scieee AI-readable full text Open interactive document viewer

A Cost-side Analysis on Collusive Sustainability

Lambertini, Luca,Sasaki, Dan

Abstract

EconStor is a publication server for scholarly economic literature, provided as a non-commercial public service by the ZBW.

Full text

Lambertini, Luca; Sasaki, Dan Working Paper A Cost-side Analysis on Collusive Sustainability Quaderni - Working Paper DSE, No. 355 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Lambertini, Luca; Sasaki, Dan (1999) : A Cost-side Analysis on Collusive Sustainability, Quaderni - Working Paper DSE, No. 355, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4954 This Version is available at: https://hdl.handle.net/10419/159196 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ D Frvw0vlgh Dqdo|vlv rq Frooxvlyh Vxvwdlqdelolw| Oxfd Odpehuwlql Gdq Vdvdnl Ghsduwphqw ri Hfrqrplfv Ghsduwphqw ri Hfrqrplfv Xqlyhuvlw | ri Erorjqd Xqlyhuvlw| ri H{hwhu Vwudgd Pdjjlruh 78 H{hwhu/ Ghyrq H[7 7SX L073458 Erorjqd/ Lwdo| Xqlwhg Nlqjgrp odpehuwlCvser1xqler1lw g1vdvdnlCh{hwhu1df1xn Vhswhpehu 4<<< Dfnqrzohgjhphqwv = Zh duh judwhixo wr Jhrujh Qrupdq/ Vrxjdwd Srggdu/ Fkulvwldq Vfkxow} dqg [dylhu Zdxwk| iru lqvljkwixo glvfxvvlrqv/ zlwkrxw zklfk wklv uhvhdufk zrxog qrw kdyh ehhq srvvleoh1 Wkh dxwkruv dvvxph wkh vroh uhvsrqvlelolw| iru dq| uhpdlqlqj ghihfwv1 DFr vw0vlgh Dqdo|vlv rq Frooxvlyh Vxvwdlqdelolw| Devwudfw = Lq dq roljrsro | vxshujdph/ upv* dfwlrqv lq sulfhv dqg txdqwlwlhv duh vxe0 mhfw wr qrq0qhjdwlylw| frqvwudlqwv1 Wkhvh frqvwudlqwv fdq revwuxfw wkh sudfwlfdelolw| ri rswlpdo sxqlvkphqw + ãod Deuhx +4<;9,/ Odpevrq +4<;:,/ dqg Kçfnqhu +4<<9,, lq vxvwdlqlqj wdflw frooxvlrq1 Qrwlqj wkdw wkh survshfw ri vlqjoh0shulrg rswlpdo sxqlvk0 phqw ghshqgv lqglvshqvdeo| xsrq upv* delolw| wr fkdujh sulfhv vwulfwo| ehorz pdu0 jlqdo frvwv +orvv0pdnlqj sulflqj,/ xqghu wkh suhvhqfh ri srvlwlyh sulfh frqvwudlqwv/ pdujlqdo frvwv fdq vhuyh dv d ixgjh wr pdwhuldolvh vlqjoh0shulrg rswlpdo sxqlvk0 phqw1 Lq wklv sdshu zh fkdudfwhulvh wkh hhfwv ri surw0frvw udwlrv +ru pdun0xsv, rq wkh vxvwdlqdelolw| ri wdflw frooxvlrq/ lq oljkw ri rswlpdo sxqlvkphqw1 Nh|zrugv = Pdujlqdo frvwv/ pdun0xs/ srvlwlyh sulfh frqvwudlqw/ srvlwlyh txdqwlw| frq0 vwudlqw/ surgxfw glhuhqwldwlrq/ vxevwlwxwdelolw|1 MHO fodvvlfdwlrq = O46/ G76/ F:51 4 4 Lqwur gxfwlrq J DPH0WKHRUHWLF ROLJRSRO\ OLWHUDWXUH kdv ehhq zlgho| uhfhswlyh ri wkh vlp0 soli|lqj dvvxpswlrq wr vxssuhvv vxsso| frvwv dqg wkhuhe| wr htxdwh upv* surwv zlwk wkhlu uhyhqxhv1 Xqgrxewhgo|/ wklv sudfwlfh kdv ehhq surprwhg e| wkh lqqrfxrxv lqwhqwlrq wr vlpsoli| wkh prgho dv pxfk dv srvvleoh1 Wklv vlpsolfdwlrq/ krzhyhu/ lv dffrpsdqlhg e| d ghdu vdfulfh= zlwk }hur pdujlqdo frvwv/ qhjdwlyh sulfhv dqg sulfhv ehorz pdujlqdo frvwv duh v|qrq|prxv 1 Lq uhdolw|/ rq wkh rwkhu kdqg/ lw lv frqfhlydeoh wkdw qhjdwlyh sulfhv zrxog hqfrxqwhu lpsohphqwdwlrqdo gl!fxowlhv/ zklovw sulfhv ehorz pdujlqdo frvwv zrxog eh iuhh ri dq| vxfk frpsolfdwlrq lqvridu dv wkhlu olwhudo jxuhv duh qrq0qhjdwlyh1 Fohduo|/ wklv glvwlqfwlrq qhyhu pdwhuldolvhv zkhq wkh roljrsro| jdph lv vwdwlf 1 Iru/ erwk qhjdwlyh sulfhv dqg sulfhv ehorz pdujlqdo frvwv duh lqglylgxdoo| luudwlrqdo/ dqg wkxv fdq eh glvplvvhg iurp frqvlghudwlrq1 Hyhq zkhq wkh roljrsro| jdph lv uhshdwhg +dq roljrsro| vxshujdph,/ lqvridu dv upv dsso| wuljjhu vwudwhjlhv zlwk Qdvk uhyhuvlrq ãod Iulhgpdq +4<:4,/ wkhuh lv olwwoh qhhg wr frqvlghu dq| vwudwhjlhv ru dfwlrqv zklfk duh lqglylgxdoo| luudwlrqdo hlwkhu whpsrudulo| ru lqwhuwhpsrudoo|1 Lq idfw/ wkh survshfw ri whpsrudulo| fkdujlqj d sulfh vwulfwo| ehorz pdujlqdo frvwv uhfhlyhg olwwoh wkhruhwlfdo dwwhqwlrq xqwlo Deuhx +4<;9/ 4<;;, dqg Deuhx/ Shdufh dqg Vwdffkhwwl +4<;9, slrqhhuhg wkh frqfhsw ri rswlpdo sxqlvkphqw 1 Lq frqwudvw zlwk lwv vxevwdqwldo lpsdfw rq jdph wkhru|/ hfrqrplf dssolfdwlrqv ri rs0 wlpdo sxqlvkphqw lq pruh vshfldolvhg hogv/ lqfoxglqj lqgxvwuldo rujdqlvdwlrq/ kdyh ehhq vxusulvlqjo| ihz dqg idu ehwzhhq1 Dprqj wkhvh ihz sdwkeuhdnhuv lv Odpevrq +4<;:,1 Xv0 lqj d Ehuwudqg gxrsro| vxshujdph zlwk wzr upv vxsso|lqj shuihfw vxevwlwxwh surgxfwv / Odpevrq frqvwuxfwv dq rswlpdo vlqjoh0shulrg shqdo frgh zklfk lv whpsrudulo| lqglylgxdoo| luudwlrqdo |hw lqwhuwhpsrudoo| suhflvho| lqglylgxdoo| udwlrqdo 1 4 Krzhyhu/ wkh plqlpxp glv0 frxqw idfwru uhtxluhg lq vxvwdlqlqj sulfh frooxvlrq lq Odpevrq +4<;:, lv wkh vdph 4 25 dv wkdw lq Iulhgpdq +4<:4,1 Wklv/ dv zh glvfryhu lq wklv sdshu/ lv gxh wr Odpevrq*v vshflf dvvxpswlrq wkdw wkh wzr upv* surgxfwv duh shuihfw vxevwlwxwhv 1 Olwhudwxuh derxqgv rq wkh hhfwv ri surgxfw glhuhqwldwlrq rq wkh vxvwdlqdelolw| ri 4 Odpevrq fdoov wklv wkh vhfxulw| ohyho/ l1h1 wkh glvfrxqwhg rz ri surwv dw zklfk wkh lqglylgxdo udwlrqdolw| frqvwudlqw suhflvho| elqgv1 Lq klv pruh uhfhqw frqwulexwlrqv +Odpevrq/ 4<<7> 4<<8, lw lv vkrzq wkdw/ li upv* d sulrul v|pphwu| lv zdlyhg/ rswlpdo sxqlvkphqwv pd| qr orqjhu klw wkh vhfxulw| ohyho1 Vshflfdoo|/ li upv glhu lq vl}h/ wkh vhfxulw| ohyho sxqlvkphqw lv rshudwlyh iru wkh odujh upv exw qrw iru wkh vpdoohu rqhv1 5 wdflw frooxvlrq hlwkhu lq sulfhv ru lq txdqwlwlhv +Ghqhfnhuh/ 4<;6> Fkdqj/ 4<<4/ 4<<5> Urwkvfklog/ 4<<5> Urvv/ 4<<5> Iulhgpdq dqg Wklvvh/ 4<<6> Kçfnqhu/ 4<<7/ 4<<8/ 4<<9> Odpehuwlql/ 4<<:> lqwhu dold ,1 H{fhsw iru Kçfnqhu +4<<9,/ krzhyhu/ doo wklv olwhudwxuh xvhv wkh wudglwlrqdo Iulhgpdq +4<:4, irupxodwlrq ri iron wkhruhp1 Lq wklv sdshu/ zh dqdo|vh wkh hhfwv ri pdujlqdo frvwv rq vxvwdlqdelolw| ri wdflw fro0 oxvlrq/ lq oljkw ri rswlpdo sxqlvkphqw xqghu erwk qrq0qhjdwlyh sulfh dqg qrq0qhjdwlyh txdqwlw| frqvwudlqwv1 Vhfwlrq 5 surylghv d edvlf jhqhudo prgho1 Lq vhfwlrqv 6 dqg 7 zh suhvhqw d olqhdu gxrsro| prgho +dv lq Vlqjk dqg Ylyhv/ 4<;7, wr ghyhors lqwxlwlrq e| ghulylqj vxejdph shuihfw htxloleuld h{solflwo|1 Lq olqhdu Frxuqrw gxrsro| vxshujdph suh0 v hqwhg lq vhfwl rq 6 wkh sul fh rr u l v q hyhu d elq g lq j frq f hu q / zk lov w lq olqh du Ehu wu dq g gxrsro| vxshujdph suhvhqwhg lq vhfwlrq 7 wkh sulfh rru fdq elqg li u pv duh vxsso|lqj forvh vxevwlwxwhv 1 V h fwlr q 8 eu lh | loo xv wu d whv zk h q wk h gxdolw| ehwzhhq sulfh frpshwlwlrq dqg txdqwlw| frpshwlwlrq krogv dqg zkhq lw idlov/ lq whupv ri wkh pdjqlwxgh ri pdujlqdo frvwv uhodwlyh wr ghpdqg sulfhv1 Vhfwlrq 9 vxppdulvhv wkh srvvleoh lqflghqfh ri ydulrxv lqgxvwuldo wd{dwlrq dqg vxevlglvdwlrq rq frooxvlyh vxvwdlqdelolw|/ lq oljkw ri wkhlu hhfwv rq sulydwh upv* frvw vwuxfwxuh1 Vhfwlrq : frqfoxghv wkh sdshu1 5 Jhqh udo vhw0xs 514 Wkh prgho Zh frqvlghu wkh iroorzlqj vx shujdph1 Wzr d sulrul lghqwlfdo upv rshudwh lq wkh pdunhw ryhu wkh wlph krul}rq | ' c 2 c  c  / vhoolqj +srvvleo| lpshuihfw , vxevwlwxwh surgxfwv1 Dw hdfk wlph | / up  fkrrvhv lwv dfwlrq k  / zklfk pdwhuldolvhv hlwkhu lq d sulfh R  ru lq d txdqwlw| ^  lq prvw ri wkh h{lvwlqj wkhruhwlfdo prghov/ dowkrxjk rxu jhqhudo vhw0xs grhv qrw suhfoxgh rwkhu dfwlrq vsdfhv lqvridu dv wkh| duh vxevhwv ri zhoo0ghqhg phwulf vsdfhv1 Zh dgrsw wkh iroorzlqj dvvxpswlrqv +fi1 Deuhx/ 4<;9/ s1 4<8,= D4 = Wkh glvfrxqw idfwru B 5 Ef c  lv frqvwdqw ryhu wlph dqg frpprq wr erwk upv1 D5 = Wkh xqlw surgxfwlrq frvw lv frqvwdqw dqg htxdo wr & 1 Wkhuhiruh/ wkh uhvxowlqj shu0shulrg surw ixqfwlrq iru up  lv Z  E k  ck  'E R   &  ^  / zkhuh i c j ' i  c 2 j 1 6 D6 = Hdfk lqyhuvh ghpdqg ixqfwlrq R  E ^  c^   lv vwulfwo| prqrwrqh dqg frqwlqxrxv lq ^  jlyhq dq| ^  1 D7 = R  Ef c f : f dqg/ iru dq| ^  wkhuh h{lvwv d 5 E ^   : f vxfk wkdw R  E 5 E ^   c^  'f 1 D8 = ^  5 df c lE B o / zkhuh lE B  lv vxfk wkdw surgxflqj ^  : lE B  zrxog ylrodwh wkh lqgl0 ylgxdo udwlrqdolw| frqvwudlqw wr wkh frqwlqxdwlrq r i wkh jdph1 Wklv vwdwhv wkdw lw zloo qhyhu eh lq wkh lqwhuhvw ri up  wr surgxfh dq| rxwsxw odujhu wkdq lE B  / iru dq| jlyhq B 5 Ef c  1 D9 = @h} 4@ i Z  E k  ck   m k  5 df c lE B o j k W  d k  o lv d vlqjohwrq1 Ilup  *v surw Z  E k  ck   ghfuhdvhv xqlprgdoo| dv wkh glvwdqfh ehwzhhq k  dqg k W  d k  o lqfuhdvhv1 D: = Wkh rqh0vkrw jdph lq wkh vsdfh i k  ck 2 j kdv d xqltxh htxloleulxp lq sxuh vwudwhjlhv/ E k   ck  2  1 Zh dvvxph khuhlqdiwhu wkdw wkh xqltxh vwdwlf Qdvk htxloleulxp lv v|pphwulf / l1h1/ k   ' k  2 ' k  1 Wkurxjkrxw wklv sdshu/ rxu irfxv lv h{foxvlyho| wr glvfxvv wkh vxvwdlqdelolw| ri d sdwk wkdw frqvlvwv ri vlpsoh uhshwlwlrq ri wkh vdph v|pphwulf dfwlrq suroh E k  c k   / uhihuuhg wr dv frooxvlyh dfwlrqv ru vlpso| frooxvlrq xqohvv frqwh{wxdoo| frqixvlqj1 Rxu suhplvh lv wkdw wklv frooxvlyh suroh hqwdlov surwv wkdw duh vwulfwo| deryh wkh surwv iurp uhshwlwlrq ri wkh vwdwlf Qdvk htxloleulxp E k  ck   1 Lq jhqhudo/ iru dq| suhvfulehg sur oh E k  ck   wkhuh h{lvwv d xqltxh fulwlfdo glvfrxqw idfwru B W d k  o vxfk wkdw wkh suroh lv vxvwdlqdeoh zlwk vxejdph shuihfwlrq li dqg rqo| li wkh dfwxdo glvfrxqw idfwru B lv htxdo wr ru kljkhu wkdq B W d k  o 1 Wkh jhqhudo ghulydwlrq ri wklv fulwlfdo glvfrxqw idfwru kdv ehhq hvwdeolvkhg e| Deuhx +4<;9> 4<;;, dqg Deuhx/ Shdufh dqg Vwdffkhwwl +4<;9,1 Krzhyhu/ wkhlu v|pphwulf rswlpdo sxqlvkphqw vfkhphv fdq eh dhfwhg e| wkh srvlwlylw| frqvwudlqwv lpsrvhg rq upv* dfwlrqv +hlwkhu txdqwlwlhv ru sulfhv,1 Wklv vkdoo eh forvho| lqvshfwhg lq wkh iroorzlqj 515 dqg 5161 515 Vlqjoh 0shulrg v|pphwulf rswlpdo sxqlvkphqw Ilupv lqlwldoo| iroorz d suhvfulehg frooxvlyh sdwk/ ghqhg dv d v|pphwulf rxwfrph |lhoglqj vwulfwo| kljkhu surwv wkdq wkh vwdwlf Qdvk htxloleulxp rxwfrph/ xqwlo dq| ghyldwlrq lv 7 ghwhfwhg1 Li d ghyldwlrq lv ghwhfwhg lq shulrg | / wkhq lq wkh qh{w shulrg | n / upv vzlwfk wr wkh sxqlvkphqw skdvh zkhuh erwk upv dgrsw wkh sxqlvkphqw dfwlrq k do luuhvshfwlyh ri zklfk up lv sxqlvklqj wkh rwkhu1 Li erwk upv iroorz wkh suhvfulehg shqdo frgh dw | n / wkhq wkh| uhyhuw wr wkh lqlwldo frooxvlyh sdwk iurp | n2 rqzdugv1 Rwkhuzlvh/ wkh sxqlvkphqw skdvh frqwlqxhv xqwlo wkh shqdo frgh lv dgrswhg e| erwk upv dw wkh vdph wlph1 Deuhx +4<;9/ Ohppd 4:/ s1 537, suryhv wkdw wklv v|pphwulf shqdo frgh/ zkhq @  vdwlvhv wkh v|vwhp ri htxdwlrqv Z  E k W  d k  o ck    Z  E k  ck  ' B W d k  o  Z  E k  ck    Z  E k do c k do   ( +4, Z  E k W  d k do o c k do   Z  E k do ck do ' B W d k  o  Z  E k  ck    Z  E k do c k do   ( +5, lv rswlpdo lq wkdw lw uhtxluhv d orzhu glvfrxqw idfwru B W d k  o wr vxvwdlq frooxvlrq wkdq dq| rwkhu sxqlvkphqw uxoh1 516 Frqvwudlqhg pxowl0shulrg v|pphwulf rswlpdo sxqlvkphqw Dowkrxjk v|vwhp +4,0+5, frqvlvwv ri wzr htxdwlrqv zlwk wzr xqnqrzqv/ gxh wr h{rjhqrxv frqvwudlqwv lpsrvhg rq dfwlrq vhwv/ d vroxwlrq q k do cB W d k  o r pd| qrw dozd|v h{lvw1 Zkhq qr vroxwlrq h{lvwv/ wklv uh hfwv wkh vlwxdwlrq zkhuh hyhq wkh wrxjkhvw vlqjoh0shu lrg shqdo dfwlrq dgplvvleoh xqghu wkh h{rjhqrxv frqvwudlqwv lv vwloo qrw vhyhuh hqrxjk wr pdnh wkh upv lqglhuhqw ehwzhhq ghyldwlqj iurp wkh shqdo frgh dqg frpso|lqj1 Wr oo wklv jds zh frqvlghu wkh iroorzlqj prglfdwlrq1 Zh dgrsw wkh wrxjkhvw dgplvvleoh lqvwdqwdqhrxv shqdo dfwlrq k  / zkhuh wkh h{rjhqrxv frqvwudlqwv duh douhdg| elqglqj1 Wkhq zh dovr lpsrvh d vpdoo dprxqw ri dgglwlrqdo sxqlvkphqw lq wkh shulrg diwhu 1 Wklvvhuyhvwr lqfuhdvh wkh wrxjkqhvv ri wkh sxqlvkphqw +wkdw lv/ uhgxfh wkh lqfhqwlyhv iru wkh lqlwldo ghyldwlrq, rq rqh kdqg/ dqg wr lqfuhdvh wkh ghyldwlrq lqfhqwlyh iurp wkh sxqlvkphqw rq wkh rwkhu kdqg/ zkhuhe| uhgxflqj wkh diruhphqwlrqhg jds1 Dv zh lqfuhdvh wkh dprxqw ri sxqlvkphqw lq wkh vhfrqg shqdo shulrg/ pruh ri wkh jds lv oohg1 Li wkh jds lv qrw frpsohwho| oohg e| wkh wzr0shulrg sxqlvkphqw/ l1h1/ li erwk wkh uvw dqg wkh vhfrqg shqdo shulrgv fduu| wkh wrxjkhvw shqdo dfwlrq k  dqg upv vwloo kdyh vwulfw lqfhqwlyhv wr frp so| zlwk wkh shqdo frgh lq wkh uvw shqdo shulrg / wkhq zh ordg dgglwlrqdo sxqlvkphqw lq wkh wklug shqdo shulrg1 Wkh surwudfwlrq ri wkh shqdo skdvh frqwlqxhv xqwlo wkh jds lv frpsohwho| oohg1 Wkhuhe| lq jhqhudo/ zkhq rxu shqdo frgh lv  shulrgv orqj/ wkh vhyhuhvw shqdo dfwlrq k  dgplvvleoh xqghu wkh h{rjhqrxv frqvwudlq wv lv lq lfwhg gxulqj wkh uvw    shulrgv/ dqg 8 wkhq wkh qdo  0wk shulrg ri wkh shqdo skdvh slfnv xs wkh uhpdlqghu ri wkh wrwdo suhvfulehg dprxqw ri sxqlvkphqw1 +Vhh Dsshqgl{ iru dx{loldu| h{sodqdwlrqv1, Pruh irupdoo|=  Dw | '  / erwk upv vhw k  ' k  1  Dw | + |  2 ,/ erwk upv vhw k  ' k  li/ dw |   / k  ' k 2 ' k  / l1h1/ li upv kdyh suhylrxvo| dgkhuhg wr wkh frooxvlyh suhvfulswlrq1 Rwkhuzlvh/ upv vzlwfk wr dq  0shulrg sxqlvkphqw skdvh/ gxulqj wkh uvw    shulrgv ri zklfk erwk upv dgrsw wkh shqdo dfwlrq k  / lq wkh qdo  0wk shulrg wkh| dgrsw wkh dx{loldu| shqdo dfwlrq k  d  o 1 Li dq| ghyldwlrq iurp wkh shqdo frgh lv ghwhfwhg gxulqj wkh sxqlvkphqw skdvh/ wkhq wkh zkroh  shulrgv ri wkh sxqlvkphqw skdvh uhvwduw doo ryhu djdlq> rwkhuzlvh li erwk upv kdyh dgkhuhg wr wkh shqdo frgh wkurxjkrxw wkh hqwluh  shulrgv/ wkhq wkh| uhyhuw wr wkh lqlwldo frooxvlyh sdwk wkhqfhiruwk1 Wkh lqfhqwlyh frpsdwlelolw| ri wklv shqdo frgh fdq eh h{suhvvhg e| wkh v|vwhp ri vlpxo0 wdqhrxv lqhtxdolwlhv= Z  E k W  d k  o ck    Z  E k  ck     3  [  ' B   Z  E k  ck    Z  E k  ck    n B   Z  E k  ck    Z  E k  d  o c k  d  o   ( +6, Z  E k W  d k  o ck    Z  E k  ck    B  3   Z  E k  d  o ck  d  o   Z  E k  ck    n  3  [  '  3  n B   Z  E k  ck    Z  E k  ck     '  c  c  n B   Z  E k  ck    Z  E k  d  o c k  d  o   +7, Z  E k W  d k d  o o c k d  o   Z  E k d  o c k d  o    3  [  ' B   Z  E k  ck    Z  E k  ck    n B   Z  E k  ck    Z  E k  d  o c k  d  o   ( +8, ri zklfk +6, uhsuhvhqwv wkh lqfhqwlyh qrw wr ghyldwh iurp wkh frooxvlyh sdwk/ +7, uhsuhvhqwv wkh lqfhqwlyh qrw wr ghyldwh iurp wkh shqdo frgh dw wkh  0wk shulrg ri wkh sxqlvkphqw skdvh +  '  c  c    ,/ dqg qdoo| +8, wkh lqfhqwlyh qrw wr ghyldwh iurp wkh qdo  0wk shulrg ri wkh shqdo frgh1 Iurp wkh h{suhvvlrq lq wkh uljkw0kdqg vlghv ri wkhvh lqhtxdolwlhv lw hphujhv wkdw dprqj wkhvh  n  lqhtxdolwlhv rqo| wkh uvw wzr/ l1h1/ +6,/ dqg +7, zlwk  ' / fdq elqg zklovw wkh rwkhu    lqhtxdolwlhv +  '2 c  c   ri +7, / dv zhoo dv +8,, duh vodfn1 9 Lq dgglwlrq/ wkh lqwhuwhpsrudo lqglylgxdo udwlrqdolw| frqglwlrq  3  [  ' B  Z  E k  ck  n B  Z  E k d  o ck d  o n " [  '  n B  Z  E k  ck    f +9, pxvw dozd|v eh vdwlvhg1 Li frqvwudlqw +9, zhuh ylrodwhg/ upv zrxog qg lw suhihudeoh wr fhdvh doo wkh surgxfwlrq dfwlylwlhv shupdqhqwo|/ ehfdxvh wkh kduvkqhvv ri wkh sxqlvkphqw zrxog rxwzhljk wkh glvfrxqwhg ydoxh ri wkh uhlqvwdophqw ri frooxvlyh surwv1 Wr vxppdulvh/ zkhq h{rjhqrxv frqvwudlqwv elqg /wkh frqvwudlqh g fulwlfdo glvfrxqw idfwru B WW d k  o lv ghwhuplqhg wkurxjk wkh v|vwhp ri wzr htxdwlrqv Z  E k W  d k  o ck    Z  E k  ck  '  3  [  ' E B WW d k  o   Z  E k  ck    Z  E k  ck    n E B WW d k  o    Z  E k  ck    Z  E k  d  o c k  d  o   ( +:, Z  E k W  d k  o ck    Z  E k  ck    E B WW d k  o  3   Z  E k  d  o ck  d  o   Z  E k  ck    n E B WW d k  o    Z  E k  ck    Z  E k  d  o c k  d  o   +;, zlwk wzr xqnqrzqv B WW d k  o dqg k d  o +qrwh wkdw wkh sulqflsdo shqdo dfwlrq k  lv qr orqjhu dq xqnqr zq ehfdxvh lw lv qrz ghwhuplqhg e| wkh frqvwudlqwv qrw e| lqfhqwlyhv,/ vxemhfw wr lqglylgxdo udwlrqdolw| +9,1 Wklv revhuydwlrq lpphgldwho| lpsolhv wkh iroorzlqj1 Wkhruhp = Zkhq wkh vhw ri dgplvvleoh dfwlrqv hqodujhv +uhvs1/ glplqlvkhv,/ wkh uh0 txluhg gxudwlrq ri sxqlvkphqw  vkruwhqv +uhvs1/ ohqjwkhqv, dqg wkh frqvwudlqhg fulwlfdo glvfrxqw idfwru B WW d k  o ghfuhdvhv +uhvs1/ lqfuhdvhv,/ dw ohdvw zhdno|1 517 Frvw hhfwv Kdylqj frqvwudlqhg shqdo dfwlrqv fkdudfwhulvhg lq jhqhudo devwudfw whupv/ qrz zh uhwxuq wr rxu pdlq lqwhqwlrq lq wklv sdshu/ wkdw lv/ wkh hhfwv ri pdujlqdo f rvwv rq wkh vxvwdlqdelolw| ri frooxvlrq1 Wkh edvlf suhplvh zh dffhsw lv wkdw upv duh doorzhg wr fkdujh sulfhv vwulfwo| ehorz pdujlqdo frvwv/ exw qrw olwhudoo| qhjdwlyh sulfhv1 Wklv dxwrpdwlfdoo| lpsolhv wkdw/ zkhq pdujlqdo frvwv duh qhjoljleoh/ qr orvv0pdnlqj dfwlrqv duh dydlodeoh/ zklfk uhvwulfwv wkh vhw ri lpsohphqwdeoh shqdo frghv1 Lq rxu qrwdwlrq iurp 516/ wklv lv h{suhvvhg dv Z  E k  ck  'f > :  iru dq| sdlu & /  / wkhuh lv d xqltxh lqwhjhu  vxfk wkdw wkhuh h{lvwv d vroxwlrq ^  d  o 5 d f c ^   / B WW d R  o 5 E f c  wr wkh v|vwhp +55,0+56, zkhq  '  e xw qrw zkhq   >  iru dq|  / wkh plqlpxp dgplvvleoh glvfrxqw idfwru B WW d R  o uhvxowlqj iurp  '  prqrwrqlfdoo| ghfuhdvhv & 1 Wklv/ lq frqmxqfwlrq zlwk Sursrvlwlrq ll/ lpsolhv wkh iroorzlqj uhvxow zklfk lv frpprq wr erwk vlqjoh0 dqg pxowl0shulrg v|pphwulf sxqlvkphqw1 Sursrvlwlrq lll = Lq d sulfh0vhwwlqj vxshujdph zlwk olqhdu vwdjh0ghpdqg +<,/ wkh vhw ri vxvwdlqdeoh frooxvlyh rxwfrphv i  cBcR  j +dw ohdvw zhdno|, lqfuhdvhv lq wkh pdujlqdo frvw & 1 8 Uhh{dplqdwlrq ri sulfh0txdqwlw| gxdolw| Lq wklv vhfwlrq/ zh lqyhvwljdwh wkh vlplodulwlhv dqg glhuhqfhv ehwzhhq sulfh frpshwlqj dqg txdqwlw| frpshwlqj vxshujdphv1 Lq jhqhudo/ wkhuh h{lvwv gxdolw| ehwzhhq d sulfh vhwwlqj jdph dqg d txdqwlw| vhwwlqj jdph1 Iru lqvwdqfh/ lq olqhdu gxrsro| zlwk ghpdqg vwuxfwxuh +<,/ wkh gxdolw| ehwzhhq sulfh vhwwlqj jdphv dqg txdqwlw| vhwwlqj jdphv fdq eh h{suhvvhg hvvhqwldoo| e| lsslqj wkh vljq ri  1 Wklv gxdolw| kdv ehhq zhoo nqrzq lq wkh olwhudwxuh/ dqg wkhuhiruh frqqrlvvhxuv pd| kdyh ehhq sx}}ohg zk| lq rxu sdshu/ rq wkh frqwudu|/ wkhvh wzr irupv ri frpshwlwlrq hqwdlo vxevwdqwldoo| glvwlqfw jdph0wkhruhwlf fkdudfwhulvwlfv1 Wkh dv|pphwu| ehwzhhq sulfh frpshwlwlrq dqg txdqwlw| frpshwlwlrq lv qrw lqkhuhqw lq Deuhx*v rswlpdo sxqlvkphqw uxoh/ exw vwhpv sxuho| iurp qrq0qhjdwlylw| frqvwudlqwv1 Iru lqvwdqfh/ Ghqhfnhuh +4<;7, vkrzv wkh vlplodulw| ehwzhhq Ehuwudqg jdphv zlwk srvl0 wlyh txdqwlw| frqvwudlqwv exw zlwkrxw srvlwlyh sulfh frqvwudlqwv/ dqg Frxuqrw jdphv zlwk srvlwlyh sulfh frqvwudlqwv exw zlwkrxw srvlwlyh txdqwlw| frqvwudlqwv1 Qrwh wkdw/ vlqfh Gh0 qhfnhuh*v dqdorj| ehwzhhq Frxuqrw dqg Ehuwudqg jdphv lv derxw wkh rqh0vkrw ghyldwlrq iurp wkh frooxvlyh sdwk / doo wkh uhvxowv wkhuh pxvw eh lqghshqghqw ri zkdw shqdo frghv duh hpsor|hg lq rughu wr vxvwdlq wkh frooxvlrq1 Lqvwhdg/ wkh nh| lv= zkhq zh lqwhufkdqjh upv* vwudwhjlf yduldeohv ehwzhhq sulfhv dqg txdqwlwlhv/ zh dovr qhhg wr lqwhufkdqjh olnhzlvh doo wkh uhohydqw frqvwudlqwv vxfk dv qrq0qhjdwlylw|/ lq rughu wr pdlqwdlq wkh gxdolw|1 47 Lq rxu frqwh{w/ lw lv rqo| wkh srvlwlyh sulfh frqvwudlqw ri zklfk wkh lpsolfdwlrq wr fro0 oxvlyh vxvwdlqdelolw| ydulhv zlwk wkh pdujlqdo frvw & / qrw wkh srvlwlyh txdqwlw| frqvwudlqw1 Lqvridu dv wkh pdujlqdo frvw & lv odujh hqrxjk wr sxvk wkh sulfh rru/ R  f / vx!flhqwo| idu ehorz wkh pdujlqdo frvw + &    2 s 2  f  .S lq rxu olqhdu gxrsro | vxshujdph h{dpsoh,/ wkh srvlwlyh sulfh frqvwudlqw qhyhu elqgv1 Dv & ghfuhdvhv/ wkh srvlwlyh sulfh frqvwudlqw vwduwv wr elqg lq d Ehuwudqg vxshujdph zlwk upv surgxflqj forvh vxevwlwxwhv1 Wklv vhuyhv wr uhgxfh wkh vxvwdlqdelolw| ri frooxvlrq1 Lq wkh h{wuhph/ zkhq & ' f / lw lv lqwxlwlyho| fohdu wkdw wkh gxdolw| ehwzhhq Ehuwudqg dqg Frxuqrw jdphv lv uhvwruhg1 Qrwh lq sduwlfxodu wkdw/ dv vxshuprgxodulw| lqfuhdvhv wr wkh olplw/ wkh frqvwudlqhg pxowl0shulrg sxqlvkphqw dv|pswrwlfdoo| frlqflghv zlwk rqh0vkrw Qdvk uhyhuvlrq/ wkhuhe| ehfrphv vhfxulw|0ohyho sxqlvkphqw +vhh Odpevrq/ 4<;:/ 4<<7/ 4<<8, hyhq wkrxjk wkh gxudwlrq ri sxqlvkphqw whqgv wr lqqlw|1 Wklv lv reylrxv lq d Ehuwudqg vxshujdph zlwk upv surgxflqj shuihfw vxevwlwxwhv1 Lq d Frxuqrw vxshujdph zlwk upv vxsso|lqj shuihfw frpsohphqwv / rq wkh rwkhu kdqg/ wkh gxudwlrq ri sxqlvkphqw djdlq jurzv wr lqqlw|1 Lw lv vwudljkwiruzdug wr yhuli| wkdw/ lq rxu olqhdu gxrsro| h{dpsoh/ lq wkh olplw zkhuh  &  / Z  E ^ W  d ^  o c^   Z  E ^  c^   $ 2 c Z  Ef c f ' f vr wkdw wkh fulwlfdo glvfrxqw idfwru lq vxvwdlqlqj prqrsro|0ohyho frooxvlrq frqyhujhv wr 425/ wkh vdph ohyho dv lq wkh Ehuwudqg vxshujdph zlwk shuihfw vxevwlwxwh surgxfwv1 9 Srolf| dqg uhjxodwru| lpsolfdwlrqv Dv zh kdyh vkrzq lq vhfwlrqv 5 dqg 7/ lq Ehuwudqg vxshujdphv zlwk upv vxsso|lqj forvh vxevwlwxwhv/ vxvwdlqdelolw| ri wdflw sulfh frooxvlrq klqjhv xsrq wkh survshfw ri fkdujlqj whpsrudulo| d sulfh ehorz wkh pdujlqdo frvw/ dqg krz idu ehorz lw fdq eh1 Wklv ohdgv wr wkh iroorzlqj vwudljkwiruzdug srolf| lpsolfdwlrqv1  Surgxfwlrq vxevlglhv dqg vdohv vxevlglhv vhuyh wr uhgxfh pdujlqdo surgxfwlrq frvwv shufhlyhg iurp wkh up*v sulydwh surw frqfhuq/ zkhuhe| lqfuhdvh wkh pdun0xs1 Wklv/ lq oljkw ri rxu iruhjrlqj dqdo|vlv/ fdq khos ghvwdelolvh sulfh frooxvlrq li upv* surgxfwv duh forvh vxevwlwxwhv1 E| wkh vdph wrnhq/ vdohv wd{hv gr wkh rssrvlwh/ eulqjlqj dq dgyhuvh hhfw ri surwhfwlqj frooxvlyh vxvwdlqdelolw|1 48  Frusrudwh wd{dwlrq dw d dw p dujlqdo wd{ udwh lv nqrzq wr eh qrq0glvwruwlrqdu|/ exw wklv lv wuxh rqo| lqvridu dv wkh dw udwh h{whqgv wr qhjdwlyh surwv/ l1h1/ rqo| li orvvhv duh sursruwlrqdwho| vxevlglvhg1 Lq uhdolw|/ orvvhv duh prvw w|slfdoo| qrw vxevlglvhg1 Wklv vhuyhv wr pdjqli|/ lq uhodwlyh whupv/ wkh hhfwlyh orvvhv lqfxuuhg e| shqdo sulfhv ehorz pdujlqdo frvwv1 Lw khqfh lqfuhdvhv wkh hhfwlyhqhvv ri sxqlvkphqw dqg wkhuhe| vhuyhv wr surwhfw frooxvlyh vxvwdlqdelolw|1  Vxevlglhv dqg wd{ fuhglwv jlyhq wr lqqrydwlyh lqyhvwphqw / zklfk lv w|sl0 fdoo| dlphg dw uhgxflqj pdujlqdo surgxfwlrq frvwv/ hqfrxudjh frvw uhgxflqj surfhvv lqqrydwlrq 1 Frvw uhgxfwlrq/ dv diruhphqwlrqhg/ fdq eulqj dq d!updwlyh hhfw ri fxuwdlolqj frooxvlyh vxvwdlqdelolw|1  Dqwl0gxpslqj uhjxodwlrq / ohjdoo| surklelwlqj sulfhv ehorz pdujlqdo frvwv/ lv d vwudljkwiruzdug zd| wr fxuwdlo wkh survshfw ri sulfh frooxvlrq hvshfldoo| zkhq wkh hqylurqphqw lv xqvxlwdeoh iru gluhfw lpsohphqwdwlrq ri dqwlwuxvw sulfh uhjxodwlrqv1 Lw ghvhuyhv khljkwhqhg dwwhqwlrq wkdw wklv uhjxodwlrq vhuyhv d!updwlyho| li dqg rqo| li lw lv ohjdoo| hqirufhg1 Li/ rq wkh rwkhu kdqg/ gxpslqj lv vxemhfwhg wr hfrqrplf vdqfwlrqv vxfk dv qhv ru shqdo wd{hv lqvwhdg ri ohjdo survhfxwlrq/ wkhq vxfk glvlqfhqwlyh vfkhphv fdq pdjqli| wkh hhfwlyhqhvv ri sxqlvkphqw dqg wkhuhe| khos vxvwdlq wdflw frooxvlrq1  Suhvhqfh ri vl}hdeoh {hg frvwv shu up shu shulrg dhfwv wkh vhfxulw| ohyho/ l1h1/ wkh lqwhuwhpsrudo lqglylgxdo udwlrqdolw| frqglwlrq1 Qdpho|/ lw pdnhv h{lw uhodwlyho| pruh dwwudfwlyh/ uhqghulqj kduvkhu sxqlvkphqw qr orqjhu lqglylgxdoo| udwlrqdo1 Wklv fdq eulqj dq d!updwlyh hhfw ri uhgxflqj wkh vxvwdlqdelolw| ri frooxvlrq e| qduurzlqj wkh fkrlfh vhw ri dydlodeoh sxqlvkphqw1 Lq wklv vhqvh/ ydulrxv vxevlglhv dqg wd{ frqfhvvlrqv jlyhq wr {hg lqgxvw uldo h{shqvhv kdyh d zhoiduh0uhgxflqj vlgh0 hhfw ri hqfrxudjlqj wdflw sulfh frooxvlrq1 Lw vkrxog dovr eh qrwhg wkdw rqo| {hg frvwv shu shulrg /qrw vxqn frvwv xsrq hqwu| / fdq vhuyh wr ghvwdelolvh wdflw sulfh frooxvlrq1  Frusrudwh wd{dwlrq rq d oxps0vxp edvlv / vxfk dv frpsxovru| uhjlvwudwlrq ru olfhqvlqj/ lv nqrzq wr eh qhxwudo lq d vwdwlf vhwwlqj/ exw qrw qhfhvvdulo| vr lq rxu uhshdwhg0jdph iudphzrun1 Iru/ lw dxjphqwv {hg frvwv shufhlyhg iurp sulydwh upv* srlqw ri ylhz/ zklfk fdq fxuwdlo frooxvlyh survshfwv dv diruhphqwlrqhg1 Qrwh hvsh0 fldoo| wkdw rqo| d oxps0vxp vxevfulswlrq wd{ / l1h1/ d oxps vxp shu up shu shulrg / 49 fdq vhuyh wr ghvwdelolvh sulfh frooxvlrq/ qrw d rqfh0dqg0iru0jrrg vxqn sd|phqw xsrq hqwu|/ wkh odwwhu ehlqj wuxo| qhxwudo hyhq lq rxu g|qdplf roljrsro| jdphv1 : Frqfoxglqj gl vfxvvlrq Wkh lpsdfw ri pdujlqdo frvwv rq frooxvlyh vxvwdlqdelolw| kdv iuhtxhqwo| ehhq ryhuorrnhg lq pdq| ri wkh h{lvwlqj wkhruhwlfdo vwxglhv rq uhshdwhg roljrsro| jdphv1 Xvlqj whfkqlfdoo| vwudljkwiruzdug dssolfdwlrq ri rswlpdo sxqlvkphqw +Deuhx/ 4<;9/ 4<;;> Deuhx/ Shdufh dqg Vwdffkhwwl/ 4<;9> Odpevrq/ 4<;:> Kçfnqhu/ 4<<9, dqg prgli|lqj lw lq oljkw ri srvlwlyh sulfh dqg txdqwlw| frqvwudlqwv/ wklv sdshu kdv fkdudfwhulvhg vrph ri wkh v|vwhpdwlf uhodwlrqv ehwzhhq wkh pdjqlwxgh ri pdujlqdo frvwv dqg wkh vxvwdlqdelolw| ri frooxvlyh rxwfrphv1 Pdujlqdo frvwv dhfw roljrsrolvwv* fdsdelolw| ri vxvwdlqlqj wdflw frooxvlrq lq wzr iurqwv1 Rq rqh kdqg/ wkh suhvhqfh ri vxevwdqwldo pdujlqdo frvwv idflolwdwhv frooxvlrq dw dq| sulfh0 txdqwlw| ohyho e| orzhulqj wkh frqvwudlqhg fulwlfdo glvfrxqw idfwru1 Rq wkh rwkhu kdqg/ zkhq wkh glvfrxqw idfwru lv qrw kljk hqrxjk wr vxvwdlq prqrsro|0ohyho frooxvlrq/ wkh suhvhqfh ri vl}hdeoh pdujlqdo frvwv hqdeohv frooxvlrq wr eh vxvwdlqhg dw d kljkhu +forvhu wr prqrsro|, ohyho1 Dvlgh iurp lwv kljko| sudfwlfdo lpsolfdwlrqv/ rxu uhvxow rhuv dq h{wud dgydqwdjh/ wkdw lv/ lw derxqgv lq srwhqwldo frqqh{lrqv wr ixwxuh uhvhdufk vxemhfwv1 Wkh hhfw ri frvw uh0 gxfwlrq lpphgldwho| jlyhv ulvh wr wkh txhvwlrq ri hqgrjhqlvlqj pdujlqdo frvwv e| phdqv ri vrph suhfrpplwwhg lqyhvwphqw1 Vxfk lqyhvwphqw fdq eh pdgh hlwkhu dv fdsdflw| lqvwdo0 phqw/ whfkqrorjlfdo lqqrydwlrq/ ru wkh fkrlfh ri glhuhqw phwkrgv lq frusrudwh qdqflqj1 Srolf| lpsolfdwlrqv duh dqrwkhu gluhfwlrq wr sureh1 Wkh survshfw ri hqgrjhqlvlqj pdujlqdo frvwv dovr uhodwhv wr wkh lvvxh ri mrlqw yhqwxuhv lq U)G / lqfoxglqj ohjlvodwlyh dwwlwxgh hlwkhu iru ru djdlqvw vxfk mrlqwlqj1 Odvw/ exw qrw ohdvw/ wkh zlgho| vwxglhg vxemhfw ri rujdqlvd0 wlrqdo ghvljq / hvshfldoo| wkrvh txhvwlrqv vxfk dv zk| upv dsshdu wr uhwdlq lqh!flhqw surgxfwlrq whfkqrorjlhv rq sxusrvh/ dqg zk| upv whqg wr rsw iru dqg dgkhuh wr lqh!0 flhqw pdqdjhuldo sudfwlfhv dqg vhhplqjo| xqqhfhvvdulo| exuhdxfudwlf frusrudwh vwuxfwxuhv/ fdq srvvleo| eh glvhqwdqjohg lq oljkw ri frvw0vlgh wkhru| rq wdflw frooxvlrq1 4: Dsshqgl{ D pruh jhqhudo irup ri pxowl0shulrg sxqlvkphqw fdq eh ghvfulehg dv iroorzv1 Ilupv vwd| rq d suhvfulehg frooxvlyh sdwk k  / xqwlo dq| ghyldwlrq lv ghwhfwhg1 Rqfh d ghyldwlrq lv ghwhfwhg lq shulrg | / wkhq lq wkh qh{w shulrg | n  / upv vzlwfk wr d pxowl0shulrg sxqlvkphqw skdvh zkhuh erwk upv dgrsw wkh sxqlvkphqw dfwlrq k  d o luuhvshfwlyh ri zklfk up lv sxqlvklqj wkh rwkhu 1 Lq wkh sxqlvkphqw skdvh/ zkhqhyhu erwk upv iroorz wkh suhvfulehg shqdo frgh k  d 5 o dw | n 5 E 5 ' c  c  / wkhq wkh| sod| k  d 5 no lq wkh qh{w shulrg 5 n  1 Diwhu  shulrgv/ zkhuh  lv wkh vshoo ri wkh shqdo frgh/ upv uhyhuw wr wkh lqlwldo frooxvlyh sdwk iruhyhu/ l1h1/ k  d  no ' k  1 Li dq| ghyldwlrq iurp wkh shqdo frgh lv ghwhfwhg gxulqj wkh sxqlvkphqw skdvh/ wkhq wkh sxqlvkphqw skdvh uhvwduwv dqhz iurp k  d o doo ryhu djdlq1 Wkh lqfhqwlyh frpsdwlelolw| frqglwlrqv lq vxvwdlqlqj wklv  0shulrg shqdo frgh fdq eh ghvfulehg e| wkh iroorzlqj v|vwhp ri  n  lqhtxdolwlhv= Z  E k W  d k  d 5 o o c k  d 5 o   Z  E k  d 5 o c k  d 5 o    [  '  B WW d k  o    Z  E k  d 5 n  o c k  d 5 n  o   Z  E k  d  o c k  d  o   5 '  c  c n +57, zkhuh/ iru qrwdwlrqdo frqyhqlhqfh/ ohw k  d u o ' @  zkhqhyhu u: / wkdw lv/ wkh odvw ri wkhvh  n  lqhtxdolwlhv +zlwk 5 '  n , uhsuhvhqwv upv* lqfhqwlyh qrw wr ghyldwh iurp wkh ruljlqdo frooxvlyh sdwk 1 Lw lv lqwxlwlyho| fohdu/ krzhyhu/ wkdw qrw doo ri wkhvh  n  lqhtxdolwlhv vkrxog elqg +l1h1/ krog zlwk vwulfw htxdolwlhv,1 Iru/ d ghyldwlrq iurp hduolhu vwdjhv ri wkh shqdo skdvh jhqhudoo| jdlqv vwurqjhu lqfhqwlyhv wkdq wkdw iurp odwhu vwdjhv1 Wklv lpsolhv wkdw wkh uvw lqhtxdolw|/ zlwk 5 ' / wrjhwkhu zlwk wkh lqlwldo qrq0ghyldwlrq frqglwlrq iurp wkh frooxvlyh suhvfulswlrq/ zlwk 5 '  n / vkrxog elqg/ zklovw rwkhu    lqhtxdolwlhv/ zlwk 5 '2 c  c  c /qhhgq rw elqg1 Dv zh vhh iurp Deuhx +4<;9/ 4<;;,/ wkh rswlpdolw| ri sxqlvkphqw vwdqgv rq wzr frxqwhuirufhv= rq rqh kdqg wkh lqlwldo ghyldwlrq iurp wkh suhvfulehg frooxvlyh sdwk vkrxog eh glvfrxudjhg e| pdnlqj wkh sxqlvkphqw dv vhyhuh dv srvvleoh/ zklovw rq wkh rwkhu kdqg wkh ghyldwlrq iurp wkh uvw shqdo shulrg vkrxog dovr eh suhyhqwhg/ lq rughu iru zklfk wkh uhp dlqghu ri wkh sxqlvkphq w/ l1h1/ wkh sruwlrq ri sxqlvkphq w lq lfwhg iurp wkh vhfrqg shqdo shulrg rqzdugv/ vkrxog qrw eh wrr kduvk wr frpso|1 Wkh frxqwhuedodqfh ehwzhhq 4; wkhvh wzr irufhv qhfhvvlwdwhv wkdw wkh uvw shqdo shulrg pxvw fduu| dv pxfk sxqlvkphqw dv ihdvleoh1 Zklovw wkh lqfhqwlyh frqglwlrq qrw wr ghyldwh iurp wkh uvw shqdo shulrg elqgv/ wkh frqglwlrqv gr qrw elqg dv iru wkh odwwhu    shqdo shulrgv1 Wklv lpsolhv wkdw wkhuh uh0 pdlq fhuwdlq ghjuhhv ri iuhhgrp rq wkh doorfdwlrq ri s xqlvkphqw dprqj wkhvh    shulrgv zlwkrxw dhfwlqj wkh ryhudoo rswlpdolw| ri wkh shqdo frgh / lqvridu dv wkh wrwdo glvfrxqwhg dprxqw ri sxqlvkphqw uhpdlqv xqfkdqjhg +zklfk dovr lpsolhv wkdw wkh rswlpdo shqdo whqxuh  pd| qrw eh xqltxh,1 Lq wkh suhvhqfh ri vxfk pxowlsolflw| ri rswlpdo shqdo frghv/ lq wklv sdshu zh vhohfw wkh iurqw ordghg sxqlvkphq w/ lq lfwlqj dv p xf k sxqlvkphq w dv lpphgldwho| dv srvvleoh1 Wklv fohduo| ohdgv wr wkh shqdo frgh ghvfulehg lq vxevhfwlrq 516/ zkhuhe| wkh v|vwhp +57, uhgxfhv lqwr +6,0+7,1 Rxu dvvhuwlrq lv vlpso| wkdw wklv lv dq rswlpdo sxqlvkphqw/ qrw qhfhvvdulo| wkh xqltxh rswlpdo sxqlvkphqw1 Uhihuhqfhv Deuhx/ G1M1 +4<;9,/ H{wuhpdo H txloleuld ri Roljrsrolvwlf Vxshujdphv/ Mrxuqdo ri Hfr0 qrplf Wkhru| / 6< / 4<405581 Deuhx/ G1M1 +4<;;,/ Rq wkh Wkhru | ri Lqqlwho| Uhshdwhg Jdphv zlwk Glvfrxqwlqj/ Hfrqrphwulfd / 89 / 6;60<91 Deuhx/ G1M1/ G1 Shdufh dqg H1 Vwdffkhwwl +4<;9,/ Rswlpdo Fduwho Htxloleuld zlwk Lp0 shuihfw Prqlwrulqj/ Mrxuqdo ri Hfrqrplf Wkhru| / 6< / 58409<1 Doeén/ V1 dqg O1 Odpehuwlql +4<<;,/ Frooxvlrq lq Glhuhqwldwhg Gxrsrolhv Uhylvlwhg/ Hfrqrplfv Ohwwhuv / 8< / 63803;1 Fkdqj/ P1K1 +4<<4,/ Wkh Hhfwv ri Surgxfw Glhuhqwldwlrq rq Frooxvlyh Sulflqj/ Lq0 whuqdwlrqd o Mrxuqdo ri Lqgxvwuldo Rujdql}dwlrq / < / 78609<1 Fkdqj/ P1K1 +4<<5,/ Lqwhuwhpsrudo Surgxfw Fkrlfh dqg Lwv Hhfwv rq Frooxvlyh Ilup Ehkdylru/ Lqwhuqdwlrqdo Hfrqrplf Uhylhz / 66 / ::60<61 Ghqhfnhuh/ U1 +4<;6,/ Gxrsro| Vxshujdphv zlwk Surgxfw Glhuhqwldwlrq/ Hfrqrplfv Ohwwhuv / 44 / 6:0751 4< Gl{lw/ D1N1 +4<:<,/ D Prgho ri Gxrsro| Vxjjhvwlqj d Wkhru| ri Hqwu| Eduulhuv/ Ehoo Mrxuqdo ri Hfrqrp lfv / 4 3 / 530651 Iulhgpdq/ M1Z1 +4<:4,/ D Qrqfrrshudwlyh Htxloleulxp iru Vxshujdphv/ Uhylhz ri Hfrqrplf Vw xglhv / 6 ; / 40451 Iulhgpdq/ M1Z1 dqg M10I1 Wklvvh +4<<6,/ Sduwldo Frooxvlrq Irvwhuv Plqlpxp Surgxfw Glhuhqwldwlrq/ UDQG Mrxuqdo ri Hfrqrplfv / 57 / 9640781 Kçfnqhu/ M1 +4<<7,/ Frooxvlyh Sulflqj lq Pdunhwv iru Yhuwlfdoo| Glhuhqwldwhg Surgxfwv/ Lqwhuqdwlrqdo Mrxuqdo ri Lqgxvwuldo Rujdql}dwlrq / 4 5 / 4880::1 Kçfnqhu/ M1 +4<<8,/ Hqgrjhqrxv Surgxfw Ghvljq lq dq Lqqlwho| Uhshdwhg Jdph/ Lq0 whuqdwlrqdo Mrxuqdo r i Lqgxvwuldo Rujdql}dwlrq / 4 6 / 5::0<<1 Kçfnqhu/ M1 +4<<9,/ Rswlpdo V|pphwulf Sxqlvkphqwv lq d Ehuwudqg Glhuhqwldwhg Surg0 xfw Gxrsro|/ Lqw huqdwlrqdo Mrxuqdo ri Lqgxvwuldo Rujdql}dwlrq / 4 7 / 9440631 Odpehuwlql/ O1 +4<<:,/ Sulvrqhuv* Glohppd lq Gxrsro| +Vxshu,Jdphv/ Mrxuqdo ri Hfr0 qr plf Wkhru| / :: / 4;40<41 Odpevrq/ Y1H1 +4<;:,/ Rswlpdo Shqdo Frghv lq Sulfh0Vhwwlqj Vxshujdphv zlwk Fdsdflw| Frqvwudlqwv/ Uhylhz ri Hfrqrplf Vw xglhv / 87 / 6;80<:1 Odpevrq/ Y1H1 +4<<7,/ Vrph Uhvxowv rq Rswlpdo Shqdo Frghv lq Dv|pphwulf Ehuwudqg Vxshujdphv/ Mrxuqdo ri Hfrqrplf Wkhru| / 95 / 77709;1 Odpevrq/ Y1H1 +4<<8,/ Rswlpdo Shqdo Frghv lq Qhduo| V|pphwulf Ehuwudqg Vxshujdphv zlwk Fdsdflw| Frqvwudlqwv/ Mr xuqdo ri Pdwkhpdwlfdo Hfrqrplfv / 57 / 40551 Urvv/ W1Z1 +4<<5,/ Fduwho Vwdelolw| dqg Surgxfw Glhuhqwldwlrq/ Lqwhuqdwlrqdo Mrxuqdo ri Lqgxvwuldo Rujdql }dwlrq / 4 3 / 40461 Urwkvfklog/ U1 +4<<5,/ Rq wkh Vxvwdlqdelolw| ri Frooxvlrq lq Glhuhqwldwhg Gxrsrolhv/ Hfrqrplfv Ohwwhuv / 73 / 660:1 Vlqjk/ Q1 dqg [1 Yl yhv +4<;7,/ Sulfh dqg Txdqwlw| Frpshwlwlrq lq d Glhuhqwldwhg Gxrsro|/ UDQG Mrxuqdo ri Hfrqrplfv / 4 8 / 8790871 53