The Economics of Administering Import Quotas with Licenses-on-Demand

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1 The Ecoomcs of Admserg Impor uoas wh Lceses-o-Demad Jaa Hraaova, James Falk ad Harry de Gorer Prepared for he World Bak s Agrculural Trade Group Jauary 2003

2 Absrac Ths paper exames he effecs of raog mpor uoas by lceses-o-demad. We aalyze he Nash eulbrum for a game where przes are allocaed o a proraed bass ad bddg s cosless. Facors affecg he degree of effcecy ad re shares amog frms are assessed. Wh lceses-o-demad, a reduco of -uoa arffs may resul decreased uoa fll, ad a crease he uoa may resul a 00 perce uoa fll rae. Ths resul s oppose o ha whe lceses are allocaed o a hsorcal share bass, for example. Oher polcy mplcaos for he mplemeao of lceses-o-demad clude he effcacy of o-use peales ad he effcecy of (a) lcese fees (euvale o a crease uoa arffs); ad (b) lms o he umber of lceses a frm s allowed o receve. Keywords: mpor uoas, re dsspao, lceses-o-demad, Nash eulbrum, re dsrbuo JEL Classfcao: F3 ; D45 Auhors are Asssa Professor a he Uversy of New Mexco, Professor of Operaos Research a The George Washgo Uversy ad Assocae Professor a Corell Uversy, respecvely. Correspodg auhor: Jaa Hraaova, Aderso Schools of Maageme, Uversy of New Mexco, 924 Las Lomas NE, Albuuerue, NM 873. Ph: (505) , emal hraa@um.edu The fdgs, erpreaos, ad coclusos of hs paper are he auhors ow ad should o be arbued o he World Bak, s maageme, s Board of Execuve Drecors, or he coures hey represe.

3 The Ecoomcs of Admserg Impor uoas wh Lceses-o- Demad. Iroduco Impor uoas rema a mpora polcy srume wheher he form of a smple uoa or combao wh arffs as a arff rae uoa. For example, he Agreeme o Agrculure he Fal Ac of he Uruguay Roud 994 esablshed,37 arff-uoas aloe. Res geeraed by mpor uoas provde a opporuy for frms o sped resources compeg for hese res, wh he degree of dsspao depedg crcally o he mehod by whch mpor lceses are allocaed. Of he seve prcpal mehods of uoa admsrao repored by he World Trade Orgazao (WTO), a lceses-o-demad s he mos commo mehod represeg 47 perce of he oal cases where he uoa s bdg (WTO, 2000). Frs-come, frs-served, hsorcal mpor shares ad auco are he ex mos commo mehods of allocag mpor uoas, represeg 2, 9 ad 8 perce of he oal cases where he uoa s bdg, respecvely. The frs-come, frs-served mehod does o eal allocao of mpor or expor lceses. Whle aucos have bee wdely dscussed he leraure ad hsorcal shares mehod has bee gve some aeo, leraure s scarce o he mos commo mehod of lceses-o-demad. Ths paper ams o fll hs gap. The purpose of hs paper s o aalyze he ecoomcs of lceses-o-demad ad assess he effecs o re shares ad ecoomc effcecy. The lceses-o-demad mehod assgs lceses based o he level of lceses reuesed by dvdual frms. If he sum of all reuess s greaer ha he uoa, he each frm receves a proraed umber of lceses. Hece, lceses-o-demad s aoher way whch he goverme raos uoa res. The way whch a uoa s admsered ca have a drec fluece o Ths excludes appled arffs as a mehod of arff uoa admsrao where he uoa s o-bdg.

4 boh rade flows ad he dsrbuo of res, ad s, herefore, a hghly polcal ssue. There s a urge eed o provde more formao o he ecoomcs of arff uoa admsrao mehods. By comparg he ecoomc mplcaos of lceses-o-demad o hose of aucos ad frs-come, frsserved mehods, our paper ams o corbue o he dscusso o arff uoa reform ad rade lberalzao, ad beer rules for arff uoa admsrao. Aucos allocae mpor lceses o he hghes bdders ad he frs-come, frs-served mehod allocaes mpors whou lceses o he frms ha arrve he frs o he por of mpors ery. We prese a game-heorec aalyss of he compeo for mpor uoa lceses uder dffere ecoomc codos whe lceses-o-demad are mplemeed as he admsrao mehod. We show ha here exss a uue eulbrum for a exeded game where przes are allocaed o he proraed bass ad bddg s cosless. Ieffcecy occurs because lceses-o-demad mehod of uoa admsrao eables hgh cos frms o operae. I addo, hgher cos frms receve he umber of lceses closer o her desred allocao, whle lower cos frms receve lceses progressvely furher from her desred allocao. We cofrm some uve resuls lke greaer effcecy of he lceses o demad sysem of allocao compared o he deal of a well fucog auco or radable lcese marke. Bu we also show ha ) he level of wase depeds more o he varace he cos srucure amog frms ha o he level of coss, 2) presece of fxed coss has a ambguous effec o effcecy 3) re dsspao may be lower ha wh he frs-come, frs-served mehod bu dead-wegh cos ca be larger due o effce allocao of resources, 4) a reduco of -uoa arffs may resul decreased uoa fll, ad a crease he uoa may resul a 00 perce uoa fll rae (a resul oppose o ha whe lceses are allocaed o a hsorcal share bass). Oher polcy mplcaos for he mplemeao of lceses-odemad clude he effcacy of o-use peales ad he effcecy of (a) lcese fees (euvale o a crease -uoa arffs); ad (b) lms o he umber of lceses a frm s allowed o receve. Effecs of rade lberalzao are examed hrough a crease he uoa amou ad a chage he per u 2

5 uoa re due o a chage arffs or marke prces. I addo, codos affecg uoa uder-fll are defed. The paper s orgazed as follows. The ex seco dscusses he leraure o uoa admsrao mehods ad hghlghs he corbuo of hs paper o he leraure. Seco 3 roduces he model of a game whe mulple przes (lceses) are allocaed o a proraed bass, followed by some umercal examples ha llusrae he Nash eulbrum for hree frms. Seco 4 hghlghs he ecoomc mplcaos of he resuls ad dscusses some ecoomc ad polcy facors ha ca affec he oucome. Seco 5 explores he mplcao of relaxg several of he assumpos of he base model by allowg for cosa margal coss ad o pealy for leavg lceses uused. The cocludg seco summarzes he polcy mplcaos ad offers suggesos for fuure research. 2. Leraure o uoa admsrao mehods From he four mos commo mehods of uoa admsrao, auco has bee mos wdely aalyzed he leraure as a commo mehod of allocag res (Bergse e al.; Krsha 990; 993a,b) or przes (Hol; McAfee ad McMlla). Ye, oly 8 perce of he oal agrculural uoas bdg are allocaed usg hs mehod. The ecoomc aalyss of frs-come, frs-served ca be raced o he wag--le leraure (Hol ad Sherma; Sue; Deaco ad Sosele), whle ha of hsorcal shares has bee aalyzed he case of agrculure by Gervas ad Surprea. However, he mos commo mehod of lceses-o-demad has o bee gve ay formal aeo. Ye s he mos commo mehod used 47% of cases he agrculural secor whe he uoa s bdg. I also s used as a uoa admsrao mehod secors oher ha agrculure such as for exle mpor uoas he mul-fber agreeme. Our paper ams o fll hs gap he leraure. Lke Krsha ad Ta, ad McCorrso ad Sheldo, we focus o he mplemeao of mpor uoas erms of he rules goverg allocao ad he effecs o he dsrbuo of res ad ecoomc effcecy. Our paper makes wo maor corbuos, oe raher echcal ad he oher volvg polcy 3

6 mplcaos for mplemeao of he lceses o demad as a sysem of lcese allocao. Frs, we aalyze he Nash eulbrum of a game where przes are allocaed o a proraed bass ad bddg s cosless ad show ha a uue eulbrum exss for ay gve umber of bddg frms. Secod, we deerme he codos affecg he degree of effcecy ad re shares amog frms ad compare he ype ad degree of effcecy o uoa admsrao mehods. Alhough lceses-o-demad are mpora bu o aalyzed he leraure, here s a sgfca leraure o he effecs of aucos ad frs-come, frs-served mehods of allocao. If lceses are aucoed, he o res are dsspaed ad he reveue o he goverme s he arff euvale of he uoa (Bergse e al.; Krsha 990; 993a,b; Hol). Ths assumes perfec compeo, perfec formao, ceray ad he lke. Krsha (990; 993a,b) for example, shows he effecs of mperfec compeo reducg auco reveues, resulg re rasfers away from axpayers. Lceses are awarded o he lowes cos frms whe auco s used as a mehod of uoa admsrao, resulg a effce allocao of resources. The wag--le leraure mples re dsspao hrough re seekg (Barzel; Sue). Barzel shows ha wh perfec formao res are compleely dsspaed hrough wag--le f ages are decal. Wh asymmerc valuaos of he good, re s dsspaed oly for he margal parcpa. The fra-margal parcpas are sll able o ear a par of he re, resulg uder-dsspao of res. Sue argues ha he degree of re dsspao depeds o he degree of heerogeey dvdual valuaos. A effce arff uoa admsrao mehod s he oe ha allows for full ulzao of he mpor uoa ad s allocao o he lowes cos frms. Rules such as radably of uoa lceses ad lcese fees wll affec he ceves for ulzg arff uoas. Furhermore, uderlyg ecoomc codos lke cosa margal coss affec effcecy of resource allocao. The mehod of allocag uoas ca have mpora mplcaos for he mpac of rade lberalzao. For example, s show he leraure ha f lceses are allocaed effcely by he hsorcal share mehod o hgher cos mporers, a reduco of -uoa arffs may resul creased uoa fll, whereas a crease he uoa may 4

7 resul uoa uder-fll (IATRC). However, we wll show ha he oppose occurs wh a lceses-odemad mehod of allocag mpor uoas. 3. Model of Lceses-o-Demad Cosder a small coury mposg a mpor uoa for a sgle commody. The goverme allocaes he rghs o hs uoa by a lceses-o-demad allocao sysem. Lceses-o-demad allocae lceses based o he level of lceses reuesed by dvdual frms. If he sum of all reuess s greaer ha he uoa, he each frm receves a proraed umber of lceses. Tha s, f frm asks for lceses, he s share of oal lceses avalable wll be, where s a umber of mporg frms. 2 No dvdual frm s allowed o reues more lceses ha he uoa self. The lceses are o-radable. Oly boa fde mporg frms ualfy for lceses he curre perod, whch meas ha each frm had o be a mporer he prevous perod. Thus, he umber of mporg frms s deermed from he prevous perod ad s kow o everyoe. Each mporg frm derves per u reveues deermed by he dfferece bewee he world prce P w ad he domesc prce P d, e of he -uoa arff case of arff uoas. 3 Ths uoa re per u mpored, (P d P w ), s he same for all frms. Each frm has a creasg cos srucure of he form C ( ), where s he acual mpor uay for frm. We cosder boh he cases of decal ad asymmerc cos srucures. Perfec formao s assumed, such ha frms kow each oher s cos fucos ad desred uaes. The game proceeds wo sages. I he frs sage, frms deerme her desred uaes ha hey wa o mpor,,2,,. Based o her desred uaes, he secod sage frms deerme he uaes hey ask for (bds),,,2,,. Workg backwards, we frs deerme he opmal bds for gve arge uaes ad he deerme he opmal uaes desred. 2 The frms are assumed o be mporers oly, wh o domesc produco. Alhough our aalyss s carred ou for a mporg coury, he resuls hold for allocag expor lceses as well. 5

8 Sage 2: For gve arge uaes, frm asks for lceses such ha hey receve as close as possble o he desred (arge) mpor uay, subec o he cosra ha o dvdual frm ca ask for more lceses ha he uoa self, for all, 2,,. Ially, we assume ha here s a prohbve pealy mposed for leavg lceses uused, such ha each frm wll use all he lceses receves. For example, he Europea Uo reures a dow payme of 20 perce of he value of mpors ad he frm loses hs f o mpors occur ha year. For a lear margal cos fuco, he per u profs foregoe for mporg less ha he desred uay s he same as ha of mporg more ha he opmal amou. The opmal uaes asked for (bds) are as follows: If, he for all, 2,,. Ths s because he goverme allocaes he exac umber of lceses reuesed whe he umber of reuesed lceses s less ha he uoa. Thus, every frm bds s desred uay. Noe ha uoa may be uder-flled hs case. If >, he he goverme allocaes he proraed umber of lceses such ha. Thus, he opmal bd s such ha f < + ad oherwse. The opmal uay of each frm s a fuco of he oher frms opmal bds ad he soluo s hus a Nash eulbrum. Because he frms wll bd her desred uay oherwse, he case > s he oly eresg oe o aalyze. Symmerc frms: 3 For he aalyss o follow, deals such as -uoa ad ou-of-uoa arffs ad ou-of-uoa ad over-uoa mpors are gored. 6

9 Whe all frms have decal cos srucures, ( ) C( ), her desred mpor uaes are also C decal,. I eulbrum, all frms ask for lceses ad receve. Ths s because sce >, he allocaed uay s less ha he desred uay for a represeave frm, >. Thus, o frm has a ceve o ulaerally lower her bd, as hs would brg hem eve furher from her desred uay. Also, o bd below s a Nash eulbrum because frm he has a ceve o ulaerally rase her bd ad hus ge closer o her desred uay. Asymmerc frms: Now cosder asymmerc cos srucures bewee dvdual mporg frms. The esug desred uaes are rak ordered o he erval (0,A), where + A R, 0 < < 2 <... <. If A >, all he frms whose desred uaes exceed or eual he uoa auomacally bd he uoa amou. The opmal bd ssue s eresg oly for frms who desre o mpor a uay lower ha he uoa. We herefore assume ha o sgle frm has suffce capacy o mpor he ere uoa;.e., A <. Noe ha he lower dces dcae frms wh hgh mporg coss, as hgh cos frms desre lower uaes. To llusrae he Nash eulbrum, frs cosder wo mporg frms, 2, wh dffere cos srucures whose desred mpor uaes are ad + > < 2 2. Proposo : I eulbrum, he low cos frm always bds he maxmum amou. The hgh cos frm eher also bds he uoa or bds such ha receves exacly he amou desred. The hgh cos frm bd depeds o he desred level of lceses. Tha s, frm ad 2 s `bes respose fucos are: 2 ad f < 2 ad oherwse. 7

10 The lower cos frm wll always bd he maxmum;.e., he uoa amou ad he hgher cos bds such ha receves he desred amou f hs s less ha a half of he uoa amou. Oherwse he hgher cos frm also bds he uoa. Thus, he hgher cos frm ges exacly or closer o wha was. Ths s because compeg wh he oher frm he lower cos frm s he frs oe o have he cosra bdg ad hus s always cosraed by he maxmum. Proof: Cosder ad 2 2. Ths s obvously o a Nash eulbrum sce 2 2 > ad > ad he frms have a ceve o devae by rasg her bds. Cosder frm 2 rasg s bd o k. Frm ca be a leas as well off as before by rasg s bd by he same amou k. Thus, frm ca mach he crease ul 2. Frm ow opmzes s bd kowg wha frm 2 bds. Frm would lke o se o sasfy he euao + subec o Ths wll be possble f or. 2 For > 2, we aga assume rak orderg of desred uaes 0 < < 2 <... < ad >. Proposo 2: There exss a uue eulbrum, where he lowes cos frm always bds he uoa amou ad addoal -- low cos frms may also bd he maxmum uoa. The remag frms bd such ha hey receve exacly her desred levels of lceses. The eulbrum profle for he frs frms, 8

11 <, ca be foud by solvg he sysem of lear euaos ( ) ( ),... subec o he cosra ha. / for The umber of frms ha wll bd s -. I wll be show ha a uue eulbrum exss for he hghes ha sasfes he above euao. Frms,..., acually ge he allocao ha hey desre, whle frms +,..., all ge he same allocao a allocao less ha wha hey desre, where he dfferece s progressvely larger for frms wh lower mporg coss. For all frms bddg, hgher cos frms ge he same amou of lceses as low cos frms eve hough he desred amou of he laer frms s hgher. Therefore, hgh cos frms ge closer o her desred levels ha low cos frms. Hgh cos frms are effecvely able o overbd more ha he low cos oes ad hereby receve lceses closer o her desred levels. For frms who bd less ha, he desred level of lceses s obaed. A closed form soluo for (frm s `bes respose ) s preseed a laer proposo. Proof: Each frm would lke o se o mach he uay / o subec o he cosra ha o dvdual bd ca be greaer ha he uoa amou. Nog ha / /, 2 > 0, we see ha a frm ca crease (decrease) s allocao by creasg (decreasg). Suppose a parcular -uple o ceve for a frm o crease s bd ;.e., he umber,..., s eulbrum. The here ca be / cao be smaller ha 9

12 . Lkewse here ca be o ceve for frm o decrease s bd;.e., he umber / cao be larger ha. I eulbrum, here are wo possbles: < whch case / or whch case / Noe our assumpo ha 0 < < <... <. Le 2 < ad le ( ),..., be a eulbrum -uple. I ca be show ha he bds are rak ordered he same way as he desred uaes, < (see Appedx). By a argume smlar o ha used for he case 2, we ca show ha. From he prevous resul, we kow ha here s some maxmal eger < such ha < 2 + <... < <.... Suppose for he mome ha we kow. To fd he eulbrum profle, we eed o solve he sysem of euaos: / for,.... or, recallg ha,..., + 0

13 ( ) ( ) / for,.... Ths s a sysem of lear euaos ukows. As we do o kow he eger beforehad, we mus sar solvg he sysem for, - 2,... ad fd he hghes, for whch he sysem of euaos yelds a feasble eulbrum. I ca be show ha he defg euaos are also solvable for egers less ha ;.e., hese soluos also sasfy he ecessary codos, bu hey do o cosue a Nash eulbrum. Cosder a soluo where -s frms, s { 0,,..., }, bd,.e., s The he frs s frms receve her desred allocao ad -s frms receve less ha wha hey desre. However, ay frm, where s+, s+2,,, ca ge closer o her allocao by lowerg her bd below. A uue Nash eulbrum occurs a he maxmal eger, for whch he sysem of defg soluos solves ad ha sasfes he ecessary codos. Proposo 2a shows how o deerme he larges value of for whch he euaos hold. Alhough we ca show ha he euaos hold for all smaller (posve) values of, hese soluos do o cosue a Nash eulbra ad are herefore of o eres o us. Proposo 2a: The closed form soluo for a eulbrum bd for he larges -h frm s ( ), where sasfes he codos > 0 ad ( ). Proof: see Appedx.

14 The followg examples for 3 llusrae he procedure for fdg he Nash eulbrum. I example boh hgher cos frms are perfecly sasfed, whle example 2 oly he hghes cos frm s perfecly sasfed. Example 3 llusraes he case whe oe of he frms obaed her desred allocao - all frms bd a he maxmum ad oe oba wha hey asked for exacly. Bu eve he, he hgher cos frm allocao s closer o her desred uay. Example : Le 3,.0, ad 0.2, 0.3, ad 0.8. We kow ha. A 2, approprae euaos are he ( / 0.2 ) 2 ( / 0.3 ) + 2 ad he soluo s 0.4, 0.6. The eulbrum 3-uple s (0.4,0.6,.0) ad he 2 correspodg allocaos are ( 0.2,0.3,0.5 ). Frms ad 2 oba her desred allocao, ad Frm 3 ges he bes allocao ha ca wh a bd of. Now suppose ha. The seg also, he approprae euao s 2 (/0.2 ) 2or Bu he rple of bds (0.5,,) ad he correspodg allocao (0.2, 0.4, 0.4) s o a Nash eulbrum because frm 2 would wa o lower s bd order o ge a allocao closer o

15 Example 2: Now le.0, ad 0.3, 0.5, ad Aga we kow ha. If we 2 assume 2, we expec,. The approprae euaos are 2 < 3 3 ( / 0.3 ) 2 ( / 0.5 ) + 2 ad he soluo s 3/ 2, 5/ 2. whch volaes he codo ha [ 0, ].. The 2 soluo does o sasfy ecessary codos. Now assume ha, so ha as well. The approprae euao s ( / 0.3 ) 2 2, resulg 6 / 7. The correspodg allocaos are ( 0.3,0.35,0.35). Frm ges s desred allocao, ad Frms 2 ad 3 do o. Ths soluo sasfes boh ecessary ad suffce codos. Example 3: Now le.0, ad 0.5, 0.6, ad 0.8. Assume 2. The approprae euaos 2 3 are ( / 0.5 ) 2 ( / 0.6 ) + 2 ad he soluo s 6, 7. Ths s o feasble. Now assume ha. The 2 approprae euao s ( / 0.5 ) 2 ad he soluo s 2, aga feasble. The oly eulbrum 3-uple for hs example has for all. 3

16 Sage : Kowg how frms wll behave sage, each frm sraegcally decdes abou s desred uay. Proposo 3: Behavg sraegcally, frms desred uaes are Couro uaes f he oal uay desred Couro eulbrum s less ha he uoa bu compeve uaes f he oal uay desred Couro eulbrum exceeds he uoa. Whou he eraco of he secod sage, each frm behaves sraegcally by maxmzg s prof gve he uaes mpored by he oher frms. The eulbrum yelds he Couro uaes C for all as he opmal uaes desred. If he oal ucosraed uay desred Couro eulbrum s less ha he uoa, C, he uoa s udersubscrbed. Whou he uoa cosra, all frms bd ad also receve her Couro uaes, C ad he uoa s uderflled. If he oal ucosraed uay desred Couro eulbrum exceeds he uoa C >, he uoa s oversubscrbed ad wll be flled. Ths s because each frm bds a leas her desred uay, C, hus he sum of he bds exceeds he uoa ad he acual uaes awarded wll be deermed o a proraed bass. Bu f he uoa s flled, he prce s gve ad he Couro uaes are o loger he opmal desred uaes. I fac, each frm akes he prce (a he uoa flled level) as gve ad hus re-solves for s opmum uay desred, amely each frm would lke o mpor her compeve uay ce. Thus, he compeve uaes become he releva desred uaes hs case, ce, for,2,,. 4. Ecoomcs of lceses-o-demad Ths seco dscusses he ecoomc mplcaos of he heorecal resuls for he game ha characerzes lceses-o-demad mehod ad compares he ype ad degree of effcecy o aucos ad frs-come, fs-served mehods. Facors affecg he degree of effcecy are defed as well as he effecs of 4

17 rade lberalzao hrough a decrease he -uoa arff (for arff-rae uoas) ad a crease uoa. Oe of he ma resuls of he above aalyss s ha he hgher cos he frm, he closer her lcese allocao o her desred uay ad he hgher he probably ha hey receve exacly her desred uay. Ths mples effcecy resource allocao. Allocag lceses-by-demad eables hgh cos frms o rema busess ad acheve lcese allocao ha uder a effce oucome would be assged o low cos frms. The effce dsrbuo of lceses across frms geeraes ecoomc wase of uoa res wh he exra coss assocaed wh mporao. Thus, relave o boh he auco ad frs come frs served mehods, a lcese o demad admsrao mehod geeraes wase hrough s ably o elmae he effce frms. No re seekg occurs uder lceses o demad. Ths s a resul of he oe-perod seg ha we assume for our aalyss, cosless bddg, ad o ery allowed. Beg a boa fde mporg frm esures a frm he rgh o compee for lceses, hus o frm has a ceve o sped resources he effor o oba hs rgh. Also, o resources are expeded whe compeg for lceses, as bddg s cosless. Ths resul s he same for a oe-me auco; sce oly he parcpas who ca bd he hghes amou receve ad pay for he lceses ad here s o ceve o re seek. Uder frs-come, frs-served, however, resources are spe by wag--le ad res are dsspaed eher compleely (f decal valuaos) or compleely (asymmerc valuaos). As log as he oal uay demaded exceeds he uoa amou, he uoa wll be fully flled. Ths s he resul of our assumpo of a hgh pealy for falure o use awarded lceses. Ths pealy may ake a form of a o-refudable dow payme whe frms receve her awarded lceses a he begg of he year. I case of agrculure, Europea Uo mporers are ofe 5

18 reured o pay 20% of he value of he produc advace. We relax hs assumpo he ex seco. If perfec formao s assumed, boh auco ad wag--le resul a 00 perce fll rae. The presece of fxed coss has a deermae effec o deadwegh cos. I may decrease he effcecy f he fxed coss preve he hghes cos mporers from bddg. Relave o he case wh zero fxed coss ad he same varable cos fuco, fxed coss add o he deadwegh cos because hey cosue a addoal cos for he frms ha should be ou of busess. The same reasog apples o a decrease he reveue marg due o a crease he -uoa arff (for arff uoas) or he world prce, or a decrease he domesc prce due o some ecoomc shock. The absolue level of effcecy may decrease due o a elmao of he hghes cos mporers bu relave dsoro for he remag frms sll exss. A crease he uoa, o he oher had, decreases effcecy hrough reducg he relave dsoro. The hgh cos frms ha orgally receved her opmal amou wll rema a her desred levels ad he uoa expaso s rasferred o he lower cos frms. I addo, per u re decles, creasg he probably ha he hghes cos frm wll o parcpae. Hece, rade lberalzao by reducg -uoa arffs or expadg uoas wll reduce he effcecy of he lceses-o-demad mehod. Whe a lm o he lceses receved by each frm s mposed, effcecy creases because lm wll be more bdg o low cos frms. Ths resul s sharp coras o ha of o-rasferable res wh hsorcal allocao (as assumed Lo, for example). If frms are allowed o rade he lceses, Pareo opmaly of he eulbrum oucome s resored. All frms bd he maxmum allowable amou for all, 2,, ad each frm s allocaed / lceses. Subseuely, he hgh cos frms sell her lceses o he low cos frms. Thus, effcecy s maxmzed bu re s rasferred o he hgh cos frms. 6

19 The followg seco explores he mplcaos of relaxg (oe by oe) several assumpos of he base model. We cosder he case of cosa margal coss ad zero o-use pealy. 5. Cosa margal cos ad zero o-use pealy Cosa margal cos Assume ow ha each mporg frm has dffere varable coss ha are vara o he level of mpors. Each frm bds he maxmum ad so receves / lceses. The deadwegh coss for he example of 4 Fgure are gve by he shaded areas. If fxed coss are also prese, he deadwegh coss crease by he fxed coss of he wo hgh cos frms remag he bddg ad decrease by he deadwegh cos of he hghes cos frm ha exs. A crease he per u uoa re brough abou by eher a decrease he -uoa arff or chage world or domesc prces wll resul a decle deadwegh coss f he hghes cos frm s forced o ex he bddg process. The per frm deadwegh coss of he remag hgher cos frms crease bu oal deadwegh coss decle. The decal effec o deadwegh coss occurs f a lcese fee s mposed ha forces he hghes cos frm o ex. Fgure : Deadwegh coss for four frms wh dffere levels of cosa margal cos P P d MC 4 MC 3 MC 2 MC P w A crease he uoa hrough rade egoaos wll have a deermae effec o deadwegh coss because domesc prces fall (ad world prces crease f a large mporer) ad 7

20 so hgh cos mporers may ex he bddg process (he oucome depeds o he elascy of excess demad (ad excess supply f a large coury mporer)). If here s o ex, he deadwegh coss crease. A lm o he mpor lceses receved by a frm ca crease (bu o decrease) deadwegh coss bu uoa uder fll ever occurs uder he assumpos of our model uless he oal uay demaded s less ha he uoa. Noe ha he varace of coss s mpora addo o he level of coss amog mporg frms deermg he degree of ecoomc effcecy. Zero o- use pealy I may cases, he goverme does o mpose a pealy for leavg lceses uused. Sce bddg for lceses ad coseuely leavg hem uused s cosless uder hs scearo, each frm wll leave uused he lceses ha exceed s desred amou. All frms ask for he maxmum umber of lceses eual o he uoa amou, for all, 2,, ad each frm s allocaed / lceses. Ieffcecy creases because low cos frms o average ge fewer lceses ha wh a pealy for uused uoas ad uoa uder fll occurs ha creaes a addoal dead-wegh cos. Trasfer of lceses o he hgh cos parcpas creases he gap bewee he desred ad acual umber of lceses for he low cos parcpas. I addo, hese rasferred lceses are lef uused by he hgh cos frms as hese oly rea her desred levels. Proposo 4: Whe o pealy s mposed o o-use of lceses, he degree of re dsspao creases wh greaer heerogeey of frms. A crease varace of mporg cos srucures uder o pealy causes a crease he umber of lceses lef uused ad hus a crease effcecy. Ths s because he hgher he cos varao, he more very hgh cos frms here are. The dfferece bewee he desred uay ad he allocaed 8

21 uay s larger for hese, geerag more uused lceses ha uder pealy were allocaed o lower cos frms. Proof: The umber of lceses uused, L U, s he dfferece bewee he allocaed uay uder o pealy ad he desred uay of he frms ha would receve hese uaes uder pealy, ( ). LU Le + σ ε, whereε has a mea 0 ad varace for, 2,. The L U ε σ ad L U σ > ε 0. Ths s because ε 0, < adε < ε + <... < ε, resulg ε < Cocludg remarks I hs paper, we dscuss he mplcaos of raog mpor uoas by lceses-o-demad where lceses are based o he level of lceses reuesed by dvdual frms. If he sum of all reuess s greaer ha he uoa, he each frm receves a proraed umber of lceses-o-demad. We assess he effecs of such a scheme o re shares ad ecoomc effcecy, ad compare hese o aucos ad frscome, frs-served mehods. Ths paper aalyzes he Nash eulbrum for a game whe mulple lceses are allocaed o a proraed bass ad shows ha a uue eulbrum exss for ay umber of frms. Numercal examples provde sghs o he properes of he model ad ecoomc mplcaos of alerave suaos. We show ha he eraco bewee deermg desred uaes ad subseuely deermg he uaes asked for (bds) causes he frms o choose Couro uaes 9

22 he ucosraed case (f he sum of Couro uaes desred s less ha he uoa) ad compeve uaes f he oal Couro uay desred exceeds he uoa. We he aalyze he compeo of mpor uoa lceses wh lceses-o-demad uder dffere ecoomc codos. We defy several codos affecg he degree of effcecy ad re shares amog frms. Uder codos of perfec compeo ad perfec formao, we aalyze he mplcaos of varous facors acually observed lke fxed coss, pealy for o-use of lceses, ad a lm o he umber of lceses a frm s allowed o receve. Effecs of rade lberalzao are examed hrough a crease he uoa amou ad a chage he per u uoa re due o a chage arffs or marke prces. I addo, codos affecg uoa uder-fll are defed. As expeced, hs sysem of allocao s more effce ha a well fucog auco or radable lcese marke. We show ha he level of wase depeds more o he varace he cos srucure amog frms ha o he level of coss. Ieresgly, he lceses-o-demad mehod has very dffere mplcaos for he mpac of rade lberalzao where a reduco of -uoa arffs may resul decreased uoa fll, ad a crease he uoa may resul a 00 perce uoa fll rae. Ths resul s oppose o ha of whe lceses are allocaed o a hsorcal share bass, for example, where opporuy coss may chage overme, preveg he leas cos-mporg frms from operag (Lo). Oher polcy mplcaos for he mplemeao of lceses-o-demad clude he effcacy of o-use peales ad he effcecy of (a) lcese fees (euvale o a crease -uoa arffs); ad (b) lms o he umber of lceses a frm s allowed o receve. Some coures ad commody secors mpleme each of hese rules for he lceses-o-demad allocao mehod. Fuure research should focus o relaxg he assumpo of a fxed umber of mporg frms. Res may be such ha pays for frms o eer he busess by mporg a ou-of-uoa arffs he shor ru ad so ga saus as a mporer o bd for lceses. Ths wll have he effec of dsspag res furher, o oly because of he re seekg coss of mporg a ou-of-uoa arffs bu also addg o he 20

23 umber of hgher cos mporg frms. The aalyss ca also be exeded o clude mperfec formao ad rsk averso o he par of frms whe hey make sraegc decsos her bddg levels. 2

24 Refereces Barzel, Y A Theory of Raog by Wag Joural of Law ad Ecoomcs 7 (Aprl): Bergse, C.F., K.A. Ello, J.J. Scho ad W.E Takacs, 987. Auco uoas ad Ued Saes Trade Polcy. Polcy Aalyses Ieraoal Ecoomcs No. 9. Isue of Ieraoal Ecoomcs, Washgo, D.C. Deaco, R.T., ad J. Sosele. 99 Prce Corols ad Re Dsspao wh Edogeous Trasaco Coss Amerca Ecoomc Revew Volume 8, Issue 5 (December): Gervas, J-P. ad D. Surprea "A Ecoomc Ivesgao of he Impor Lcesg Mehods ad TRs Agrculure". Paper preseed a he Caada Agrculural Ecoomcs Socey, (Jue) Vacouver, Caada. Hol, C.A Compeve Bddg for Coracs uder Alerave Auco Procedures. Joural of Polcal Ecoomy Vol. 88, No. 3 (Jue): Hol, C.A. ad R. Sherma. 982 Wag-Le Aucos Joural of Polcal Ecoomy Volume 90, Issue, 2 (Aprl): Ieraoal Agrculural Trade Research Cosorum (IATRC) 200 Issues Reformg Tarff-rae Impor uoas he Agreeme o Agrculure he WTO Commssoed Paper #3 (May), Uversy of Mesoa, S Paul, Mesoa. Krsha, K., 990. The Case of he Vashg Reveues: Auco uoas wh Moopoly. Amerca Ecoomc Revew 80 (Sepember 990): , 993a Theorecal Implcaos of Imperfec Compeo o uoa Lcese Prces ad Aucos. World Bak Ecoomc Revew (7): , 993b Aucos wh Edogeous Valuaos: The Perssece of Moopoly Revsed. Amerca Ecoomc Revew 83(March 993b):

25 Krsha, K. ad L.H. Ta Rags ad Rches, A Arbor, MI: The Uversy of Mchga Press. Krueger, A.O., 974. "The Polcal Ecoomy of he Re-Seekg Socey." Amerca Ecoomc Revew Vol. 64(3): Lo, J.R Lcesg ad Norasferable Res. Amerca Ecoomc Revew Vol. 7, No. 3., (Jue): McAfee, R.P., ad J. McMlla 987. Aucos ad Bddg. Joural of Ecoomc Leraure, Vol. 25, No. 2. (Jue): McCorrso, S. ad I.M. Sheldo. Sellg Impor uoa Lceses: The U.S. Cheese Case, Amerca Joural of Agrculural Ecoomcs 76(November 994): Skully, D Ecoomcs of TR Admsrao. Ieraoal Agrculural Trade Research Cosorum, Workg Paper Sue, W Raog ad Re Dsspao he Presece of Heerogeeous Idvduals Joural of Polcal Ecoomy Vol. 97, Issue 6 (December): World Trade Orgazao (WTO), Tarff uoa ad Oher uoas Backgroud paper G/AG/NG/S/7 May 23 23

26 24 Appedx Proof ha bds are rak ordered he same way as he desred uaes: There are four possble cases:, <, <, ad <,. Cases ad 2 are rval. I case 3, he eualy < mples ha k k / so ha / k k. The < mples ha > > / / k k k k

27 Sce he lef-had sde s smaller ha or eual o, we have he coradco > ad we coclude ha hs case s feasble. The las case mples ha / k < / k k k so ha / k < / k k k ad he resul s mmedae. Proof of proposo 2a: The geeral form of he euaos s: ( ) / ( ) for,..., For each,..., rao ( / ), subrac euao from euao o ge ( ) / 0. Noe ha he s smaller ha uder our assumpo. Ths meas ha f (0, ] we are doe. To deerme, subsue he above expressos o he euao ( ) / ( ) for,..., ad solve for. You ge he closed form soluo 25

28 ( ). Recallg ha we are doe f (0, ] we see ha he oly permssble s are hose such ha a) > 0 so ha > 0 ad b) ( ) so ha. Ay such ha hese wo codos are rue wll lead o a eulbrum. Oe mgh oe ha codo a) s acually mpled by codo b), as he rgh had sde of b) becomes egave for s larger ha he larges ha sasfes a). The oppose s o rue as he followg example shows. However sce a) s so easy o check, mgh be prude o fd he larges whch sasfes, ad work dow from here. For example, wh:, ad (0.,0.2,0.3,0.5,0.6) we see ha he larges for whch codo a) holds s 3. Tesg codo b), we see ha he larges for whch holds s 2. I order o acually compue he eulbrum, you do eed o solve he approprae euaos. We have ad ( ) 26

29 ( ) / 0. Fally we show ha he euaos are sasfed for all smaller ha he larges ha sasfes he above euaos. Suppose > sasfes b). The we kow ha or ( ) ( ) + We wa o show ha he frs of hese expressos s rue whe s replaced by -;.e., ( ) +. Bu hs follows mmedaely from he prevous expresso sce we kow ha <. 27