenue (net of taffc acquton cot pad to publhe) ae aound 10% of total evenue. Th mple t go magn on AdSene 90%.It oveall go magn (fo each and noneach ad pogam) ha been between 50-70% n the pat fve yea. We ue 75% a eaonable. Revenue $325m $196m Google 2004 evenue on thd paty ad afte payng publhe. DoubleClck 2004 evenue fo Tech Soluton whch appea to manly be comped of DART poduct. Table 1. Data and Souce. We want to nvetgate how the one-ded and two-ded technque dffe n the pedcton of whethe the meged Google-DoubleClck entty wll have the ablty to nceae the pce of DFP by X%, holdng all ele contant. The potental 38 The evenue pad by advete by publhe etmated at aound $2 CPM of whch publhe keep appoxmately 80%. See 78-evenue-hae/ and 31

32 Davd S. Evan and Mchael D. Noel fo an nceae n the pce of DFP wa a cental pont of concen wth the mege. Google AdSene an ntegated poduct, and o chage hghe makup than DoubleClck DFP. The concen wa that t mght be advantageou fo Google to ae the pce of DFP and hft publhe to t AdSene netwok. 39 In the analy, we take X to be ethe 5% o 10%, and nce the platfom ae nheently aymmetc, we ue the fomula et out n Appendx A.1. ecaue of aymmetc platfom and aymmetc pce change, the decton of ba fom ung the one-ded calculaton n the two-ded ettng unknown ex ante. Gven the lmted data avalable, calbaton the mot feable appoach. 40 Fo the one-ded calculaton, thee ae fou paamete to etmate (all on the publhe de), ung a combnaton of data and etcton baed n economc theoy. In the two-ded model thee ae xteen paamete total n the demand ytem that we need to etmate ung a combnaton of data and economc theoy. Appendx A.2 dcue the pecfc of the theoetcal etcton ued n calbatng the paamete unde both one-ded and two-ded calculaton. The fomula ae n Appendx A.1, whch extend the model to the cae of aymmetc platfom, a elevant hee. ecaue we calbate, the one-ded calculaton wll be ubect to the Lene ba. Followng common pactce, we epot the moe ealy ntepetable ctcal dveon ato and ctcal wtchng level athe than the ctcal elatcte (β o γ themelve). 41 The ctcal dveon ato defned a the facton of the quantte lot at DoubleClck DFP that need to be mmedately ecaptued by Google AdSene platfom, fo a pce nceae n DFP to be poftable once the ndect netwok feedback effect wok themelve out. It effectvely the quanttyweghted ato of the co-pce elatcty (of AdSene quantty wth epect to the 39 In the two-ded calculaton, we attbute 2/5 th of the Google unt pce and evenue to the publhng de and 3/5 th to the advetng de, to match the DoubleClck ato. Thee ae the expected de-pecfc pce that Google would chage had advete pad publhe dectly fo the advetng pace and each pad Google a common fo the value of the tool and ntemedaton evce povded. Th avod the need fo negatve pce and negatve extenalty paamete n the calbaton, whch add tanpaency. 40 Gven enough tme a competton authoty could pobly obtan uffcent data fom membe of the nduty and though uvey to obtan etmate fom demand-ytem etmaton. 41 See Shapo (1996). 32

33 Davd S. Evan and Mchael D. Noel pce of DFP) to the own-pce elatcty (of DFP). The Ctcal Swtchng Level defned a the facton of the total quantte of DFP that need to be mmedately ecaptued by AdSene afte a pce nceae fo the nceae to be poftable once all feedback effect ae woked out. It calculated a the AdSene-quantty-weghted co-pce elatcty to total DFP quantty. Ctcal dveon ato Ctcal wtchng level 5% Ctcal Pce Inceae 10% Ctcal Pce Inceae One-ded Two-ded One-ded Two-ded Calculaton Calculaton Calculaton Calculaton 0.83% 0.00% 1.67% 0.01% 0.06% 0.00% 0.22% 0.00% Table 2. Ctcal Dveon Rato and Swtchng Level Table 2 epot the ctcal dveon ato and ctcal wtchng level unde ou bet data aumpton, fo both the one-ded and two-ded calculaton, and fo ctcal pce nceae (X) of 5% and 10%. 42 Whle all the numbe ae low gven the concentated natue of the popoed mege, the ctcal dveon ato and wtchng level mpled by the one-ded eult tun out to gnfcantly oveetmate the two-ded calculaton. In othe wod, the one-ded calculaton undetate the potental fo unlateal pce effect fom the mege n th ccumtance. Wheea the one-ded numbe allow fo a mall poblty that the pce nceae would not be poftable, the two-ded calculaton ugget that Google lkely to ae pce on DFP even f vtually no cutome wtched to AdSene. 42 We peent th analy to demontate the effect of two-ded condeaton on tandad dveon ato analy. Whethe and unde what ccumtance t appopate to conclude fom th ot of analy that a mege hould be blocked a much moe complcated ue whch we do not adde n th atcle. 33

34 Davd S. Evan and Mchael D. Noel Th ceate a egon of eo between the ctcal dveon ato. If the actual dveon ato below the one-ded fgue and above the two-ded fgue, t would eult n dffeent concluon dependng on the calculaton ued. The oneded calculaton would ugget poftable pce nceae, the two-ded calculaton would not. The ame tue fo actual wtchng level. Geneally peakng, the fndng of poftable pce nceae wth an effectvely zeo co-pce elatcty n the two-ded calculaton mght be upng. Megng fm n a one-ded wold only ae pce above t fomely poft-maxmzng level f dong o dectly caue cutome to wtch to t othe poduct,.e. a lage enough co-pce elatcty. The eaon why zeo wtchng level ae plauble n the two-ded cae becaue of the ndect netwok extenalte. y ang the pce of DFP, DoubleClck loe publhe and, va the feedback effect, alo loe advete, then moe publhe, moe advete and o on. A the DoubleClck platfom hnk and t value deteoate, advete and publhe wtch to othe platfom, ncludng Google AdSene. 43 It tun out that the nceae n poft to Google fom th wtchng, whch dven by change n platfom ze athe than change n elatve pce dectly, make the pce nceae on DFP poftable. Hence, Google beneft fom contactng and devalung the low (abolute) magn DoubleClck platfom to nceae the elatve value of t hgh (abolute) magn AdSene platfom. 44 In ummay, the one-ded and two-ded calculaton yeld dffeent ctcal dveon ato (and ctcal wtchng level) and open up a egon of eo between them. The ze of th egon of eo depend on the data and extenalty aumpton, but non-tval a a geneal ule. If the actual dveon ato fall n between the one- and two-ded calculaton, the analyt would gve an oppote ecommendaton about unlateal pce effect. Th hghlght the need fo ncopoatng two-ded effect nto any economc analy nvolvng MSP. 43 Cutome who ae entve to platfom ze, even f pefectly pce nelatc, make th wtch. 44 The fact that Google can poft fom DFP pce nceae that ae puely contactonay ugget that othe nonpce method of hnkng the elatve ze of the DoubleClck platfom can alo be poftable. 34

35 Davd S. Evan and Mchael D. Noel Th ecton ha hghlghted the eo that ae fom ung appoache baed on the one-ded Lene Index.e. ubect to the Lene ba. Suppoe, howeve, that an analyt had ued econometc technque fo aeng maket defnton and compettve effect n ngle-ded maket to ae the Google-DoubleClck tanacton. In that cae, ou concluon would be eveed (the Etmaton ba). The analyt would tend to defne maket too naowly and ovetate the compettve conequence of the tanacton. VI. CONCLUSIONS Tadtonal method fo evaluatng mege between ngle-ded fm can lead to eoneou concluon when mege nvolve MSP. The decton of the ba depend on the analytcal technque ued, wth tadtonal demand etmaton tendng to daw maket too naowly and ovetatng compettve effect, and Lene Index baed calbaton method dawng maket too boadly and undetatng compettve effect. The decton of ba can alo vay wth the degee of platfom aymmety and the patcula et of poduct that ae ubect to pce nceae. When mege nvolve MSP, the coect analy mut account fo the ndect netwok effect between the multple de and the conequent effect on pce and output fo the multple de. Falng to do o can lead to mateal mtake a we have hown though the mulaton epoted above. 35

36 Davd S. Evan and Mchael D. Noel ILIOGRAPHY Agente, E. and L. Fltucch (2005). Etmatng Maket Powe n a Two-Sded Maket: The Cae of Newpape, Jounal of Appled Econometc, fothcomng. Agente, E. and M. Ivald (2005). Maket Defnton n Pnted Meda Induty: Theoy and Pactce, CEPR Dcuon Pape No. 5096, Avalable at SSRN: Amtong, Mak (2006). Competton n Two-Sded Maket, Rand Jounal of Economc, Vol. 37, No. 3, pp Amtong, M. and J. Wght (2007). Two-Sded Maket, Compettve ottleneck and Excluve Contact, Economc Theoy, Vol. 32, No. 2, pp ake, J., and T. enahan (1985) The Gan fom Mege o Colluon n Poduct- Dffeentated Indute, Jounal of Indutal Economc, 33(4), pp Calton, Denn (2007). Maket Defnton: Ue and Abue, Competton Polcy Intenatonal, Vol. 3, No 1. DOJ and FTC (1997). U.S. Hozontal Mege Gudelne. Avalable at: Dubo, P., A. Henandez -Peez and M. Ivald (2007). The Maket of Academc Jounal: Empcal Evdence fom Data on Fench Lbae, Jounal of the Euopean Economc Aocaton, Vol. 5, No. 2, Apl-May 2007, pp Emch, E. and T.S. Thompon (2006). Maket Defnton and Maket Powe n Payment Cad Indute, Revew of Netwok Economc, Vol. 5, No. 1, pp Evan, D. (2003a). The Anttut Economc of Two-Sded Maket, Yale Jounal of Regulaton, Vol. 20, No. 2, pp Evan, D. (2003b). Some Empcal Apect of Mult-Sded Platfom Indute, Revew of Netwok Economc, Vol. 2, No. 3, pp Evan, D., A. Hagu and R. Schmalenee (2006). Invble Engne: How Softwae Platfom Dve Innovaton and Tanfom Indute. MIT Pe, Evan, Davd and Rchad Schmalenee (2005a). Payng wth Platc: The Dgtal Revoluton n uyng and oowng, 2d Ed. MIT Pe, Cambdge, MA. 36

37 Davd S. Evan and Mchael D. Noel Evan, D. and R. Schmalenee (2005b). The Economc of Intechange Fee and The Regulaton: An Ovevew. Poceedng Payment Sytem Reeach Confeence, Fedeal Reeve ank of Kana Cty, May 2005, pp Evan D. and R. Schmalenee (2007a). The Indutal Oganzaton of Two-Sded Platfom, Competton Polcy Intenatonal, Vol. 3, No. 1. Evan, D. and R. Schmalenee (2007b). Catalyt Code: The Statege behnd the Wold Mot Dynamc Compane. Havad une School Pe, Faell, J and C. Shapo (1990). Hozontal Mege: An Equlbum Analy, The Amecan Economc Revew, Vol. 80, No. 1, pp Feldman, R. (1994) The Welfae Economc of a Health Plan Mege, Jounal of Regulatoy Economc, 6(1), pp Ha,. (2003). Recent Obevaton about Ctcal Lo Analy. Avalable at: Ha,. and J.J. Smon (1989). Focung Maket Defnton: How Much Subttuton Neceay? Reeach n Law and Economc, Vol. 207, pp Ha,. and C. Velanovk (2003). Ctcal Lo: It Gowng Ue n Competton Law, Euopean Competton Law Revew, Vol. 5, pp Ivald, M. and F. Veboven (2005). Quantfyng the Effect fom Hozontal Mege n Euopean Competton Polcy, Intenatonal Jounal of Indutal Oganzaton, Vol. 23, pp Kae, U. and J. Wght (2006). Pce Stuctue n Two-Sded Maket: Evdence fom the Magazne Induty, Intenatonal Jounal of Indutal Oganzaton, Vol. 24, Iue 1, pp Katz, M. and C. Shapo (2003). Ctcal Lo: Let Tell the Whole Stoy, Anttut Magazne, Vol. 17, No. 2, pp Klen,., Ande V. Lene, Kevn M. Muphy and Lacey L. Plache (2006). "Competton n Two-Sded Maket: The Anttut Economc of Payment Cad Intechange Fee," Anttut Law Jounal, 73(3), pp Nevo, A. (2000). Mege wth Dffeentated Poduct: The Cae of the Ready-to- Eat Ceeal Induty, RAND Jounal of Economc, 31(3), pp O en, D. and A.Wckelgen. (2003). A Ctcal Analy of Ctcal Lo, FTC Wokng Pape

38 Davd S. Evan and Mchael D. Noel Rochet, J-C. and J. Tole (2003). Platfom Competton n Two-Sded Maket, Jounal of the Euopean Economc Aocaton, 1:4, pp Rochet, J-C. and J. Tole (2006). Two-Sded Maket: A Poge Repot, RAND Jounal of Economc, Vol. 37, Iue. 3, pp Ryman, M. (2004). Competton etween Netwok: A Study of the Maket fo Yellow Page, Revew of Economc Stude, 71, pp Ryman, M. (2007). An Empcal Analy of Payment Cad Uage, Jounal of Indutal Economc, 55, pp Scheffman, D. and J. Smon (2003). The State of Ctcal Lo: Let Make Sue We Undetand the Whole Stoy, The Anttut Souce, Vol. 3, No. 2, pp Shapo, Cal (1996). Mege wth Dffeentated Poduct, Anttut, 10, pp Weman, Denn L. (2005). Aeng Maket Powe: The Tade-off etween Maket Concentaton and Mult-Maket Patcpaton, Jounal of Competton Law and Economc, 1 (2), pp Weden, G.J. and L. M. Foeb (1994). "The Effect of Mege n Dffeentated Poduct Indute: Logt Demand and Mege Polcy, Jounal of Law, Economc, & Oganzaton, 194, pp Wllg, R. (1991). Mege Analy, Indutal Oganzaton Theoy, and Mege Gudelne, ookng Pape on Economc Actvty: Mcoeconomc, 281, pp Wght, J. (2004). The Detemnant of Optmal Intechange Fee n Payment Sytem, Jounal of Indutal Economc, Vol. 52, No. 1, Mach, pp A1. APPENDIX. N-PLATFORM AND ASYMMETRIC PLATFORM CASES We extend the eult n the text to the cae of aymmetc platfom and to the cae of moe than two platfom. The Ctcal Lo equaton fo two aymmetc platfom gven by: 38

39 Davd S. Evan and Mchael D. Noel 39 0 ) (, 2 1, = + + = = A X R Q Q M X R (A.1) The N platfom fomula dffe only n the numbe of ummed tem. Th fomulaton allow dffeent pce change at each platfom on each de fo ue n a vaety of queton. Fo Actual Lo, conde agan the oelatc demand ytem gven by p p q q q γ β δ α µ + + = (A.2) fo, = 1,2, and = A,, whee lowe cae q and p epeent log value. Paamete ae potve (though th need not be the cae) and etcted uch to pevent the two-ded effect fom explodng followng pce change. Snce th a demand ytem, ownehp patten do not matte fo etmaton. Alo, f thee ae two platfom that both ell to de A, t not neceay that they both ell to de. The two de can efe to completely dffeent good. It may alo be that one platfom ell to de A and, wheea anothe fm ell only to de A, and a thd fm only ell to de. The educed fom value of q a a functon only of paamete and pce, accountng fo all the feedback n the ytem, : ( ) ( ) q Ω + + Ψ + Γ = / ] [ θ θ δ θ α θ θ δ θ α (A.3) whee ( ) ( ) ( ) p p α δ δ α δ δ α α δ δ α α α δ δ α γ β µ θ + + Γ = Ψ Ω = Ψ = Γ + = 1 1

40 Davd S. Evan and Mchael D. Noel Totally dffeentatng, and eplacng all the Actual Lo fomula: dp wth X and dq wth L, we deve L = ( Γ γ Ψ β ) X / Ω ( Γ β + Ψ γ ) X / Ω [ Γ ( α γ + δ β ) + Ψ ( α β δ γ )] X / Ω [ Γ ( α β δ γ ) + Ψ ( α γ + δ β )] X / Ω (A.4) The analyt then compae Actual Lo and Ctcal Lo a decbed n the text. The analy can futhe be extended to N platfom. The Actual Lo fomula deved fom the followng ytem of 2N equaton: q N = δ q + θ k=1 k k (A.5) fo = 1..N;, = A,;, whee θ = µ + N k = 1 γ k p k Quantty at platfom on de depend on the quantty at each platfom k (ncludng ) on the othe de (the δ k ), and the pce at each platfom (ncludng ) on de (the γ k ). 45 Subttutng each q equaton nto each q equaton, the ytem can be ewtten n matx fom: ϑ = Φ fo each de, whee an NxN matx wth th element λ equal to N k = λ = 1( = ) δ δ (A.6) 1 k k 45 We have eplaced the notaton α fom the two-platfom veon wth δ and the coeffcent on own pce fom β wth γ. 40

41 Davd S. Evan and Mchael D. Noel whee 1( = ) an ndcato functon equal to one when = and zeo othewe. Alo, ϑ a N-vecto wth th element equal to element equal to φ, whee: q, and Φ an N-vecto wth th φ = θ + N k= 1 δ k θ k (A.7) Actual Lo calculated fo each q by total dffeentaton,.e. L = 1 ( ) dφ, fo = A,, eplacng each dp wth X n the dφ tem. To cloe the model, we note that the ft ode condton defnng makup n the two-platfom ymmetc cae ae the ame a thoe n the 2-platfom and N- platfom aymmetc cae, nce each et of equaton platfom pecfc. A befoe, the calculated Actual Lo amount X ae ubttuted nto the Ctcal Lo equaton and the ACR checked. (Altenatvely, one can fx all paamete except one, and ue the ACR = 1 dentty to back out the ctcal value of the emanng paamete.) The compaatve tatc fom the ymmetc and two-platfom cae cay though to the N fm aymmetc cae. A2. APPENDIX. CALIRATION OF ELASTICITIES FOR GOOGLE- DOULECLICK MERGER ANALYSIS We conde the queton of whethe t may be poftable fo Google to ae the pce of DFP pot-mege by 5% o 10%. Due to the pae natue of the avalable data, we ue a calbaton technque to get a ft look at the potental unlateal effect of the mege. Fo the one-ded calculaton, thee ae fou paamete to be calbated, all on the publhe de ( β, PULISHER GOOGLE PULISHER β DOULECLICK, PULISHER γ GOOGLE, PULISHER γ DOULECLICK ) nce all ndect netwok effect ae eoneouly aumed to be zeo. Ft, we ue the theoetcal one-ded Lene Index to fx the own-pce elatcte, gven the obeved makup (two etcton). Th yeld a baed etmate of the tue hot- 41

42 Davd S. Evan and Mchael D. Noel un pce elatcte. We then aume Slutky ymmety, whch equate evenueweghted co-pce elatcte aco platfom (one etcton), whch commonly done. Th eentally equate the co-patal Q / P = Q / P, wtten n level ntead of log. 46 We then ut need to etmate o calbate one of the co-pce elatcte and then we could calculate Ctcal Lo and Actual Lo and compae them. Howeve, we ntead employ the common and ueful technque n calbaton exece to et Ctcal Lo equal to Actual Lo (the fouth etcton) and then back out the value of the co-pce elatcte (connected togethe by Slutky ymmety) that would exactly equate CL and AL. Rathe than epot thee ctcal co pce elatcte dectly, a explaned n the text, we follow the common pactce of epotng ctcal dveon ato and ctcal wtchng level, whch ae deved fom the ctcal co pce elatcte. Fo the two-ded calculaton, whoe fomula ae n Appendx A.1, we mut calbate xteen paamete, ethe dectly o ung etcton guded by economc theoy. Ft, we ue the tue two-ded fomula fo the Lene Index gven by equaton (9). Condtonal on the extenalty paamete (α and δ ), th yeld a lnea elaton between each own-pce elatcty and t coepondng co-pce elatcty (on each de fo each platfom), a total of fou etcton. We agan aume Slutky ymmety to equate the evenue-weghted co-pce elatcte aco platfom on each de (two moe etcton), though eult ae mla fo othe eaonable aumpton. We alo ue a mla type of Slutky ymmety fo the elatve ze of the ndect netwok effect. Gven the abence of dect data on the ze of the netwok effect, th eaonably elate pa of extenalty elatcte and yeld fou moe etcton. Effectvely, we et fo each de Q / Q = Q / Q and Q / Q = Q / Q, wtten n level ntead of log. Ung othe eaonable aumpton doe not affect eult qualtatvely. We dectly et Google ownplatfom co-de extenalty to 0.1 (10%) on each de, and t co-de co- 46 Th mut be exactly tue wth Hckan demand cuve o f thee wee no ncome effect, and an appoxmaton fo the Mahallan (o egula) demand cuve etmated hee. 42

43 Davd S. Evan and Mchael D. Noel platfom extenalty to 0.05 (5%) on each de (fou moe etcton). Slutky ymmety pn down the coepondng extenalty paamete fo DoubleClck. Thee etcton add to 14 and equatng Actual Lo equal to Ctcal Lo count fo a 15 th etcton. We need only pecfy one own-pce elatcty o one co-pce elatcty to complete the calbaton. A we do not have dect data on any of thee elatcte, t moe pudent to eek out the mot ymmetc oluton. Techncally peakng, many combnaton of β (own) and γ (co) ae poble on a gven de and tll atfy t makup condton. Howeve, note that the mpact on makup of a change n β about 1/α tme the mpact of a change n γ. So f α = 0.1, the mpact of β ten tme that of γ. Theefoe, a elatvely low β could ext on one de a long a t coepondng γ extemely hgh to compenate. ut nce AL mut equal CL, th caue an oppote te on the othe de. It tend to foce the othe β to be hgh, and the othe γ to be extemely mall and the latte can ealy come out negatve (wth a mlaly lage magntude a the γ on the ft de) whch not poble. The mot eaonable oluton, abent good data, that whch yeld the mot ymmetc β and γ, condtonal on atfyng all the othe contant. In a fully ymmetc model th enue a puely ymmetc oluton; n an aymmetc model the β and γ tll dffe aco de but only to the extent the extenalty paamete eque th. We mplement the mot ymmetc oluton by mnmzng the um of quae of the γ aco de (altenatvely, the um of quae of the β aco de.) Th the 16 th and fnal etcton. We ae now able to back out the ctcal β and γ (ted togethe by the above contant) that would eult n CL equalng AL. Of coue, n cae whee moe and bette data avalable, one need not ely a heavly on theoetcal etcton and ntead etmate elatcte dectly fom the data telf. Th alway pefeed. 43