t the propensity to consume the resource good. Maximizing U t in (9) subject to the budget constraint (8) yields

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1 ISB Innaonal Confn on Issus n Busnss onoms Mang an Mamas (IBMM-6) Sngapo Busnss Cls Capal nvonmn an Rnabl Rsous W-Bn Zang Rsuman Asa Paf Unvs Bppu-s Japan Absa: Ts pap nfs busnss ls n a nam onom mol nognous psal apal polluon an nabl sous popos b Zang () T mol sbs a nam npnn among psal aumulaon nvonmnal nams sou ang an vson of labo n ompv mas un govnmn s nvnon n nvonmnal poon T fn onom suu mas possbl o su naons among onom vaabls a no foun n sng lau of onoms n a sngl analal famo moonom founaon Ts su gnals Zang s mol b allong all m-pnn paams o b m-pnn os: busnss ls nabl sou avsng nvonmnal ang apal aumulaon Inouon Ts pap nfs busnss ls n a nam onom mol nognous psal apal polluon an nabl sous popos b Zang [] Ts su amps o pov ano onbuon o lau b nfng onom fluuaons n an onom go mol b Zang [] T pap s ogan as follos Son gnals Zang s mol Son sos o solv nams an smulas mol Son 4 smulas mol o monsa busnss ls u o som po sos on onom ssm Son 5 onlus su T Bas Mol Ts son s bul on Zang [] b allong all m-pnn paams o b m-pnn T onom as sos an on govnmn ( olls as fo nvonmnal poon) T sos a pouon nvonmnal an nabl sou sos Housols on asss of onom an sbu noms o onsum an sav Pouon sos o fms us labo an apal as npus angs a pla n pfl ompv mas W assum a omognous an f populaon T labo fo s sbu among sos W sl ommo o sv as numa L an s spf as san fo spvl labo an psal apal npus T pouon funon A A an a posv paams H A s a funon of nvonmnal qual masu b lvl of polluon T magnal onons a gvn b / / () s gvn paon a of psal apal an L san fo so of sou L () s f a a san fo mamum ps://oog/7758/rpubirh66 98

2 possbl s fo sou so fo unongs o nns go a of nabl sou T ang a n so s n qual o naual go a mnus avs a an / () L spvl san fo labo fo an apal sos mplo b sou so W assum a avsng of sou s a ou aong o avsng pouon funon b A A b A b an a paams an masu b lvl of polluon L p an a a on avsng W nou (4) s a funon of nvonmnal qual spvl san fo p of sou an f T magnal onons a gvn p / p / (5) W spf nams of so of polluans as follos C C Q (6) n an A Q a posv paams an A A an an a posv paams an ( ) a spvl labo fo an apal sos mplo b nvonmnal so s a funon of W no p apa al b / L an spvl san fo a as on ns pamn an ag nom P apa un nom s gvn b an T bug onsan s an T p apa sposabl nom s gvn b (8) s p (9) a spvl a as on onsumpon of goos an sou o smpl of analss spf ul funon as follos U u s popns o onsum popns o on al an popns o onsum sou goo Mamng U n (9) subj o bug onsan (8) ls s p () / (7) () / / Aong o fnon of s ang n ousol s al s gvn b s () ps://oog/7758/rpubirh66 99

3 T quaon smpl sas a ang n al s qual o savng mnus ssavng T govnmn s a nom s Y p C p C () As a onl o npu faos n nvonmnal so govnmn bug s gvn b T govnmn s opmal poblm s gvn b T opmal soluon s gvn b Y (4) Ma s: Y Q Y Y (5) / / T man fo an suppl of sou balan a an pon of m (6) L an san fo spvl labo suppl an oal apal so T labo fo s alloa bn sos As full mplomn of labo an apal s assum av W av us bul nam mol W no amn nams of mol T nams an s Pops (7) Ts son amns nams of mol s nou a n vaabl b / W no so a nams an b pss b ffnal quaons Lmma T moon of ssm s mn b ffnal quaons (8) funons n (8) a funons of an gvn n appn Moov all o vaabls an b mn as funons of an a an pon of m b follong pou: b (A) b (A6) an b (A) an b (A) b () Q b (7) p an b () / ŷ b (8) an s b () b (4) W spf paam valus as follos 5 A 4 A 7 6 A b 7 b b b 4 5 (9) Un (9) nf qulbum valus as follos Q p 6 ps://oog/7758/rpubirh66

4 4 94 s 649 () T gnvalus a alula as: W 6 Z 5 an 4 plo moon of onom ssm n gu Q p Compaav nam Analss g : Moon of onom Ssm W ons paams n (9) as long-m avag valus s nou a vaabl o u o angs n paam valu gu sos osllaons sn san fo ang a of vaabl n ang apa of sou a spf as Q p g : luuaons n ang apa of sou gu sos osllaons n popns o sav follos: 6 sn Q p 5 g : luuaons n popns o sav ps://oog/7758/rpubirh66

5 5 Conlusons Ts pap nf busnss ls n a nam onom mol nognous psal apal polluon an nabl sous popos b Zang [] 6 Appn T appn sos lmma om () an (5) an (5) oban (A) om m n an / j j j j Ins (A) n n (8) (A) Ins (A) an () n () A A (A) om fnon of Y av p Y (A6) us () an Ins (8) n (A6) Y (A7) also us () an (5) om (A7) Y an / av (A8) Subsung p n () no (6) ls: p Ins (8) n p (A9) also us () an (5) om (A9) an / av (A) / om (A) (A8) an (A) solv (A) Subsung (A) no (A) an g (A) ps://oog/7758/rpubirh66

6 Solv (A) (A) I s sagfoa o a pov ompuaonal pou n lmma om () an (5) av / p Ins s quaon n p (A4) also us om () an (A) av A (A5) Ins (A5) n (A4) (A6) also us (A) an (A) Insng (A) n (A6) solv as a funon of an as follos (A7) om () an (6) av (A8) o no gv pssons of an as pssons a ous om (A7) av (A9) Mulplng o ss of () an usng s ŷ oban (A) om (A9) an (A) onlu poof (A) 7 Anolgmns T auo s gaful fo fnanal suppo fom Gans-n-A fo Snf Rsa (C) Poj o 5846 Japan So fo Pomoon of Sn 8 Rfns [] WB Zang A nam naon among apal nvonmn an nabl sous nvonmn an sou pols n a -so go mol Malasan Jounal of onom Sus Vol 49 pp -9 ps://oog/7758/rpubirh66

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