STRATEGIC CHOICE OF TRADE POLICY INSTRUMENTS

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1 КОНСОРЦИУМ ЭКОНОМИЧЕСКИХ ИССЛЕДОВАНИЙ И ОБРАЗОВАНИЯ РОССИЯ И СНГ ECOOMICS EUCATIO A RESEARCH COSORTIUM RUSSIA A CIS V.. Melk STRATEGIC CHOICE OF TRAE POLICY ISTRUMETS Fl Reor

2 V.. Melk STRATEGIC CHOICE OF TRAE POLICY ISTRUMETS Resume Wh s he omum mx of rde oly srumes? Usully oermes hoose mo suh srumes s uos rffs exl of ml subsdes. The ol of he roe s o osder he ossbly of smuleous use by he oerme of uos d orresod Lese fees d rffs. The use of uos d rffs s omlemes rher h subsues llows o rry ou rde oly whh domes from he effey o of ew - oer oly bsed o smle uos or smle rffs. The ule ouomes of he lyss deed o he ye of oerme wheher mxmzes s reeue or ubl welfre mrke sruure d he os sruure of frms oer he mrke. The sudy ms mro our udersd of he lk bewee oerme ereo - he oml mx of rde oly srumes d omeo he home oods mrke.. Iroduo Wheer o he reso for he beef of free rde would be rde brrers sll exs. Usully rde brrers er he form of he roeos rffs uos orff brrers d olury exor resr VER. The rffs for roduo rese he re rese erl roduo redue osumo redue mor d ree rff flows o he se; he uos o mor mke he sme bu ree flows for he fore roduers b o of for he se whh rodued he uos. Besdes he rffs resul loss of eoomy effeeess whh ome from dsoro of moo of behour of he domes roduers d usomers. O he oher hd he rese of de from mro he odos of rde whh s oseuee of redued fluee of he rff o he res of he fore exorers. I se of mor oury whh o fluee he res world mrkes he ee effe of he rff o eoomy s obous. The ehue of he of he rff lyss be led for sudy of oher ses of rde oly: exor subsdy mor uos d VER. The exor subsdes resul losses eoomy effeeess. The mory of rumes for he beef of rde roeosm usully defed sel eress. The e reor s deoed o he roblems of relzo of he se wo-r rde oly se of wo oures wo mrkes my roduers odos of merfe omeo where he usul rumes of free rde re lble. The omum oly of oerme s osdered from he o of ew of wo uroses:

3 mxmzo of ersol omes; mxmzo of domes welfre. The bse model s wo-leel me. A he frs leel oermes oue rde oly d o he seod- home d fore roduers behe s Couro omeors. The reor osders: The uos d rffs omleme eh oher he oml wo-r rde oly: he mor lese for ere o he mrke uo d yme for u of mor rff; The fors whh fluee he omum rde oly; The eulres of he wo-r rde oly odos of rso o mrke; The eulry of he wo-r rde oly he erl d exerl mrke; 5 The des of he modfed rde oly. We he show h he wo-r rde oly domes he smle uo d smle rff d he ls wo meoed re he sel ses of. Thus he effeeess of he wo-r rde oly deeds o he umber of ome frms o he mrke mude of heeroeey of fuos of oss derees of oexy of fuos of oss d hus o wh frms he e oly wll be led d he oermes of whh oures wll exeue he oly. Besdes he effeeess d ouome of he rde oly we he osdered uder he follow odos: yoff fuos of oerme G s ome of oerme or W - domes welfre. We he foud odos whh he omum wo-r rde oly of oerme wll eoure fore frms o behe s moolh Skelber leder o he seod leel of he me.. The reew of he lerure. The lssl roblem he heory of he oles of erol rde oers he effe of he rffs d uos or he effe of rey of ossble oles. I bsoluely omee models of rde rffs d uos - re usully eule h s he effe of he rff be duled by he ordly hose model of uo. As s sed by Bhw 965 wll o be rue merfe omeo. He hs demosred h he rffs dome boe he uos whe here s merfe omeo home mrke. I be exled by he f h he kee resose of fore frms he uo s more ex h he rff. Thus he uo omrso wh he rff rses moools fore of erl frms. Aderso 988 d Krsh 989 eerlzed he reous resuls. Aderso osdered he duooly model d showed h uder he er odos uos ed o lower omeo. Krsh hs show model of Berrd h he uo osrs he bly of frms o omee effeely whe he oods re erfe subsues. Aordly we ould exe

4 some eres omrsos bewee he rffs d uos s sre srumel mes of rde oly. The lyss of he uos olooly e ddol eeros. My works uoer he ses of hs roblem for exmle Ioh d Oo 98 Hrrs 985 Hw d M 988 Cooer d Rezm 989 Ishkw 99 Krsh 989 Res 99 b d ohers. There re lso works whh he dome of he uos boe he rffs s roed. Some eoomss osdered ubl models of hoe whh lyze he rffs d uos. For exmle Css d Hllm 985 he show h he uos dome boe he rffs. Kemfer 989 hs roed h he uos re more referble h rffs d h exly uos o erl oerroduo. Roember d Sloer 989 used reeed model of he me o show relee of he uos boe he rffs mk of he reeme of he eoom es more dfful. Perhs he m dfferee bewee rffs d uos s oly srumes s reled o her effes o fore frms. Ay rff o fore frms redues her rofs d y subsdy o domes frms lso redues he rofs of fore frms. Quos o he oher hd e muh reer ossbly for fore frms o beef rulrly f he uo s mlemeed s olury exor resr VER me h fore frms kee y uo res rher h h o buy uo leses. I effe VER s s dee h fles more olluse ouome for fore frms. Ths mles h VER s less lkely o be he eres of oerme whh mxmzes domes welfre. A losely reled ossbly s h VER mh led o he he mode of rlry bewee frms s Hrrs 985 who ssumes h he moso of VER he exerl free-rde leel oers he Berrd rlry o sruure whh he domes frm beomes he Skelber re leder. Eo d Grossm 986 us he wo-se me model for wo frms rodu subsue oods he foud h he er odos of reulry esur uueess d sbly of eulbrum he omum hoe wll be: - rodu of he exor xes f he dfferee bewee exeos of he lol roduer oer he rer s behour d hs rue behour s ee; - esblsh he exor subsdes se he boe meoed dfferee s ose. I ddo o he hoe bewee he rffs d uos here re my oher losely reled roblems. Ee f he eo s lmed oly o rffs here exss roblem eher wh he oueme of he re or er rffs. There should be hoe. As s show Brder d Seer 98b merfe omeo er d he d lorem rffs re o eule d her rele reess deeds o he fuol

5 5 form of demd d oher sel ses of he model. I Corde 9 he wde reserh of effe of he rff effe uos d oher ses of rde oly s e. I he work of Roussl d Suomel 985 he roblem of how he ools of he rde oly be used re s osdered. The uhor of he roe del wh some erreos he moder lerure of he modfed rde oly ruh o for wo-r oly d for smle rff. So x 98 hs osdered he mor rffs he exor subsdy or subsdy for domes sles. Allow subsdy o lol sles o shf he emhss of he lyss wy from rde oly beuse oerme hs ee o use suh subsdy smly o offse he ouuresr effe of olooly. Ee he bsee of rde hs obous eo o subsdze moooles d olooly lwys exss. Thus lo of wo-r rde oly for se of he smle rff s usfed wh he frmework of osdered models he ddol sre effes. As fr s s usfed roduos of he uo o eror frms we see he moder lerure. So x 988 uses lbro ehue o ssess he effes of sre rde oles o he U.S. uomoble dusry. Hs uderly model s rerol-mrkes model wh Jese d Amer roduers where frm odu s hrerzed by odu rmer model. He fouses o us he U.S. mrke. Coer bou he rs leel of Jese mor eero he U.S. mrke led U.S. olsy-mrke 98 o mose olury exor resr VER o Jese mors. O hs x hs reeed eres ouomes of omrso of oer oles of USA wh oml oles. I he e reew s show h he uos d rffs re dffere hoes. I s suosed he roe o osder ossbly of us he uos d rffs s ddo o eh oher bu o s releme. The wor rde oly rodes for osder he mor lese for ere losde wh he rff for he u of mor. Suh oly ws frs rodued by O 9 he lssl lyss of re dlemm of seyld. Phls 98 d Wlso 99 lso osdered he exmles of oler ss of he res. For he se of sole mrke wh homoeeous fuos of oss Fuers d Km 99 he osdered he wo-r rde oly omlee bu merfe formo. I he mrke model of oe oury wh homoeeous fuos of oss hey he foud odos whe he oml wo-r rde oly domes oer he smle rff d smle uo. I s lso fr for he oerme whh s eresed oly mxmzo of he ome d for beeole oerme eresed erl welfre. The effe rses beuse he lre yme for he mor lese moses smller mou of dsoros h rff. A oerme reh he eurl ome redu urre rffs d remburs he los omes by he yme for he lese. Wh homoeeous fuos of

6 oss Fuers d Km 99 he osdered umerl exmles whh lso he show de of he wor rde oly.. The me sruure of sre rde oly. The sudy of sre rde oly s fudmelly lo of o-ooere me heory d herefore uses he sh eulbrum [s frs defed by sh 95] s he erl eulbrum oe. The eerl oooere me wh erso s lled he sysem Г I{ X } I { f x} I > Here I { } s se of lyers umbers; {X } I se of srees he lyer wh umber I; he olleo of srees xx x. x x X s lled he suo of he me Г d X X X X he se of ll suos; for eh lyer I fuo f : X R lled he yoff fuo of lyer. Eh lyer seles srey x from srey se X so s o deedely d oooerely mxmze yoff fuo f x x x. Le x e x e x e x e be fesble eor of srees oe seleed by eh lyer. The swer o roblem o exsee of sh eulbrum es he follow heorem: Theoremsh: Le s ssume wh he me Г for y lyer he se of srees X s o emy om d oex d yoff fuo f. s oe o x d ouous. The here s sh eulbrum. To sole dym mes wh omlee formo we use bkwrd duo.. Two-r rde oly. Les osder bse model of he rerol mrkes wo-r rde oly. There re wo oures oe s home oury he oher s fore oe. There re - of home frms d - of fore frms rodu he homoeeous oods. Suose s roduo leel of -home frm for he home mrke; 6 - leel of exor of - fore frm for he home mrke. Aordly we use lbel by sersk o dese rbles whh re reled o he fore mrke. Suose - leel of exor of home frm for he fore mrke; - leel of roduo of fore frm for he fore mrke. The he omlee sles hese wo oures eul Q d Q: Q. Q.

7 The erse demd ures home d fore oury Q Q where C ;. I s lso kow с - fuo of oss of home frm; с - fuo of oss of fore frm where C > > d C > >. The eoom resul of he frms y s deermed by he oseue fuos of rof: π Q Q e.... π Q Q e.... Where e e - yme for he lese o home d fore oerme ordly; - he rff er u of roduo mosed o home d fore frms ordly. Les dese by eor z e z e wo-r of rde oles of home d fore oerme here re he uos o home d mor frms. The s obous h z e - s he smle uo; z - he smle rff.. Trde oly he hrd-mrke model. I sre rde oly he hrd-mrke model s well kow. I hs model oe or more frms from domes oury d oe or more frms from fore oury omee oly he hrd mrke. Thus hese frms herefore rodue oly for exor. Ths smlfo ers ery useful; llows oe o see sre effes of oree rde oly s ure odo. I he hrd-mrke model domes oerme do oh o drely hder fore frm.e. here s o ossbly for mor rffs or uos d he url oly s exor subsdy whh dre effe s o hel domes frm omeo wh s fore rl. I he roe s suosed model of he hrd mrke o use he wo-r rde oly. The suoso s exressed h hs model he omum oly wll er urlly he form of ee rff subsdy he ose yme for he lese. The seuel sruure of model osss of wo ses. A he frs se of oerme esblsh wor oly e d e for eror frms. A he seod se eror d exeror frm smuleously hoose ouu leel or exor for he hrd mrke. Us erse duo o fd erfe subme sh eulbrum sh eulbrum he seod se frs s osdered d he sh eulbrum he frs se bewee oermes s osdered whh omleely relzes h her oly wll ffe he

8 8 lue of ouus of frms he seod se. Thus he yoff fuos of frms re defed by relos.. roded h QQ. π Q e....5 π Q e....6 Where e e - yme for he lese o home d fore oerme ordly; - he rff er u of roduo mosed o home d fore frms ordly. We shll osder se of homoeeous os fuos: ;. Muh of he lyss of sre rof-shf mkes use of he Couro model of olools behor. By se rffs d hs bee redeermed se d s herefore reed s exoeous. The frs order odos ssoed wh mxmzo of.5.6 s π π ; ;.. Beuse of homoeey.5.6 s ;. The seod order odos ssoed wh mxmzo of π π ;..8 Frs order odo. mkes ler h Couro eulbrum s sh eulbrum ouus s. s mled by sh odo for he se whh eh lyers srey se s smly he se of ossble ouu ues mh rodue oe-sho smuleous-moe me. The Couro eulbrum herefore hs he sme o surrses roly roery h y sh eulbrum hs. Frs order odo. ould be soled rle for he rof-mxmz hoe of for y e se of ouu hoes by he oher frms. Ths resul ml fuo s he reo fuo or bes-resose fuo. The ommo erseo of he besresose fuos oe for eh frm s he Couro eulbrum. A ddol reulry odo h urs ou o be erl o he hrerzo of he Couro eulbrum s he follow. π π ;..9

9 9 Ths odo obously holds for ll ooex demd ures lud ler demd bu be oled f demd s ery oex. Codo.9 s lked o my roeres of he Couro model. Mos morly odo.9 mes h srey rbles d re sre subsues. If π hs mes he mrl lue π of res frm srey rble dereses whe he srey rble of rl reses. Lemm.. Suose h he os fuos d s we-ouously dffereble d oex for y ; he erse demd ure Q s we-ouously dffereble d derese for y Q ; ~ ~ he fuo Q s oe for y Q. The he hrd-mrke model wo-r rde oly: > >. Corollry.. α where α d β where β. As he bs model we shll osder he wo-se me wh omlee bu merfe formo. O he frs se he lyers d he home d fore oermes smuleously hoose her srey d form bou hem d - lyers home d fore frms whh o he seod se smuleously hoose her srey. I mes h eh frms mrl reeue deles s he ouu of y oher frm rses. I s he solled Hh sbly odo for er roosed dym dusme mehsms. oe howeer h he ure Couro model s oe-sho s me wh o rel-me dyms. Ay roosed dym dusme s exeso o he model. Presum h seod order odos re loblly ssfed lobl ssfo of.9 hs oex s lso he Gle-kdo odo for uueess of he Couro eulbrum. Codo.9 lso esures dl rous omre s roeres of he model re well-behed.

10 Les dese hrouh x e X x e X he srees of he frs d he seod lyer where X k R R R - se of srey k of he lyer k. Le x X ; - srey of - lyer d x X - srey of - lyer where X k R R - se of srey of k - lyer k. I f x ; f x ; f x π ; f π ; x X X X X X. x x The s ossble o defe he wo-se me ersos wh omlee bu merfe formo Г I{}{ X } I { f x} I > x x x x x x x x x x x x x x x x x x x x x x x x x x x x x The follow exsee heorem of sh eulbrum me Г s fr. Theorem.. Suose h he os fuos d s we-ouously dffereble res d oex for y ; he erse demd ure Q s we-ouously dffereble d derese for y Q ; ~ ~ he fuo Q s oe for y Q. Q h Q Q Q he me Г exss erfe subme sh eulbrum.

11 From he e heorem we e remrkble orollry. Corollry.. I he hrd-mrke model omum wo-r rff whh mxmzes he oerme s omes s ee subsdy d he omum yme for he lese s eul o flow sles roeeds of erl frm. Exmle.. model of he hrd mrke. Oe mrke wo oermes wo frms. The erse fuo of demd Q b Q. The oss fuos of home d fore frms: C ; C. For serh he omum wo-r rde oly we ly mehod of erse duo. Thus we osder rous ombos of ly or o ly he wo-r rde oles by dffere oermes. The ouomes re e Tb.. From he e exmle s sble h he omum wo-r rde oly s he subsdy he ose yme for he lese. If he wo-r rde oly s led oly by oe oerme s lso eessry o oe h he omum subsdy s resed beuse of de rele oss of eror frm. Frms whh eed hel omeo wh exeror frms rerese less re obes for subsdz from he o of ew of oerme. Besdes we see h hs se subsdy fores eror frm o more resse fuo of he bes swer h ur fores fore frm o rodue less. The omum eror subsdy moes frm o led Skelber ouu leel d fore subsdy mkes leel of he follower. The oerme oer h de h les he soluo frs o eule de of eror frm. The eror frm hs smulus for ee of rmry soluo whh hes sre ero bewee frms. If he wo-r oly s led by boh oermes mxmzo G k her omum oly sll wll be he subsdy he ose rff. Howeer se of mxmzo of welfre G k π k he me leel of oermes looks lke rsoers` dlemm mde s boh oures re he worse oso odo of sre eulbrum h free rde howeer eh hs smulus for deo from free rde. Les osder for exmle. wheher he omum wo-r rde oly of he Preo-oml wh rese o he oles of eh oerme GG.e. he se whe bewee oermes s rese olluso. I hs se we he he follow frs-bes ouome: -/ > whh rher dffers from he ddully rffs - - /5. For exmle f -/ GG- /8b>- /5b; π π; -/b; ee- /6b. Here he me lso hs he

12 rsoers dlemm flor he sese h olluso bewee he wo oermes would he resuled reer reeue for eh ssum eul dso of ol reeue h ddully rol oles.. Two-r rde oly model of he rerol mrkes wh homoeeous sruure of os fuo. I hs se с d с. The eoom resul of he frms y s deermed by he oseue fuos of rof: π Q Q e... π Q Q e....8 Where e e - yme for he lese o home d fore oerme ordly; - he rff er u of roduo mosed o home d fore frms ordly. Lemm. : If C > > > ; C > > > ; Q Q C ; Q Q Q Q ; Q Q Q ; Q Q Q ; Q Q ; Q Q ;... ;... he he model of he rerol mrkes uder he wo-r rde oly he odo re exeued: > ; > ; > ; > ; for... ;... The more of hs Lemm.. s h for he rerol-mrkes model esblshes ery mor feure: «he mor rffs of he wo-r rde oly redue he leel of erl sles of exerl frms d rese domes sles of erl frms». Thouh he e f s kow bu for he model uder osdero s ew. From he roed Lemm.. s lso esy o e: Corollry.. α where α d β where β.

13 .. Poly of mxmzo of he oermel omes. The uroses of oerme re defed by fuos. { } G - ome of home oerme.5 { } G - ome of fore oerme.6. The e ye of oerme we shll lled G- ye. For he oermes of G-ye he leel of omum wor rde oly s defed by he odos of euly o zero of he ome from sles of fore frms. As he bs model we shll osder he wo-se me wh omlee bu merfe formo. O he frs se he lyers d he home d fore oermes smuleously hoose her srey d form bou hem - lyers -home d - fore frms whh o he seod se smuleously hoose her srey. Les dese hrouh x e ~ X x e ~ X he srees of he frs d he seod lyer where X k R R R - se of srey k of he lyer k. Le x X ; - srey of - lyer... d x X - srey of - lyer... where X k R R - se of srey of k - lyer k. I f x G ; f x G ; f x π x... ; x x f π... ; x x X X X X... formo The s ossble o defe he wo-se me ersos wh omlee bu merfe Г I{ }{ X } I { f x} I >

14 e~ e~ The follow exsee heorem of sh eulbrum me Г s fr. Theorem.. If C > > > ; C > > > ; Q Q C ; Q Q Q Q ; Q Q Q ; Q Q Q ; Q Q ; Q Q ; 5 Q h Q Q Q ; Q h Q Q Q... ;... he me Г exss erfe subme sh eulbrum. From he e heorem we e remrkble orollry. Corollry.. I he homoeeous se for omum wo-r rff whh mxmzes he oerme s omes s ee subsdy d he omum yme for he lese euls o he urre of fore frm. Les osder orl exmle of he wo-r omum rde oly. Exmle.. Two mrkes wo oermes wo frms. The erse fuos of demd he home d fore mrke Q -Q re kow; Q -Q. Fuos of oss of home d fore frms: C /; C /.

15 The fuos of frms rof d he fuos of he ome of oermes re defed uder he formuls.8.5 d.6. I ould be redly erfed h hs modell exmle he odos of Lemm. d Theorem. re rred ou. So he omum ou us of frms deed o leel of wo-r rff: Thus of yoff fuo of oermes: G ; ; G Fuos re ouous d oe by d ordly. Thus he omum rff: ;. 6 6 Thus omum ouu of frms hs leel he uos ; re lso esblshed: ; 6 ; 6 ; 6 6 The omum yme for he lese: e 6 6 C 6 > ; 6 6 e C 6 >. The exmle shows h he omum wo-r oly se of wo oures wo oermes d wo frms s he subsdy he ose yme for he lese. Thus suh oly eoures frms o exor reer h eror ouu leel.

16 6.. Poly of mxmzo of he domes welfre. The uroses of oerme re defed by fuos. Q s ds W с. - domes welfre of home oury. W Q s ds с. - domes welfre of fore oury. The e ye of oerme we shll lled W- ye. I hs se oerme mxmzes domes welfre oss of he sum of exess of he usomer rof of erl frm d s ow omes from he x. For he oermes of W ye he leel of omum wo-r rde oly s defed by he odos of euly o zero of he ome from sles of fore frms. As he bs model we shll osder he wo-se me wh omlee bu merfe formo. O he frs se he lyers d he home d fore oermes smuleously hoose her srey d form bou hem - lyers -home d - fore frms whh o he seod se smuleously hoose her srey. Les dese hrouh x e ~ X x e ~ X he srees of he frs d he seod lyer where X k R R R - se of srey k of he lyer k. Le x X ; - srey of - lyer... d x X - srey of - lyer... where X k R R - se of srey of k - lyer k. I h x W ; h x W ; h x π x... ; x x h π... ; x x X X X X... formo The s ossble o defe he wo-se me ersos wh omlee bu merfe Г W I{ }{ X } I { h x} I >

17 e~ e~ The follow exsee heorem of sh eulbrum me Г s fr. Theorem. : If C > > > ; C > > > ; Q Q C ; Q Q Q Q ; Q Q Q ; Q Q Q ; Q Q ; Q Q ; 5 Q что Q Q Q ; Q что Q Q Q... ;... he me Г exss erfe subme sh eulbrum. Proof s reseed he Aedx. Les osder orl exmles of he wo-r omum rde oly. ow we shll osder exmles whh ofrm exressed before hyohess. We mke he omre lyss of ouomes of exmles...6. See. Alo d before he obed ouomes Fuers d Km 99. All ouomes we shll oe he ble.:

18 8 Tb.. Melk V.. Fuers & Km Z G Z G Z W Z W Z G Z G Z W Z W low subsdy subsdy subsdy subsdy subsdy - subsdy - hh subsdy subsdy subsdy subsdy subsdy - subsdy - low subsdy subsdy subsdy subsdy rff - subsdy - hh subsdy subsdy subsdy rff > rff - subsdy - low rff > subsdy subsdy subsdy rff > - subsdy - hh subsdy subsdy subsdy rff > rff > - subsdy - low subsdy subsdy subsdy subsdy hh subsdy subsdy subsdy subsdy low subsdy subsdy subsdy subsdy hh subsdy subsdy subsdy subsdy From he ble s sble h for he osdered exmles A subsdy er boh for G-oerme d for W-oerme more ofe d uder oher odos h Fuers d Km99 models d deeds o dfferee mo fore d home frms d from os lue. For G-oerme whe ll frms he hh oss deedely of umber of frms he mrke he oml oly s subsdy; A erl oerme se of G he oml oly er by he wy of ose rff whe ll frms he low oss d umber of exerl frms s more erl frms o or more. Thus he oml oly of exerl oerme wll be lwys subsdy; A erl oerme se of W he oml oly wll be lwys subsdy f s more erl frms h he mrke h exerl frms. Thus he oml oly of exerl oerme wll be subsdy low oss d ose rff hh oss. I se of euly of umber of frms he mrke he oml oly s lwys subsdy. Here lbel - mes h hs se ws o lyss Fuers & Km99 Geerlly resuls o reee ery dffully

19 9 I exmles. d. wh rese of rmeer с he lue of he oermel ome he be wll rese he exese of he reer lue of he subsdy hese oss of oerme omese by hh ose yme for he lese d he he ome dereses s he oss of frms wll rese so h he oermes o omese oss o subsdz by yme for he lese. I hs se ll he frms he del os sruure reeue-mxmz oerme uses s wo-r srey o eoure he exeror frms o behe s moolh Skelber leder he seod se of me. Ths mles h he reeuemxmz er u of fee s eher ee whe he os fuos of frms re hh y mou of frms or ose whe he os fuos of frms re smll d umber of exeror frms lre. These smulus re modfed se of oerme W h lso s oered wh osumer surlus. I rulr welfre-mxmz oerme wll lwys hoose ee er u fee subsdy o smule ol roduo. Ths suo s ossble hh yme for he lese. Thus f he os fuos of frms re hh eror d exeror he er u of fee of eror frm s ose he eror frms do o buy he lese. I ddo for exmle.6 he se s osdered wheher he omum wo-r rde oly of he Preo-oml oer summrzed welfre WW.e. he se whe bewee oermes s rese olluso. I hs se we he he follow frs-bes ouome: -.85 whh lle b dffers from he ddully oml rffs -.95 hs se WW.55. Besdes hs se whe bewee oermes s rese olluso WW.55>.55;.9.86;.86.9; e e.6. Here he me lso hs he rsoers dlemm flor he sese h olluso bewee he wo oermes would he resuled reer summrzed welfre for eh h ddully rol oles.. Two-r rde oly model of he rerol mrkes wh homoeeous sruure of os fuo. I hs se ll he fuos of oss re dffere d we o redue he rff he exese of res he yme for he lese beuse he frms wh hh oss fll ou of he mrke f he yme for he lese s hh. If d re exreme frms h s he frms wh umbers d he ee rof he omum wo-r rde oly z e z e.

20 .. Poly of mxmzo of he oermel omes. I hs se yoff fuos of oermes: с I G.8 с I G.9 where I I - leel of mor home d fore oury ordly. The omum oly s defed by omzo o d. I hs model he omum oly of oerme wll lso deed o deree of oexy d deree of heeroeey of fuos of oss. The exmle shows h he omum wo-r oly se of wo oures wo oermes d wo frms s he subsdy he ose yme for he lese. Thus suh oly eoures frms o exor reer h eror ouu leel. Furher we shll osder exmles for homoeeous se... Poly of mxmzo of he domes welfre. I hs se yoff fuos of oermes: с I ds s W I. с I ds s W I. where I I - leel of mor home d fore oury ordly. The omum oly s defed by omzo o d. I hs model he omum oly of oerme wll lso deed o deree of oexy d deree of heeroeey of fuos of oss. The exmle shows h he omum wo-r oly se of wo oures wo oermes d wo frms s he subsdy he ose yme for he lese. Thus suh oly eoures frms o exor reer h eror ouu leel.

21 Codued exmles.8-. lyss llows o se more dee d ew ouomes h Fuers &Km99 for homoeeous se. Besdes ow s ossble o odu he omre lyss of ouomes exmles.8-. see lo. All ouomes we shll bule.: Tb.. Melk V.. Fuers & Km Heeroe ey Z G Z G Z W Z W Z G Z G Z W Z W Low subsdy subsdy subsdy subsdy rff - rff - mddle subsdy subsdy subsdy subsdy rff - rff - hh subsdy subsdy rff subsdy subsdy - subsdy - Here rmeer - edoeous From he ble s sble h for he osdered exmles 5 For G-oerme y deree of heeroeey he erl oerme wll esblsh he hh yme of ere for exerl frms before h s he oly wll be reled from subsdy wh ose rff.e. he oml oly wll be lwys subsdy. For W-oerme he suo s smlr exe for se whe umber of exerl d erl frms s eul o oe d he oss of erl frms exeed oss of exerl frms he he oml oly of erl oerme s ose rff. 5. Modfed wo-r rde oly. I he work of Melk for he smler models ws offered o eer rmeer τ- rff for he lol roduer hoe h olooly se wll resul he subsdy. For oerme suh s G- ye he rff ured o be ose. For oerme suh s W-ye hs relly resuled he subsdy τ. Moreoer here wll be re umber of he wo-r oles s for he omum rffs odo mus be obsered: τ h es home oerme ddol ools of reul. Here lbel - mes h hs se ws o lyss Fuers & Km99 5 Geerlly resuls o reee ery dffully

22 We shll use hs effe. I s offered o ly he wo-r rde oly o oly o fore bu lso o lol frms e ~ ~ τ ~ ~ e τ. The modfed wo-r rde oly hus s defed ~ z e e ~ ~ τ ~ ~ z e e ~ τ. Thus he e rde oly eerlzes my exs rde oles: ~ z - free rde; ~ z - smle rff; ~ z e - smle uo; ~ z e - wo-r rde oly o fore frm; 5 ~ z τ τ - subsdz of exor; 6 ~5 z e ~ ~ - olury exor resro; ~6 z e ~ ~ τ - wo-r rde oly o home frm; 8 ~ z e ~ ~ τ τ ~ e > - exor red subsdes. Thus he yoff fuos of frms re hed: ~ π Q Q e τ e~ ~ π e ~ Q Q e τ ~ G 5.. Poly of mxmzo of he oermel omes. I hs se yoff fuos of oermes: { } { τ } { } { τ } ~ G τ - ome of home oerme 5. τ - ome of home oerme 5. The hyohess s ded h se oerme of mxmzes s ome he modfed wo-r rde oly wll o be he subsdy y odos. These des re bes llusred he oex of oree exmles. Exmle 5.. Les ssume re kow erse demd fuo he home d fore mrke d os fuos of frms: Q b Q Q ; Q Q b Q ; > > b > b > C d ; C d. I hs se oml modfed wo-r rde oly s defed by odos: > ; > ; 5.5

23 ; b b ; b b b b ;. 5.6 b b G 8d b b ; G 8d b b. Prooso 5... I se of ler os fuos d ler erse fuos of demd here s fely my oml modfed wo-r rde oly mxmz he oermel omes. Thus he se s ossble whe he eror roduo leel re o eul o zero d he se of he subsdy s mossble. Proof. As we he fe umber of soluos of he euos 5.5 here s fe umber oml modfed wo-r rde oly mxmz he oermel omes. Le subsdy he from 5.5 > d fromа 5.6. Bu he roduo leel o be ee he.e. b he subsdy s mossble. Exmle 5.. We shll ssume h odos of exmle 5.. here s еру olluso bewee oermes whh mxmze ommo summrzed ome G G. Besdes le b b. I hs se we ob ouome omleely oermous wh ouome of exmle 5... I hs se: > ; > ; b b ; ; b b b b ; ; b b 8d b G ; b G 8d b. b Thus s fr: Prooso 5... I se of del os fuos d del ler erse fuos of demd he modfed wo-r rde oly mxmz he oermel omes es he Preo omum ouome oer he o ome. Corollry. I se of ler os fuos d ler erse fuos of demd oml modfed wor rde oly mxmz he oermel omes domes o oher rde oly srumes. 5.. Poly of mxmzo of he domes welfre. The uroses of oerme re defed by fuos.

24 Q s ds W с 5. - domes welfre of home oury. W Q s ds с domes welfre of fore oury. I se of mxmzo of domes welfre he modfed oly s he subsdy. Exmle 5.. Les ssume re kow erse demd fuo he home d fore mrke d os fuos of frms: Q b Q Q ; Q Q b ; > > b > b Q > C d ; C d. I hs se oml modfed wo-r rde oly s defed by odos: ; ; 5.9 b ; ; b ; b. 5. b W d b b ; W d b b. Prooso 5.. I se of ler os fuos d ler erse fuos of demd here s fely my oml modfed wo-r rde oly s he subsdy mxmz he domes welfre. Thus he se s ossble whe he eror roduo leel rereses he omee ouome. Proof. As we he fely my of soluos of he euos 5.9 here s fely my oml modfed wo-r rde oly mxmz he domes welfre. Le > he from 5.. Bu roduo o be ee he. Aloously. From 5.9 follows h d o eul o zero smuleously.е. oml modfed wo-r rde oly s subsdy. Exmle 5.. We shll ssume h odos of exmle 5.. here s еру olluso bewee oermes whh mxmze ommo he domes welfre W W. Besdes le b b. I hs se

25 5 we ob ouome omleely oermous wh ouome of exmle 5... I hs se: ; ; ; b ; b b ; b W d b ; b W d b. b Thus s fr: Prooso 5... I se of del os fuos d del ler erse fuos of demd he modfed wo-r rde oly mxmz he domes welfre es he Preo omum ouome oer he o domes welfre. Corollry. I se of ler os fuos d ler erse fuos of demd oml modfed wor rde oly mxmz he domes welfre domes o oher rde oly srumes. 6. Choe of rde oly srumes. A he frs leel oermes oue rde oly d o he seod- home d fore roduers behe s Couro omeors. Les osder hree se me. A he frs leel oermes oue rde oly srume o he seod oermes se oree lue of rmeers of hs rde oly d o he hrd- home d fore roduers behe s Couro omeors. O frs se of oerme hoose he follow oles: ~ z - free rde; ~ z - smle rff o exeror frm; ~ z - smle rff o erl frm; ~ z - smle rff o exeror d erl frms; 5 ~ z e - wo-r rde oly; 6 ~ z e - modfed wo-r 5 rde oly. Iero of rde oly srumes -6 we shll osder o exmles. Exmle 6.. Les ssume re kow erse demd fuo he home d fore mrke d os fuos of frms: Q Q Q ; Q Q ; C. ; C. Q. Thus he oermes mxmze domes welfre. Oml rde oles for eery ossble ombos of hoes of oermes we redue he ble 6.

26 6 The lyss of he ble 6. shows h oml rde oly wll be wo-r rde oly or modfed wo-r rde oly. For se ~ ~ z here s fely my of oml rde oles d s defed by 5 z 5 odos. 9 ;. 9 for hs se he ble 6. oe of ossble rs s refleed oly. Two-r rde oly d modfed wo-r rde oly re eule oer mxm of domes welfre. Howeer he modfed wo-r rde oly he yme for he lese s muh lower d he rof s ds from zero. Prooso 6. I se of oler os fuos d ler erse fuos of demd modfed wo-r rde oly mxmz he domes welfre domes o oher rde oly srumes. The roof of he e seme s o rese. Le s llusre he e rooso by exmle. Exmle 6.. Les ssume re kow erse demd fuo he home d fore mrke d os fuos of frms: Q Q Q ; Q Q Q ; C. 5 ; C. 5. Thus he oermes mxmze domes welfre. Oml rde oles for eery ossble ombos of hoes of oermes we redue he ble6.. The lyss of he ble 6. shows h oml rde oly wll be modfed wo-r rde oly. A he modfed wo-r rde oly he rof of frms yme s more d he mrke re of he oods s lower h for oher srumes.. Coluso Wh s he omum mx of rde oly srumes? I he reor he ossbly of smuleous use by he oerme of uos d orresod Lese fees d rffs s lyzed. The use of uos d rffs s omlemes rher h subsues llows o rry ou rde oly whh domes from he effey o of ew - oer oly bsed o ohers rde oly srumes. The ule ouomes of he lyss deed o he ye of oerme wheher mxmzes s reeue or ubl welfre mrke sruure d he os sruure of frms oer he mrke. The reor lyses he roblems of relzo of he se wo-r rde oly se of wo oures wo mrkes my roduers odos of merfe omeo.

27 We he show h he wo-r rde oly domes he smle uo d smle rff d he ls wo meoed re he sel ses of. Thus he effeeess of he wo-r rde oly deeds o he umber of ome frms o he mrke mude of heeroeey of fuos of oss derees of oexy of fuos of oss d hus o wh frms he e oly wll be led d he oermes of whh oures wll exeue he oly. I he be we he show h for he hrd-mrke model he oml wo-r rde oly s subsdy. For hs se he lyl resuls Lemm. d Theorem. re obed. I hs r we esed subsl sese of roeres of os fuos d erse demd fuos whh defe exsee of oml rde oly. I model of he rerol mrkes wh homoeeous sruure of os fuos he odos of exsee of oml rde oly s for se of mxmzo of he oermel ome Theorem. d for se of mxmzo of he domes welfre Theorem. re foud. All hese resuls re llusred wh se of exmles. For homoeeous se we he esblshed h A subsdy er boh for G-oerme d for W-oerme more ofe d uder oher odos h Fuers d Km models d deeds o dfferee mo fore d home frms d from os lue. For G-oerme whe ll frms he hh oss deedely of umber of frms he mrke he oml oly s subsdy; A erl oerme se of G he oml oly er hrouh ose rff whe ll frms he low oss d umber of exerl frms s more h erl frms o or more. Thus he oml oly of exerl oerme wll be lwys subsdy; A erl oerme se of W he oml oly wll be lwys subsdy f here s more erl frms h he mrke h exerl frms. Thus he oml oly of exerl oerme wll be subsdy low oss d ose rff hh oss. I se of euly of umber of frms he mrke he oml oly s lwys subsdy. I model of he rerol mrkes wh homoeeous sruure of os fuos o he bss of umerl model ke Mle we he esblshed h : For G-oerme y deree of heeroeey he erl oerme wll esblsh he hh yme of ere for exerl frms before h s he oly wll be reled from subsdy wh ose rff.e. he oml oly wll be lwys subsdy.

28 8 For W-oerme he suo s smlr exe for se whe umber of exerl d erl frms s eul o oe d he oss of erl frms exeed oss of exerl frms he he oml oly of erl oerme s ose rff. We he lysed lso ee se of he wo-r rde oly whh osss of he f h odos of rsol eoomy he e oly hs ee oseuee for he erl roduers. I he frs le fll he derese of erl roduo whe oly oe oerme us wo-r rff. Is worh remd h oerme whh mxmzes omes eoures mor frms o rodue Skelber ouu leel. Ad se of mxmzo of domes welfre we he omee ouome bu wh os shr reduo of erl roduo d oseuely by reer deedee of oury o exor. The modfed wo-r rde oly ludes ly he wo-r rde oly o he erl roduers s well h se of olooly hs redued he subsdy s well s for he fore roduers. I se of mxmzo of oerme omes he modfed wo-r rde oly s o he subsdy y odos houh he roeo of he domes roduer s ossble hs se. I se of mxmzo of domes welfre he modfed oly s he subsdy. The resuls of omrso of rde oly srumes show h he modfed wo-r oly s dom. The wo-r rde oly s osdered for Berrd omeo. There re wo oures oe home oher fore. There s oe home d oe fore frm. Le - re of he oods frm o he home mrke; Le - re of he oods frm he fore mrke; The mrke demd fuo s d he home d fore mrke. Eh frm urs os с er u of roduo с. Therefore he rof of frm s e с π e с π where he demd for he ouu of frm deoed s e by > f f f ; > f f f ;

29 9 e e - yme for he lese o home d fore oerme ordly; - he rff er u of roduo mosed o home d fore frms ordly. The yoff fuos of oermes re defed smlrly of formuls. d.5. Beuse of mrke semeo d beuse of he osy of mrl os we roeed by exm us oe ol mrke. The π с e π. Lemm 5. I e Berrd model oml wo-r oly s he ose rff m f m f > m where m mxmzes. The oml oly e Berrd model dffers from oml oly Couro model. So Couro model for se of wo frms oml wo-r oly lwys ws subsdy whh wh rowh of umber of frms ssed he ose rff. I Berrd model for se of wo frms s oml oly we he he ose rff o subsdy. He wo-r rde oly ully bee used he erol rde? He bee used he mrke sruures lyzed he roe? The swer s yes. There s defed umber of exmles of use of suh oles: Two-r rffs TPT I s se of wo-r rde oly z e Two-r rffs re r shemes h ole fxed fee whh mus be d o osume y mou of ood d he rble fee bsed o use. Two-r rffs re ommoly used re. Tble TPT es few exmles: Tble TPT. Fxed remum Chre ry ord o Telehoe s elery Rel umber of us Polrod mer Cmer urhse Amou of flm Amuseme rk Входной билет umber of rdes Tx Il meer red se

30 I erol rde he wo-r rff s used by oermes o suh frms: he sulers of he eler ower seres of ellulr oeo Iere of seres seres of rsor. Trff-re uo TCR I s se of wo-r rde oly z A rff-re uo s uo for olume of mors lower rff. Afer he uo s rehed hher rff s led o ddol mors. Suose oury reles s uo of os wh TRQ of os. The TRQ ers o dffer from he bsolue uo. The dso s h uder bsolue uo s lelly mossble o mor more h os wheres uder TRQ mors exeed os bu hher oer-uo rff s led o he exess. I rle TRQ rodes more mrke ess o mors h uo. I re howeer my oer-uo rffs re rohbely hh d effeely exlude mors exess of he uo. I s ossble o des TRQ so h rerodues he rde-olume lm of he uo reles. Trff-re uos TRQs re wo-leel rffs. TRQs were doed dur he Uruuy Roud s mehod for rod reer ess o mrkes wh hh rffs. A lmed olume of mors s llowed he lower rff d ll subseue mors re hred he hher rff. If he demd for mors he low rff s reer h he olume llowed by he TRQ he mors mus be roed. A TRQ hs hree omoes: - uo h defes he mxmum olume of mors hred he -uo rff - -uo rff d - oer-uo rff. The wo-leel rff resuls seed mor suly fuo. Imors wh he uo re hred he lower rff; oer-uo mors re hred he hher rff. Ths resuls erl se whe he uo olume s flled. The fure llusres se whh domes demd s suffe o mor he full uo olume he uo rff bu he oer-uo rff s rohbe. Th s he domes re s below he re of mors wh he oer-uo rff hus here s o ee o mor beyod he uo. Were domes demd o rese mh beome rofble o mor he oer-uo rff. Ths ooruy would o be ossble wh sdrd bsolue uo. TRQ dmsro oles dsrbu he rhs o mor he -uo rff. Whoeer obs suh rhs mke rsk-free rof of he dfferee bewee he domes re d he world re luse of he -

31 uo rff. The re lbeled RET he fure rereses he lue of hese rofble oorues. Res de h he demd o rde wh he uo s reer h he suly of uo; hus he eessy o ro or dmser he TRQ. World re Oer-uo rff Trff-re uo omes re World re -uo rff RET I-uo rff Oeruo rff World re Quo Imor olume Whh oures he TRQs? Of he WTO members oures ermely use TRQ s. The oures wh he rees umber of TRQs re oered mo relely welhy eoomes wh hsorlly roeos rulurl oles. I ddo seerl Cerl d Eser Euroe oures he doed TRQs o ese he rso of her rulurl seors o mrke-oreed eoomy. Trff uo dmsro s fudmelly ro roblem. The ssue for TRQ dmsro s o deerme wheher some wys of ro re beer h ohers. The follow exmle s osdered: Russ Threes Trff d Quo Hkes h llusre he heorel r of sudy: Me d oulry exorers o Russ fe hey rffs ex yer f ls by he Russ Arulure Msry ome o fore. The msry hs sd eds o rse mor rffs s roee mesure d mose mor uos o beef ork d oulry. The msry sd he mesures re med o roe he domes dusry from dum of he mors. The rffs ome s r of he Russ relo o r uos h he bee mosed by he EU d whh re exeed o effe exors from Russ.

32 I s beleed h he ew rff o ork wll be se 8 er e omred o he rese 5 er e. O beef he rff wll rse from 5 er e o 5 er e d o oulry from 5 er e o 5 er e. The uos h re be roosed would lm mors of ork o Russ o oes beef oes d oulry 5 oes. Ls yer Russ mored 8 oes of ork of whh 5 oes me from he EU mly from emrk wh some from Germy Fre d he eherlds d 6 oes om from he US. Russs ork mors moued o urer of he ourys ow ouu Russ lso mored 5 oes of beef d.9 mllo oes of oulry me. Below he ble. he omre lyss o he oulry me for d omum wo-r oly wh resuls of he smle rff of s e. Poulry me Tb. Smle rff Trffuo Trffuo oml 5% 5%5 5% Home ouu 56 58% 5% Imor 9 5-6% -59% Goerme reeues 6-6% 8 6% Pyoff of home frm 586% 8 % Pyoff of fore 6 5-5% 6-6%

33 frm Pre % % The meoed boe rl exmles of sre rde oles sek bou ul of he heorel resuls obed he roe. 8. The bblorhy. Aderso Jmes E. The Rele Ieffey of Quos. The MIT Press 988. Bhw Jdsh. O he Eulee of Terffs d Quos. I Rober E. Bldw e l. es Trde Growh d he Ble of Pymes: Essys Hoor of Gofred Hberler. Cho: Rd Mlly 965. Brder J A. d B. J. Seer 98. Trff roeo d merfe omeo : H. Kerzkowsk ed. Moools Comeo d Ierol Trde Oxford Clredo Press. Brder J. A.. d B. J. Seer 98b Trde wrfre: Trffs d rels J. ofll Eo Css J.H. d A.L.Hllm Poll Ifluee Moes d he Choe bewee Trffs d Quos Jourl of Ierol Eooms Cooer R. d R. Rezm 989 Uery d he hoe of rde oly olools dusres. Reew of Eoom Sudes

34 Corde W. M. The Theory of Proeo. Oxford: Clredo Press. 9 x A. K. 98 Ierol rde oly for olools dusres Eoom J. 9 suleme - 6 x A. K. 988 Oml rde d dusrloly for he U.S. uomoble dusry : Feesr R. 988 ed. Cmbrde Cmbrde Uersy Press. Eo Joh d Gee M. Grossm Oml Trde d Trde Poly uder Olooly Qurerly Jourl of Eooms Fuers Tmohy S. d Km Kyoo H. Two - Pr Trde Poly uder Imerfe Comeo Reew of Ierol Eooms 5 99 :6- Gude Gerrd d Sl Sehe W. Uueess of Couro Eulbrum: ew Resuls from old mehods Reew of Eoom Sudes Hrrs R. 985 Why olury exor resrs re olury Cd J. of Eo Hw H.. d C. M 988 O he eulee of rffs d uos uder duooly: A oeurl ro roh J. of Il Eo Ishkw J. 99. Rk lere rde-resr oles uder erol duooly J d he World Eoomy Ioh M. d Y. Oo 98 Trffs s. uos uder duooly of heeroeeous oods J. of Il Eo Kemfer Wllm H. J.Hrold MClure Jr. d Thoms. Wlle Iremel Proeo d Effe Poll Choe bewee Trffs d Quos Cd Jourl of Eooms My Krsh Kl Trde Resros s Fl Pres. Jourl of Ierol Eooms Krsh. K Trde resros s fl res J. of Il Eo Melk V.. Ime Modell he eso Mk Theory uder Uery// Вестник Псковского Вольного университета. Математика и информатика - Псков: Псковский Вольный ун-т вып C.8-8.

35 5 O. Wler Y. A seyld lemm: Two-Pr Trffs for Mkey Mouse Moooly Qurerly Jourl of Eooms Phls Lous The Eooms of Pre srmo. Cmbrde Uersy Press 98. Res J. 99 Volury exor resrs rofs d uly dusme. Cd J. of Eo. -. Res. J. 99 Wdfll rof d erl reloshs: Who ed he Jese uo dusry from VERs? J. of Idusrl Eo Roember Julo J. d Grh Sloer Trffs d Quos wh Iml Colluso Cd Jourl of Eooms My Roussl. d Suomel A. Clul he Cosumer d e Welfre Cos of Imor Relef. U.S. Ierol Trde Commsso Sff Reserh Sudy 5. Wsho.C.: Ierol Trde Comsso 985. Wlso Rober B. oler Pr. Oxford Uersy Press 99. Ларбани М. Мельник В.Н. Существование равновесие Нэша-Слейтера// Сложные управляемые системы: Сб. науч. трудов.м: РосЗИТЛП 996 с.6-9. Мельник В.Н. Модифицированная двухчастная торговая политика // Вестник Псковского Вольного университета. Математика и информатика - Псков: Псковский Вольный ун-т вып. - C.-8. Proof of Lemm..: 9. Aedes. The roofs of he heorems. The soluo o he frs order odos.5.6 wll yeld d s fuos of rffs d. The omre s effes be obed by olly dffere frs order odos. wh rese o s follows.

36 6 π π π π. d π π π π. These euos be soled us Crmer s rule: π ; π ; π ; π where π π π π s he deerm of he lef-hd mrx. d.. From.8 d.9 >; > >.. Proof of Corollry..: Le ~ d ~ be domes frm s bes resose d fore frm s bes resose. By he frs-order odo α ~. The us odos - of Lemm.. we e α. ex we he h ~ α. I s smlrly roed h β where β. Tb.. Home oerme z free rde e z wo-r rde Fore oerme z free rde G π- /9b; G π- /9b; -/b;-/b; ;;e;e; G- /8b π; G π- /6b; -/b;-/b; --/;e- /b;e;

37 z e wo-r G π- /6b; G- /8b π; -/b; -/b; ; --/b; e; e- /b; G- /5b π; G- /5b π; -/5b -/5b; --/5--/5; e- /5b;e- /5b; Exmle.. homoeeous se Two mrkes wo oermes se of G d hree ses: wo frms ; hree frms ; four frms ; my frms. Ierse fuos of demd he home d fore mrke: Q-Q; Q-Q; he oss fuos of home d fore frms: C /; C /. Ouomes of omum oly for rous lues of rmeer.. were smuled Mle d re llusred o he rhs: ome of home oerme ome of fore oerme oml wo-r rff of home oerme oml wo-r rff of fore oerme

38 8 Exmle.. Two mrkes wo oermes se of G d hree ses: wo frms ; hree frms ; four frms ; my frms. Ierse fuos of demd he home d fore mrke: Q-Q; Q-Q; he oss fuos of home d fore frms: C /; C /. Ouomes of omum oly for rous lues of rmeer.. were smuled Mle d re llusred o he rhs: oml wo-r rff of home oerme & oml wo-r rff of fore oerme ome of home oerme & ome of fore oerme Exmle.5. Two mrkes wo oermes wo frms. All rmeers re smlr o Exmle. exe for elmo с5 for smlfo of he omre lyss. The omum oles for dffere ombos of hoes of oermes re e Tb... Home oerme Tb... z z z e free rde smle rff wo-r rde Fore oerme z free rde G; π85; G; π85; 5; 5; 5; 5; G; π89; G; π9; 85; 5; 5; 5; G6; π665; G; π58; 86;9; 95;9; ; e; ; e; -85;e6; ; e; ; e; ;e;

39 9 G; π9; G8; π6; G6; π; G; π89; G8;π6; G8;π59; z 5;5; 8;6; 5;; smle rff 85;5; 8;6; 8;68; ;e; 8;e; -5;e9 ;e; 8;e; ;e; G; π58 G8; π59; G68; π9; G6;π665; G6; π; G68; π9; z e wo-r rde 95;9; 86;9; 8;68; 5;; 5;; ;5; ;e; ;e9; -55;e6; -85;e6; -5;e; -55;e6; The osdered exmle s lso ew s s rodued for he frs me for he wo-r rde oly se of wo oures d wo mrkes houh s omred o kow resuls for se of free rde d smle rff. The referees re o sefed s he e ouomes were obed by he uhor s sel se of he wo-r rde oly. From he e exmle s sble h he omum wo-r rde oly s he subsdy he ose yme for he lese. From he e exmle s sble h omum wo-r rde oly s he subsdy he ose yme for he lese. If he wo-r rde oly s led oly by oe oerme he omum subsdy of exeror frm moes o he led Skelber ouu leel d he eror frm s moed o he leel of he follower. Thus he ome of oerme he wo-r oly s he lres. If he wo-r oly s led by boh oermes mxmzo Gk her omum oly sll wll be he subsdy he ose rff. Howeer se of mxmzo of welfre Gk π k he me leel of oermes looks lke rsoers` dlemm mde s boh rodu oures re worse off he sre subsdy eulbrum h hey would be uder free rde bu eh hs

40 ulerl ee o eree. Thus hs deo oes o o he smle rff d o he wo-r rde oly whh obously domes boe he smle rff. Les osder for exmle.5 wheher he omum wo-r rde oly of he Preooml wh rese o he oles of eh oerme GG.e. he se whe bewee oermes s rese olluso. I hs se we he he follow frs-bes ouome: -.85 whh rher dffers from he ddully wo-r rffs -.55 GG.68. I se whe bewee oermes s rese olluso GG.85> ;..65;e e.9. Here he me lso hs he rsoers dlemm flor he sese h olluso bewee he wo oermes would he resuled reer reeue for eh ssum eul dso of ol reeue h ddully rol oles. Exmle.6. Two mrkes wo oermes se of W d hree ses: wo frms ; hree frms ; four frms ; my frms.. Ierse fuos of demd he home d fore mrke: Q-Q; Q-Q; he oss fuos of home d fore frms: C /; C /. Ouomes of omum oly for rous lues of rmeer.. were smuled Mle d re llusred o he rhs: domes welfre of home oury domes welfre of fore oury

41 Exmle.. Two mrkes wo oermes se of W d hree ses: wo frms ; hree frms ; four frms ; my frms.. Ierse fuos of demd he home d fore mrke: Q-Q; Q-Q; he oss fuos of home d fore frms: C /; C /. Ouomes of omum oly for rous lues of rmeer.. were smuled Mle d re llusred o he rhs: oml wo-r rff of home oerme & oml wo-r rff of fore oerme domes welfre of home oury & domes welfre of fore oury Exmle.8. homoeeous se Two mrkes wo oermes se of G d hree ses:: wo frms ; hree frms ; four frms ; my frms. Ierse fuos of demd he home d fore mrke: Q-Q; Q -Q; he oss fuos of home d fore frms: C /..; C /..

42 .... Here rese of rmeer redues derese of heeroeey of oss fuos. Ouomes of omum oly for rous lues of rmeer.. were smuled Mle d re llusred o he rhs: ome of home oerme ome of fore oerme oml wo-r rff of home oerme oml wo-r rfff of fore oerme As homoeeous se work Fuers d Km ws osdered oly oe umerl exmle for he uroses of omrso wh our model we shll odu more ou of models Fuers d Km for he reer umber of ses for dffere C d Exmle.9. homoeeous se Fuers d Km Oe mrke oe oerme se of G d hree ses: wo frms ; hree frms ; four frms. Ierse C.

43 fuos of demd he home d fore mrke: Q-Q; Q -Q; he oss fuos of home d fore frms: C /..; C /.. 9. Here rese of rmeer redues derese of heeroeey of oss fuos. Ouomes of omum oly for rous lues of rmeer.. 5 were smuled Mle d re llusred o he rhs: ome of home oerme oml wo-r rff of home oerme Exmle.. homoeeous se Two mrkes wo oermes se of W d hree ses: wo frms ; hree frms ; four frms. Ierse fuos of demd he home d fore mrke: Q-Q; Q -Q; he oss fuos of home d fore frms: C /..; C / Here rese of rmeer redues derese of heeroeey of oss fuos. Ouomes of omum oly for rous lues of rmeer.. 8 were smuled Mle d re llusred o he rhs:

44 oml wo-r rff of home oerme oml wo-r rff of fore oerme As homoeeous se work Fuers d Km ws osdered oly oe umerl exmle for he uroses of omrso wh our model we shll odu more ou of models Fuers d Km for he reer umber of ses for dffere C d C. Exmle.. homoeeous se Fuers d Km Oe mrke oe oerme se of W d hree ses: wo frms ; hree frms ; four frms. Ierse fuos of demd he home d fore mrke: Q-Q; Q -Q; he oss fuos of home d fore frms: C /..; C /.. 9. Here rese of rmeer redues derese of heeroeey of oss fuos. Ouomes of omum oly for rous lues of rmeer.. were smuled Mle d re llusred o he rhs:

45 5 Tble 6. z z z z ~ z ~ z W.6W e ---e --- π.8π.8.. W.W e ---e --- π. π..8. W.W e ----e --- π.π W.W e ---e --- π.π... W.6W e ---e ---- π. π...8 W.W e ---e ---- π.6 π W.W e ---e ---- π.8 π..8.8 W.W e ---e----- π.6 π...8 ~ z W.6W e ----e ---- π. π W.W e ---e----- π.π W.W e ---e --- π.6 π W.W e ---e ---- π.π.6..8 ~ z W.6W e ----e---- π. π... W.W e--e ---- π. π.6.8. W.W e ---e ---- π.6 π..8. W.W e ---e ---- π.π... ~ z W.W e ---e.8 π.9 π.9.. W.W e ---e.8 π. π..8. W.W e --- e.8 π. π..8. W.W e ---- e.8 π. π... ~ z 5 W.6W e --- e.5 π.9 π.56.. W.W e ----e.5 π. π W.W e ----e.5 π.π.8.8. W.5W e ---e.5 π. π.8..

46 6 z z 5 W.W e.8e ---- π.9π.9.. W.W e.5e ---- π.56π.9.. W.W e.8e---- π. π...8 W.W e.5e---- π.596 π...8 W.W e.8e --- π. π...8 W.W e.5e ---- π.8π...8 W.W e.8e---- π. π... W.W e.5e --- π.8π... W.W e.8e.8 π π.. W.W e.5e.8 π.5 π.. W.W e.8e.5 π π.5.. W.W e.5e.5 π.5 π.5.. Табл. 6. z z z z ~ z ~ z W.8W e ---e --- π.6π W.5W e ---e --- π. π W.5W e ----e --- π.π W.W e ---e --- π.π. W.9W e ---e ---- π. π W.6W e ---e ---- π.5 π W.5W e ---e ---- π.9 π W.8W e ---e----- π. π.6 ~ z W.8W e ----e ---- π. π W.5W e ---e----- π.6π W.5W e ---e --- π.6 π W.8W e ---e ---- π.6π. ~ z W.W e ----e---- π. π W.W e--e ---- π.6 π..6.9 W.W e ---e ---- π. π W.9W e ---e ---- π.5π.5 ~ z W.W e ---e. π.5 π..5.6 W.W e ---e. π. π W.W e --- e. π.5 π.9..8 W.6W e ---- e. π. π.9 ~ z 5 W.5W e --- e. π. π W.W e ----e.8 π. π.9.. W.W e ----e. π.5π... W.5W e ---e.9 π. π.

47 z z W.W. W.9W. W.W. W.W.6 W.8W.8 W.9W e.e ---- e.e---- e.e --- e.e---- e.e. e.e. π.5π. π.6 π. π.9 π.5 π.9 π. π. π. π. π W.W e.e ---- π.6π...66 W.W e.8e---- π.9 π... W.W e.e ---- π.π.5.. W.W e.9e --- π.π...8 W.W e.e. π. π...5 W.W e.8e.8 π. π... Proof of Theorem..: I Tk o ou he mos of uo by d we e h [ ] [ ]. Thus mxmzo π by be osdered o om se X [ ] d mxmzo π by - o om se X [ ]. II By he d fuos π d π re ouous. III As ord o he odos - he heorems uree he follow odos: π π. The odos. uree oy of fuos π d π. IV Thus from I II d III o he bss of he heorem of sh follows h here s Curou eulbrum o he seod se of he me. ow we shll reur o he frs se of he me d we shll osder he me bewee oermes. Les show h he odos of he heorem uree he exsee of sh eulbrum