Optimal firm behavior under environmental constraints 1

Transcription

1 Opil fi bhvio u viol cosis ouf Bouckki, Nli Hioko 3 Yui Ysko 4 Absc Th pp xis h Po iuc-iovio hypohss i fi ol wh: i h fi hs vig cpil chology wih wo coply fcos, gy cpil ; ii scppig is ogous; iii chologicl pogss is gy-svig ogous hough puposiv &D ivs; iv h iovio icss wih &D ivs css wih coplxiy; v h fi is subjc o issio quos which pu upp bou o is gy cosupio y ; vi gy cpil pics xogous. Blc gowh phs fis chciz, copiv sic lysis is pfo o suy ki of log- Po iuc-iovio hypohss. I picul, i is show h igh issio quos o o pv fis o gow i h log-u, hks o ogous iovio, bu hy hv ivs ffc o h gowh of pofis. So sho- yics lso pouc, picully, o lyz h ol of iiil coiios gy pics i opil fi bhvio subjc o viol gulio. Aog uous suls, w show h i fis which hisoiclly sll pollus fi i opil o ssivly pollu i h sho u: uig h siio, w cl chis will co-xis wih ol iy chis i h pouciv scos, iplyig ubiguously iy siio; ii high gy pics iuc sho lifi fo cpil goos bu hy pss ivs i boh w cpil &D, fuig ki of vs Hicksi chis. Kywos: Vig cpil, &D, Eissio quos, Po hypohsis, Iuciovio hypohsis, Opiizio JEL ubs: C6, D, D9, Q55, Q56 W woul lik o hk picips of h 7 hi Vi Vig Wokshop of h 8 MIMI Wokshop hl i Lill, spcilly Polo Bio, fo ivlubl cos. Bouckki ckowlgs h ficil suppo of h Blgi sch pogs PAI P5/ AC 3/8-3. Th usul iscli pplis. Cospoig uho: Uivsié choliqu Louvi, Blgiu, Uivsiy of Glsgow, UK. Plc Mosquiu, 3, 348 Louvi-l-Nuv, Blgiu. ouf.bouckki@uclouvi.b 3 Pii Viw A&M Uivsiy, USA. NHioko@pvu.u 4 Houso Bpis Uivsiy, USA. YYsko@hbu.u

2 . Ioucio Th gus fo viol gulio usully bs o wh hs co o b kow s h Po hypohsis. Po 99 Po v Li 995 gu h ls i so scos, cfully sig viol gulio s ky fu of iusil policy c ics fi copiivss by cougig iovio i viol chologis. So f, his hypohsis hs b h g of uous suis i svl isciplis, icluig cooics, wih highly ivgig coclusios. I picul, y cs suis hv b pfo, chig iff coclusios pig o fis, iusis, couis. A xcll copilio of such cs suis c b fou i Po Hb-Coply 7. A siil hypohsis, populiz by Hicks 93 wily ppli o viol cooics, spcilly i is gy p s Nwll, Jff Svis, 999, fo sil coibuio, is h so-cll iuc-iovio hypohsis. Accoig o Hicks, h chg of liv pics of poucio ipus siuls iovio, iovio of picul yp, ic o sv h poucio fco h bcos livly xpsiv. I h cox of h gy cosupio b, his hypohsis siply sipuls h i pios of pily isig gy pics liv o oh ipus, cooic gs will fi i o pofibl o vlop liv chologis, h is, gy-svig chologis. Jus lik h Po hypohsis, h iuc-iovio hypohsis i is gy-svig vsio hs b isivly sui i c ys, wih gi highly ivgig oucos, pig ily o h gggio lvls cosi i h suis. I hi wll-kow wok, Nwll, Jff Svis 999 coclu

3 h lg poio of fficicy ipovs i US ufcuig ss o b uooous, hfo o iv by h Hicksi chis ouli bov. B i siul by ighig viol gulio, cus by h gul xhusio of fossil soucs, ic by iiol gs lik h Kyoo Poocol o by pily icsig gy-pics, h ol of iovio h fi lvl is h ky i h wo hypohss scib bov. I xplis why hs hypohss cully shpig subsil p of h viol liu i cooics. If h fis o ffcivly spo o h l cosis cicuscs by oig o &D, h h viol pobl, usoo s h bu ivolv by viol cosis o cooic vlop, c b pilly solv. This fs o h so-cll Wi-Wi ouco io by Po: ioviv fis woul o suff y pouciviy slup whil coibuig cisivly o cl viol susibl vlop. This pp is vo o usig how u which coiios, if y, fis woul gg i &D ivss u viol cosis /o isig gy pics. I cos o uous pps wi i his obly i h cocooic liu, which ypicl cosi h &D couc ousi h fis by spciliz iis s, fo xpl, H, 4, w s wih h ky ssupio h fis, cofo wih viol cosis, y ci o iiviully gg i &D civiis. W o cosi such xsio s ssil o g hough h puzzl, h svl sos fo his ppoch o b pf:

4 3 i Fis of ll, h ol of poucio fis i h vlop of cl chologis co b u-sco bcus os viol pobls fi o iusy spcific co b siply solv by ipoig chologis. W shll vlop his i i h x scio wh scibig h coc cs of h chlo-lkli iusy i Jp Yi, 7. ii Sco, i hs b ply sblish h ls i h cs of lg copoios s Co Siisclco, 994, fis o spo o viol policy sus hough iovios, o by swichig ipus o ucig oupu. iii Ls bu o ls, s io by svl uhos og h, Co Siisclco, quo jus bov, vy high xs o big ow CO issios i h bsc of iovios. This jusifis h ppoch k i his pp: usig how h fis fo xpl, subjc o polluio quos gg iiviully i &D is i ky sk. Thoughou his pp, w shll cosi vig cpil chologis. Cpil goos pouc iff s boy iff chologis, h yougs vigs h os gy-svig,, hfo, h ls polluig. Bsi lis, wokig wih vig cpil poucio fucios llows o cpu so ky ls of h pobl u cosiio, which woul b los u h ypicl ssupio of hoogous cpil. Fo isc, fcig issio x, fis p o owsiz. Howv, i ypicl fwok wh h fi lso chooss h opil g sucu of cpil, which is h i iiol cool vibl i vig cpil ols, owsizig ils oizio: h ol, hus, h ii chis chologis h

5 4 ov. Fo pouciviy lyss, his is goo ws: coy o h ypicl fwok wih hoogous cpil, w hv cl pouciviy-hcig ffc of issio xs i such fwok, hus givig chc o h Po ``Wi-Wi ouco o is, v i h bsc of fis ioviv civiis. I, whh such iic oizio ffc c cops h so-cll pofi-issio ffc ccoig o which pofis cli u issio xs sous s highly iiguig qusio. Vy fw pps hv i o l wih his issu so f, ly u o h sophisic hicl sucu of vig cpil ols. Two vlubl xcpios shoul b io h. Xpps Zuw 999 povi h fis ispcio io his pobl. Thy coclu h h coss of viol gulio w iig if fis spo o issio xs by scppig h ol ii chologis. Thfo, h iic oizio ffc offss subsil p of h giv pofi-issio giv ffc, bu o olly. Fichig, Hl, Ko Vliov 5 iouc b spcificio of boi chologicl pogss ulyig h cosi vig cpil sucu. Thy coclu h if lig coss icopo io h lysis h s uig w chis hi full pouciviy poil ks i, h h giu of h oizio ffc is sogly uc, viol gulio hs kly giv ffc o iusy pofis. Ou pp xs h wo pvious pps, wh h pc of chologicl pogss is kp xogous, ogizs &D cisios. W hv ly jusifi lgly why

6 his ogizio is cssy fo pop ppisl of h ``viol pobl s fi bov. W shll fi ou gus i his spc i h x fcul scio. 5 W chciz opil fi bhvio boh sypoiclly i h log-u, w xc svl w suls, hks o h ogous u of chologicl pogss. I picul, w ouli h h cucil suls: i I h log-u, igh issio quos coupl wih liquiiy cosis o o pv fis fo gowig i h log-u, hks o ogous iovio, his is goo ws. Howv, hs cosis hv ivs ffc o h gowh of pofis. I oh s, whil &D is cucil fo fis o kp o gowig spi viol ficil cosis, w g h ul ouco ls, h fi lvl h o Po-hypohsis is xpc o is i h log-u, ly, sghig viol gulio os o ipov h siuio of h fis i h log-u, u h coiios of h ol pickig liquiiy-cosi fis. ii I h sho-u, h suls v cl. Fo xpl, w sblish h fis which hisoiclly sll pollus fi i opil o ssivly pollu i h sho u: uig h siio, w cl chis will co-xis wih ol iy chis i h pouciv scos, iplyig ubiguously iy siio. Thfo, h ol povis ico-fouios fo ssil p of h so-cll Eviol Kuzs Cuv. iii Ls bu o ls, w show h u so spcific bu sobl cicuscs, high gy pics iuc sho lifi fo cpil goos bu

7 hy pss ivs i boh w cpil &D, fuig ki of vs Hicksi chis. 6 Th pp is ogiz s follows. Scio is vo o scibig so sli chcisics of h viol gulio k h coc fi lvl, boowig fo h wiig of so chologiss. Scio 3 folly scibs ou fi opiizio pobl oulis so of is pculiiis. Scio 4 ivs h opiliy coiios ips h. Scio 5 is coc wih h log- opil bhvio of fis Scio 6 pss so iplicios fo opil sho yics. Scio 7 coclus.. Isigh fo chologiss W s wih sho scipio of h cs of h chlo-lkli Jps iusy, which is i ou viw xcll illusio of fi s bhvio u viol gulio i gy-svig cox. W h swich o oh sli fus of h pobl, s pic by svl chologiss... A illusio: h chlo-lkli iusy i Jp This sub-scio is ily bs o Yi 7. Th chlo-lkli iusy poucs chloi cusic so hough lcolysis. Bcus i ivolvs lcolysis, i is o of h jo gy cosus i h Jps iusy. 5 I his cox, jo coc 5 Yi 7 pos h bou 3% of ol iusy lciciy cosupio i Jp c b ibu o h chlo-lkli iusy i 996, which lso ccous fo bou o-fifh of ol chicl iusy i his y.

8 7 of h fis opig i his iusy is o vlop ioviv chiqus i o o uc gy cosupio. Of cous, h &D civiis couc o his w o ll ic by viol cosis o isig gy pics. This ws cily o h cs i h 6s fo xpl. O h oh h, h chologicl cox of such iusy is highly isig fo h suy of gy-svig iovio pocsss. To his cox, o hs o ssiiv viol issu, lik o h lcolysis chiqu us, which hs oiv icsigly sv viol gulio fo h l 6s. I, h i, h lcolyic pocss ploy ws cuy pocss, hus bs o highly oxic subsc. I ws livly quickly sblish h h cuy ls by h chlo-lkli iusy o h ighboig ss ws h cus of h so-cll Mii iss, which cus bou 7 vicis i h i. 6 Th Jps uhoiis s ulig gis chlo-lkli iusy fo h i-6s, sipulig og ohs quiiv liis o cool h lvls of cuy ls o vio. I 974, h Jps uhoiis ook sp fuh gis h iusy qui h covsio of s y cuy pls s possibl o h uiqu liv h i, h -i-usa iphg lcolyic pocss, by h of Now, cos h os isig p of h soy. Bcus h liv iphg pocss ws clly isvgous i s of gy cosupio cop o h cuy pocss, giv h pio of pily icsig gy pics cll h icuy pocss gulio ws k uig h fis oil cisis, i quickly pp o 6 Mii iss fs o Mii By i h Souh p of Jp, wh h fis css of cuy poisoig w iscov. 7 Isigly, s io by Yi 7, h fil cisio o ul ou h cuy pocss ws k wh h pocss ws ccouig fo 95% of ol cpciy, which of cous c hvy sios bw h poucs h Jps uhoiis. S o i Yi s coibuio.

9 8 boh poucs uhoiis h h ws ug o vlop liv lcolyic pocss, lss gy-cosuig h h iphg pocss lss polluig h h cuy pocss. 8 This oiv ssiv &D ffo i vlopig hi lcolyic pocss, h io xchg b pocss, h suspsio by My 977 of h covsio pog o h iphg pocss chology. As io by Yi 7, lhough h i of usig io xchg bs h b kow by y ys h i, sigific &D ffo ws o vlop io xchg bs p o h chlo-lkli iusy, h ub of p pplicios by Jps fis ics kly f h i-7s uil h ly 8s i his fil. I 998, bou 9% of h Jps chlo-lkli pls us h io xchg b pocss... Oh fus Svl oh isighs c b gi fo h chology liu cocig h ioviv pocsss i h iusy subjc o viol cosis. W shll io wo of h, which will b xplicily cosi i ou hoicl s-up. i Th ol of ficil cosis: This yp of cosis is, of cous, cucil s log s o is coc wih chologicl ovio, spcilly wh i is ipos by lw. If h fis o o fc y yp of ficil cosis, h hy coul fic &D xpius wih o lii, which is cily ulisic. I h cs of h Jps chlo-lkli iusy scib bov, ficil cosis v o cucil sic h whol iusy ws qui o swich 8 Yi lso io so pobls l o h poo quliy of h cusic so pouc by h iphg chiqu. This poi gos byo ou fwok bu i is cily highly iiguig.

10 9 chology i lii ou of i s h vy isig scipio of h b bw h chlo-lkli iusy h Jps uhoiis o h ficig of h qui &D pogs i Yi s pp. ii Th ol of chologicl coplxiy: I is vy wll kow h h succss of &D pogs ps, og ohs, o h coplxiy sophisicio of h chologis o b up-g. Coplxiy is hfo ful igi of ly chology opio hois à l Nlso Phlps 964 of o c s gowh hoy s fo xpl, Bo Sl-i- Mi, 995, chp 7, o Sgso,. Nlss o sy, h pobl of chologicl sophisicio is lso ssiiv bi o chologicl pogss bcus of lii ou of vilbl skills hi-ch cpil s Chuowsky Lopz, 7, pp 88-, fo h Agii cs. W shll k hs spcs io ccou i h fi gic pobl ss hf. 3. Th fi pobl W shll cosi h pobl of fi skig o xiiz h pofi h ks io ccou h gy cosupio E, h ivs o &D, h ivs µ io w cpil: I = [ Q p E k µ ] x µ,, wh k is h giv ui cpil pic p cpciy ui, p is h giv gy pic, - is h iscouig fco. H Q is h ol pouc oupu, Q = µ,

11 c = Q pe kµ 3 is h pofi o csh flow. W hfo posul Loif vig cpil poucio fucio s i Bouckki, Gi Lico 997, 999 o Hioko Ysko 996, 5. I quio, sus h vig ix of h ols chi sill i us i, o i oh wos, - sus h scppig i. Th whol coplxiy of h opiizio pobl cosi i his pp cos fo h fc h is cool vibl, which is qui uusul i cooic hoy. W shll co bck o his poi i il l. Fo ow, l us oic h w o o ssu y oupu-ugig boi o isboi chologicl pogss: whv h vig is, ll chis pouc o ui of oupu. I ou fwok, h chologicl pogss is xclusivly gy-svig, which is h ky copo of h b ou chologicl pogss viol susibiliy. I cos o h l liu obly o Fichig l., 5, 6 7, w ssu h fis ivs i &D. I flcs h fc h h viol pobls h lik o gy cosupio subsqu CO issios fi-spcific, so, h fis co siply ipo pxisig cl chologis. A v if lv chology coul b ipo lik h iphg chiqu i ou Jps iusy cs, cosly opio wok is. L us cll h lvl of h gy-svig chologicl pogss. W posul h his lvl volvs ogously ccoig o: ' f =, >, 4 wh f is icsig cocv: f/>, f/ <. Equio 4 svs fw cos. I bsiclly sipuls h h of gy-svig chicl pogss is

12 icsig cocv fucio of h &D ffo csig fucio of is lvl. Th l spcificio is sig o flc h giv ipc of chologicl coplxiy o &D succss. Th p sus h x o which coplxiy ipcs h of chologicl pogss jus lik i Sgso,, fo xpl. I will ply ipo ol hf, which is cosis wih h vilbl vic, io i Scio, o h ol of chologicl coplxiy i h opio of cl chologis. W lso ssu h h gy-svig chologicl pogss is fully boi i w cpil goos, which iplis, kpig h Loif sucu ouli bov, h ol gy cosupio is giv by µ E =. 5 W ow iouc h viol cosi o h fi, hough sipl issio quo cosi: E E x, 6 wh h gulio fucio E x is giv. Iplici i ou sig, h cosupio of of gy is h sol souc of polluio hough CO issios. sicig gy cosupio is hfo ic wy o lii polluio. Th fis lso subjc o sco yp of cosi, ficil cosi, which w lso ol i sighfow wy by iposig h posiiviy of csh-flows, c, y, s w will s l. L us ow suiz h opil cool pobl o ckl. Th ukow fucios : h ivs µ, µ, io w cpil su i h cpciy uis

13 h &D ivs,, h chology, h cpil scppig i -,, <, h oupu Q, csh-flow c, gy cosupio E, [,. Th cosis giv by h viol cosi 6, plus h posiiviy, liquiiy cosi oh guliy coiios:, c, µ,, <, 7 Th coiio is s cosi i vig cpil ols iplyig h scpp chis co b us. W shll lso spcify h iiil coiios s follows: = <, =, µ µ,, [,]. 8 Th opil cool pobl -8 hs svl hicl pculiiis cop o h ypicl opil cool pobl i cooics, which ks i qui h o ckl. W co bck o h chicl p i h x Scio 4 wh h cssy opiliy coiios vlop. Bfo, l us sss h followig cooic spcs: i Tchologicl pogss ollig : Ou folizio siplifis o gbl hicl coplxiy h chlo-lkli iusy xpl scib i Scio. I picul, whil h icivs o vlop liv chologis w iv by isic puly cologicl oivios g i of h cuybs lcolyic pocss gy-svig sos, h wo oivios g i ou ollig: h fi is vlopig gy-svig chologis o low is gy xpius o cop wih viol gulio. O h oh h, whil h chologicl us s o b lii o h i h

14 3 chlo-iusy cs cuy, iphg io xchg b pocsss, h &D ffo ws cully coiuous i i, sulig i o-lupy jcoy of ps s ocu i Yi 7. Hc, ou coiuous i sig is sill qu. ii Tchologicl pogss ollig : I ou ollig, chologicl ipovs ffc oly h w cpil goos. This is cysl cl i quio 5 givig ol gy cosupio. Of cous, his o b h cs i gl. A p of gy-svig iovios is pobbly isboi, o gl foulio of h pobl kig io ccou his spc woul, i picul, plc h ODE o, by PDE o,. This xsio is ou of h scop of his pp. As o c guss, ou opil cool pobl -8 is ly xly icky. Movig o PDEs spcificios of chologicl pogss woul oblig us o so ssivly o uicl siulio s i Fichig l., 6, which w w pcisly o voi. O h oh h, p of chologicl iovios i h wokplc of cous ipo, bu vhlss hly zo cos. Thfo, hy c b ``ipo i h chologicl vibl wihou y cisiv loss of gliy. iii Tchologicl pogss ollig 3: As i H 4, w c x h ol by isiguishig bw &D vo o ics oupu, &D viol-fily. This igh pobbly chg so of h suls of h pp. Giv h iuc lgbic cos, w hv ci o sic ou io o gy-svig chologicl pogss, which lso hpps o b h viol-fily iovios i ou s-up.

15 4 iv Eviol gulio: I his pp, w focus o issio quos, s his ss o b o of h sli chcisics of viol gulio boh h iol siol lvls. Oh policy isus coul hv b cosi lik issio xs s Xpps D Zuw, 999 fo xpl. Moov, i coul b isig o cop policy ools gig h fulfill of h Po hypohsis. This gos byo h scop of his pp. 4. Exu coiios W ow ov h ivio of h opiliy coiios. Fo hicl covic, w chg h ukow cisio vibl µ o = µ/, 9 which is lso h ivs io w cpil bu su i h gy cosupio uis h h i cpciy uis. I h vibls, h opiizio pobl -8 bcos I = [ Q p E k ] x,, c = Q pe k, Q =, E =, E E x, 3,, c,, <, 4 = <, =,,, [, ]. 5

16 5 Th subsiuio 9 ovs fo quio 5 s i o h ls i h fuciol. Equio 4 fo h ukow is h s. I h cs >, h soluio of 4 hs h fo: / = f v v B, 6 wh h cos B= = f v v / is uiquly i by h iiil coiios 8 o 5. Fo ow o, w wok wih h followig xplici spcificio fo ogous chologicl pogss: f=b, <<, b>. 7 By 4, his iplis h h lsiciy of h of chologicl pogss wih spc o &D xpius is cos qul o. Th lg is, h bigg is h fficicy of ivsig i &D. Th opiizio pobl OP -7 iclus sv ukow fucios,,,, Q, c, E coc by fou quliis,, 3, 6. Followig Hioko Ysko 996, Ysko 4, Ysko Hioko 5, w will choos,, s h ip vibls o cools of h OP cosi h s of h ukow fucios,,, Q, c, E s h p s vibls. Th joiy of opiizio ols of hicl cooics usig FOC fis-o coiios fo iio jcois oly. I cos, h u of h OP -7 quis kig io ccou h iquliis E E x,,,, <, c o ukow vibls i h cosis 3 4. Ths iquliis hv ssil ipc o xu coiios opil yics

17 6 iffly i h blow lysis. Th iquliis h s cosis o cool vibls, which coo i h opiizio hoy. Th o-s cosis < hl followig h chiqu vlop by Hioko Ysko i svl pps ly ci. Th cosi E E x is cosi i wo css of Tho blow. Filly, h cosi c is h os icovi hiclly is chck posioi s k blow. L h giv fucios p, k, E x b coiuously iffibl, b coiuous. To kp h OP s coc, h soohss of h ukow vibls shoul b cosis. W will ssu h h cisio vibls wh cssy subl los vywh.. o [,. Th, h ukow s vibls, c, Q, E i -5.. coiuous o [,, s sblish i Hioko Ysko 6. W lso ssu pioi h h ipop igl i covgs i will b u i ll subsqu Thos -4. Th cssy coiio fo xu NCE i h OP -7 is giv by h followig s Tho. L *, *, *, *, Q*, c*, E*,, [,, b soluio of h OP -7. A If E*=E x c*> [,, E x, h I ' *=, I '= *>, 8 I ' *=, I '= *>,, 9 wh

18 7, ' k b I = [ ] ' k I =, h s vibl is i fo 3, is h ivs fucio of, B b =. B If E*<E x c*>, h I ' *=, I '= *>, I ' *=, I '= *>, 3 I ' */=, I '= */>,, wh [ ] ' k p I =, 4 p I ] [ ' ' =, 5 I ' is s i, is s i. Th poof is vy log chicl w po ll h ils i h Appix. Th xpssios,, 4, 5 h Fsh ivivs of h fuciol I i vibls,,. Th iviv I hs iff fos 4 pig o whh h sicio 3 is civ o iciv. Bfo givig h cooic ipio of h opiliy coiios, so chicl cos i o.

19 8 k. If 3 is civ Cs A, h h s vibl is i fo = E x h s sicio o h vibl i 4 is sisfi if E x, [,. If h coiio E x fils fo so [,, h Tho is sill vli i Cs A if w plc h iffil cosi i 4 wih h sic cosi x{, E x } o h cool s Hioko Ysko, 6, fo poof. k. To kp hicl coplxiy sobl, w o o iclu h cosi c io h NCE. To b copl, Tho hs o iclu wo o css: E*>E x, c*=, E*=E x, c*=. Th pobl -7 i hs css shoul b s OP wih s cosis, which ls o sigific hicl chllgs s Hl, Shi Vickso, 995, fo isigh io his issu. As w shll s, h gi c*= os o usully pp i h log- yics Scio 5 y hv ipc oly o h siio yics s o of possibl scios Scio 6. k 3. Suffici coiios fo xu fo such OPs coplic ivolv h sco Fsh ivivs of h fuciol I. Th uhos iv lyz such coiio i I I h fo J = < =*, =* fo h Cs A wih civ sicio 3. I I I is o iclu io his pp. k 4. Th vig ols wih ogous TC uli-xl u ul coiios, s Chp 6 i Hioko Ysko 996. W c show h h OP -7 y lso possss wo locl x: h ivil soluio,,, [,. Th soluio is vifi by is subsiuio io,4,5, h I <, I <, I <, i.., h NCE 3 hols. This locl soluio scibs cooic yics wih o ivs o chologicl ovio wh h i pofi gos o h cosupio goos. Th ivil soluio is o sbl i h ss h so sll posiiv ivss i w cpil &D c foc h cooic sys o jup o h x soluio. h o-ivil soluio, wh *, *, * posiiv, ls, o so ps of h plig hoizo [,. I scibs h cs wh h cooic sys islls w quip ivss io scic chology. Th pp focuss o h sucu of h o-ivil soluio *, *, *.

20 9 L us ov ow o so cooic ipios of h obi fis-o opiliy coiios. I o o cop o sily wih h xisig liu, w s wih h cs A, h is, wh h viol cosi is biig. I, i such cs, h biig viol cosi c b boly viw s quilibiu coiio i h gy k, wh h quo plys h ol of supply. L us ip h opiliy coiios wih spc o ivs &D, h cs of scppig big ivilly fix by k bov. Usig quios 9, h iio opil ivs ul y b wi s: = k Th ipio of such ul is qui ul hvig i i h ly vig cpil liu obly Solow l., 966, Mlcoso, 975 s xploi i Bouckki, Gi Lico 997. I ou ol, o ui of cpil coss k o k i ps vlu. This is h igh-h si of h opil ul bov. Th lfh si shoul hfo giv us h gil bfi fo ivsig. Effcivly, i is h igl of iscou gis fo ivsig ov h lifi of chi bough sic - is by cosucio h lifi of such chi. A y copis bw -, chi bough will povi o ui of oupu bu h fi hs o py h cospoig gy xpius. Giv ou Loif spcificios, is h gy qui of y chi bough. plys hfo h ol of h ffciv pic of h ipu pi by h fi. How coul his b ioliz? Siply by oicig h u biig viol cosi, h

21 l iics clig k coiio s i h ly vig cocooic liu s fo xpl, Solow l., I such fwok, h gil pouciviis of gy shoul b quliz coss vigs, iplyig igh cocio bw h ffciv pic of gy h gy qui of h ols chi sill op. Mo pcisly, h l pic, which hpps o b h Lgg ulipli ssoci o h biig viol cosi, is qul o h ivs of h gy qui of h ols chi sill i us, which is qul o y copis bw -. Noic h i such cs, h ffciv pic of gy is o glly qul o p. Th l os o ply y ol sic gy xpius bco pi qul o pe x i h cosi gi. Thigs coplly iff i h cs wh h viol cosi is o biig cs B of Tho. I such cs, h opil ivs ul bcos followig quio 4: p = k, = p s i h fi pobl sui by Mlcoso 975 wih gi lbo plyig h ol of gy, kig cl iffc wih spc o h cosi cs A. Ou fwok hus xs sigificly h bchk hoy o llow fo siuios i which ipu ks o o cssily cl u o isiuiol cosis. L us ip ow h &D opil ul, which is lso w i h liu. Usig, i is giv by 9 I Solow l., h ol of gy is ply by lbo.

22 b k = Th igh-h si is siply h ps vlu of gil ivs i &D. Th gil bfi is giv by h lf-h si. Coy o h opil ivs ul, h gis fo oig &D ls fov: h &D ivs iucs kowlg ccuulio pocss, which is o subjc o obsolscc i ou cs, i cos o cpil goos. Th ig c b usoo if o hs i i h xiiz fucio i h fo I = [ p k ] h giv ogous lw 6,7 of oio of chologicl pogss. I shoul b oic h wiig h pobl i s of, h h i s of ivs i physicl uis µ, os o wiig pobl wih ipu-svig chicl pogss s pobl wih oupu-ugig chicl pogss. As o c s, fix, ics of, hfo, icss o oly h oupu Q bu lso h ivs xpius hough h k. Th lf-h si of h opil &D ul ks pcisly io ccou his -off. O o h, h gil ics i,, followig h gil is i, h is b, ipcs posiivly oupu by ipovig h fficicy of ll vigs f. Noic h sic chis hv fii lifi, his ffc shoul b copu bw - fo ch vig, which xplis h fco = s s i h ig. O

23 h oh h, h isig icss ivs xpius fo fix, which xplis h giv, k, i h ig. W ow ov o h suy of h sys of h opiliy coiios xc bov. W fis s by skig fo xpoil soluios fo ully gowig vibls lik, h so-cll blc gowh phs Scio 5, which c fu ki of log yics, h w ov o sho- yics Scio Alysis of opil log yics. Th opil log yics of h OP c ivolv iio gis such h I ' I '. L us ssu h h viol cosi 3 is civ i h log u: E=E x [ l,, l w will suy h liv cs l. Th cospoig log- iio gi Λ, Λ, Λ is i by h sys of h oli igl quios I '=, I '=, x E =, [ l,. 6 wh I ' I ' i by. Th quios I '= I '= l o k B b b = /, 7 k B b B b = / / / 8

24 3 [ l,. W will xplo h possibiliy of xpoil soluios fo, whil - cos, o h sys 6-8 sply i h css =, > <. Fis of ll, w s wih h followig pliiy sul: If is xpoil, h is los xpoil pciclly uisiguishbl fo xpo lg i h ss of h followig l: L. If = C fo so C>, h / / b C C / 9 / / C / lg. I picul, = b C / if b = CB. Poof. A = C, / / Cv b C b = b v B = B. C C ~ Diviig by = / b C / C /, w obi / / b C B b CB C / C / b / C C C b = = ~ Expig h fucio x c io h sis, w obi ~ = ε, wh h sll p CB C CB C ε =... css s b b C. Th l is pov. Fo bviy, w will oi h xpssio lg wh usig h oio f g

25 4 W ow fi h cocp of blc gowh phs cosi. Dfiiio. Th Blc Gowh Ph BGP is soluio,, o 6, 7 8, wh is xpoil - posiiv coss. If h viol cosi 3 is o biig, h h sys o b solv is I '=, I '=, I ' '=, [ l,, 3 wh I ', I ' I ' ' i by, 4, 5. As show blow, h opil log- gowh wih iciv gulio, E<E x, is possibl oly > s Scio 5... k 5. I h cs of h iciv viol cosi 3, i is covi o iouc h Fsh iviv I ' = ρ [ p ], 3 of I i is of h Fsh iviv 5 i us i uig BGP lysis. I, i is sy o s h if I ' [ l, fo so l, h I ' [ l,. 5.. Blc gowh i cs =. I his cs, h p of &D fficicy, <<, is qul o h p of &D coplxiy, <<. I his cs, h opil log- gowh ivolvs h civ viol gulio ul coiios. Nly, L. A =, y iio soluio,, of h OP -7 wih xpoilly gowig ivolvs h civ viol gulio: E=E x sig so f, if h followig coiios hol: h viol cosi E x is bou o [,,

26 5 b h giv gy pic p os o ics o icss slow h h opil : li p / =. / Poof. L us cosi = C, h C b / C by L. W ssu h E<E x [ l,, l. Th, by Tho, OP iio gi,, hs o sisfy h oli sys 3. Subsiuig h bov io h xpssios 3 fo I ' I ', w obi fo 3 h / C b / C p =, 3 b b / C C C k, [ l,. 33 Equio 3 is, which is such h - bcus of h coiio b. Equio 33 is giv. Af ioucig h fucio f = [ [ ] ]/ k iffiig 33, w hv = [ C ] C / b / b / f. Sic f</ fo y possibl k, h >cos= [ C ] C / b / b / >. Thfo, by 3, E icss ifiily. A h coiio, ou ssupio is wog E=E x so > l. Dpig o h yics of h giv E x, i c bco E<E x so >, bu E=E x. Th l is pov. Though i ks us of cool vibl h is, h sicio b o h pic of gy is cully qui ul. I will b fi log h wy whc h opil cool b chciz. I, s flc i Scio 6. blow, wh h gy pic is oo high i h spii of L, h fi gos io copl collps wih zo opil ivs i boh quip &D. Hcfoh, gy

27 6 cosupio will islf go o zo, h issio quo cosi will o b biig sypoiclly. I his ss, gy pics ply ol i h iio: oo high pics will iscoug y yp of ivs, lig h fi io collps i h logu. This s h such siuio h ucovs cs wh h Hicksi chis os o wok, which is hly supisig: x ipu pics c v u io ivs icivs. Coiio b is suffici. I Scio 5.., w will s o spcific posioi sicio 45 o h gy pic ics, u which blc gowh wih h civ viol gulio ks plc Gowh u o-cos vio Th pupos of his scio is o pouc so ul o-xisc suls. I ffc, o woul xpc h oo sig viol gulio c by o s iply y cou-blcig Po o iuc-iovio chis. Ou suls cofi his iuiio. O h oh h, s clly highligh i h 975 Mlcoso s wok o h so-cll Tbogh-Sih popy l o h coscy of opil scppig i, fo h ol o g gul xpoil soluios wih cos xpos, so sog coiios o h focig fucios of h pobl. Aoh isigh gi by h lysis blow is h ol ply by h pic of cpil quip s flc i h followig ho. Tho. If = h coiios of L hol, h o xpoil BGP wih posiiv gowh xiss if h viol cosi E x oooiclly css o icss O h cpil pic k oooiclly css o icss.

28 7 Poof. By L, E=E x [ l,, l. Th, by Tho, OP iio gi,, hs o sisfy h oli sys 6-8. Cs : E x css icss. Th =E x / by 6, hc, css icss fo cycl o cycl =cos is o possibl. Cs : k css icss. L us subsiu = C io h FOC 7 8 fo h civ vio gulio cs si h obi xpssios. / Applyig L, w fi h C 8 ls o C [ ] k b / C, h 7 ls o quio Th quliy 34 is h giv k. Is lysis shows h -=cos [ l,, is possibl oly if k=cos, [ l,. If k css icss, h - css icss - cos. Th ho is pov. I is isig o cop h ipc of h viol cosi cpil pic o log- yics. By Tho, if E x css /o k icss ov i, which cov h wo ufvobl css of icsigly sig gulio icsigly xpsiv cpil goos spcivly, h h BGP i h ss of Dfiiio os o xis. I gl, quio 33 oss h h cosi k < /, 35 is cssy fo h xisc of y iio gi. Howv, s follows fo h poof of Tho, h giv cy o sig gulio c b cops ci x wih chp cpil goos, h, log- gi wih

29 8 xpoil csig - is possibl. Nly, h followig fi is isig o po: Coolly. L = h viol cosi 3 b civ. Th: If k gowhs up o h vlu /, h o iio gi wih xpoil gowig is possibl. b If E x, h o such iio gi is possibl. c If boh E x k cs, h, iio gis wih xpoil gowig possibl i so gs of E x k chg. I picul, if k oooiclly css o, h E x is lg h posiiv cos. Poof coius Cs of h pvious poof. L us ssu h h log- = C, C>, is coiuous. Subsiuig io 6-8, w obi Th s iily follows fo h posiivss of h lf-h p of 33. L k. Th, i follows fo 34 h h ukow - css -. By h vlu ho, E x =[-], wh <<, E x [-]. Nx, o c s h 33 c hol oly if [ ] k C E =cos>, 36 wh C E =[C-]C/b - /b is fou fo 33. Sic -, h [ ] fucio f = [ ]/ k - k. Thfo, 36 ls o [ - k] C E o [k] C E. Hc, E x C E k

30 >C E > E x c o cs o h s c. If w ssu E x, h 36 c o b hol. I povs ou s b. 9 Coolly oss h h ipc of h viol cosi o h log opil yics is o ssiiv h h cpil pic. Mo spcificlly, ssil cs i h viol gulio E x co b cops wih h vilbiliy of chp cpil goos v if k. No xpoil gowh is possibl if E x. Howv, xpoilly csig cpil pics sill copibl wih xpoilly isig &D ivs csig fii ozo quo issios. W ow ov o h cs of cos cooic isiuiol vio, which is h cs wh blc gowh phs ypiclly is s Mlcoso, Blc gowh u cos vio Th followig ho sblishs h xisc of blc gowh phs i h ss of Dfiiio wh h cooic isiuiol vio is hl cos. Tho 3 bou blc gowh. If =, E x = E =cos, k = k =cos, 37 h h iio opil gi BGP Λ, Λ, Λ xiss, Λ C, Q Λ, Λ,c Λ ~ C, Λ =M =cos, Λ = E /M, 38 wh h coss C M i by h oli sys C / [ / C ] = M b / E / M k, 39

31 3 C E / M CE / M E / M = k, 4 h hs posiiv soluio, ls, sll. Nly, if << / / < E b [ k ], 4 h C, <C<, is soluio of h oli quio C / [ C ] = E b / k C C o 4 M = E C / k o. Th uiquss of h soluio is gu if / / < Eb 4 / k. 43 C If li p =, h h iio opil c Λ > lg. Poof. By L, b / C Λ C =. Th subsiuio of 37, 38, Λ io 7 ls o bm C, f igio, o b C C E / M k =, E / M M b C k C = h c b wi s 39. Subsiuig 37, 38, Λ o 8 givs E / M C E / M C [ ] k which bcos 4 f igio.,,

32 3 Equios 39 4 y hv posiiv soluio C M ul ssupios. I picul, l <<. Th, psig h xpos i 4 s h Tylo sis, w obi k o M E M E C o M CE M CE C o M E M E = / / / / / / o k o M E C C M E M E M E = / / / / o [ ] k o C M E / =, which hs h soluio / o k C E M =. Now, xpssig h xpo i 39 s h Tylo sis, w obi = k o M E M E b M C C ] [ / / 44 Subsiuig h obi M io 44 ls o o quio 4 fo C. To lyz his quio, w us h w vibl C x = wi 4 s F x = F x, wh F x= / x x, = / x x k b E x F Ths fucios show i Figu such h F =, F x> <x<, F x= x=, F x> <x<, F x= x=. Also, F x<<f x sll <x<<. Thfo, o hv soluio < x < o h l quio, i is

33 3 cssy suffici h F >F, which ls o h iquliy 4. Th suffici coiio fo h uiquss of x is F x<f x <x<, which ls o 43. Filly, l us pov h c Λ > lg. By, C M CE C C b M Q / / Λ. Thfo, c Λ = Q Λ k Λ Λ Λ E p / / p E k C C b M C M CE. Expssig h xpo s h Tylo sis usig 44, w obi / p E C C p E C C p E k o M E C M E C b M c C C C = > = Λ 45 If li = C p, h c Λ > lg ough fo y posiiv vlu Λ. Th ho is pov. Th uiquss coiio 43 is suffici. A lysis shows h h soluio is usully uiqu wihou his coiio. Th oly possibl cs of o-uiquss wh w his coiio is wh h opil C is vy clos o. A iiol lysis will b povi l o xplo his issu. W ow s so qui isig copiv sics suls highlighig how h blc gowh phs c o chgs i h viol gulio o pic ps.

34 33 Coolly 3. A 37 <<, cs of E ls o h cs of boh opil ps C M, lv h log- lifi of cpil goos ul sic M ~E. A cs of k css h opil C, icss h opil M iiishs h log- lifi of cpil goos s M ~k /. Mo sig viol gulio hough cs i E is b fo h gowh of fis oupu pofi. Though fis spo o viol gulio by xpoil &D ivs ffos, h pc of such ffos is ubiguously givly ffc by icsigly sig issio quos. Sicly spkig, ou log lysis uls ou h occuc of ki of Po hypohsis sic o sig viol gulio os uc h gowh of fis oupu pofis. This xs h suls of Xpps Zuw 999 Fichig l. 5 i h issig icio. Ev hough h fis c spo o igh issio quos by o iovio, such isu os o llow o coplly cicuv h ipc of o sv gulio. I cos, ou sul ss o go os wih H s picios 4 ccoig o which issio x y v boos h gowh of poucio i h cooy. Howv, h l pp is bs o cocooic fwok wh h poucs, hus h pollus, o il o sp o iovio. This igh xpli h iffc, og oh possibl sos. Low cpil pics goo fo ivs i gy cosupios uis bu pov b fo h gowh of fis oupu pofi. This igh sou s supisig. Nohlss, o shoul kp i i h low cpil pics y l o cliig &D ivs pcisly bcus hy o siul ivs i physicl cpil,

35 34 fuig ki of subsiuio bw ivs i physicl cpil ivs i &D. Th is, h fi pfs o k pofi fo h xogously csig cpil pics h h icsig is cosly &D xpius. Sic ivs i &D is h uiqu souc of gowh i his fi s pobl, h gowh y b pliz by csig cpil pic ps. This is xcly wh ou ol pics i h log u. A fuh isig sul cocs h opil log- lifi of cpil goos. Sic Λ = E /M, M ~E, i follows h igh viol gulio lvs h opil lifi of cpil goos ul. Whil low E os uc h opil lifi of chis, h fc h such igh gulio os lso push ivs oww pushs h xiizig fi o us h fw chis log. Th wo ffcs xcly offs ch oh i ou fwok. U csig pics fo cpil goos, h fi ivss o uss h chis fo sho i. This is sohow cosis wih h c liu o boi chologicl pogss obsvig h o pi ivs-spcific chologicl pogss lik h o covy by h ifoio couicio chologis ucs h liv pic of cpil goos css hi lifi u o isig obsolscc coss s fo xpl Kusll, 998. k 6. I Tho 3, h BGP scl p pps o b ui. W hv h iicy of h log- yics u h BGP bcus chicl pogss is ogous. I hpps fo siil pobls i h ogous gowh hoy. A ypicl xpl is h Lucs-Uzw ol s h book of Bo Sl-i-Mi, Ecooic Gowh, Chp 5, Bouckki, uiz-ti 8.

36 35 Filly, i shoul b o h h gy pic p is o ivolv i h BGP 38. This is f fo supisig sic w hv cosi biig viol cosis so f. I, u h civ viol cosi, h gy pic p is o ps i h NCE fouls 8- h opil log yics Λ, Λ, Λ will b h s fo y p up o ci lvl h ps o h chos iicy p. By Tho 3, if h giv gy pic p icss slow h h opil Λ s lso coiio b of L, h c Λ sypoiclly. Th gy pic p lso hs iic ffc o h opil cools *, *, *, sic p ipcs h ogous c*: high p s low lvl of csh c*, lss oy i h pock. Howv, whil h csh flow c* is posiiv, h log- fi opil policy BGP is o ivs h s i chis i &D. W shll s i Scio 6 h h gy pic ipcs h siio yics i ou ol, i y b i such wy h w will v ch h BGP s Scio 6 blow. Th ol of his pic i h log-u yics is vli qusio wh > h h viol gulio is o biig will b cosi i Scio 5. hf. k 7. If quio 4 hs soluio < C <, h, i h gl cs, i hs oh soluio C, <C </-. Howv, h lg soluio C hs o ss, sic C> h vlu of is ifii c*< by 45. Nuicl Expl. L =.5, =.5, b=., E =.5, k=.. Th, h soluio of h oli sys is C=. Λ =M =., which c b vifi by is ic subsiuio io I such cs, h pe of h objciv fucio bcos pe x, xogous.

37 Css < >. I hs css, o BGP i h ss of Dfiiio xiss. Howv, log- gi wih xpoilly gowig csig pps o b possibl spcil cobiio of giv ps. Tho 4. L E x = E =cos k= k=cos. Th: If <, h o iio opil gi wih xpoilly gowig xiss. b If >, h iio opil gi Λ, Λ, Λ such h Λ gows xpoilly, Λ, E<E x, is possibl ONLY if p xpc/ wh C is h ogous of Λ. Poof. L us subsiu = C = M D io 7 8 si h gowh o of h obi xpssios. / b C / Applyig L Tho, w fi h, C / I / C b C D ' b M k C 46 If E=E x, h I ' [ ] k 47 h s vibl is fou fo 8 s = [ D M E ] D / D 48

38 37 Cs <: To kp I '= by 46, w xpoilly gowig wih D=C/>. Th by 48 I '< by 47, hc h opil. Th is o iio gi wih C> possibl. Cs >: By 46, h sicio k</ 49 is cssy fo I '. If 49 is vli, h, o kp I '= by 46, w icsig ~ C csig ~ D wih D=C-/<. Th ogous C> is o b i. Sic css xpoilly, w hv h cs E<E x wih h iciv viol gulio fo y icsig. Th, by 4 3, I ' = [ p ] k = { p }, 5 I ' = = 5 Th quio 5 hs o soluio if p cos. L p=p s, s>. Th 5 hs h fo / C / b s I ' p =. 5 C Equio 5 hs uiqu soluio such h s/c. So, w hv o ssu s C fo kpig h cosi <. L s<c. Th by 5. Subsiuig p=p s io 5, w obi I / C C / C b ' b = C k k k > C C C C,

39 38 fo y C> bcus of 49. Thfo, o xpoilly gowig iio gi is possibl i his cs. Filly, l s=c. Th, by 5, =L, wh L=cos> p <B. Subsiuig p=p C/ io 46 5, w obi sys of wo oli quios wih spc o C M. Th sys is siil o h quios 39-4 i Tho 3. Is lysis shows h possibiliy of posiiv soluios C M so sicios o p oh ps. Th ho is pov. Wh >, h fficicy of h &D ivs pps o b high s cop wih h ivs io h w cpil. Tho 4 coclus h, i h opil log-i gi, los ll h oupu gos o &D ivs h p of cpil ivss xpoilly css i h ol isibuio of h oupu. Also, h vio cosi is o biig w c kp lg ou of ol sss sic w buy icsigly sll ou of w cpil. By 49, h sicio k</ o h giv cpil pic is cssy fo h xisc of y posiiv opil gi. Th gy pic p plys ipo ol i h cs >, i picul, iio gi wih xpoil Λ opil ph is ipossibl if h gy pic p os o ics. Oly if p icss wih ci, h iio gi wih xpoilly icsig Λ csig Λ is possibl. Th ics of p iss Λ, h is, css h lifi of cpil goos. I oh wos, ki of iuc-iovio chis ss o b civ i h cs >, h is, wh h &D civiy is highly ffici, so ffici h h ivs vo o quip gos o zo. I such cs, h fi is i ppully shp oizio, is o suffig ll fo viol gulio. W hv o oic h his

40 39 iio gi is o BGP i h ss of Dfiiio bcus Λ sypoiclly s o zo. W shll isg such cofiguio i h sho- yics scio blow. 6. Tsiio yics Fo ow o, w s =. Sic w hv o l wih sho- yics i his scio, so cos o h iiil coiios i o. Th OP soluio *, *, * sisfis h iiil coiios 5. A ssil iiil coiio is = bcus h ukow is coiuous. If Λ, h h yics of *, *, * ivolvs siio fo h iiil s = o h log iio jcoy Λ if i xiss. By 4, c = Q-pE--k h iiil s =, o p E k B v v 53 ohwis, h cooic sys is o possibl = bcus of oo high gy cpil pics p, k. Coiio 59 iplis wo sipl cosis: p < B k < E. 54 Ev if 53 hols, h opil yics y b such h h cooic sys will v ch h viol sicio E=E bcus of oo high gy /o cpil pics. L us os h cospoig scios. 6.. Th collps css.

41 4 L E<E x h iiil i. Scio : Th cs of oo high gy pic. L us ssu h h xl k gy pic p icss fs h h opil.g., if is xpo wih h lg h C i h cs =. Th, by 5, I ' '> fo ll h opil sgy is o kp h lifi of h cpil * s sho s possibl bcus of h high gy cos p. I his cs, h opil * soo bcos *= h opil w ivs *= is i by h sig I '< i 4. By, I '< h opil *=. So, h opil yics is siuio of cooic collps o cpil ovio copl scppig of xisig cpil bcus of oo high pic of h souc. By 3, h vibl E sivs o is lwys lss h E x. If p icss wih xcly h s s h opil, h h cooy y gow bu v ch h viol cosi E=E x. Scio : Th cs of oo high cpil cos. L h k pic k of w cpil icss o v ifiily bcos k / c fo so c >. Th, by 4, I '< h opil w ivs *= c. So, h opil sgy is o buy o w cpil. By, I '< h opil *=. By 5, I ' '<, hc, *=. Th opil yics is h cooic cli o &D ivs, o cpil ovio o cpil scppig bcus of oo high pic k of h w cpil. Th vibl E E<E x =E x, i.., h viol cosi is v ch.

42 4 Th bov scios o o flc h u of chologicl cpil plc. I Scio 6. blow, w cosi css wh h opil sys yics ivolvs cpil ovio. Th OP poucs quliivly iff opil gis *, *, *, [,, pig o whh h viol blc sicio 3 is civ, E=E x, o iciv, E<E x. I ou ol, h fis-pollus h fis fo which h sicio is civ. W will cosi h css of fis-pollus fis-o-pollus sply. A =, h log- BGP yics ivolvs h civ viol sicio 3 s Tho 3. As show blow, h siio yics chs h sicio Opil isiv gowh h cs of iy fi. L us ssu h E k =E x k sig wih h is k, k. Also k</, ohwis o gowh is possibl s Scio bov. Scio 3: Th isiv gowh civ vio gulio. L k =. Th opil yics k follows Cs A of Tho wih h civ E=E x sicio. This gi is gowh wih isiv cpil ovio iuc by chicl pogss. I o o k w cpil ivs k, h fi s o scp so obsol cpil, followig quliy 3 u h giv E=E x. I h log- yics cosi i Scio 3., h opil &D iovio * is h iio jcoy Λ. Th opil * chs h jcoy Λ iily f k. Th OP hs h iio upik jcoy Λ fo h cpil

43 4 lifi, i fo I '=. If Λ =, h h opil * Λ. If Λ, h w c show h h opil * will ch Λ f so i l k. If Λ <, h h opil ivs *= is iil < l. L, > l, h opil * hs cycls h plc chos s i Bouckki, Gi Lico, 997 i by h phisoy of o [, k ]. A fol poof of his opil *, * yics c b o siilly o Hioko Ysko 5. U Scio 3, h gy pic p is o ps i h NCE fouls 8-, hfo, i os o ipc h opil siio * * siilly o h log yics whil sicios hol. Of cous, ics of h gy pic p ucs h cospoig opil Q* c*. Figu h followig siulio xpl illus his scio. Expl. L =.5, ==.5, b=., E x = E =.5, k=., p=.5, =, =, =, =5.5, [,]. 55 Th, B== by 6. Th is h BGP, clcul i Expl bov, Λ = C, C=., Λ =M =., Λ = 5, [,, 56 iic by h gy lis i Figu. I his cs, E= =5.5*=.5 is qul o E x, hc, h viol blc 3 is civ sig =. Sic Λ =5 < =, h h opil *= *= < l =3. Af l, h opil * coicis wih h BGP Λ *=*-5 xhibis plc chos Opil xsiv gowh h cs of fi-o-pollu. This cs s h h gy polluio blc E h iiil s = is low h h lii E x. L us ssu h E<E x < k, wh h o k will b

44 43 i. Mhiclly, his cs is o coplic ivolvs h gi c*=, o cov by h NCE of Tho. So, w sic ouslvs wih uic xpl is cooic ipio o o povi y fol poofs. Scio 4: Exsiv gowh. If p os o ics, h by 5, 3, 54 I ' '< I '<. Hc, * is opil whil E<E x s Expl 3 blow. A h s i, if * icss h giv k os o ics, h I '> by 4, hc, h opil ivs * is xil. So, o c buy w cpil h is o o ov h ol o, i.., w hv xsiv gowh. O h oh si, by, I '> sll *, hc, h opil * is posiiv hfo, * icss i. I his cs, h cosi c* i 4 liis boh cools * *: Q* * k** pe*. 57 Th, h siio opil yics o so iiil pio [, k ] is i by h sicio c*= o * k** = Q* pe* 58 uil E k =E x k. Sic h opil * icss, h gy gulio lii E=E x will b ch soo h opil ovio yics will swich o Scio 3 wih h civ cosi 3. Th k of h iiil siio pio [, k ] is i fo coiio E k = E x k. If h giv p icss ifiily, h * is i by 35, I ' '=, I '=, *=p, hc, * icss. If h p ics is slow h h opil pouciviy, h h opil cpil lifi * lso icss whil E<E x.

45 44 Expl 3. L ll giv ps b s 55 i Expl bu =, [,]. 59 Th h BGP 56 is h s s i Expl bu h siio yics is iff. I his cs, E= =*=4 is lss h E x =.5, hc, h viol blc 3 is iciv o iiil ivl [, k ] h bgiig of h plig hoizo. Th yics of h opil * * o [, k ] follows h sicio c*= is show i Figu 3. Th iio of * * ivolvs iiol hoicl cosiios bs o vyig h quliy 58. I pps h *=7.8, *=.3 k. Th, h cospoig E* icss fs chs h lii vlu E x =.5 k.36. Th l opil yics o [ k, is scib by Cs A of Tho is siil o Scio 3. Nly, sic Λ.36< =, h *= h opil *= is iil uig h sco p of siio yics,.36 < l =3. L, >3, *= Λ h opil *=*-5 hs plc chos i by h pvious yics o [-, 3]. k 8. If h posiivss of c is o ssu, h h opil * jups o ifiiy iily f = bcus of h possibiliy of boowig, so h blc E=E x will b ch iily f =. Mhiclly, * ivolvs h l-fucio =. Th h lgh of h siio pio [, k ] is zo. Th opil yics highligh i his scio qui w i h l cooic liu s fo xpl, Bouckki, Gi Lico, 997. Thy sv so cos: i A fis, o h h oizio policy chos by h fi cosiss i icsig ivs i w quip &D wihou scppig h ol o polluig chis. I Hioko Ysko 996 Bouckki l. 997, h oizio policy lso copsss scppig p of h ol cpil goos i wy siil o h isiv gowh scio scib i Scio 6.. Th so bhi his iffc is qui ly:

46 45 whil i Scio 6., ivsig i w chis fo fix lvl of chologicl pogss is o possibl wihou scppig so obsol ol chis bcus of k clig coiios o biig viol cosis spcivly, fi wih low ough iiil cpil sock so wih low ough iiil polluio sock hs o iciv o scp is ol chis s log s is issio quo cosi is o biig. ii No h i ou cs fis which hisoiclly sll pollus pcisly hos which hisoiclly sll poucs. Ex o couy lvl, ou xcis pics h hisoiclly poo couis will fi i opil o ssivly ivs hfo o ssivly pollu uig hi vlop pocss. Duig such siio, w cl chis will co-xis wih ol iy chis i h pouciv scos, iplyig ubiguously iy siio. I his ss, ou ol povis w ico-fouios o ssil p of h viol Kuzs cuv s og ohs, Chili B, 5. Th x scio sblishs h uig his siio, h uiqu bk o polluio is h gy pic, which suggss fiscl of h viol pobl uig h siio. Nohlss, h -off is cl: if gy xs is o cu gy cosupio, h i will ffc h pc of chologicl pogss ivs givly, fuig ki of vs Hicks chiss, s pov i h x scio Th ipc of gy pic o xsiv gowh.

47 I h cs of xsiv gowh Scio 4, h siio yics is icly ipc by h bhvio of h gy pic p bcus of L p oooiclly ics. Th * icss is uiquly i fo I '= 5 kow *, whil E*< E x. Th log iio jcoy Λ fi i Scio 5.. sisfis h quio I ' Λ ; =. W ssu h p is o oo high, so h I '*; > i * is xil uig siio yics h liv cs is Scio i Scio 6.. Th, h siio yics is gi c*= * * sisfy 58 whil E*<E x o iiil ivl [, k ]. W will cop h siio yics u wo iff icsig gy pics p p, p < p, iic cospoig opil *, *, * wih h subscips. By 5, h sucu of h quio I '= is such h *< * whil E*<E x. Th ogous Q*, *, E* o iil h * *. O h oh h, h xsiv gowh p [, k ] of siio yics is usully vy sho s Expl 3. Th, by 58, * k* * > * k* * 6 [, k ]. Ivolvig iiol soig bs o vyig h quliy 58, w c pov h *> * *> *. Thfo, boh * * sll high gy pic p. This sul c b suiz s h followig popy: Duig h siio yics wih iciv viol cosi, ics of h gy pic p focs o isiv cpil ovio wih sho cpil lifi -* bu css boh cpil &D ivss * *.

48 47 L us highligh h x cs of h pics p p such h Qp E> bu Qp E=. Th, by 58, * o * posiiv, bu * =* = sic ll giv oupu Q is sp = o buy gy bcus of oo high gy pic. U ul ssupios, h poucio will v bco pofibl h pic p. As ouli bov, w g h cs fo ivs iuc-iovio chis u iciv viol cosi. High gy pics iuc sho lifi fo cpil goos bu hy pss ivs i boh w cpil &D. 7. Cocluig ks I his pp, w hv sui i ph h opil bhvio of fis subjc o issio quos liquiiy-cosi. W hv sp subsil p of h fis scios of h pp o jusify why such pobl u ogous chicl pogss h is, wh fis sp o &D is cucilly ipo o ckl. I iio, h vig sucu s lis o h pobl u suy cosibly ichs h iscussio. W hv xc uous w suls, ih i h ivsigio of sho yics o i h lysis of log-u gowh gis. I os css lyz, h Po iuc-iovio hypohss ul ou. A fw ks i o. Of cous, ou suls bs o pic-kig fis ou olig of liquiiy-cosis is pobbly oo sipl. Aig k pow is o pobl if w follow h sgy of Fichig l. 6, lhough i is o likly h ou suls woul b iclly l. Mollig ig liquiiy cosis o cculy is uch o coplic sk boh hiclly cocpully.

49 48 W bliv h llowig h fis o icu io b o fs is oizio coplic o viol ss is qui cisiv issu h shoul b cosi i o cophsiv fwoks i h s of cooic policy. I his spii, cl pl ols s o qu, sic hy woul llow uch o pcis iscussio of wlf iplicios of iff viol cooic policis. This is ou x sp. 8. Appix Poof of Tho : Th poof uss pubio chiqus of h opiizio hoy vlop fo h clss of ols u suy i Hioko Ysko 996, Ysko 4, Ysko Hioko 5. L us cosi Cs B fis. Cs B. If h sicio 3 is iciv, E*<E x, h w choos,, v=' s h ip ukow vibls of h OP. Th, h iffil sicio ' i 4 hs h s fo v. W ssu h,, v subl -, -, v - bou.. o [,. Subsiuig 7 o 6, w obi xpssio fo. W f o subl fucios,, v s h issibl viios, if,, v,,, vv, sisfy cosis 4-5. L us giv sll issibl viios,, v, [,, o,, fi h cospoig viio I = I,, v v I,, v of h objciv fuciol I. Usig -3, w obi h

50 49 ] [ ] [ B b k p B b B b k p B b I = A wh = v. To pov h Tho, w shll sfo h xpssio A o h fo,, v o v I I I I v =, A wh h o is sup [, f ss f =. I will ivolv svl sps. Fis, usig h Tylo xpsio fxx=fxf xxox wic, w hv h. = = o b B o b B b A3 Nx, usig A3 h ly popy f f f = of igls, w sfo A o

51 5,, - ] [ [,} x{,} x{ o b k k p p b I = A4 wh x{,} phsizs h h viios, o-zo oly o h ivl [,. Nx, w ichg h liis of igio i h sco of A4 s, [ p p = i h fis s, ] [,} x{ b b = i h fifh siilly. To sfo h hi, w us h Tylo xpsio,, o f f =. Collcig cofficis of,,, w wi A4 s:.,, ] [ ] [ o p k p k b I =

52 5 Filly, cllig = v, w cov h ls xpssio o,, ] [ ] [ v o v p k p k b I = A5 Foul A5 i oios, 4, 5 povis h qui xpssio A. Th oi 4 of issibl cools,, v hs h sipl s fo,, v. So, h NCE 3 follows fo h obvious cssy coiio h h viio Ι of fuciol Ι c o b posiiv fo y issibl viios,, v, [,. Cs A. If h sicio of 3 is civ: E = E x [,, h w choos s h ip ukows of h OP. Th p s vibl is uiquly i fo h iiil pobl = E x, =, obi f iffiig 3. As show i Hioko Ysko 6, if E x, h fo y subl, uiqu.. coiuous fucio < xiss.. hs ' s k bou h possibl cs E x >. Thfo, h s sicios ' < i 4 sisfi uoiclly, so w c xclu fo h xu coiio. Siilly o h pvious cs, l us giv sll issibl viios, [,, o fi h cospoig viio,, I I I =

53 5 of h fuciol I. I his cs, h viio is i by. To fi hi cocio, l us ps 3 s E = = x h,,} x{ o =. A6 W will us h bov foul A4 fo h viio I s fucio of,, lii fo A4 usig A6. To o h, w wi h hi of D4 s o p o p p p = = =,} x{,, A7 by ig ± pplyig A6. Th igl i A7 hs h o o bcus is coiuous. Subsiuig A7 io A4 collcig h cofficis of, w obi h xpssio, o I I I = A8 i h oios. Th s of h poof is iicl o Cs B.

54 53 Th Tho is pov. fcs [] Bo Sl-i-Mi, 995, Ecooic Gowh, McGw-Hill. [] Bouckki,.,. uiz-ti, 8, Spcil fucios fo h suy of cooic yics: Th cs of h Lucs-Uzw ol, Joul of Mhicl Ecooics 44, [3] Bouckki,., M. Gi, O. Lico, 997. plc chos i h vig cpil gowh ol, Joul of Ecooic Thoy 74, [4] Bouckki,., F. l io O. Lico, 999, Exogous Vs ogously iv flucuios i vig cpil gowh ols, Joul of Ecooic Thoy 88, [5] Co, C. D. Siisclco, 994, Eviol policy cosi: Th ol of chologicl iovio, Euop Ecooic viw 38, [6] Chili, A., J. B, 5, Tol fco pouciviy h viol Kuzs cuv, Joul of Eviol Ecooics Mg 49, [7] Chuowsky, D. A. Lopz, 7, Eviol g ioviv cpbiliis i Agi iusy, i [], 8-4. [8] Fichig, G.,. Hl, P. Ko V. Vliov, 5, Eviol policy, h Po hypohsis h coposiio of cpil: Effcs of lig chologicl pogss, Joul of Eviol Ecooics Mg 5, [9] Fichig, G.,. Hl, P. Ko V. Vliov, 6, Cpil ccuulio u chologicl pogss lig: vig cpil ppoch, Euop Joul of Opio sch 7, [] Fichig, G.,. Hl, P. Ko V. Vliov, 7, Ficilly cosi cpil ivss: Th ffcs of isboi boi chologicl pogss, Joul of Mhicl Ecooics, fohcoig. [] H,, 4, Gowh, vio iovio: A ol wih poucio vigs violly oi sch, Joul of Eviol Ecooics Mg 48, [] Hl,., S. Shi,. Vickso, 995. A suvy of h xiu picipls fo opil cool pobls wih s cosis, SIAM viw 37, 8-8. [3] Hicks, J., 93. Th hoy of wgs. McMill Loo. [4] Hioko, N. Y. Ysko, 996. Molig Opiizio of h Lifi of Tchologis Kluw Acic Publishs, Doch.

55 [5] Hioko, N., Y. Ysko, 5, Tupik opil jcois i igl yic ols wih ogous ly, Joul of Opiizio Thoy Applicios 7, 9-7. [6] Hioko, N., Y. Ysko, 6, Cocviy i vig cpil ol wih oli uiliy, Appli Mhics Ls 9, [7] Kusll, P., 998, Ivs-spcific &D h cli i h liv pic of cpil, Joul of Ecooic Gowh 3, 3-4. [8] Mlcoso, J., 975, plc h l vlu of cpil quip subjc o obsolscc, Joul of Ecooic Thoy, 4-4. [9] Nlso,., E. Phlps, 966, Ivs i hus, chology iffusio cooic gowh, Aic Ecooic viw 56, [] Nwll,., A. Jff.Svis, 999, Th Iuc Iovio Hypohsis Egy-Svig Tchologicl Chg, Th Quly Joul of Ecooics 4, [] Po, S., B. Hb-Coply Es., 7. Iusil iovio viol gulio. Th UN Uivsiy, Msich. [] Po, M., 99, Aic's G Sgy, Sciific Aic 64, 4. [3] Po, M. C. v Li, 995, Tow w cocpio of h vio-copiivss lioship, Joul of Ecooic Pspcivs 9, [4] Sgso, P.,, Th log-u gowh ffcs of &D subsiis, Joul of Ecooic Gowh 5, [5] Solow,., J. Tobi, C. Vo Wizsck M. Yi, 966, Noclssicl Gowh wih Fix Fco Popoios, viw of Ecooic Suis 33, [6] Xpps, A. A. D Zuw, 999, Eviol policy copiivss : Th Po hypohsis h coposiio of cpil, Joul of Eviol Ecooics Mg 37, [7] Yi, M., 7, Iovio o cl chology hough viol policy: Egc of h io xchg b pocss i h Jps chlo-lkli iusy, i [], [8] Ysko, Y., 4, Mxiu picipl fo Vol igl quios wih cooll ly i, Opiizio 53, [9] Ysko, Y. N. Hioko, 5. Opiizio of h lifi of cpil quip usig igl ols, Joul of Iusil Mg Opiizio,

56 55 F x F x x Figu. Solvig h oli quio 45 wih spc o h ukow x = C.

57 56 * = k l * M * Figu. Tsiio log- yics u civ vio gulio fo Expl spcific iiil coiios. Th o lis iic h BGP gi. Th sh li shows h ivs fucio -.

58 57 * k l * Q* c* Figu 3. Tsiio log- yics u iciv vio gulio fo Expl 3. Th opil yics civ gulio Expl is show i gy colo.