Gains and losses from trade when countries differ in public knowledge stocks

Working Paper No 45/00

Gains and Losses from Trade when Countries differ in Public Knowledge Stocks

by

Hans Jarle Kind

SNF project no 1035

”Foreign direct investment and development:

Lessons for Southern Africa from the Southeast Asian Experience”

SNF project no 1070

”Internationalization and economic policy”

The projects are financed by the Research Council of Norway Grants nos 131700/730 and 124559/510

SIØS - Centre for International Economics and Shipping

FOUNDATION FOR RESEARCH IN ECONOMICS AND BUSINESS ADMINISTRATION BERGEN, SEPTEMBER 2000

ISSN 0803 - 4028

© Dette eksemplar er fremstilt etter avtale med KOPINOR, Stenergate 1, 0050 Oslo.

SIØS - CENTRE FOR INTERNATIONAL ECONOMICS AND SHIPPING

SIØS – Centre for international economics and shipping – is a joint centre for The Norwegian School of Economics and Business Administration (NHH) and The Foundation for Research in Economics and Business Administration (SNF). The centre is responsible for research and teaching within the fields of international trade and shipping.

International Trade

The centre works with all types of issues related to international trade and shipping, and has particular expertise in the areas of international real economics (trade, factor mobility, economic integration and industrial policy), international macroeconomics and international tax policy. Research at the centre has in general been dominated by projects aiming to provide increased insight into global, structural issues and the effect of regional economic integration. However, the researchers at the centre also participate actively in projects relating to public economics, industrial policy and competition policy.

International Transport

International transport is another central area of research at the centre. Within this field, studies of the competition between different modes of transport in Europe and the possibilities of increasing sea transport with a view to easing the pressure on the land based transport network on the Continent have been central.

Maritime Research

One of the main tasks of the centre is to act as a link between the maritime industry and the research environment at SNF and NHH. A series of projects that are financed by the Norwegian Shipowners Association and aimed directly at shipowning firms and other maritime companies have been conducted at the centre. These projects include studies of Norwegian shipowners' multinational activities, shipbuilding in Northern Europe and the competition in the ferry markets.

Human Resources

The centre’s human resources include researchers at SNF and affiliated professors at NHH as well as leading international economists who are affiliated to the centre through long-term relations. During the last few years the centre has produced five PhDs within international economics and shipping.

Networks

The centre is involved in several major EU projects and collaborates with central research and educational institutions all over Europe. There is particularly close contact with London School of Economics, University of Glasgow, The Graduate Institute of International Studies in Geneva and The Research Institute of Industrial Economics (IUI) in Stockholm. The staff members participate in international research networks, including Centre for Economic Policy Research (CEPR), London and International Association of Maritime Economists (IAME).

Jdlqv dqg Orvvhv iurp Wudgh zkhq Frxqwulhv glhu lq Sxeolf Nqrzohgjh Vwrfnv1

Kdqv Mduoh Nlqg

Kdqv1NlqgCqkk1qr

Devwudfw

Iroorzlqj wkh lqvljkw iurp hqgrjhqrxv jurzwk wkhru|/ zh dvvxph wkdw frxqwulhv zlwk dgydqfhg surgxfwlrq vwuxfwxuhv kdyh kljk ohyhov ri sxeolf nqrzohgjh1 Wkh sxusrvh ri wklv sdshu lv wr dqdo|}h zkhwkhu d ghyhorslqj frxqwu| vkrxog wudgh zlwk frxqwulhv wkdw duh pruh ru ohvv dgydqfhg wkdq lwvhoi1 Zh dujxh wkdw lw lv sduwlfxoduo|

kdupixo wr wudgh zlwk dgydqfhg frxqwulhv li lqwhuqdwlrqdo wudqvdfwlrq frvwv duh kljk dqg fdslwdo lqwhuqdwlrqdoo| lppreloh/ lq zklfk fdvh zhoiduh pd| eh kljkhu lq dxwdun|

wkdq zlwk wudgh1 Iru orz ohyhov ri wudqvdfwlrq frvwv lw pd| eh prvw ehqhfldo wr wudgh zlwk uhodwlyho| dgydqfhg frxqwulhv/ lq sduwlfxodu li fdslwdo lv lqwhuqdwlrqdoo| preloh1

Qrq0whfkqlfdo vxppdu|

Gxulqj wkh odvw wzr ghfdghv zh kdyh zlwqhvvhg dq lqfuhdvlqj uhvhdufk lqwhuhvw lq wkh txhvwlrq ri krz shulskhudo uhjlrqv duh dhfwhg e| wudgh olehudol}dwlrq zlwk fhqwudo uhjlrqv1 Wkh uhvhdufk w|slfdoo| lqglfdwhv wkdw olehudol}dwlrq lv ehqhfldo li lqwhuqdwlrqdo wudgh frvwv duh vx!flhqwo| uhgxfhg/ exw wkdw shulskhudo uhjlrqv rwk0 huzlvh pd| eh kduphg1 Wklv lqvljkw lv ydoxdeoh/ exw wkh prghov lqyduldeo| dvvxph wkdw frxqwulhv kdyh dffhvv wr wkh vdph surgxfwlrq whfkqrorj|1 Wkh| duh wkxv qrw sduwlfxoduo| vxlwdeoh iru dqdo|}lqj krz Ph{lfr lv dhfwhg e| forvhu lqwhjudwlrq zlwk wkh XV/ krz Wxunh| dqg Juhhfh duh dhfwhg e| forvhu lqwhjudwlrq zlwk Jhupdq| dqg Iudqfh/ ru krz wkh Sklolsslqhv lv dhfwhg e| forvhu lqwhjudwlrq zlwk Vrxwk Nruhd dqg Vlqjdsruh1 Lq wklv sdshu zh h{whqg wkh suhydlolqj iudphzrun lq rughu wr doorz wkh frxqwulhv wr kdyh glhuhqw surgxfwlrq whfkqrorjlhv1 Wkh sxusrvh ri wklv h{whqvlrq lv wr vkhg vrph oljkw rq wkh txhvwlrq ri zkhwkhu ghyhorslqj frxqwulhv vkrxog sul0 pdulo| wudgh zlwk rwkhu ghyhorslqj frxqwulhv ru zlwk whfkqrorjlfdoo| pruh dgydqfhg frxqwulhv1

Lq olqh zlwk wkh fodvvlfdo ghyhorsphqw olwhudwxuh zh dvvxph wkdw ghyhorslqj frxq0 wulhv kdyh d frpsdudwlyh dgydqwdjh lq dq djulfxowxuh vhfwru/ zkhuh wkh zdjh ohyho lv kljkhu wkh ohvv oderxu lw hpsor|v1 Dgglwlrqdoo|/ zh iroorz wkh qhz wudgh wkhru|

dqg dvvxph wkdw wkhuh lv lqwhuqdwlrqdo wudgh lq vshfldol}hg surgxfhu vhuylfhv wkdw duh pdqxidfwxuhg xqghu lqfuhdvlqj uhwxuqv wr vfdoh1 Pruh vshflfdoo|/ zh dvvxph wkdw qhz surgxfhu vhuylfhv duh ghyhorshg e| xvlqj oderxu dqg d qdwlrqdo vwrfn ri sxeolf nqrzohgjh dv lqsxwv/ dqg wkdw wkhvh vhuylfhv duh xvhg dv lqsxwv lq wkh pdqxidfwxulqj vhfwru1 D frxqwu| zklfk kdv d uhodwlyho| kljk vwrfn ri sxeolf nqrzohgjh lv dgydqfhg lq wkh vhqvh wkdw lw lv deoh wr ghyhors d uhodwlyho| odujh vhw ri surgxfhu vhuylfhv1 Wklv frxqwu| kdv d frpsdudwlyh dgydqwdjh lq wkh pdqxidfwxulqj vhfwru1

Lq wkh irupdo prgho zh vkrz wkdw grphvwlf idfwru lqfrph lq ghyhorslqj frxq0 wulhv idoov li wkh| wudgh zlwk pruh dgydqfhg frxqwulhv/ dqg wkdw hpsor|phqw lq wkh pdqxidfwxulqj vhfwru ghfuhdvhv1 Wkh odwwhu phdqv wkdw wkh srru frxqwu| ehfrphv pruh ghshqghqw rq lpsruwv ri surgxfhu vhuylfhv1 Wklv lv sduwlfxoduo| kdupixo li lq0 whuqdwlrqdo wudgh frvwv duh kljk dqg fdslwdo lqwhuqdwlrqdoo| lppreloh/ lq zklfk fdvh zhoiduh pd| eh kljkhu lq dxwdun| wkdq zlwk wudgh1 Zh dovr vkrz wkdw wudgh zlwk

dgydqfhg frxqwulhv whqgv wr eh ohvv ehqhfldo wkh ohvv uhvsrqvlyh zdjhv duh zlwk uhvshfw wr fkdqjhv lq djulfxowxudo hpsor|phqw1 Wklv fdq eh h{sodlqhg e| wkh idfw wkdw wkh frvw dgydqwdjh iru wkh hqwuhsuhqhxuv lq wkh ohvv ghyhorshg frxqwu| lv wkhq uhodwlyho| vpdoo1

Dq dgydqwdjh ri wudglqj zlwk uhodwlyho| dgydqfhg frxqwulhv lv wkh idfw wkdw gr0 phvwlf pdqxidfwxuhuv jdlq dffhvv wr d zlghu udqjh ri vshfldol}hg surgxfhu vhuylfhv/

zklfk whqgv wr uhgxfh surgxfwlrq frvwv1 Wklv hhfw lv sduwlfxoduo| vwurqj iru orz ohyhov ri wudgh frvwv1 Ixuwkhupruh/ surylghg wkdw fdslwdo lv lqwhuqdwlrqdoo| preloh/

dq dgydqfhg wudglqj sduwqhu rhuv pruh surwdeoh lqyhvwphqw rssruwxqlwlhv wkdq grhv ohvv dgydqfhg wudglqj sduwqhuv1 Frqvhtxhqwo|/ wudglqj zlwk dq dgydqfhg frxq0 wu| whqgv wr eh ehqhfldo li wudgh frvwv lqlwldoo| duh orz dqg fdslwdo lv lqwhuqdwlrqdoo|

preloh1

4 Lqwurgxfwlrq

Zh kdyh zlwqhvvhg dq lqfuhdvhg lqwhuhvw lq wkh txhvwlrq ri krz shulskhudo uhjlrqv zloo eh dhfwhg e| wudgh olehudol}dwlrq zlwk fhqwudo uhjlrqv/ qrw ohdvw gxh wr wkh Hxurshdq lqwhjudwlrq surfhvv1⁴ Nuxjpdq dqg Yhqdeohv +4<<3,/ lq d yhu| lpsruwdqw sdshu/ kdyh vkrzq wkdw wudgh olehudol}dwlrq pd| kdup shulskhudo uhjlrqv1 Lq sduwlfxodu/ upv surgxflqj xqghu lqfuhdvlqj uhwxuqv wr vfdoh pd| hh wr fhqwudo uhjlrqv zlwk kljk orfdo sxufkdvlqj srzhu zkhq wudgh lv olehudol}hg1 Krzhyhu/ shulskhudo uhjlrqv qhhg qrw eh kduphg1 Wkh uhdvrq lv wkdw wkh| w|slfdoo| kdyh orz idfwru frvwv/ dqg wklv hhfw whqgv wr pdnh wkhp pruh dwwudfwlyh zkhq wudgh lv olehudol}hg1 Lq d vhulhv ri sdshuv Nuxjpdq dqg Yhqdeohv +h1j1/ 4<<3/ 4<<8d/ 4<<8e, kdyh vkrzq wkdw wkh uvw hhfw lv olnho| wr grplqdwh iru kljk ohyhov ri wudqvdfwlrq frvwv/ zkloh wkh odwwhu hhfw lv olnho| wr grplqdwh iru orzhu ohyhov ri wudqvdfwlrq frvwv1 Wklv lqvljkw lv ydoxdeoh/ exw wkh prghov lqyduldeo| dvvxph wkdw wkh frxqwulhv kdyh dffhvv wr wkh vdph surgxfwlrq whfkqrorj|1 Wkh| duh wkxv qrw sduwlfxoduo| vxlwdeoh iru dqdo|}lqj krz Ph{lfr lv dhfwhg e| forvhu lqwhjudwlrq zlwk wkh XV/ krz Wxunh| dqg Juhhfh duh dhfwhg e|

forvhu lqwhjudwlrq zlwk Jhupdq| dqg Iudqfh/ ru krz wkh Sklolsslqhv lv dhfwhg e|

forvhu lqwhjudwlrq zlwk Vrxwk Nruhd dqg Vlqjdsruh1

Wkh sxusrvh ri wkh suhvhqw sdshu lv wr vkhg vrph oljkw rq wkh txhvwlrq ri zkhwkhu ghyhorslqj frxqwulhv vkrxog sulpdulo| wudgh zlwk rwkhu ghyhorslqj frxqwulhv ru zlwk whfkqrorjlfdoo| pruh dgydqfhg frxqwulhv1 Zh dgguhvv wkh txhvwlrq e| frpelqlqj lqvljkw iurp wkh qhz wudgh wkhru| dqg wudglwlrqdo ghyhorsphqw hfrqrplfv1

Dv lv zhoo nqrzq/ wkh vlpsohvw Khfnvfkhu0Rkolq dqg Ulfdugldq iudphzrunv suh0 glfw wkdw wkhuh duh jdlqv iurp lqwhuqdwlrqdo wudgh li/ dqg rqo| li/ wkh sduwlflsdwlqj frxqwulhv duh dv|pphwulf lq vrph uhvshfw1 V|pphwulf frxqwulhv/ rq wkh rwkhu kdqg/

vkrxog kdyh qr lqfhqwlyhv wr wudgh1 Wklv fohduo| vxjjhvwv wkdw ghyhorslqj frxqwulhv zrxog eh ehwwhu r wudglqj zlwk lqgxvwuldol}hg frxqwulhv wkdq zlwk rwkhu ghyhorslqj frxqwulhv1

Wkh suhglfwlrq wkdw zh vkrxog qrw revhuyh wudgh ehwzhhq vlplodu frxqwulhv grhv

4Wkurxjkrxw wklv sdshu zh zloo xvh wkh whupv wudgh olehudol}dwlrq/ hfrqrplf lqwhjudwlrq dqg uhgxfhg lqwhuqdwlrqdo wudqvdfwlrq frvwv lqwhufkdqjhdeo|1

4

qrw frqirup zhoo zlwk hpslulfdo gdwd1 Wkh qhz wudgh wkhru|/ lqlwldwhg e| Qrupdq +4<:9,/ Nuxjpdq +4<:<,/ dqg Gl{lw dqg Qrupdq +4<;3,/ ghsduwv iurp qhrfodvvlfdo wudgh wkhrulhv lq wkdw lw suhvxssrvhv vfdoh hfrqrplhv/ lpshuihfw frpshwlwlrq dqg surgxfw glhuhqwldwlrq1 Lq wklv vhw0xs zh pd| h{shfw lqwudlqgxvwu| wudgh lq frq0 vxphu jrrgv dqg surgxfhu vhuylfhv wr jhqhudwh jdlqv iurp wudgh ehwzhhq v|pphwulf dv zhoo dv ehwzhhq dv|pphwulf frxqwulhv1 Dw ohdvw vlqfh wkh vhplqdo sdshuv ri Hwklhu +4<:</ 4<;5, lw kdv ehhq uhfrjql}hg wkdw lpsruw dqg h{sruw ri glhuhqwldwhg sur0 gxfhu vhuylfhv/ zklfk uhgxfh surgxfwlrq frvwv iru pdqxidfwxuhg jrrgv/ frqvwlwxwh d pdmru uhdvrq iru wudgh wr eh zhoiduh hqkdqflqj1

Wkhuh lv dovr d odujh vwudqg ri olwhudwxuh dujxlqj wkdw wudgh pd| uhgxfh zho0 iduh/ sduwlfxoduo| iru ghyhorslqj frxqwulhv wkdw wudgh zlwk lqgxvwuldol}hg frxqwulhv1 Dffruglqj wr fodvvlfdo ghyhorsphqw hfrqrplvwv olnh Suhelvfk +4<83,/ Vlqjhu +4<83,/

Edudq +4<8:,/ P|ugdo +4<8:,/ dqg Kluvfkpdq +4<8;, wudgh pd| ohdg wr uvw0pryhu dgydqwdjhv iru dgydqfhg frxqwulhv/ dqg klqghu ghyhorsphqw dqg lqgxvwuldol}dwlrq lq srru frxqwulhv1 Wkhuhe| srru frxqwulhv ehfrph vshfldol}hg lq orz0whfk vhfwruv wkdw duh lqwhqvlyh lq qdwxudo uhvrxufhv1 E| wudglqj zlwk rwkhu srru frxqwulhv/ rq wkh rwkhu kdqg/ ghyhorslqj frxqwulhv zloo eh ohvv ghshqghqw rq qdwxudo uhvrxufhv dqg pd| eh deoh wr lpsuryh wkhlu whfkqrorjlfdo fdsdelolwlhv1

Lq olqh zlwk wkh fodvvlfdo ghyhorsphqw olwhudwxuh zh dvvxph wkdw ghyhorslqj frxq0 wulhv kdyh d frpsdudwlyh dgydqwdjh lq dq djulfxowxuh vhfwru zlwk ghfuhdvlqj uh0 wxuqv wr vfdoh1 Dgglwlrqdoo|/ zh iroorz wkh qhz wudgh wkhru| dqg dvvxph wkdw wkhuh lv lqwhuqdwlrqdo wudgh lq vshfldol}hg surgxfhu vhuylfhv wkdw duh pdqxidfwxuhg xqghu lqfuhdvlqj uhwxuqv wr vfdoh1 Pruh vshflfdoo|/ zh dvvxph wkdw eoxhsulqwv iru glhuhq0 wldwhg surgxfhu vhuylfhv duh ghyhorshg e| xvlqj oderxu dqg d qdwlrqdo vwrfn ri sxeolf nqrzohgjh dv lqsxwv/ dqg wkdw wkhvh vhuylfhv duh xvhg dv lqsxwv lq wkh pdqxidfwxulqj vhfwru1 D frxqwu| wkdw kdv d uhodwlyho| kljk vwrfn ri sxeolf nqrzohgjh lv dgydqfhg lq wkh vhqvh wkdw lw lv deoh wr ghyhors d uhodwlyho| odujh vhw ri surgxfhu vhuylfhv1 Wklv frxqwu| kdv d frpsdudwlyh dgydqwdjh lq wkh pdqxidfwxulqj vhfwru1

Rwkhu wklqjv ehlqj htxdo/ pdqxidfwxulqj frvwv duh orzhu wkh odujhu wkh vhw ri surgxfhu vhuylfhv wkdw d frxqwu| kdv dffhvv wr1 Wklv hhfw vxjjhvwv wkdw wkh zhoiduh jdlqv iurp wudgh duh kljkhu wkh pruh dgydqfhg wkh wudglqj sduwqhu1 Krzhyhu/ gr0

phvwlf idfwru lqfrphv zloo ghfuhdvh li wkh wudglqj sduwqhu lv pruh dgydqfhg/ vlqfh d odujhu vkduh ri wkh frxqwu|*v oderxu irufh zloo eh hpsor|hg lq wkh djulfxowxuh vhfwru1 Wkh kljkhu hpsor|phqw lq wkh djulfxowxuh vhfwru pruhryhu phdqv wkdw d vpdoohu vhw ri surgxfhu vhuylfhv zloo eh surgxfhg grphvwlfdoo|1 Wklv odwwhu hhfw lv sduwlfxoduo|

glvdgydqwdjhrxv li wkhuh duh odujh lqwhuqdwlrqdo wudqvdfwlrq frvwv rq surgxfhu vhu0 ylfhv1 Lq wkh irupdo prgho zh vkrz wkdw lw pd| eh prvw ehqhfldo wr wudgh zlwk dgydqfhg frxqwulhv li wudqvdfwlrq frvwv duh orz/ zkloh lw lv prvw ehqhfldo wr wudgh zlwk ohvv dgydqfhg frxqwulhv li wudqvdfwlrq frvwv duh orz1

Wkh frqvxphuv rzq wkh upv wkdw ghyhors eoxhsulqwv iru surgxfhu vhuylfhv/ dqg zh frqvlghu erwk wkh fdvhv zlwk lqwhuqdwlrqdoo| preloh dqg lppreloh fdslwdo1 Wkh idfw wkdw d vpdoohu vhw ri surgxfhu vhuylfhv zloo eh surgxfhg grphvwlfdoo| wkh pruh dgydqfhg wkh wudglqj sduwqhu/ ehfrphv sduwlfxoduo| vhyhuh li fdslwdo lv lqwhuqdwlrq0 doo| lppreloh1 Wkh uhdvrq lv wkdw wkh lqyhvwphqw rssruwxqlwlhv zloo wkhq eh vpdoohu1 Lqghhg/ zh vkrz wkdw wkh zhoiduh ohyho pd| eh orzhu zlwk wkdq zlwkrxw wudgh li wudqvdfwlrq frvwv duh kljk dqg wkh wudglqj sduwqhu lv uhodwlyho| dgydqfhg1 Ixuwkhu0 pruh/ zh vkrz wkdw wudgh zlwk dgydqfhg frxqwulhv whqgv wr eh ohvv ehqhfldo wkh ohvv uhvsrqvlyh zdjhv duh wr fkdqjhv lq djulfxowxuh hpsor|phqw1 Wklv fdq eh h{sodlqhg e| wkh idfw wkdw wkh frvw dgydqwdjh iru hqwuhsuhqhxuv lq wkh ohvv ghyhorshg frxqwu|

wkhq lv uhodwlyho| vpdoo1

Wkh uhvw ri wklv sdshu lv rujdql}hg dv iroorzv1 Wkh irupdo prgho lv suhvhqwhg lq vhfwlrq 5/ dqg lq wkh iroorzlqj vhfwlrqv zh glvfxvv krz wkh zhoiduh ohyho ghshqgv rq wkh wudglqj sduwqhu*v vwrfn ri sxeolf nqrzohgjh/ dqg rq wkh ohyho ri wudqvdfwlrq frvwv1 Vhfwlrq 6 wuhdwv wkh fdvh zkhuh fdslwdo lv iuhho| preloh/ zkloh fdslwdo lv dvvxphg wr eh lqwhuqdwlrqdoo| lppreloh lq vhfwlrq 71 Frqfoxglqj uhpdunv/ dqg vrph vxjjhvwlrqv iru ixuwkhu uhvhdufk/ duh rhuhg lq vhfwlrq 81 Vrph pdwkhpdwlfdo ghulydwlrqv duh uhoh0 jdwhg wr wkh dsshqgl{1

5 Wkh prgho

Wkhuh duh wzr frxqwulhv lq wkh irupdo prgho/ fdoohg frxqwu| +krph, dqg s +iru0 hljq,1 Hdfk frxqwu| frqwdlqv wzr surgxfwlrq vhfwruv/ djulfxowxuh dqg pdqxidfwxulqj1

6

Frxqwu| 'c s lv hqgrzhg zlwku xqlwv ri oderxu/ 8 xqlwv ri odqg/ dqgg xqlwv ri frxqwu| vshflf sxeolf nqrzohgjh1 Zh ghqrwh dv wkh zdjh udwh dqg Z dv wkh odqg uhqw1 Idfwru lqwhqvlwlhv glhu ehwzhhq vhfwruv/ exw qrw dfurvv frxqwulhv1 Iru vlpsolflw| zh vkdoo dvvxph wkdw odqg lv xvhg lq wkh djulfxowxuh vhfwru rqo|/ zkloh sxeolf nqrzohgjh 0 zklfk grhv qrw uhfhlyh dq| uhqwv 0 lv xvhg dv lqsxw lq surgxfwlrq ri eoxhsulqwv iru vshfldol}hg surgxfhu vhuylfhv wr wkh pdqxidfwxulqj vhfwru1 Oderxu lv dvvxphg lppreloh ehwzhhq frxqwulhv/ dqg zh devwudfw iurp srsxodwlrq jurzwk1

514 Ghpdqg vlgh

D uhsuhvhqwdwlyh frqvxphu ghpdqgv jrrgv iurp dq djulfxowxuh +5, dqg d pdqxidf0 wxulqj +6, vhfwru/ dqg fkrrvhv frqvxpswlrq vr dv wr pd{lpl}h wkh krprwkhwlf dqg wlph vhsdudeoh xwlolw| ixqfwlrq

L ' ] _"

f 6E|^#5E|^3# e^34|_|c +4, zkhuh 4 : f lv wkh vxemhfwlyh glvfrxqw udwh +dqg f # 1 Zlwk wklv xwlolw|

ixqfwlrq zh pd| zulwh wkh prphqwdqhrxv frqvxphu sulfh lqgh{ dv

^ 'R^#₆R^3#₅ c +5, zkhuhR6 lv wkh sulfh ri wkh pdqxidfwxulqj jrrg/ dqgR5 wkh sulfh ri wkh djulfxowxuh jrrg1

Hdfk frqvxphu krogv rqh xqlw ri oderxu dqg d vkduh*u ri wkh {hg idfwru odqg/

81 Erwk idfwruv duh vxssolhg lqhodvwlfdoo|/ dqg wkh lqwhuwhpsrudo exgjhw frqvwudlqw lv jlyhq e|

"

]

f

dR6E|6E| nR5E|5E|oe³

U| foE_

'

"

]

f

E| n ZE|8

u

e³

U| foE_

nlEf u

+6, Wkh v|perolEfghqrwhv wkh suhvhqw ydoxh ri djjuhjdwh qdqfldo zhdowk lq frxqwu|

c o wkh lqwhuhvw udwh/ wkh zdjh ohyho/ dqgZ wkh odqg uhqw1

Ohw.E|ghqrwh frqvxphu h{shqglwxuh dqg ghqh_.E|*_|.E|Pd{lpl}dwlrq ri +4, vxemhfw wr +6, |lhogv wkh Hxohu htxdwlrq

.E|*.E| 'oE|4c +7, zklfk ghvfulehv wkh rswlpdo frqvxpswlrq sdwk1

515 Wkh vxsso| vlgh

Wkhuh lv iuhh hqwu| lq erwk wkh djulfxowxuh dqg wkh pdqxidfwxulqj vhfwru1 Wkh djulfxowxuh jrrg lv surgxfhg e| xvlqj oderxu dqg odqg lq d frqvwdqw uhwxuqv wr vfdoh whfkqrorj|/ dqg wkh surgxfwlrq ixqfwlrq lv jlyhq e| ~ 'u^q₅8^3q Wkh fruuh0 vsrqglqj xqlw frvw ixqfwlrq lv htxdo wr &q^qZ^3q c zkhuh &q 'q^3qEq^q31 Wkh djulfxowxuh jrrg pd| eh wudghg frvwohvvo| dfurvv wkh frxqwulhv/ dqg zloo wkxv kdyh d xqltxh zruog sulfh1 E| wdnlqj wkh djulfxowxuh jrrg dv qxphudluh ER₅ 'R₅ ,/ lw iroorzv wkdw lq htxloleulxp

&q^qZ^3q c ~ fc E&q^qZ^3q ~ ' f +8, Lw ixuwkhu iroorzv wkdw

u₅ '

qZ

Eq

_3q

~ +9,

Gxh wr wkh vkdsh ri wkh xwlolw| ixqfwlrq zh dovr nqrz wkdw

R5E~n~s ' E#E.n.s +:, Wkh pdqxidfwxulqj jrrg lv surgxfhg e| xvlqj glhuhqwldwhg surgxfhu vhuylfhv/

zklfk duh lqwhuqdwlrqdoo| wudghdeoh/ dv lqsxwv1 Zh dvvxph wkh vlpsoh FHV surgxf0 wlrq ixqfwlrq

 '

% _? [

&'

%^Ej3*j_&

&_j*Ej3

c +;,

zkhuh ? ' ? n?s lv wkh dydlodeoh qxpehu ri vhuylfhv/ %& wkh txdqwlw| ri vhuylfh qxpehu &cdqg j :  lv wkh hodvwlflw| ri vxevwlwxwlrq ehwzhhq dq| sdlu ri ydulhwlhv1 Surgxfhu vhuylfhv duh wkxv wkh rqo| lqsxwv lq surgxfwlrq ri wkh pdqxidfwxulqj jrrg1⁵

5Zh frxog hdvlo| kdyh dvvxphg wkdw wkh prghuq jrrg lv pdqxidfwxuhg e| xvlqj erwk oderxu dqg surgxfhu vhuylfhv/ exw wklv zrxog qrw dgg dq|wklqj qhz txdolwdwlyho|1

8

Wkh uhvwulfwlrq wkdw wkh hodvwlflw| ri vxevwlwxwlrq lq +;, lv juhdwhu wkdq rqh/

j : c lpsolhv wkdw qr lqsxw lv hvvhqwldo lq surgxfwlrq/ dqg lw lv hdv| wr vkrz wkdw wkh surgxfwlylw| ri wkh lqwhuphgldwh lqsxwv lv vwulfwo| lqfuhdvlqj lq ?1⁶ Dv lq Hwklhu +4<;5,/ Urphu +4<;:,/ dqg Hydqv/ Krndsrkmd/ dqg Urphu +4<<;, zh lqwhusuhw wklv dv wkrxjk wkh surgxfwlrq surfhvv lv pruh vshfldol}hg wkh kljkhu wkh qxpehu ri lqwhuphgldwhv wkdw lv dydlodeoh1 Zh vkdoo wkxv wdnh ?Er dv dq lqgh{ ri wkh joredo whfkqrorjlfdo ohyho dw wlph r

E| fkrlfh ri vfdoh/ lw wdnhv rqh xqlw ri oderxu wr vxsso| rqh xqlw ri surgxfhu vhuylfh1 Doo surgxfhuv lq d jlyhq frxqwu| zloo fkdujh wkh vdph sulfh vlqfh wkh lqsxwv hqwhu v|pphwulfdoo| lq wkh surgxfwlrq ixqfwlrq dqg duh surgxfhg zlwk wkh vdph whfkqrorj|1 Zh zloo iroorz Gl{lw dqg Vwljolw} +4<::, dqg dvvxph wkdw ? lv odujh1 Wkhuhe|/ zh pd| devwudfw iurp vwudwhjlf lqwhudfwlrqv/ dqg fdq xvh wkh lqyhuvh hodv0 wlflw| uxoh wr qg wkdw wkh sJK sulfh htxdov

R ' j

j +<,

Lqwhuqdwlrqdo wudgh lq surgxfhu vhuylfhv lqyroyhv vrph wudqvdfwlrq frvwv1 Wkhvh frvwv vkrxog eh lqwhusuhwhg dv hyhu|wklqj wkdw/ rwkhu wklqjv ehlqj htxdo/ pdnhv lw pruh h{shqvlyh wr ex| vhuylfhv wkdw duh surgxfhg deurdg wkdq grphvwlfdoo|1 Wklv lqfoxghv idfwruv vxfk dv sxuh frppxqlfdwlrq dqg wudqvsruwdwlrq frvwv dqg kdqgolqj ri uhg wdsh1⁷ Zh prgho wkh wudqvdfwlrq frvwv wr eh ri wkh Vdpxhovrq lfhehuj w|sh/

dqg dvvxph wkdw rqo| * ri hdfk xqlw vklsshg dfwxdoo| uhdfkhv lwv ghvwlqdwlrq E  Wklv lpsolhv wkdw wkh f1l1i1 sulfh ri dq lpsruwhg jrrg lv wlphv kljkhu wkdq wkhi1r1e1 sulfh/ vr wkh surgxfwlrq frvwv iru wkh pdqxidfwxulqj jrrg +wkh gxdo

6Wklv lv prvw hdvlo| vhhq li zh dvvxph wkdw{n @ { bn> lq zklfk fdvh +;, vlpsolhv wr Pm @ q⁴ {= Zh wkhq vhh wkdw wkh dyhudjh surgxfwlylw| ri lqsxwv/ ^P_q{^m @q⁴⁴ > lv vwulfwo| lqfuhdvlqj lq q1

7Sduw ri wkhvh frvwv pd| eh srolf| ghwhuplqhg/ wkrxjk zh wuhdw wkhp dv sxuho| h{rjhqrxv lq wklv sdshu1 Wkhgh idfwr lqwhuqdwlrqdo wudqvdfwlrq frvwv iru upv lq Hdvw Dvld/ iru lqvwdqfh/ zhuh suhvxpdeo| vljqlfdqwo| uhgxfhg zkhq flufxpvwdqwldo wudgh surfhgxuhv dqg exuhdxfudwlf lqwhuihu0 hqfh zhuh judgxdoo| derolvkhg iurp wkh odwh 4<93*v +vhh/ h1j1/ Drnl/ Nlp/ dqg Rnxqr0Ixmlzdud/

4<<:,1

ri , lv

'

?R^3j n?ER^3j_3j^

+43,

Wkhuh lv shuihfw frpshwlwlrq lq wkh pdqxidfwxulqj vhfwru/ lpso|lqj wkdw wkh frqvxphu sulfh lv htxdo wr surgxfwlrq frvwv> R₆ ' Frqvxphuv doorfdwh d vkduh

# ri wkhlu lqfrph wr wkh pdqxidfwxulqj jrrg/ dqg zh wkxv kdyh

 ' E#. +44,

Zlwk wkh FHV sulfh lqgh{ lq htxdwlrq +43,/ wkh djjuhjdwh pdunhw vkduhv grphv0 wlfdoo| dqg deurdg iru vxssolhuv ri surgxfhu vhuylfhv duh htxdo wrr '?ER*^3j dqgr '?ER*^3j/ uhvshfwlyho|1 Xvlqj wklv/ lw lv vwudljkwiruzdug wr vkrz wkdw +jurvv, vdohv yroxphv ri hdfk ydulhw| htxdo

% ' r#.

R? / dqg %' r#.

R? c +45,

zkhuh wkh uvw vxevfulsw uhihuv wr surgxfhu frxqwu| dqg wkh vhfrqg vxevfulsw wr frqvxphu frxqwu|1 Zh wkhq kdyh% %n%

Wkh lqvwdqwdqhrxv surw rz dffuxlqj wr d vxssolhu ri surgxfhu vhuylfhv htxdov ER% 'R%*j Zh zloo irfxv rq vwhdg| vwdwh vroxwlrqv/ lq zklfk fdvh o '4c dqg fdq h{suhvv wkh suhvhqw ydoxh ri pdnlqj d surgxfhu vhuylfh dv

' R%

j4 +46,

Eoxhsulqwv iru qhz surgxfhu vhuylfhv duh ghyhorshg e| xvlqj oderxu dqg wkh qdwlrqdo nqrzohgjh vwrfn g dv lqsxwv/ dqg wkh lqqrydwlqj up uhfhlyhv d sdwhqw zlwk lqqlwh olih wkdw krogv lq erwk frxqwulhv1⁸ Zh fkrvh wkh vfdoh vxfk wkdw lw wdnhv

*g xqlwv ri oderxu wr ghyhors d qhz ghvljq1 Wkh frvw ri pdnlqj d eoxhsulqw lv wkxv *gLi wklv frvw lv juhdwhu wkdq wkh suhvhqw ydoxh ri d surgxfhu vhuylfh/ wkhq lw fdqqrw eh surwdeoh wr ghyhors d qhz ydulhw|/ dqg zh pxvw kdyh? ' f Rwkhuzlvh/

8Wkh frpprq nqrzohgjh vwrfn lv wdnhq wr eh d qrq0ulydourxv lqsxw wkdw uhfhlyhv qr uhqw1 Vhh Urphu +4<<3 d/e, dqg Jurvvpdq dqg Khospdq +4<<4, iru ghwdlohg glvfxvvlrqv1

:

iuhh hqwu| hqvxuhv wkdw '*g lq htxloleulxp1 Wkh iuhh hqwu| frqglwlrq wkhuhiruh lpsolhv

*g fc ? fc E *g ? ' f +47,

Wkh oderxu uhtxluhphqw ri pdnlqj d eoxhsulqw lv wkxv lqyhuvho| uhodwhg wr gc uh hfwlqj wkh idfw wkdw lqqrydwruv duh pruh surgxfwlyh wkh kljkhu wkh qdwlrqdo nqrzo0 hgjh vwrfn1 Zh zloo vd| wkdw frxqwu|lv pruh dgydqfhg wkdq frxqwu|s lig : g_s/ dqg ylfh yhuvd1⁹

Frpelqlqj htxdwlrqv +46, dqg +47, zh qg wkdw wkh htxloleulxp txdqwlw| ri hdfk ydulhw| ri surgxfhu vhuylfhv htxdov

% '4Ej*g +48,

Wkh frqvxphuv krog wkh vkduhv lq wkh upv wkdw vxsso| surgxfhu vhuylfhv/ dqg gr qrw srvvhv dq| rwkhu qdqfldo dvvhwv1 Lq wkh iroorzlqj zh zloo glvwlqjxlvk eh0 wzhhq vwdwhv zkhuh qdqfldo fdslwdo lv lqwhuqdwlrqdoo| preloh +, dqg qrw preloh +,1 Ghqrwlqj wkh qdqfldo zhdowk lq wkhvh wzr vwdwhv e| l^rc r'c / lqvwdqwdqhrxv frqvxphu h{shqglwxuh lq wkh vwhdg| vwdwh pd| eh zulwwhq dv wkh vxp ri idfwru lqfrph soxv wkh dqqxlw| ri wkh qdqfldo zhdowk=

. 'Z8 nun4l^r +49, Zhoiduh lq frxqwu| lq wkh vwhdg| vwdwh pd| eh h{suhvvhg dv wkh udwlr ri lqfrph ryhu wkh frqvxphu sulfh lqgh{=

' .

R^#₆R^3#5 +4:,

9Zlwk wklv vshflfdwlrq zh kdyh lpsolflwo| dvvxphg wkdw nqrzohgjh grhv qrw rz iurp rqh frxqwu| wr dqrwkhu1 Wkh txdolwdwlyh uhvxowv ri wklv sdshu zrxog qrw fkdqjh li zh kdg doorzhg lpshuihfw lqwhuqdwlrqdo nqrzohgjh vslooryhuv1 Zkdw lv hvvhqwldo lv wkdw nqrzohgjh rzv pruh hdvlo|

zlwklq wkdq ehwzhhq frxqwulhv1 Wklv lv lq dffrugdqfh zlwk hpslulfdo vwxglhv/ vhh/ h1j1/ Eudqvwhwwhu +4<<9,/ dqg Hdwrq dqg Nruwxp +4<<9,

Lw wdnhv?% zrunhuv wr vdwlvi| ghpdqg iru surgxfhu vhuylfhv/ zkloh?*g zrun0 huv duh qhhghg wr ghyhors eoxhsulqwv1 Oderxu pdunhw htxloleulxp wkxv uhtxluhv +zlwk

? f

u '?% n ?

g nu₅c +4;,

zkhuh djulfxowxuh hpsor|phqw u5 lv jlyhq iurp htxdwlrq +9,1 Lq wkh vwhdg| vwdwh zh kdyh ? ' f

Wkurxjkrxw wklv sdshu wkh frxqwulhv duh dvvxphg wr srvvleo| eh dv|pphwulf lq rqo| rqh uhvshfw/ qdpho| lq wkhlu ohyho ri sxeolf nqrzohgjh +g 9'gs1 Lq sduwlfxodu/

zh zloo dvvxph wkdw hqgrzphqwv ri oderxu dqg odqg duh wkh vdph1

Iru dq dxwdun|/ dqg lq d wudgh htxloleulxp zlwk frpsohwho| v|pphwulf frxqwulhv/

wkh zhoiduh ohyho lv vwulfwo| lqfuhdvlqj lq wkh vwrfn ri sxeolf nqrzohgjh1^: Pruhryhu/

uhgxflqj wkh ohyho ri wudqvdfwlrqv frvwv ehwzhhq v|pphwulf frxqwulhv xqdpeljxrxvo|

lqfuhdvhv zhoiduh1^; Krzhyhu/ lq wkh vxevhtxhqw vhfwlrqv zh zloo vkrz wkdw lw lv dpeljxrxv zkhwkhu lw lv suhihudeoh wr kdyh d wudglqj sduwqhu zlwk d uhodwlyho| kljk ru d uhodwlyho| orz nqrzohgjh vwrfn1 Zh zloo dovr vkrz wkdw zhoiduh pd| idoo li wudqvdfwlrq frvwv duh uhgxfhg ehwzhhq dv|pphwulf frxqwulhv1 Lq sduwlfxodu/ zlwk lqwhuqdwlrqdoo| lppreloh fdslwdo/ d frxqwu| pd| eh ehwwhu r dv dq dxwdun| wkdq li lw wudghv zlwk d pruh dgydqfhg frxqwu|1

6 Iuhh fdslwdo prelolw|

Lq wklv vhfwlrq zh zloo dvvxph wkdw qdqfldo fdslwdo lv shuihfwo| preloh lqwhuqd0 wlrqdoo|/ vr wkdw frqvxphuv duh iuhh wr lqyhvw lq zkdwhyhu frxqwu| wkh| olnh1 Zlwk Free0Grxjodv xwlolw| ixqfwlrqv frqvxphuv vdyh d {hg vkduh ri wkhlu lqfrph/ dqg wkh djjuhjdwh vwhdg| vwdwh qdqfldo zhdowk lq frxqwu| htxdov

l^ ' .

.n.s d?n?sso +4<, Frqvxphuv lq frxqwu| rzq d vkduh .*E. n .s ri wkh upv lq frxqwu|

sc dqg iru wklv wkh| uhfhlyh d glylghqg htxdo wr 4?_ss.*E. n._s hdfk shulrg1

:Vhh Dsshqgl{ D41

;Vhh Dsshqgl{ D51

<

Frqvxphuv lq frxqwu| s olnhzlvh uhfhlyh 4?.s*E.n.s iurp frxqwu| Qhw lpsruw ri surgxfhu vhuylfhv dqg ri wkh djulfxowxudo jrrg lq frxqwu|htxdo?sRs%s

?R%_s BfdqgE#.R₅5 Bfc uhvshfwlyho|1 Edodqfhg wudgh wkxv uhtxluhv 4d?ss. 4?.so

.n._s ?_sR_s%_sn?R%_s dE#.R₅5o ' f +53, Zh zloo irfxv rq glyhuvlhg htxloleuld/ zkhuh erwk frxqwulhv surgxfh erwk wkh djulfxowxudo jrrg dqg surgxfhu vhuylfhv +wkh odwwhu lpso|lqj wkdw '*g,1 Wkh vwhdg| vwdwh htxloleulxp ydoxhv duh wkhq irxqg e| vlpxowdqhrxvo| vroylqj htxdwlrqv +8,0+45,/ +49,/ dqg +4;,0+53,1 Gxh wr wkh idfw wkdw wkh v|vwhp lv kljko| qrq0olqhdu/

zh zloo edvlfdoo| uho| rq qxphulfdo vlpxodwlrqv1^<

614 Zhoiduh hhfwv ri wudgh ehwzhhq dv|pphwulf frxqwulhv

Wkh vl}h ri wkh iruhljq sxeolf nqrzohgjh vwrfn dhfwv wkh krph frxqwu| lq irxu glhuhqw zd|v1 Wzr ri wkhvh duh srvlwlyh li wkh krph frxqwu| wudghv zlwk d pruh dgydqfhg frxqwu| zkloh wkh rwkhu wzr duh qhjdwlyh/ dqg ylfh yhuvd1

Srvlwlyh hhfwv ri wudglqj zlwk d pruh dgydqfhg frxqwu|

E Wkh odujhu wkh vwrfn ri sxeolf nqrzohgjh lq wkh iruhljq frxqwu|/ wkh orzhu wkh iruhljq lqqrydwlrq frvwv1 D kljk ydoxh ri gs wkxv lpsolhv wkdw ?s lv odujh1 Wklv vljqlhv d kljk joredo whfkqrorjlfdo ohyho/ dqg whqgv wr uhgxfh wkh frvw ri surgxflqj wkh pdqxidfwxulqj jrrg1 Wr vhh wklv irupdoo|/ zh pd| glhuhqwldwh iurp htxdwlrq +43, z1u1w1 ?s wr qg=

Y

?cRcRs

'*EjrsY?_s

?s f +54,

Wklv vshfldol}dwlrq hhfw jrhv edfn wr \rxqj +4<5;,> surgxfwlrq frvwv duh ghfuhdvlqj lq wkh qxpehu ri glhuhqwldwhg surgxfhu vhuylfhv/ ehfdxvh lw doorzv iru pruh lqgluhfw xvh ri oderxu1 Wkh frvw uhgxfwlrq lv lqyhuvho| uhodwhg wr wkh vl}h ri jc dqg uh hfwv wkdw wkh lqsxwv duh ohvv glhuhqwldwhg wkh odujhu wkh hodvwlflw| ri vxevwlwxwlrq +wkh

<Lw lv d vwdqgdug surfhgxuh wr xvh qxphulfdo vlpxodwlrqv lq wklv nlqg ri jhqhudo htxloleulxp prghov> vhh Ixmlwd/ Nuxjpdq dqg Yhqdeohv +4<<<,1

lqsxwv ehfrph krprjhqrxv lq wkh olplw j $ 4⁴³ Qrwh wkdw/ vlqfh wkh iruhljq upv* pdunhw vkduh lq wkh krph frxqwu| +rs lv lqyhuvho| uhodwhg wr c wkh ehqhw ri d kljkhu ydoxh ri?_s lv ghfuhdvlqj lq wkh ohyho ri wudqvdfwlrq frvwv1⁴⁴

E Wkh idfw wkdw lqqrydwlrq frvwv lq wkh iruhljq frxqwu| duh ghfuhdvlqj lq lwv vwrfn ri sxeolf nqrzohgjh/ dovr lqglfdwhv d srvlwlyh qdqfldo lqfrph hhfw ri wudglqj zlwk dq dgydqfhg frxqwu|1 Wkh uhdvrq lv wkdw/ zlwk iuhh lqwhuqdwlrqdo fdslwdo pr0 elolw|/ d uhodwlyho| kljk ydoxh rigs phdqv wkdw frqvxphuv lq wkh krph frxqwu| jdlq dffhvv wr pruh surwdeoh lqyhvwphqwv1 Rwkhu wklqjv ehlqj htxdo/ wkh vwhdg| vwdwh lqfrph ohyho lv wkhuhiruh dq lqfuhdvlqj ixqfwlrq rig_s +f1i1 htxdwlrqv +49, dqg +4<,,1

Qhjdwlyh hhfwv ri wudglqj zlwk d pruh dgydqfhg frxqwu|

E D qhjdwlyh hhfw ri wudglqj zlwk dq dgydqfhg frxqwu| lv wkh idfw wkdw wkh ohvv dgydqfhg frxqwu| zloo eh uhodwlyho| vshfldol}hg lq djulfxowxuh surgxfwlrq1 Wkxv/

wkh kljkhu wkh ydoxh ri gsc wkh odujhu wkh djulfxowxuh hpsor|phqw lq frxqwu|

Vlqfh wkhuh lv ghfuhdvlqj uhwxuqv wr oderxu lq wkh djulfxowxuh vhfwru/ idfwru lqfrph lq lv ghfuhdvlqj lq g_s⁴⁵ Wklv hhfw kdv ehhq pxfk ghedwhg lq wkh ghyhorsphqw olwhudwxuh1

EIlqdoo|/ lw vkrxog eh qrwhg wkdw kljkhu djulfxowxuh hpsor|phqw lv pluuruhg lq orzhu hpsor|phqw lq wkh pdqxidfwxulqj vhfwru1 Wkhuhe| d kljk ydoxh ri gs phdqv wkdw d vpdoohu qxpehu ri wkh lqsxwv lv surgxfhg grphvwlfdoo|/ dqg wklv lqwhuqdwlrqdo uhorfdwlrq whqgv wr lqfuhdvh surgxfwlrq frvwv iru pdqxidfwxuhg jrrgv lq ⁴⁶

43Vhh dovr Hwklhu +4<;5, iru dq hduo| irupdo glvfxvvlrq ri zhoiduh jdlqv ri lqwhuqdwlrqdo wudgh lq surgxfhu vhuylfhv/ dqg Hydqv/ Krndsrkmd dqg Urphu +4<<;, iru dq dssolfdwlrq wr hqgrjhqrxv jurzwk wkhru|1 Pdwvx|dpd +4<<8, rhuv dq h{fhoohqw vxuyh|1

44Dvvxph@ 4=3=Lisk dqgqk zhuh htxdo wrsi dqgqi>uhvshfwlyho|/ wkh sduwldo hhfw ri d rqh shu fhqw lqfuhdvh lqqi zrxog eh wr uhgxfh surgxfwlrq frvwv iru wkh pdqxidfwxulqj jrrg lqke|

5+4,4 shu fhqw1 Wkh frvw uhgxfwlrq dssurdfkhv }hur dv$ 4=

45Vhh Dsshqgl{ D61

46Htxdwlrq +45, vkrzhg wkdw{m @+4,@Nm>dqg wkxv lqghshqghqw ri wkh iruhljq nqrzohgjh vwrfn1 Vlqfh djulfxowxuh hpsor|phqw lqklv lqfuhdvlqj lqNi/ wkh qxpehu ri ydulhwlhv surgxfhg lq klv ghfuhdvlqj lqNi=

44

Wkh uhodwlrqvkls ehwzhhq wkh iruhljq nqrzohgjh vwrfn dqg grphvwlf zhoiduh Wkh uhorfdwlrq hhfw lv zhdn zkhq wudgh lv lqh{shqvlyh/ dqg dw ' fjhrjudsk0 lfdo orfdwlrq grhv qrw pdwwhu shu vh1 Wkxv/ hyhq wkrxjk grphvwlf idfwru lqfrphv idoo li wkh wudglqj sduwqhu lv uhodwlyho| dgydqfhg/ zhoiduh whqgv wr eh dq lqfuhdvlqj ixqfwlrq ri gs li wudqvdfwlrq frvwv duh orz1 Li wudqvdfwlrq frvwv duh kljk/ krzhyhu/

wkh uhodwlrqvkls ehwzhhq grphvwlf zhoiduh dqggs lv pruh dpeljxrxv1 Wklv lv looxv0 wudwhg lq Iljxuh 4/ zklfk phdvxuhv zhoiduh rq wkh yhuwlfdo d{lv dqg gs rq wkh krul}rqwdo d{lv1 Khuh zh kdyh dvvxphg wkdw ' 2fc zklfk phdqv wkdw wudqvdfwlrq frvwv frqvwlwxwh iw| shu fhqw ri wkh lpsruw sulfh1⁴⁷ Lq wklv fdvh zh kdyh d X0vkdshg uhodwlrqvkls ehwzhhq zhoiduh lq wkh krph frxqwu| dqg wkh iruhljq nqrzohgjh vwrfn1 Wr vhh zk| wkh fxuyh lv X0vkdshg/ vxssrvh uvw wkdw wkh wudglqj sduwqhu lv ohvv dgydqfhg wkdq wkh krph frxqwu| Eg_s g1 Wkhq oderxu zloo eh vkliwhg iurp wkh djulfxowxuh vhfwru wr wkh pdqxidfwxulqj vhfwru lq wkh krph frxqwu|/ dqg lqfuhdvh grphvwlf idfwru lqfrph1 Dgglwlrqdoo|/ wkh uhorfdwlrq hhfw zloo dovr eh srvlwlyh/ vlqfh wkh krph frxqwu| ehfrphv uhodwlyho| vshfldol}hg lq wkh pdqxidfwxulqj vhfwru dqg vdyhv wudgh frvwv rq lpsruw ri surgxfhu vhuylfhv1 Li wkh wudglqj sduwqhu lv uhodwlyho|

dgydqfhg Egs : g/ rq wkh rwkhu kdqg/ wkh frqvxphuv ehqhw iurp pruh ehwwhu lqyhvwphqw rssruwxqlwlhv dqg d kljkhu joredo whfkqrorjlfdo ohyho1

Qrwh wkdw wkhuh zloo eh qr fkdqjh lq up orfdwlrq/ qr fkdqjh lq djulfxowxuh hpsor|phqw/ dqg qr fkdqjh lq lqyhvwphqw rssruwxqlwlhv lig 'gsWkh rqo| hhfw ri wudgh ehwzhhq v|pphwulf frxqwulhv lv wr hqodujh wkh dydlodeoh vhw ri glhuhqwldwhg surgxfhu vhuylfhv1 Zh wkhuhe| hqg xs zlwk wkh uhvxow wkdw wkh jdlqv iurp wudgh duh odujhvw zkhq wkh frxqwulhv duh glhuhqwEgs 9'gdw wklv ohyho ri wudqvdfwlrq frvwv1

47Lq doo wkh vlpxodwlrqvOk@Oi @ 4> Ik @Ii @ 4> Nk @ 4> @ 6> @ 3=34dqg @ 3=8= Lq wkh jxuhv lq wklv vhfwlrq zh kdyh fkrvhq@ 3=:=Wkh txdolwdwlyh uhodwlrqvkls ehwzhhqxkdqgNi

grhv qrw ghshqg rq0 wkh vkduh ri oderxu lq wkh djulfxowxuh jrrg 0 zkhq fdslwdo lv lqwhuqdwlrqdoo|

preloh1 Zlwk lppreloh fdslwdo/ rq wkh rwkhu kdqg/ wkh vl}h risrvvleo| sod|v d ghflvlyh uroh1 Wklv zloo eh vkrzq lq wkh qh{w vhfwlrq1

2.58 2.62 2.66 2.70

1/4 1/3 1/2 1 2 3 4

X_K

._I

Iljxuh 4= c q ' f.c ' 2fc g ' 

Wkh uhodwlrqvkls ehwzhhq wkh iruhljq nqrzohgjh vwrfn/ wudqvdfwlrq frvwv dqg gr0 phvwlf zhoiduh

Iljxuh 4 looxvwudwhg krz wkh grphvwlf zhoiduh ohyho ghshqgv rq gs/ kroglqj doo rwkhu yduldeohv frqvwdqw1 Lq Iljxuh 5/ zklfk phdvxuhv rq wkh krul}rqwdo d{lv dqg rq wkh yhuwlfdo d{lv/ zh h{whqg wkh dqdo|vlv e| vkrzlqj krz wkh zhoiduh ghshqgv rq erwk wkh ohyho ri wudqvdfwlrq frvwv dqg rq wkh vwrfn ri iruhljq sxeolf nqrzohgjh +l1h1/

iru gs ' ec gs ' c gs ' *e1 Lq wklv jxuh zh fdq lghqwli| wkuhh txdolwdwlyho|

glhuhqw duhdv=

Sursrvlwlrq 4= Vxssrvh wkdw lqwhuqdwlrqdo wudqvdfwlrq frvwv duh

+l, orz E Wkh jdlqv iurp wudgh duh odujhu wkh pruh dgydqfhg wkh wudglqj sduwqhu>Eg_s ' e: Eg_s ' : Eg_s ' *e

+ll, prghudwh E 2 Wkh jdlqv iurp wudgh duh vpdoohvw ehwzhhq v|p0 phwulf frxqwulhv/ dqg odujhvw li wkh krph frxqwu| lv ohvv dgydqfhg wkdq wkh wudglqj sduwqhu>Eg_s ' e: Eg_s ' *e: Eg_s ' 

+lll, kljk + : 2Wkh jdlqv iurp wudgh duh vpdoohvw ehwzhhq v|pphwulf frxq0 wulhv/ dqg odujhvw li wkh krph frxqwu| lv pruh dgydqfhg wkdq wkh wudglqj sduwqhu>

Eg_s ' *e: Eg_s ' e: Eg_s '  46

Wkh lqwxlwlrq ehklqg Sursrvlwlrq 4 +dqg Iljxuh 5, lv yhu| pxfk wkh vdph dv wkdw iru Iljxuh 4/ dqg lv prvw hdvlo| xqghuvwrrg li zh frqvlghu wkh h{wuhphv ri orz dqg kljk wudqvdfwlrq frvwv/ uhvshfwlyho|1 Dv glvfxvvhg deryh/ wkh jhrjudsklfdo orfdwlrq ri upv lv uhodwlyho| xqlpsruwdqw iru orz ohyhov ri / dqg lw lv dgydqwdjhrxv wr wudgh zlwk d uhodwlyho| dgydqfhg frxqwu|1 Wklv doorzv grphvwlf upv wr xvh d pruh vrsklvwlfdwhg surgxfwlrq whfkqrorj| +d odujhu vhw ri vshfldol}hg lqsxwv, dqg jlyhv wkh frqvxphuv dffhvv wr pruh surwdeoh lqyhvwphqw rssruwxqlwlhv1 Li lv kljk/

rq wkh rwkhu kdqg/ lw lv h{shqvlyh wr lpsruw lqsxwv iurp wkh rwkhu frxqwu| dqg wkh srvlwlyh vshfldol}dwlrq hhfw ri wudglqj zlwk dq dgydqfhg frxqwu| lv zhdn +f1i1 htxdwlrq +54,/ zkhuhrs zloo eh vpdoo,1 Wkxv wkh uhorfdwlrq hhfw grplqdwhv/ dqg lw lv prvw ehqhfldo wr wudgh zlwk d ohvv dgydqfhg frxqwu|1 Wkh odwwhu dovr uh hfwv wkh lpsruwdqfh ri kdylqj d odujh grphvwlf pdqxidfwxulqj edvh zkhq wudgh lv h{shqvlyh1 Lq dq| fdvh/ lw fdq eh vkrzq wkdw

Ohppd 4= Vxssrvh wkdw fdslwdo lv lqwhuqdwlrqdoo| preloh1 Lq wkdw fdvh zhoiduh lv kljkhu zlwk wkdq zlwkrxw wudgh iru doo ohyhov ri wudqvdfwlrq frvwv1 Wkh zhoiduh ohyho zlwk wudgh lv lqyhuvho| uhodwhg wr c dqg dssurdfkhv wkh dxwdun| zhoiduh ohyho dv $ 4

2.4 2.6 2.8 3.0 3.2

1.0 1.5 2.0 2.5 3.0 3.5

τ X_K

._I

._I

._I τ τ ^DXW

Iljxuh 51 c q ' f.c g ' 

7 Qr fdslwdo prelolw|

Zlwk qr fdslwdo prelolw|/ wkh upv vxsso|lqj surgxfhu vhuylfhv duh rzqhg e| grphv0 wlf vkduhkroghuv1 Lq wkh vwhdg| vwdwh wkh frqvxphuv zloo wkxv kdyh qdqfldo zhdowk htxdo wr

l^ '? +55,

Zlwk lppreloh fdslwdo wkh htxdwlrq iru edodqfhg wudgh iurp wkh iruphu vhfwlrq +htxdwlrq +53,, pxvw eh fkdqjhg wr

?R%_s ?_sR_s%_sdE#.R₅5o ' f +56, Wkh vwhdg| vwdwh htxloleulxp ydoxhv duh wkhq irxqg e| vlpxowdqhrxvo| vroylqj htxdwlrqv +8,0+45,/ +49,/ +4;,/ +55,1

714 Zhoiduh hhfwv ri wudgh ehwzhhq dv|pphwulf frxqwulhv

Wkh uhodwlrqvkls ehwzhhq zhoiduh lq wkh krph frxqwu| dqg wkh vl}h ri wkh iruhljq nqrzohgjh vwrfn srvvleo| ghshqgv fuxfldoo| rq wkh vkduhqri oderxu lq wkh djulfxowxuh jrrg zkhq fdslwdo lv lppreloh1 Iljxuh 6/ zkhuh zh kdyh fkrvhq d uhodwlyho| orz ydoxh riqcvkrzv wkdw wkh krph frxqwu| lv ehwwhu r wkh pruh dgydqfhg wkh wudglqj sduwqhu zkhq wudqvdfwlrq frvwv duh orz +Egs ' e: Egs ' : Egs ' *e dw _ Wklv lv wkh vdph uhvxow dv zh irxqg zkhq fdslwdo zhuh dvvxphg wr eh preloh1 Lw lv dovr vwloo wuxh wkdw iru lqwhuphgldwh ohyhov ri wudqvdfwlrq frvwv wkh jdlqv iurp wudgh duh orzhvw li wkh frxqwulhv duh v|pphwulf +dv looxvwudwhg e| wkh duhd _{ 2},1 Qrwh/ krzhyhu/ wkdw wkh zhoiduh ohyho lq wkh krph frxqwu| lv ghfuhdvlqj lq wkh vwrfn ri iruhljq nqrzohgjh zkhq wudqvdfwlrq frvwv duh kljk1 Lqghhg/ lw fdq eh vkrzq wkdw zhoiduh xqghu dxwdun| pd| eh kljkhu wkdq wkh rqh rewdlqhg zlwk wudgh zkhq wudgh lv h{shqvlyh dqgg_s : g

48

3.4 3.6 3.8 4.0 4.2

1.0 1.5 2.0 2.5

τ X_K

._I

._I ._I

τ τ

Iljxuh 61 c q ' fc g ' 

Wkh uhdvrq zk| lw pd| eh kdupixo wr wudgh zlwk dq dgydqfhg frxqwu| zkhq fdslwdo lv lqwhuqdwlrqdoo| lppreloh/ exw qrw zkhq lw lv preloh/ lv wkdw wkh lqyhvwphqw rssruwxqlwlhv gr qrw lpsuryh lq wkh iruphu fdvh1 Zlwk preloh fdslwdo d kljk gs

lpsolhv wkdw frqvxphuv lq wkh krph frxqwu| jdlq dffhvv wr wkh pruh surwdeoh lqyhvwphqwv deurdg> wklv lv qrw wuxh zlwk lppreloh fdslwdo1 Ilqdqfldo lqfrph lq wkh krph frxqwu| lv wkhuhiruh xqdpeljxrxvo| ghfuhdvlqj lq wkh iruhljq nqrzohgjh vwrfn1 Wkh idfw wkdw lw pd| eh kdupixo wr wudgh zlwk frxqwulhv zklfk kdyh d odujhu nqrzohgjh vwrfn zkhq fdslwdo lv lqwhuqdwlrqdoo| lppreloh/ lv prvw hdvlo| vhhq li zh dvvxph wkdw q ' 1 Zlwk frvwohvv wudgh lq wkh wudglwlrqdo jrrg/ lw pxvw wkhq eh wkh fdvh wkdw wkh zdjh ohyhov lq wkh wzr frxqwulhv duh htxdo li wkh jrrg lv surgxfhg lq erwk frxqwulhv + ' _s ' R₅,1 Vxssrvh wkdw ' fc zklfk hhfwlyho| phdqv wkdw wkh surgxfw pdunhwv duh frpsohwho| lqwhjudwhg Vxssolhuv ri surgxfhu vhuylfhv zloo wkhq fkdujh wkh vdph sulfh/ dqg kdyh wkh vdph uhyhqxh/ lqghshqghqw ri zkhwkhu wkh| duh orfdwhg lq frxqwu|ru frxqwu| s1 Hyhq lig_s lv rqo| lqqlwhvlpdoo| odujhu wkdq gclw pxvw wkhq eh xqsurwdeoh wr ghyhors eoxhsulqwv lq frxqwu|1 Wkhuhe|/

ehfdxvh wkh| kdyh qr lqyhvwphqw rssruwxqlwlhv/ frqvxphuv lq zloo eh zruvh r wkdq li g 'g_s1

Wkh frqvhtxhqfhv ri wudglqj zlwk d pruh dgydqfhg frxqwu| lv ohvv gudpdwlf li erwk odqg dqg oderxu duh xvhg wr surgxfh wkh djulfxowxuh jrrgEq 1 Wkh uhdvrq

lv wkdw wkh zdjh ohyho lq wklv fdvh zloo eh ghfuhdvlqj lq wkh ohyho ri hpsor|phqw lq wkh djulfxowxuh vhfwru/ vr wkdw s li g gs1 Wkhuhe| vxssolhuv ri surgxfhu vhuylfhv lq zloo kdyh d uhodwlyh frvw dgydqwdjh/ sduwo| rvhwwlqj wkh idfw wkdw lw lv uhodwlyho| h{shqvlyh wr pdnh eoxhsulqwv lq wkdw frxqwu|1

Vlqfh zdjhv duh ohvv vhqvlwlyh wr fkdqjhv lq wkh ohyho ri djulfxowxudo hpsor|phqw wkh odujhu wkh q/ wkh vwuhqjwk ri wkh uhorfdwlrq hhfw lv dovr lqfuhdvlqj lq q1⁴⁸ Li q lv kljk/ lw pd| eh wkhuhiruh dozd|v eh suhihudeoh wr wudgh zlwk d ohvv dgydqfhg frxqwu|/ lqghshqghqw ri wkh ohyho ri wudqvdfwlrq frvwv Wklv lv looxvwudwhg lq Iljxuh 7/ zkhuh q ' f.1 Wkh sdudphwhu ydoxhv duh wkh vdph dv lq Iljxuh 5 +zkhuh fdslwdo zdv dvvxphg wr eh preloh,/ exw xqolnh wkh hduolhu uhvxowv wkh zhoiduh lq lv qrz vwulfwo| ghfuhdvlqj lqgs iru doo ydoxhv ri 1

Vxpplqj xs wkh glvfxvvlrq lq wklv vhfwlrq/ zh kdyh=

Sursrvlwlrq 5= Vxssrvh wkdw fdslwdo lv lqwhuqdwlrqdoo| lppreloh/ dqg wkdwq lv vx!flhqwo| orz1 Wkhq lw lv suhihudeoh wr wudgh zlwk uhodwlyho| dgydqfhg frxqwulhv li wudgh lv lqh{shqvlyh1 Rwkhuzlvh/ lw lv suhihudeoh wr wudgh zlwk ohvv ghyhorshg frxqwulhv1

2.25 2.45 2.65 2.85 3.05 3.25

1.0 1.5 2.0 2.5

τ X_K

DXW ._I ._I ._I

Iljxuh 71 c q' f.c g ' 

Iljxuh 7 dovr looxvwudwhv wkdw wudgh pd| eh kdupixo li g gs= zhoiduh zrxog

48Vhh Dsshqgl{ D71

4:

eh kljkhu xqghu dxwdun| li :e Xqolnh wkh fdvh zkhuh fdslwdo lv lqwhuqdwlrqdoo|

lppreloh/ zh wkxv kdyh=

Ohppd 5= Vxssrvh wkdw fdslwdo lv lqwhuqdwlrqdoo| lppreloh1 Wkhq zhoiduh pd| eh orzhu zlwk wkdq zlwkrxw wudgh li wkh wudglqj sduwqhu kdv d uhodwlyho| odujh nqrzohgjh vwrfn1

Qrwh wkdw wkh fxuyh iru gs ' e lv X0vkdshg/ ghprqvwudwlqj wkdw lqfuhdvlqj wkh wudqvdfwlrq frvwv lv kdupixo li wudqvdfwlrq frvwv duh lqlwldoo| orz/ zkloh lw lv ehqhfldo li wudqvdfwlrqv frvwv lqlwldoo| duh kljk1 Wkh lqwxlwlrq iru wklv uhvxow lv wr eh irxqg lq wkh idfw wkdw wkhuh duh wzr rssrvlqj hhfwv ri kljkhu wudqvdfwlrq frvwv +_ :f,1 Iluvw/ wkh pdunhw dffhvv wr wkh iruhljq frxqwu| ghwhulrudwhv1 Wklv dhfwv h{sruw lqfrph qhjdwlyho|1 Vhfrqgo|/ wkh grphvwlf pdunhw ehfrphv pruh vkhowhuhg iurp lp0 sruw frpshwlwlrq/ frqwulexwlqj wr lqfuhdvh surwdelolw|1 Wkhvh hhfwv fdqfho hdfk rwkhu li wkh frxqwulhv duh v|pphwulf1 Qrz/ vxssrvh wkdw wkh nqrzohgjh vwrfn lq s lv odujhu wkdq lq Wkh iruhljq frxqwu| zloo wkhq kdyh wkh kljkhu frqvxphu lqfrph/

dqg wkxv frqvwlwxwh d odujhu pdunhw iru vxssolhuv ri surgxfhu vhuylfhv1 Hylghqwo|/

dovr upv lq zloo pdnh wkh odujhu vkduh ri wkhlu uhyhqxhv lq wkh iruhljq pdunhw zkhq wudqvdfwlrq frvwv duh orz1 Vwduwlqj iurp orz ydoxhv ri c dq lqfuhdvh lq wkh ohyho ri wudqvdfwlrq frvwv lv wkxv kdupixo wr surgxfhuv lq ehfdxvh dffhvv wr wkh prvw lpsruwdqw pdunhw lv ghwhulrudwhg1 Li lv lqlwldoo| kljk/ rq wkh rwkhu kdqg/

h{sruw lqfrph lv uhodwlyho| xqlpsruwdqw 0 wkh odujhu vkduh ri wkh uhyhqxh lv hduqhg grphvwlfdoo|1 Kljkhu wudqvdfwlrq frvwv wkhq lpso| wkdw wkh grphvwlf pdunhw eh0 frphv pruh vkhowhuhg iurp lpsruw frpshwlwlrq/ wkhuhe| lqfuhdvlqj wkh surwdelolw|

ri vxsso|lqj surgxfhu vhuylfhv1

8 Frqfoxvlrq

Wkh sxusrvh ri wklv sdshu kdv ehhq wr dqdo|}h zkhwkhu d ghyhorslqj frxqwu| vkrxog wudgh zlwk frxqwulhv wkdw duh pruh ru ohvv dgydqfhg wkdq lwvhoi1 Rqh glvdgydqwdjh ri wudglqj zlwk pruh dgydqfhg frxqwulhv lv wkdw grphvwlf idfwru lqfrphv idoo/ vlqfh hpsor|phqw lq wkh djulfxowxuh vhfwru lqfuhdvhv1 Wkh vxevhtxhqw uhgxfwlrq ri pdqx0

idfwxulqj hpsor|phqw phdqv wkdw wkh frxqwu| ehfrphv pruh ghshqghqw rq lpsruwv ri surgxfhu vhuylfhv1 Wklv lv sduwlfxoduo| kdupixo li wudqvdfwlrq frvwv duh kljk dqg fdslwdo lqwhuqdwlrqdoo| lppreloh/ lq zklfk fdvh zhoiduh pd| eh kljkhu lq dxwdun|

wkdq zlwk wudgh1 Zh dovr vkrz wkdw wudgh zlwk dgydqfhg frxqwulhv whqgv wr eh ohvv ehqhfldo wkh ohvv uhvsrqvlyh zdjhv duh zlwk uhvshfw wr fkdqjhv lq djulfxowxuh hpsor|phqw1 Wklv fdq eh h{sodlqhg e| wkh idfw wkdw wkh frvw dgydqwdjh iru wkh hqwuhsuhqhxuv lq wkh ohdvw ghyhorshg frxqwu| lv wkhq uhodwlyho| vpdoo1

Dq dgydqwdjh ri wudglqj zlwk uhodwlyho| dgydqfhg frxqwulhv lv wkdw grphvwlf pdqxidfwxuhuv jdlq dffhvv wr d zlghu udqjh ri vshfldol}hg surgxfhu vhuylfhv/ wkxv whqglqj wr uhgxfh surgxfwlrq frvwv1 Wklv hhfw lv sduwlfxoduo| vwurqj iru orz ohyhov ri wudqvdfwlrq frvwv1 Ixuwkhu rq/ surylghg wkdw fdslwdo lv lqwhuqdwlrqdoo| preloh/

dq dgydqfhg wudglqj sduwqhu rhuv pruh surwdeoh lqyhvwphqw rssruwxqlwlhv wkdq grhv ohvv dgydqfhg wudglqj sduwqhuv1 Frqvhtxhqwo|/ lw whqgv wr eh ehqhfldo wr wudgh zlwk dq dgydqfhg frxqwu| li wudqvdfwlrq frvwv duh orz dqg fdslwdo lv lqwhuqdwlrqdoo|

preloh1

Dq lqwhuhvwlqj h{whqvlrq ri wkh sdshu zrxog eh wr dvvxph wkdw wudqvdfwlrq frvwv dqg wkh ghjuhh ri fdslwdo prelolw| duh sduwo| srolf| ghwhuplqhg/ dqg dqdo|}h d jdph ehwzhhq wkh frxqwulhv1 Dq lpsruwdqw frqvlghudwlrq zrxog wkhq eh krz wkh jry0 huqphqwv zhljkw wkh glhuhqw lqfrph jurxsv 0 odqg rzqhuv dqg oderxu pd| kdyh frq lfwlqj lqwhuhvwv1 Lq wkdw uhvshfw lw frxog dovr eh uhohydqw wr lqfoxgh lqfrph jhqhudwlqj wdulv rq erwk surgxfhu vhuylfhv dqg wkh djulfxowxuh jrrg1

Ilqdoo|/ lw vkrxog eh qrwhg wkdw wkh whfkqrorj| vshflfdwlrqv lq wklv sdshu kdyh fhuwdlq vlplodulwlhv zlwk wkh rqhv xvhg e| Jurvvpdq dqg Khospdq lq d qxpehu ri jurzwk prghov1⁴⁹ D vhfrqg lqwhuhvwlqj h{whqvlrq ri wkh sdshu zrxog wkxv eh wr frqvlghu zkhwkhu lw ehfrphv pruh ru ohvv suhihudeoh wr wudgh zlwk dgydqfhg frxqwulhv zkhq orqj0whup hqgrjhqrxv jurzwk lv lqfrusrudwhg1

49Vhh/ iru lqvwdqfh/ Jurvvpdq dqg Khospdq +4<<3/ 4<<4,1

4<

9 Uhihuhqfhv

Drnl/ P1/ K|xqj0Nl Nlp dqg P1 Rnxqr0Ixmlzdud +4<<:,= Wkh Uroh ri Jryhuq0 phqw lq Hdvw Dvldq Hfrqrplf Ghyhorsphqw/ R{irug= Foduhqgrq Suhvv1

Edudq/ S1 D1 +4<8:,= Wkh Srolwlfdo Hfrqrp| ri Jurzwk1 Qhz \run= Prqwko|

Uhylhz Suhvv1

Eudqvwhwwhu/ O +4<<9,= Duh Nqrzohgjh Vslooryhuv Lqwhuqdwlrqdo ru Lqwudqdwlrqdo lq VfrshB Plfurhfrqrphwulf Hylghqfh iurp wkh X1V1 dqg Mdsdq1 QEHU Zrunlqj Sdshu 8;331

Gl{lw/ D1 N1 dqg Y1 G1 Qrupdq +4<;3,= Wkhru| ri Lqwhuqdwlrqdo Wudgh1 Fdp0 eulgjh> Fdpeulgjh Xqlyhuvlw| Suhvv1

Gl{lw/ D1 N1 dqg M1 H1 Vwljolw} +4<::,= Prqrsrolvwlf Frpshwlwlrq dqg Rswlpxp Surgxfw Glyhuvlw|1 Dphulfdq Hfrqrplf Uhylhz 9:/ 5<:063;1

Hdwrq/ M1 dqg V1 Nruwxp +4<<9,= Wudgh lq lghdv1 Mrxuqdo ri Lqwhuqdwlrqdo Hfrqrplfv 73/58405:;1

Hwklhu/ Z1 M1 +4<:<,= Lqwhuqdwlrqdoo| Ghfuhdvlqj Frvwv dqg Zruog Wudgh1 Mrxu0 qdo ri Lqwhuqdwlrqdo Hfrqrplfv 7/ 4<<05391

Hwklhu/ Z1 M1 +4<;5,= Qdwlrqdo dqg Lqwhuqdwlrqdo Uhwxuqv wr Vfdoh lq wkh Prghuq Wkhru| ri Lqwhuqdwlrqdo Wudgh/ Dphulfdq Hfrqrplf Uhylhz :5/ 6;<07381

Hydqv/ J1/ V1 Krndsrkmd/ dqg S1 Urphu +4<<;,= Jurzwk f|fohv1 Dphulfdq Hfr0 qrplf Uhylhz ;;+6,/ 7<808481

Ixmlwd/ P1/ S1 U1 Nuxjpdq/ dqg D1 M1 Yhqdeohv +4<<<,1 Wkh Vsdwldo Hfrqrp|=

Flwlhv/ Uhjlrqv dqg Lqwhuqdwlrqdo Wudgh1 PLW Suhvv

Jurvvpdq/ J1 dqg H1 Khospdq +4<<3,= Frpsdudwlyh Dgydqwdjh dqg Orqj0Uxq Jurzwk1 Dphulfdq Hfrqrplf Uhylhz ;3/:<90;481

Jurvvpdq/ J1P1 dqg H1 Khospdq +4<<4,= Lqqrydwlrq dqg Jurzwk lq wkh Joredo Hfrqrp|1 PLW Suhvv1

Nuxjpdq/ S1 U1 +4<:<,= Lqfuhdvlqj Uhwxuqv/ Prqrsrolvwlf Frpshwlwlrq/ dqg Lqwhuqdwlrqdo Wudgh1 Mrxuqdo ri Lqwhuqdwlrqdo Hfrqrplfv </ 79<07:<1

Nuxjpdq/ S1 U1 +4<<4,=Jhrjudsk| dqg Wudgh1 Fdpeulgjh= Wkh PLW Suhvv1

Nuxjpdq/ S1 U1 dqg D1 M1 Yhqdeohv +4<<3,= Lqwhjudwlrq dqg wkh Frpshwlwlyhqhvv ri Shulskhudo Lqgxvwu|1 Lq Fkulvwrskhu Eolvv dqg M1 Eudjd gh Pdfhgr +hgv,= Xqlw|

zlwk Glyhuvlw| lq wkh Hxurshdq Frppxqlw|1

Nuxjpdq/ S1 U1 dqg D1 M1 Yhqdeohv +4<<8d,= Joredol}dwlrq dqg wkh lqhtxdolw|

ri qdwlrqvTxduwhuo| Mrxuqdo ri Hfrqrplfv F[/ +4<<8,/ ;8:0;;31

Nuxjpdq/ S1 U1 dqg D1 M1 Yhqdeohv +4<<8e,= Wkh Vhdpohvv Zruog= D Vsdwldo Prgho ri Lqwhuqdwlrqdo Vshfldol}dwlrq1 QEHU Zrunlqj Sdshu 85531

Pdwvx|dpd/ N1 +4<<8,= Frpsohphqwdulwlhv dqg Fxpxodwlyh Surfhvvhv/Mrxuqdo ri Hfrqrplf Olwhudwxuh 66/ :340:5<1

P|ugdo/ Jxqqdu +4<8:,= Hfrqrplf Wkhru| dqg Xqghughyhorshg Uhjlrqv1 Orq0 grq= Gxfnzruwk1

Qrupdq/ Y1 G1 +4<:9,= Surgxfw Glhuhqwldwlrq dqg Lqwhuqdwlrqdo Wudgh1 Xq0 sxeolvkhg pdqxvfulsw/ Zduzlfn Xqlyhuvlw|1

Suhelvfk/ U1 +4<83,= Wkh Hfrqrplf Ghyhorsphqw ri Odwlq Dphulfd1 Odnh Vxf0 fhvv= Xqlwhg Qdwlrqv1

Urphu/ S1 +4<;:,= Jurzwk Edvhg rq Lqfuhdvlqj Uhwxuqv Gxh wr Vshfldol}dwlrq1 Dphulfdq Hfrqrplf Uhylhz ::/890951

Urphu/ S1 P1 +4<<3d,= Duh Qrqfrqyh{lwlhv Lpsruwdqw iru Xqghuvwdqglqj JurzwkB DH D Sdshuv dqg Surfhhglqjv ;3/ <:04351

Urphu/ S1 P1 +4<<3e,= Hqgrjhqrxv Whfkqrorjlfdo Fkdqjh1 Mrxuqdo ri Srolwlfdo Hfrqrp| +Vxssohphqw, <;/ V:40V4351

Vlqjhu/ K1 +4<83,= Wkh Glvwulexwlrq ri Jdlqv ehwzhhq Lqyhvwlqj dqg Eruurzlqj Frxqwulhv1 Dphulfdq Hfrqrplf Uhylhz 83/ Sdshuv dqg Surfhhglqjv

\rxqj/ D1 +4<5;,= Lqfuhdvlqj Uhwxuqv dqg Hfrqrplf Surjuhvv/Hfrqrplf Mrxu0 qdo 6;/ 85:0751

54

: Dsshqgl{

D4 V|pphwulf frxqwulhv= hhfwv ri fkdqjhv lq wkh ohyho ri sxeolf nqrzo0 hgjh

Zlwk v|pphwulf frxqwulhv zh pd| gurs frxqwu| vxevfulsw/ dqg zulwh frqvxphu h{shqglwxuh lq wkh vwhdg| vwdwh dv

. 'Z8 nun4? +57,

Wklv krogv zkhwkhu lqwhuqdwlrqdo fdslwdo prelolw| lv dvvxphg ru qrw1

Wkh ydoxh ri ghpdqg iru wkh djulfxowxuh jrrg htxdovE#.cri zklfk wkh {hg idfwru 8 uhfhlyhv d vkduh Eq Xvlqj +57, dqg '*g lw wkxv iroorzv wkdw

. ' un4?*g

EqE# +58,

Lqvhuwlqj iru u₅ iurp htxdwlrq +9, lqwr htxdwlrq +4;,/ oderxu pdunhw htxloleulxp fdq eh h{suhvvhg dv

u'?%n q

q

_3qZ

_3q

E#. +59,

Wkh }hur surw frqglwlrq lq wkh djulfxowxuh vhfwru lpsolhv wkdw &_q^qZ^3q '  +f1i1 htxdwlrq +8,,/ dqg iurp +45, zh nqrz wkdw%'4Ej*gXvlqj wklv wrjhwkhu zlwk htxdwlrqv +58, dqg +59, zh qg/ diwhu vrph pdqlsxodwlrqv/ wkdw

? ' #ug

ijdEqE#o#j4 +5:, Zlwk wkh Free0Grxjodv surgxfwlrq ixqfwlrq iru wkh djulfxowxuh jrrg zh nqrz wkdw _u^Z8₅ ' ^3q_q Lqvhuwlqj iru u5 iurp htxdwlrq +9,/ dqg xvlqj &q^qZ^3q ' c jlyh xv

' 

&q

EqE#Eun4?*g

EqE#

_q3

Frpelqlqj wklv zlwk +5:, zh duulyh dw 'q

jdEqE#o# qjE#u

_3q

+5;,

Lw ixuwkhu iroorzv wkdw

Z ' Eq

qjE#u

jdEqE#o# _q

+5<,

Erwk dqg Z duh wkxv lqghshqghqw ri wkh ohyho ri sxeolf nqrzohgjh/ zkloh wkh qxpehu ri ydulhwlhv?surgxfhg lq hdfk frxqwu| lv sursruwlrqdo wr g1 Htxdwlrq +57, wkxv pdnhv lw fohdu wkdw frqvxphu h{shqglwxuh lv lqghshqghqw ri g1 Vlqfh wkh sulfh R6 ri wkh pdqxidfwxuhg jrrg lv vwulfwo| ghfuhdvlqj lq ?/ lw iroorzv wkdw zhoiduh lv vwulfwo| lqfuhdvlqj lq wkh ohyho ri sxeolf nqrzohgjh1

D5 V|pphwulf frxqwulhv= hhfwv ri fkdqjhv lq wkh ohyho ri wudqvdfwlrq frvwv

Zlwk v|pphwulf frxqwulhv zhoiduh lv jlyhq e| ' _R#^.

6R^3#5 c zkhuh wkh sulfh ri wkh pdqxidfwxulqj jrrg htxdov R6 ' d?R^3jn?ER^3jo^3j Zh wkxv kdyh ^_ '

j3#

k ?ER^3j

?R^3jn?ER^3j

l_ c ru

_*

_* ' #

jr :f

Gxh wr pruh lqh{shqvlyh lpsruw ri surgxfhu vhuylfhv/ zhoiduh lv wkxv lqfuhdvlqj zkhq wudqvdfwlrq frvwv idoo dqg wkh frxqwulhv duh v|pphwulf1

D6 Wkh uhodwlrqvkls ehwzhhq djulfxowxuh hpsor|phqw dqg grphvwlf idfwru lqfrph

Wkh surgxfwlrq ixqfwlrq iru wkh wudglwlrqdo jrrg lv jlyhq e|~ 'u^q₅8^3qczkhuh vxsso| ri odqg +8, lv {hg1 Djulfxowxuh hpsor|phqw lq frxqwu| pxvw lqfuhdvh e|

E*q shu fhqw li~ lqfuhdvhv e| rqh shu fhqw>

_u5*u5 ' E*q_~*~ +63, Glhuhqwldwlrq ri htxdwlrq +9, ixuwkhu lpsolhv wkdw

_u₅*u₅ ' Eq d_Z*Z _*o n_~*~ +64, Xvlqj +63, dqg +64, wrjhwkhu zlwk &q^qZ^3q '  zh wkxv qg

_* 'Eq*q +65,

56

dqg

_o*o '  +66,

Wkh fkdqjh lq idfwru lqfrph lq frxqwu| e| rqh shu fhqw lqfuhdvh lq~ zloo wkhq eh htxdo wr _Eu n_Eo8 'u5_n_Zn Eu5_ Ohwwlqj u '8 ' c dqg lqvhuwlqj iru +65, dqg +66,/ zh kdyh

_Eu n_Eo8 ' q

q nZ +67,

Li wkh iruhljq fdslwdo vwrfn lv vr kljk wkdw frxqwu|lv frpsohwho| vshfldol}hg lq sur0 gxfwlrq ri wkh djulfxowxuh jrrg +u5'u ' / wkh zdjh udwh zloo eh htxdo wrqdqg wkh uhqwdo udwh zloo eh htxdo wrEqLq wkdw fdvh_Eun_Eo8 ' f1 Vlqfh : qdqgo qliu₅ lw iroorzv wkdw wkh fkdqjh lq idfwru lqfrph zloo eh qhjdwlyh li djulfxowxuh hpsor|phqw lqfuhdvhv1

D7 Wkh uhorfdwlrq hhfw dqg wkh vkduh ri oderxu lq wkh djulfxowxuh jrrg Vxssrvh wkdw zh duh lqlwldoo| lq d v|pphwulf htxloleulxp/ dqg frqvlghu wkh hhfw ri dq lqfuhdvh lqgs zklfk lqfuhdvhv djulfxowxuh hpsor|phqw lq dqg uhgxfhv djulfxowxuh hpsor|phqw lq s1 Lq rughu wr vlpsoli| wkh dojheud/ zh zloo frqvlghu rqo| wkh fdvh zkhuh ' f dqg wkh frxqwulhv duh lqlwldoo| v|pphwulf +?'? '?_s,1

Nhhslqj frqvxphu h{shqglwxuh {hg/ zh qg ^_%_% 'j^_R_R ^_E?_?^{R3j n_E?sR3js}

R^3j n?sR^3j_s

iurp htxdwlrqv +45, dqg +43, Dvvxplqj wkdw _~*~ ' _~s*~s : f zh nqrz iurp Dsshqgl{ D6 +f1i1 htxdwlrq +65,, wkdw ^__{_~}^*_*~ ' ^__{_~}^s_s^*_*~s^s ' ^3q_q Gxh wr frqvwdqw pdunxs lw pxvw dovr eh wuxh wkdw _{_~}^_R*R_*~ ' _{_~}^_Rs_s^*R_*~^s_s ' ^3q_q Xvlqj wklv lq wkh h{suhvvlrq iru _% dqg vlpsoli|lqj zh duulyh dw _% ' jE^3q_q %

2

_?

? n^_?_?s^s

%1 Iru wkh h{sruw vdohv wr frxqwu| s zh vlploduo| kdyh _%_s ' jE^3q_q %s^₂

_?

? n ^_?_?s^s

%sLq wkh v|pphwulf htxloleulxp zlwk }hur wudqvdf0 wlrq frvwv hdfk vxssolhu ri surgxfhu vhuylfhv zloo vhoo htxdoo| pxfk grphvwlfdoo| dqg deurdg1 Iurp htxdwlrq +48, lw wkxv iroorzv wkdw % ' %s ' ^₂^4Ej3_g c dqg dgglqj _% dqg_%ss zh kdyh

_% '  2

4Ej g

2jq q

_?

? n_?_s

?s

+68,

Lq htxloleulxp % grhv qrw ghshqg rq gsc vr _% ' f1 Htxdwlrq +68, fdq wkhuhiruh eh zulwwhq dv_? ' 2j^3q_q ?_?s1 Lqvhuwlqj iru? iurp htxdwlrq +5:,/ zh wkxv kdyh _? 'Eqc jc #_?_sc zkhuh wkh ixqfwlrq lv jlyhq e|

Eqc jc # ' 2jEq#ug

qijdEqE#o#j4 +69, Lw lv zruwk qrwlqj wkh iroorzlqj derxw wkh ixqfwlrq 1 Iluvw/ lw lv ghfuhdvlqj lq q1 Wklv uh hfwv wkh idfw wkdw wkhuh zloo eh d vwhhs idoo lq wkh zdjh ohyho lq dv djulfxowxuh hpsor|phqw lqfuhdvhv li wkhuh lv rqo| d vpdoo vkduh ri oderxu lq wkh djulfxowxuh jrrg1 Wklv jlyhv vxssolhuv ri surgxfhu vhuylfhv lq wkh krph frxqwu| d odujh frvw dgydqwdjh uhodwlyh wr wkrvh lq wkh iruhljq frxqwu|1 Wkhuhe| d orzhu q lpsolhv wkdw lw ehfrphv pruh surwdeoh wr pdnh eoxhsulqwv iru surgxfhu vhuylfhv lq / dqg wkhuh zloo eh d vpdoohu uhgxfwlrq ri ? dv ?_s lqfuhdvhv1 Vhfrqgo|/ lw fdq eh vkrzq wkdw lv lqfuhdvlqj lq j Wkh uhdvrq iru wklv lv wkdw wkh surgxfhu vhuylfhv ehfrph pruh krprjhqrxv wkh odujhu wkh hodvwlflw| ri vxevwlwxwlrq/ pdnlqj ghpdqg pruh sulfh hodvwlf1 Wklugo|/ lv lqfuhdvlqj lq#1 Wkh lqwxlwlrq iru wklv uhvxow lv wkdw wkh pruh lpsruwdqw wkh pdqxidfwxulqj jrrg lv lq frqvxpswlrq/ wkh vpdoohu lv oderxu ghpdqg lq wkh djulfxowxudo vhfwru1 Lqghhg/ lw lv hdv| wr vkrz wkdw? lv lqghshqghqw ri g_s lq wkh olplw zkhq# '  +ru liq ' f

58