2011/49. Sustainable Growth and Modernization Under Environmental Hazard and Adaptation. Natali HRITONENKO Yuri YATSENKO

Transcription

1 0/49 Susnbl Growh n Mornzon Unr Envronmnl Hzr n Apon Nl HRIONENKO Yur YASENKO

2 CORE DISCUSSION PAPER 0/5 Susnbl growh n mornzon unr nvronmnl hzr n pon Nl HRIONENKO n Yur YASENKO Jun 0 Absr W vlop n ggrg mol o suy ronl nvronmnl pon pols h ompns ngv onsquns of rn nvronmnl hzrs n hngs. h mol sngushs hr gors of pon msurs h ompns h rs of h nvronmnl mny vlu, b ompns h rs of ol prouvy, vlop n nrou nw hzr-pro pl n hnology. W nlyz h opml bln mong nvsmn, onsumpon, n ffrn gors of pon nvsmns. I pprs h h nvronmnl hzr n subsqun pon o no l n h long run o hghr lvl of pl mornzon ompr o h bnhmrk s wh no hzr. A synrgsm bwn prouvy-rl n mny-rl pon vs rss bus h prouvyrl pon posvly mps h onomy n rs br possbls for h mny pon. Kywors: nvronmnl hzr, nvronmnl pon, pl mornzon, opmzon. JEL Clssfon: C00, O, O3, Q0, Q54, Q57 Prr Vw A&M Unvrsy, xs, USA. E-ml: nhronnko@pvmu.u Houson Bps Unvrsy, xs, USA. E-ml: yysnko@hbu.u h uhors woul lk o hnk Profssor Rouf Boukkn, Profssor hrry Bréh n ohr prpns of h onfrn "Susnbl growh, hnologl progrss n h nvronmn" Insu Rhrhs Eonomqus Sols, Louvn-l-Nuv, Blgum, My 0 for vlubl ommns. h uhors r grful o CORE for s onnu suppor of hr rsrh. hs ppr ws prlly wrn urng hr vs o CORE n 00. Nl Hronnko knowlgs h suppor of NSF DMS hs ppr prsns rsrh rsuls of h Blgn Progrm on Inrunvrsy Pols of Aron n by h Blgn S, Prm Mnsr's Off, Sn Poly Progrmmng. h snf rsponsbly s ssum by h uhors.

3 . Inrouon h nvronmnl pon mns jusmns n nurl n humn sysms n rspons o ul or xp hngs n h nvronmn n orr o llv ngv mps of h hngs IPCC 00. If h pr nny of globl lm hng s orr, hn h pon wll bom n ssnl rn n onom vlopmn n omng s. h humn soy n mg ngv hngs n h nvronmn or p o h hngs. h Inrgovrnmnl Pnl on Clm Chng mphszs hs ho n s hr Assssmn Rpor IPCC 00 wh spr oumns for Mgon, n Imps, Vulnrbly, n Apon. h frs opon, mgon ons o ru mssons or nrs rbon snks, s xpnsv n provs no gurn of suss. Nw snf rsuls.g., Shkhov l 00 on Ar mhn vnng sply h nqunss of our urrn knowlg of h globl lm hng pross. Also, hr xs numrous poll, ulurl, n onom obsls for mgon ons s h 009 UN Clm Chng Confrn n Copnhgn monsr. h son opon, pon, s lso xpnsv bu prlly fsbl n mny suons. h humns hv lwys p. Apon o h nvronmnl hngs hs bn nrsngly obsrv n prsrvng h onom wll-bng ffrn spl n sol sls Agr l 005. Muh of hs pon s rggr by ps or urrn vns bu s lso npory n bs on som ssssmn of onons n h fuur. A h prsn m, h nvronmnl pon posssss ssnl ponl rsours h shoul b us wsly. Proposls h UNFCCC mng n Bl n Dmbr 007 suggs h % lvy on rbon rng oul fnn pon oss n vlopng rgons Hof l

4 009. hus, molng of nvronmnl pon srgs s of nrsng mporn for onom hory n mngmn pr. h ggrg molng of ronl pon msurs n mprov our unrsnng of pon n hlp n rmnng opml govrnmn pols on pon o lm hngs. Fnkhusr l 999 pon ou svrl yps of npory pon pols h my b lry su, mong hm: - Opmzng onom pols for rlr rplmn of long-rm whr-snsv pl h wll pr fsr h nlly np. - Rvsng long-rm vlopmn plns suh s osl vlopmn or rough onngny plns o nlu lm hng. A prsn m, molng of nvronmnl pon s h subj of muh fwr sus hn mgon molng n s rsr solly o numr smulon n h ngr ssssmn molng frmwork Hop l 993; Brun, Dllnk, n Agrwl 009; Brun, Dllnk, n ol 009; Bosllo 008; Bosllo l 00. In Hop l 993, pon s n xognous vrbl n h PAGE mol, so, no opmzon nlyss s possbl. D Brun, Dllnk, n Agrwl 009 n Brun, Dllnk, n ol 009 onsr ggrg pon xpnurs s n nognous flow vrbl of h DICE mol n monsr h pon n mgon r omplmns, pon s srongr n h shor run, mgon s srongr n h long run, n h pon s br for low nvronmnl mgs. Bosllo 008 onsrs ggrg pon xpnurs s n nognous sok vrbl of h RICE mol n rgus h h opml mgon srs rlr, pon s pospon, n mgon s br for low mgs. h mos omprhnsv rsrh s Bosllo l, 00 h sngushs hr pon gors npory sok, rv flow, R&D sok n solvs sol plnnr problm n h AD-WICH opml growh mol wh h worl spl 3

5 no rgons. hr smulon rsuls monsr h pon n mgon r omplmns or mprf subsus, opml mgon shoul sr rlr whl pon s br n long run, n npory pon s opml for rhr ounrs n som spf rgons. On n s h h ovrll pur s onflng n hvly pns n h ho of molng ools. So, nly molng of nvronmnl pon s n ul problm. A h sm m, rlvn ools for nlyzng globl pon pols xs n h onom growh hory. Mny uhors Grus n Smulrs 993; Smulrs n Grus 996; Soky 998; Elbsh n Ro 996, Hllg 009, n ohrs hv su how h opml onom growh s ff by h nvronmnl hng n nvronmnl pols. h ngv mp of h nvronmn n mroonom mols s usully hnnl hrough h uly funon rsng mny vlu of h nvronmn or h prouon funon rsng prouv vlu of h nvronmn. Smulrs n Grus 996 nrou rl nvronmnl quly whh h nvronmn fls o s lf-suppor sysm. lso ssum h h xhusbl nurl pl ffs boh h prouvy n h mny vlu. h ho of h nvronmnl onom poly n mroonom mols s usully rprsn by xpnurs on mgon msurs nvronmnl bmn or ln-up. Mols of opml lnup of hzrous wss s, Cpuo n Wln 995 hv bn probbly h frs onom mols wh h ngv mp of h nvronmn on boh prouon n uly funons. g, hr s no spf mroonom growh mol xp for Bréh, Hronnko n Ysnko 00 h provs qulv horl nlyss of h opml ho of xpnss no pon msurs. In hs ppr, w nfy n nlyz ronl srgs of pon n h gnrl onx of onom-nvronmnl 4

6 growh. In h rms of Bosllo l 00, w r fousng on plnn npory pon. Molng of ronl pon pols s pr of globl onom-nvronmnl molng hs s own sop n ssnl spfs Rlly n Shmmlpfnng 000, Sm l 000, Cllwy 004, Khn 003, n ohrs. Nmly, h sop of pon msurs s rsr o h ompnson of vrous ngv onsquns of lm hng, n prulr, of h vrg mprur nrs. h sprum of pon msurs s w n n b lssf n orn wh ngv hngs no wo gors: h pon h ompnss rs of h nvronmnl mny vlu. b h pon msurs h ompns rs of h prouvy. Our spf movon s o s whhr h ngv nvronmnl hngs n r rn pon-rl onom vngs. Suh pon of vw xss n onom-nvronmnl lrur. In prulr, Fnkhusr l 999 mphsz h mporn of pl mornzon n pon n rgu h: - In h mjory of ss, pon wll probbly nvolv h rplmn of on yp of pl by ohr. - Clm hngs wll rqur nrs flxbly n robusnss of nw pl, nrs pl urn-ovr, n shorn h onom lfm of pl. In hs ppr w nu h rol of mornzon n pon pols n nrou spr gory of mornzon-rl pon ns h gory b usng vng pl pproh. o kp nly omplxy rsonbl, w rsr ourslvs o omprv s nlyss n us h vng pl mol wh xponnl hnologl hng, n whh mornzon s mplmn hrough nsllng nw pl vngs n srppng obsol 5

7 vngs. W fous on long-run nror sy-s soluons of h formul opmzon problm. h rs of h ppr s s follows. In Son, w jusfy n formul h nrl plnnr problm for los onomy n whh ngv nvronmnl mp on onsumr uly n onom prouvy n b ompns by h nvronmnl pon. Son 3 srbs bln growh rgm n h bnhmrk problm wh no nvronmnl hng n pon. Son 4 nlyzs h opml bln mong nvsmn, onsumpon, n ffrn gors of pon xpnss n nrprs h obn rsuls. Son 5 onlus. Som proofs r prov n Appnx.. Mol o onsru mol of nvronmnl pon, w sr wh bs mol of mroonom growh Brro n Sl--Mrn 003 n vlop by nlung n nvronmnl s vrbl n svrl pon xpnss s son vrbls. Nmly, w ssum h h sol plnnr mxmzs h uly of nl onsumrs s h followng nrmporl opmzon problm: mx,,, 3 0 u, h,, whr s h soun r, h s n nvronmnl hzr prmr, s h nvsmn no h nvronmnl mny pon, n h uly funon u, h, rss n h n nrss n. h onsumpon s = y 3, 6

8 whr y s h prouon oupu, s h pl nvsmn, s h nvsmn no h prouvy-rl pon h unformly mps ll pl n srv, n 3 s h nvsmn no mornzon-rl pon h ffs only h nwly r pl. h bmn vs,, n 3 r flows s n Grus n Smulrs, 993; Vllng, 999. In orr o llusr h vry of pon vs, l us onsr h followng xmpl 3 of ngv nvronmnl mp: h wr mprur n lks n rvrs wll nrs wh h globl mprur nrs. I wll r n mny problm for onsumrs ls, n wrmr lm zons n rs h ffny of nulr powr sons h us ol wr for oolng own. hn h hr gors of pon vs r: - oolng h wr for onsumrs usng onl qupmn ns houshols, - oolng h lk n rvr wr on n nusrl sl o offs h rsng ffny of xsng powr sons, n 3 - sgn n onsruon of nw mor vn powr sons h wll work ffnly usng wrmr wr for oolng own. Apon hrough mornzon. Followng h mroonom growh hory, snr pproh woul b o srb h prou oupu by nolssl prouon funon wh homognous pl n lbor. In hs ppr, w woul lk o fn ou whhr h nvronmnl hzr rs onom nnvs for nnsf pl mornzon pon hrough mornzon. o srb h pon hrough pl mornzon, w pr from homognous pl n ssum h h ffny of ffrn pl uns pns on h m of hr onsruon n h mornzon ffor s ppl o h nws pl only Boukkn l 005. In ong so, w ngl h m-o-bul ffs n 3 h uhors r grful o Profssor hrry Bréh for provng hs nsghful xmpl" 7

9 ssum h h nsn of pl onsruon s h sm s h m of s nsllon n only h nw pl uns n b nsll o rpl h ols pl uns. I ls us o h ronl Solow-yp vng pl mols Solow l 966, Boukkn l 998, Hronnko n Ysnko 996, 999, 008. Spflly, w srb h prou oupu y by h followng vng mol y f h,, 4 3 wh mbo hnologl hng n Lonf hnology. In 4, h spf pl ffny f of h pl vng m,, pns on h hzr prmr h, h nvsmn no h ffny of ll pl vngs, n h vng-spf nvsmn 3. h nognous son vrbl s h lfm of h pl vngs srpp m. On of our gols s o sblsh how h lm hng n subsqun pon mp h pl lfm. Rmrk. Fnkhusr n ol 005 srb h oupu y by nolssl prouon funon n ssum h h roron offn of homognous pl K nrss n h hzr prmr h. In hs ppr, w o no onsr h physl pron of pl s mjor rson for s rplmn. W woul lk o fn ou whhr h nvronmnl hzr rs n onom n for nnsf pl mornzon pon hrough mornzon. h Lonf hnology mns h h ffny f os no pn on h moun of lbor us by h pl un. Followng mroonom vng mols Solow l 966, Boukkn l 998, 005, w ssum h h lbor us o prou h oupu y s 8. 5

10 Equon 5 nlus h xponnl lbor-svng hnl progrss wh h r "0 h mks nwr pl vngs lss lbor-onsumng. In 5, h ol lbor s normlz o uny, whh mns h ll vrbls y,,,,, n 3 r pr p Brro n Sl--Mrn, 003. In our mol, h nvsmns,, n 3 mus b pr p bus hy ff rlv hngs of h uly funon n h prouv funon. Ohrws, h problm wll hv srong sl ff n h sns h mor popul onomy wll b bl o mplmn mor pon msurs. hs ff s no suppor by onom rly f w ompr h pon ffny n suh ounrs s, for xmpl, Dnmrk n In. h nvronmnl mp on mny n prouvy. L us lrfy h mp of h nvronmn on h uly. Som uhors Grus n Smulrs 993; Soky 998; Byrn 997 hoos h nvronmn-pnn uly funon o b vly sprbl wh rsp o h onsumpon n nvronmnl hzr. W hoos h followng uly funon u, h,0 u v, 6 0 h n n h bsn of pon, whr h gvn funon v h srbs h rlv r rs of h mny vlu of h onomy u o h nvronmnl hzr h us by lm hng. h jusfon of h rlonshp 6 follows from h f h n nrsng onsumpon nno offs h nvronmnl mg fr s rn rl lvl s Smulrs n Grus 996. Wh rsp o h onsumpon, w hoos h CES uly funon u /, 0< <,7 0 ommonly us n rl onom-nvronmnl rsrh Smulrs n Grus 996, Soky 998. W shll no h h hosn uly spfon 6-7 mpls h h hzrs 9

11 prfrns. In ong so, w vo h ough quson of wh kn of nvronmnl mgs mp h prfrn orrng. h pnn of 6 on h hr prmr srb n 9 blow llows for hor nlyss of vrous pon srgs. In onom-nvronmnl molng, h nvronmnl hzr h s usully rprsn by h lvl of polluon.g., grnhous gss or h globl vrg mprur. h mny vlu rs hs bn horoughly sm for spf hzrs. In prulr, suh sm for h globl mp of rbon ox mssons s bs on whh s h mrgnl vlu of h mg on by n onl on of CO n mosphr onvr o mng on on of CO rn m Pr 003. W ssum h h monoonlly nrss wh m from n nl vlu h0=h 0 o h >h 0. h nl vlu h0 orrspons o h urrn s of h onomy, so w s v h 0 =0 whou loss of gnrly. As n Agr l 005, Boy 00, n IPCC 00 w ssum h h nvronmn hng wll no l o n onom ollps, so s rsonbl o k v h <. h ollps s orrspons o v h =. Smlrly o 6, w srb h mp of h nvronmnl hzr h on h vng prouvy fh,0,0 n h bsn of pon n 3 s f h,0,0 b v h # 8 whr h nrsng funon v h, 0=v h 0 <v h<, srbs h rlv prouvy rs bus of h nvronmnl hzr h, n b s fx prouvy prmr. Conpully, h prouvy rs s muh sr o sm hn h mny rs n 6. 0

12 Apon vrsus nu hnologl hng. A mjor novly of h problm unr suy s h h ngv nvronmnl mp n b ru by h nvsmns, n 3 no pon. In h oupu quon 4, n nrs of h prouvy 4 us by nvsmns n 3 n lso srb h nu oupu-ugmnng hnologl hng smbo wh rsp o n mbo n 3. A smlr onrn n b m bou h mp of h mny pon xpns on h uly. W o no wn o mx h nvsmns n 3 wh h nu hnologl hng n nrou h followng pon spfons: u, h, u v h 0=, =,,3, 9 f h,, b v h Hr,,, 3 3 rprsn ompnson bls of pon h pon ffny funons h monoonlly rs from o zro whn h orrsponng pon xpns nrss, =,,3. Formuls 9 n 0 rsr h sop of h son vrbls, n 3 o ompnsng mnmzng h ngv nvronmnl mp of h hzr prmr h. Dsp hr rlv smply, spfons 9-0 pur mjor qulv furs of pon nvsmns. Summrzng h bov formuls -0, h opmzon problm unr suy s: mx v h, 0 = y 3, y b v h, 3 3 3

13 . 4 Problm -4 nlus four son vrbls,, n 3 n hr pnn s vrbls y,,, h ssfy h onsrns y 3 5 n h nl onons 0 = 0 >0, = 0, - 0 ]. 6 h frs wo nquls 5 r snr n vng pl mols. h frs on mpls h h whrwl of nw jus nvs pl vngs s nffn. h ffrnl onsrn mns h h vng srppng m os no rs,.., rmov obsol vngs nno b nrou gn. h nl onon 6 srbs h gvn profl 0 of nsll pl vngs m =0 ovr h gvn prhsory nrvl - 0 ]. h proprs of h gvn funons r: h/>0, h0=h 0 =0, h h h nvronmnl hzr h nrss from h nl vlu h 0 o h >h 0 ; v k / h>0 h 0 h h, v k h 0 =0, v k h <, k=, boh h uly n prouvy rs bu rmn posv whn h nvronmnl hzr nrss up o h ; l/ l < l, l0=, l >0, l l=,,3 7 h pon nvsmns l prlly ompns h ngv mp of h nvronmnl hzr n Bnhmrk s: mol whou lm hng n pon

14 L us ssum h h nvronmnl hzr prmr h sys h sm, h=h 0, hn v h=v h=0 n h opmzon problm -6 s o fn,, y, n, suh h mx,8 0 = y, 9 y b, 0, 0 y, 0,, 0 = 0, = 0, - 0 ]. 3 h only son vrbl of h problm 8-3 s L lo [0, h sp of ll msurbl funons boun on ny fn nrvl from [0,, whl y, n r h s vrbls. h s vrbl s unquly rmn from h nl problm - - =, 0= 0, 4 obn fr ffrnng. Lmm nssry onon for n xrmum. L, y,, b soluon of h opmzon problm 8-3, hn I '=0 0<<y, I ' 0 =0, I ' 0 =y, whr [ ] I ' b [ ] 5 n 6 3

15 s h ul vrbl for quly 9, n s h nvrs of. S Appnx for h proof. As usully n mols wh nognous srppng of obsol pl, h uppr lm of ngrls n 5 rprsns h unknown fuur lfm of pl n s rl o h unknown srppng m - s s nvrs. Son-orr onons for n xrmum r mor ompl n obn for smlr problms n Hronnko n Ysnko 008. W fous on long-run nror sy-s soluons of h opmzon problm, whh my nlu qulbrum ss n bln growh phs. Followng $Boukkn l 998; Hronnko n Ysnko 996, 008; n ohrs, bln growh ph BGP of h vng mol 8-3 s soluon o h quons 9-,5, suh h y,, n grow xponnlly no nssrly wh h sm r n h pl lfm s onsn. h unknown nror rjory, y,,, f xss, s rmn by h quly I '=0 n 9-. h son vrbl os no nr h opmly onons 5 xplly n s foun from h s quon unr h known y n h nl onons 3. horm. For <r = <b, hr xss n opml BGP: y y,,, = ons, 8 y b,, y, 9 n h onsn opml lfm >0 s unqu soluon of h nonlnr quon r r r r. 30 b S Appnx for h proof. 4

16 Followng Brro n Sl--Mrn, 003, w rfr o r= s h ffv soun r. hus, h BGP xss n s growh rs qul o h hnologl hng r. h opml srppng rul 30 hs bn horoughly su n vng mols of Hronnko n Ysnko 996, 005, Boukkn l 998. I hs bn shown h h vlu s smllr for lrgr < <<; s 0 n s b. Morovr, f < <<, hn / b. Subsung h ls formul no 9, w obn h h onsumpon s posv h onons << n <b, whh ovr ll rsonbl onom. 4. Anlyss of h mol wh pon In hs son, w nlyz h mol -6 wh nvronmnl mp n pon. o kp h omplxy rsonbl, w wll onnu omprv s nlyss of h opmzon problm -6. Our frs quson s o fn ou whhr hs problm hs BGP srb by quls 8 n,, A prlmnry nlyss shows h problm -6 my hv BGP 8,3 f only f h pon ffny funons pn on h lvls of onrols k rhr hn on h k onrols hmslvs. So, o onnu h omprv s nlyss n mk mnngful prons, w n wo ssumpons: h nvronmnl hzr prmr h nrss up o h vlu h n rlvly shor m n sys n smll nghborhoo of h fr. h spfons 7 of h pon ffny funons r: 5

17 k k k k, 3 k / k k <, k0=, k>0, k=,,3. 33 Assumpons 3-33 smply mn h h ffny of pon hngs n m wh h sm r s h hnologl hng. W woul lk o srss h furhr qulv nlyss of problm -6 s possbl only unr hs nurl ssumpons. A 3-33, h fnl smn of h opmzon problm -6,3 s o fn funons, y,, n onsns,, 3, h lvr mx v h 34 0 unr = y 3, 35 h 3 3 ] y b[ v, 36, 37 0, y 3 0, 0, 38 0 = 0, = 0, - 0 ]. 39 h xrmum onon for hs opmzon problm s gvn by h followng lmm. Lmm. L, y,,,,, 3 b soluon of h problm 34-39, hn h followng nquls hol: I ' 0 =0, I ' 0 =0, I '=0 >0 n >0, I 0 =0, I = 0 >0, ' I 0 =0, I = 0 >0, ' ' ' 6

18 7 ' 3 I 0 3 =0, ' 3 I = 0 3 >0, whr, ] [ ] [ ' ] [ 3 3 h v b I 40, ] [ / ' h v h v I 4, ' 3 3 h bv I 4, ' h bv I 43 ] [ h v.44 h proof xns h proof of Lmm. o rv nly xprssons for h BGP, w hoos mor spf pon ffny funons:,,3, 0,, l k l k l l l l 45 h ssfy onons h onsns k, k, k 3 n 45 n b nrpr s h pon ffny prmrs. Aorng o 8 n 3, h BGP s,,, y y =ons,,,, whr h pon xpnss r onsn prs of h oupu. By Lmm, n nror soluon of h opmzon problm 34-39,46, f xss, shoul ssfy h sysm of sx nonlnr quons

19 r r r r b[ v h k k 3 3, 47 ] y b [ k v h 3 3 ] k,, 48 y, 49 3 k k v h, 50 k k 3 3 k v h, b 5 k k 3 3 k 3 v h, b 5 wh rsp o h posv lvl vrbls y,,,,, 3 n h onsn lfm. L us frs nrou h soluon, y,, of quons = = 3 =0. I rprsns h opml bln growh n h s of lm hng whn h pon s no possbl. Anlogously o horm, w n prov h followng rsul. Lmm 3. If < r < b[ v h ] 53 n = = 3 =0, hn h nonlnr sysm hs posv soluon, y,, whr s unquly rmn by 47 n, y b [ v h ], y " 54 In prulr# smll <r<<. 55 b [ v h ] 8

20 Now l us rurn o h sysm I n b spl no wo sysms: Sysm A of 47, 48, 5, 5 wh rsp o y,,, 3, n Sysm B of n n. Sysm A shoul b solv frs. W sr wh h ls wo quons 5 n 5 of Sysm A. On n s mmly h h pon n b posv only f h prmrs k, k 3 r lrgr hn som hrshol vlus. Nmly, f h ffny prmr k s oo smll suh h k </bv h, 56 hn I <0 by 4, h s, I nno b zro, h opml =0 s ornr by Lmm, ' ' n quon 5 s no rlvn. Anlogously, 3 =0 f k 3 </bv h. If boh =0 n 3 =0, hn h posv opml lfm = s rmn by Lmm 3. L us ssum h ls on of n 3 s non-zro. hn, k k 3, wo quons 5 n 5 r nonssn n, by Lmm, on of wo opml onrols n 3 shoul b zro : f k k or 0 f k k3 Hn, only on of 5 or 5 shoul b onsr f k k 3, h son on ls o h onr soluon. L k >k 3, 0, n 3 =0 for fnnss. In hs s, 3 s ornr soluon n quon 5 s no rlvn. hn k >/bv h, h opml ln k bv h 58 k s posv, h onsn opml lfm s unquly rmn from h quon r r r r b / k 59 n <r<<. b [ / bk ] 60 9

21 A h gvn,, n 3, w n sly fn y n from 48. Fnlly, f k =k 3, hn h quons 5 n 55 r h sm, = 3, boh pon possbls r unsngushbl, n solvng Sysm A s smlr o h s k k 3. hus, Sysm A hs soluon unr onon 53. L us xmn Sysm B nx. h opml mny pon n b rmn from quon 50. If h ffny prmr k s smll suh h k <- /v h -, 6 hn 50 hs no soluon n h opml =0 by Lmm. By 49 n 58, h opml onsumpon =0 s k b / v h, 6 k k b / v h, whr s rmn by Lmm 3 n k b ln k bv h 63 k k h ffrnon of 63 n k monsrs h opml onsumpon 6 s lwys posv =0. k nrss n k, hn, k " >0 n h L us xlu h nognous from h onon 6. Subsung 6 no 6, h onon 6 for =0 boms k - / v h - k b / v h, 64 k k - / v h - k b / v h. Inquls 64 lwys hol for smll k. 0

22 L us now ssum h k s no smll bu suh h 64 fls. hn, by 50, h opml mny pon lvl s k ln v h >0. 65 k Subsung 65 no quon 49 known y n, w obn h quon for : k ln ln v h k,66 k k whr k >0 s gvn by 63. h lf-hn s of hs quon s ngv =0 n nrss n up o. Hn, quon 66 hs unqu soluon >0. Knowng, w n fn by 65. hus, Sysm B s solv. W n summrz h bov rsuls n h followng smn. horm. If r <b[ v h ], hn h problm posssss n opml BGP 46 wh posv y,, n fn pl lfm. h opml pon nvsmns,, 3 r zro f h orrsponng pon ffny prmrs k, k, k 3 r smll n ssfy 56 n 64. Spflly, % 3 = 0 k </bv h n k 3 </bv h. If k >/bv h n/or k 3 >/bv h, hn on of n 3 s zro: n h ohr omponn s A < <<, h opml pl lfm s 0 f k k3 or 3 0 f k 3, k ln k bv h k 0.

23 b [ b [ v h ] / bk ] 0 0 h opml pon nvsmn s posv n gvn by 65 f h pon ffny prmrs ssfy 64. horm ls o svrl rlvn onlusons bou pon srgs.. h ho of opml pon xpnurs. h opml srgy s o nvs smulnously no, mos, wo pon vnus: h mny pon n h mor ffn ou of wo prouvy pons. In h gnrl s, w o no nvs smulnously no boh vrgprouvy n mornzon-rl pons bu no h on wh lrgr ffny prmr k or k 3.. Smlry of prouvy-rl pon msurs n h long run. h ff of h mornzon-rl mbo pon n ol prouvy smbo pon ppr o b nl n h long run. hrfor, h rlvn of mornzon n h whol sprum of pon msurs shoul no b ovrsm. h ky n mkng pon sons ls n h pon ffns k n k 3. h opml srgy s o nvs no pon msurs wh h hghr ffny, rgrlss whhr hy blong o mornzon pon or vrg-prouvy pon. For xmpl, bulng nw ms n swlls roun osl s my b lss ffn pr un of nvsmns hn mplmnng nw wrnng shm or vuon pln for h osl zon.

24 h son phnomnon s unxp bus h mp of mbo n smbo C on mornzon s rhr ffrn n onom hory Boukkn l 005. W shoul no h hs ouom s no rvl n s no gnrl fur of vng mol -6. I ours only long h BGP bus hn h mprovmns n nw pl vngs r bng vrg ovr h fuur pl lf whh s onsn long h BGP. A prlmnry nlyss shows h hs ouom wll b qu ffrn f w nlyz rnson ynms of h mol or lf h onl mol spfons W lv h ssu for fuur suy. h nx wo ouoms hv lr n mporn poly mplons. 3. Synrgsm bwn prouvy n mny pon vs. Comprng wo hrshol onons 64 monsrs rn lvl of synrgsm bwn prouvy n mny pon. Nmly, f h prouvy ffny prmr k s smll, hn h mny ffny prmr k shoul ssfy h frs hrshol onon 64 o gurn posv mny nvsmn. Howvr, f h prouvy ffny prmr k boms lrgr, hn h son hrshol onon 64 for h mny pon k boms lss rsrv bus k &. I mns h h prsn of h prouvy pon nrss h fnl prouvy n smuls h mny pon. For xmpl, lr onom rovry of osl zon ff by hurrn mks rbulng houss for h ff populon mor ffn. 4. h mp of pon on prouon, onsumpon, n pl mornzon. Unr m ssumpons, h lm hng n pon ff h opml lvls of h onomy bu o no mp s growh r whh s rmn n our mol by h hnologl hng 3

25 r. I s n xp rsul bus w hv ssum h h lm hng ffs h mny n prouvy som prng bu os no rs hm o zro Agr l 005, Boy 00. Ohrws, wll b mol of sroph hng no jus pon. L us ompr h opml lvls of onomy wh n whou lm hng n pon. o o h, w no h BGP omponns 8 n 9 whou lm hng s ~, ~ y, ~ ~, n rll h BGP, y,, wh lm hng n no pon gvn by 54 n 55. horms n n Lmm 3 prou h followng Corollry. If h pon ffny prmrs k, k, k 3 r no smll h opml pon nvsmns r posv, hn > > ~, y < y < y ~, < < ~, n < < ~. So, s xp, n nvronmnl mg supprsss onom vy n ls o smllr mny. h opml pon nrss h prouon oupu, onsumpon, n nvsmns ompr o h s of no pon, howvr, hr lvls rmn smllr hn n h s of no mg. h non-rvl rsul s h h onomlly opml pl lfm pprs o b lwys lrgr unr nvronmnl mg wh n whou pon n h orrsponng onom pron of pl s lwys lowr quls /. h onom nuon bhn hs s h sm: h nvronmnl mg rss onom prouvy n h ronl pon n ompns hs rs only prlly. 4

26 5. Conluson. h ppr ppls ronl mroonom molng ools opml growh, vng pl mols, n omprv s nlyss o suy ronl nvronmnl pon pols o ompns ngv onsquns of rn nvronmnl hzrs, prulrly, h vrg mprur nrs. Nurlly, n nvronmnl mg rss boh prouvy n uly n h ronl pon msurs n ompns hm only prlly. W fous on h ffny of spf pon msurs n, n prulr, nlyz h rol of hnologl mornzon n pon vs. h onsru mol omplly sprs h nvronmnl pon nvsmns from s mor fmous ounrpr nvronmnl mgon n nvsmns no hnl progrss. h vry of possbl pon msurs s lssf no hr gors h: ompns h rs of h nvronmnl mny vlu, b ompns h rs of vrg prouvy, vlop n nrou nw hzr-pro pl n hnology mornzon-rl pon. h pon ffny prmrs r ssnl n mkng opml pon sons n h opml srgy pprs o nvs no h pon msurs wh hghr ffny.. An mporn fur of h nvronmnl pon s h synrgsm bwn h prouvy-rl n mny-rl pon vs. I ours bus h prouvy-rl pon posvly mps h onomy, whh n urn rs br possbls for h mny pon. h onsru mol ks hs ff no oun whn lulng h opml nvsmns no ffrn pon vnus. 5

27 3. Our rsuls monsr h, sp xpons of som uhors Fnkhusr l 999, h nvronmnl hzr n subsqun pon o no l o hghr lvl of pl mornzon ompr o h bnhmrk s wh no hzr, ls, n h long run. h onomlly opml lfm of pl s lrgr unr h nvronmnl mg rgrlss whhr pon ks pl or no. hus, h nvronmnl hzr os no r n onom n for prmnnly nnsf pl mornzon. hrfor, h rlvn of mornzon-rl pon msurs shoul no b ovrsm. h lrnv pon of vw s xprss by Fnkhusr n ol 005 who nlyz mroonom growh unr lm hng n four onom frmworks Solow-Swn, Css-Koopmns, Mnkw-Romr-Wl, n Romr. hy o no us vngs n pon xpnss n srb h mp of globl mprur nrs on h longvy of pl posulng h h roron r of homognous pl s hghr for lrgr mprurs. W xp h smlr ff my our n our mol urng rnson ynms ompr o n Shubr 008 bu lv hs ssu for fuur suy. 6

28 7 6. Appnx Proof of Lmm. L us subsu 0 o 9 n wr h Lgrngn for h opmzon problm 8-3 b L 0 whr h Lgrng mulplrs for 9 n s for r ul vrbls. h nrmn of L wh rsp o mssbl nrmns,, s b b L 0 0 b b 0 Inrhngng lms of ngron 0 0 f g g f, pplyng ylor srs o n o f f, xlung b #n ollng lk rms w obn 5-6.

29 h onons I '=0 0<<y, I ' 0 =0, n I ' 0 =y follow from h gnrl nssry xrmum onon of h form: L L+ L 0 for ny mssbl vron. h lmm s provn. Proof of horm. Aorng o h fnon of h BGP, h soluon s o b xprss s 3 y y,,, ==ons. Subsung n = o, w obn h n b hl only f = n hn =/. Now, rwrng 0 w obn y y % b b, from whh follows = n h frs formul of 9. Subsuon of o 9 ls o 3= n y 3, h s, 8-9 r jusf. hn, from 5-6 n 8-9 w obn h h nror soluon s obn from b. Evlung h ngrl n nroung h noon r=, w obn 30. o prov h quon 30 hs unqu soluon, l us no s lf-hn s s r r F "Bus F0=0 n lm F / r, quon 30 hs soluon r r f r<b. h soluon s unqu bus h funon F s srly nrsng n : F r r 0 s r>. h horm s provn. 8

30 Rfrns. Agr, W.N., Arnll, W.A., omkns, E.L Sussful pon o lm hng ross sls, Globl Envronmnl Chng 5, Brro, R.J. n X.Sl--Mrn 003 Eonom Growh, h MI Prss, Msshuss 3. Boukkn, R., Grmn, M., Lnro, O., Mgnus, A Crv sruon, nvsmn volly n h vrg g of pl, Journl of Eonom Growh, 3, Boukkn, R., l Ro, F., Lnro, O Obsoln n mornzon n h growh pross, Journl of Dvlopmn Eonoms, 77, Bosllo, F 008. Apon, mgon n grn R&D o omb globl lm hng: Insghs from n mprl ngr ssssmn xrs, CCMC Rsrh Ppr Bosllo, F., Crrro, C., Cn, E. 00. Clm poly n h opml bln bwn mgon, pon n unvo mg, Clm Chng Eonoms,, Boy, J.K., 00. h Poll Eonomy of h Envronmn. Ewr Elgr, Chlnhm. 8. Bréh,., Hronnko, N., Ysnko, Y. 00. Apon n mgon n long-rm lm pols. CORE Dsusson Ppr 00/ Byrn, M Is growh ry wor? Polluon, bmn n onom growh, Journl of Dvlopmn Eonoms 54, Cllwy, J.M., 004 pur n how n w sm hm? Globl Envronmnl Chng 4, Cpuo, M., Wln, J Opml lnup of hzrous wss, Inrnonl Eonom Rvw, 36, rsour hs n mny vlu, Journl of Envronmnl Eonoms n Mngmn, 56, D Brun, K., Dllnk, R., Agrwl, S Eonom sps of pon o lm hng: Ingr ssssmn mollng of pon oss n bnfs, OECD Envronmn Workng Pprs Brun, K., Dllnk, R, ol, R AD-DICE: An mplmnon f opon n DICE mol, Clm Chng, 95, Elbsh, E.H., Ro,.L On nognous growh: h mplons of nvronmnl xrnls, Journl of Envronmnl Eonoms n Mngmn, 3, Fnkhusr, S., Smh, J.B., ol, R.S.J Whrng lm hng: som smpl ruls o gu pon sons, Eologl Eonoms 30, Fnkhusr, S., ol, R.S.J., 005. On lm hng n onom growh, Rsour n Enrgy Eonoms 7, Grus, R., Smulrs, S h r-off bwn nvronmnl r n long-rm growh polluon n hr prooyp mols, Journl of Eonoms, 58, Hllg, S. 009 Srgs o p o n unrn lm hng, Globl Envronmnl Chng, 9,

31 0. Hof, A.F., Brun, K.C., Dllnk, R.B., n Elzn, M.G.J.. vn Vuurn, D.P. 009 h ff of ffrn mgon srgs on nrnonl fnnng of pon, Envronmnl Sn n Poly,, Hop, C., Anrson, J., Wnmn, P Poly nlyss of h grnhous ff: An pplon of h PAGE mol, Enrgy Poly,, Hronnko, N., Ysnko, Yu. 996, Ingrl-funonl quons for opml rnovon problms, Opmzon, 36, Hronnko, N., Ysnko, Yu Mhml Molng n Eonoms, Eology n h Envronmn, Kluwr Am Publshrs, Dorrh /Boson /Lonon. 4. Hronnko, N., Ysnko, Yu urnpk n opml rjors n ngrl ynm mols wh nognous ly, Journl of Opmzon hory n Applons, 7, Hronnko, N., Ysnko, Yu Opml onrol of Solow vng pl mol wh nonlnr uly, Opmzon, 57, Hronnko, N., Ysnko, Yu. 00. hnologl nnovons, onom rnovon, n npon ffs, Journl of Mhml Eonoms, 46, Inrgovrnmnl Pnl on Clm Chng IPCC, 00. Clm Chng 00: Imps, Apon n Vulnrbly. Summry for Poly Mkrs. Worl Morologl Orgnson, Gnv. 8. Khn, M.E. 003 wo msurs of progrss n png o lm hng. Globl Envronmnl Chng 3, Pr, D. 003 h sol os of rbon n s poly mplons, Oxfor Rvw of Eonom Poly, 9, Rlly, J., Shmmlpfnng, D., 000. Irrvrsbly, unrny, n lrnng: porrs of pon o long-rm lm hng, Clm Chng 45, Shkhov, N., Smlov, I., Slyuk, A., Yusupov, V., Kosmh, D., Gusfsson, Ö. 00. Exnsv mhn vnng o h mosphr from smns of h Es Sbrn Ar Shlf, Sn 37, Sm, B., Buron, I., Kln, R.J.., Wnl, J., 000. An nomy of pon o lm hng n vrbly. Clm Chng 45, Smulrs, S., Grus, R Polluon bmn n long-rm growh, Europn Journl of Poll Eonomy, Solow, R., obn, J., Von Wzskr, C., Yr, M. 966 Nolssl growh wh fx for proporons, Rvw of Eonom Sus, 33, Soky, N Ar hr lms o growh? Inrnonl Eonom Rvw, 39, Vllng, N Mulplv uly n h nflun of nvronmnl r on h shorrm onom growh r, Eonom Mollng 6,