International and Development Economics

Transcription

1 Crawford School of Economics and Govrnmn WORKING PAPERS H AUSTRALIAN NATIONAL UNIVERSITY Inrnaional and Dvlopmn Economics O upu vrsus Inpu Conrols undr Uncrainy: Th Cas of a Fishry Saoshi Yamazaki Tom Kompas R. Qunin Grafon Crawford School of Economics and Govrnmn THE AUSTRALIAN NATIONAL UNIVERSITY hp://

2 Oupu vrsus Inpu Conrols undr Uncrainy: Th Cas of a Fishry By Saoshi Yamazaki Crawford School of Economics and Govrnmn Th Ausralian Naional Univrsiy Tom Kompas Crawford School of Economics and Govrnmn Th Ausralian Naional Univrsiy R. Qunin Grafon* Crawford School of Economics and Govrnmn Th Ausralian Naional Univrsiy Conac auhor: Crawford School of Economics and Govrnmn JG Crawford Buildin (13) Th Ausralian Naional Univrsiy Canbrra, ACT qunin.rafon@anu.du.au Tl: Fax: Novmbr

3 Absrac Th papr compars h manamn oucoms wih a oal allowabl cach (TAC) and a oal allowabl ffor (TAE) in a fishry undr uncrainy. Usin a dynamic prorammin modl wih mulipl uncrainis and simad rowh, harvs and ffor funcions from on of h world s lars fishris, h rlaiv conomic and bioloical bnfis of a TAC and TAE ar compard and conrasd in a sochasic nvironmn. This approach provids a dcision and modlin framwork o compar insrumns and achiv dsird manamn oals. A ky findin is ha nihr insrumn is always prfrrd in a world of uncrainy and ha rulaor s risk avrsion and wihin in rms of xpcd n profis and biomass and h rad-offs in rms of xpcd valus and varianc drmin insrumn choic. Kywords: Fishris manamn, bioconomic modl, mulipl uncrainis JEL Classificaion: C26, D81, Q22 2

4 1 Inroducion A fundamnal issu in manain common-pool rsourcs is whhr o conrol h inpus or ffors of harvsrs or hir acual lvl of cach. In a drminisic world wih prfc informaion and nforcmn boh approachs nra idnical oucoms. Howvr, in a world of uncrainy h wo mhods of rulaion diffr in hir ffcs jus as prics and quaniis diffr in hir impacs in rms of polluion wih uncrainy (Wizman 1974). W addrss h problm of how o mana undr uncrainy by comparin wo hih-ordr mhods of rulaion: a oal allowabl cach (TAC) ha limis h oal harvs and a oal allowabl ffor (TAE) ha rulas h oal lvl of ffor xpndd by harvsrs. A TAC provids dirc conrol ovr harvsin moraliy bu only indircly conrols h ffor xpndd by harvsrs whil a TAE dircly limis ffor and only indircly limis h amoun harvsd. Boh approachs can b sablishd as mark-basd insrumns if ihr h oal harvs (undr TAC conrol) or h oal fishin ffor (undr TAE conrol) wr allocad as individual and ransfrabl rihs in h form individual ransfrabl harvsin quoas (ITQs) or individual ransfrabl ffor quoas (IEQs). Whhr a TAc or TAE is prfrrd dpnds on h rlaiv coss in moniorin and nforcmn, h abiliy of fishrs o subsiu o non-itq spcis or unrulad fishin inpus, and h uncrainy bwn fishin ffor and harvs and h uncrainy bwn h fish sock and h lvl of rcruimn or rowh in h fishry. Th mor uncrain is h rlaionship bwn currn socks and fuur rcruimn h mor difficul i bcoms o ffcivly s a TAC conrol whil h lss prdicabl is h rlaionship bwn fishin inpus and lvl of cach h lss ffciv is a TAE conrol in obainin h dsird lvl of harvs. A small bu imporan liraur has dvlopd ovr h rlaiv mris of TAC and TAE conrols in fishris. Usin a on priod modl wih uncrainy in rms of h currn biomass, Hannsson and Sinshamn (1991) find ha h acual diffrnc bwn a consan 3

5 cach quoa and consan ffor is vry small and h mos imporan drminan of h rlaiv profiabiliy bwn hm is h siz of h sock ffc in h harvs funcion. Quiin (1992) xndd h Hannsson and Sinshamn modl o show ha hr is a consan ffor rul ha nras a hihr conomic rurn for vry consan cach rul. Danilsson (2002) subsqunly dvlopd a dynamic modl o compar h rlaiv fficincy of TAC and TAE conrols and also addd an addiional lvl of uncrainy. H finds ha if h pric lasiciy of dmand is low and h rlaiv variabiliy in h rowh of h sock o h cach pr uni of ffor (CPUE) is low, hn a TAC is prfrrd o a TAE. Howvr, TAE conrol is suprior if h pric lasiciy of dmand is hih and hr is hih variabiliy in h biomass rlaiv o h cach pr uni of ffor. In an xnsion of Danilsson s work, Kompas, Ch, and Grafon (in prss) dvlopd a dynamic modl uilizin annual im sris daabas from h Norhrn Prawn fishry (NPF) of Ausralia. Thy find ha ivn h simad variabiliy in h sock rcruimn rlaionship and CPUE ha h us of a TAC is prfrrd bcaus boh xpcd profis and h sock is hihr a h sady sa wih a TAC, and bcaus h variaion in h sock is always lss wih h TAC han TAE. Th prvious sudis provid usful insihs abou rulaory choic bu svral imporan qusions rmain. To wha xn can radoffs b mad bwn h oal cach lvl and h risk of ovrfishin? To wha xn do uncrainis in boh h sock rcruimn rlaionship affc h choic of TAC vrsus TAE conrol? To wha xn do comparisons of h insrumns usin cumulaiv dnsiy funcions rahr han xpcd valus provid addd insihs abou rulaory choic undr uncrainy? To addrss hs qusions, w mploy a dynamic prorammin modl undr mulipl uncrainis wih simad rowh, harvs and ffor funcions o simula h conomic and bioloical bnfis undr TAC and TAE conrols. Usin cumulaiv dnsiy funcions h wo insrumns ar compard by varyin uncrainy in rms of h pric, h sock-rowh rlaionship and h harvs-ffor funcion. Th papr is oranisd as follows. In Scion 2, w dvlop a bnchmark bioconomic modl undr mulipl uncrainis. Scion 3 dscribs h simulaion mhod and simas 4

6 h modl paramrs usin annual im sris daa from h skipjack fishry in h Wsrn and Cnral Pacific Ocan. Numrical rsuls, h rad-offs bwn TAC and TAE conrols and h ffcs of uncrainy on h rlaiv payoffs ar xplord in scion 4. Scion 5 provids concludin rmarks. 2 Modlin TAC and TAE Conrols To compar TAC and TAE conrols w spcify a monoonic harvs-ffor rlaionship rprsnd by h nral form ivn in (1) γ 1 γ 2 h = f( E, x) = qe x (1) whr h is h harvs lvl and f is h drminisic harvs funcion wih h ffor lvl E, x is h biomass lvl and q is a consan cachabiliy cofficin a im. Th paramrs γ1 and γ2 drmin h imporanc of ffor and sock lvl in h harvs funcion. Th ffor funcion, or h invrs of (1), is dfind by: E = f 1 ( h, x ) = h (, x) h = γ 2 qx 1 γ 1 (2) Uncrainy is inroducd by includin random variabls in h harvs and ffor funcions, i.., h h γ 1 γ 2 h = F( E, x z ) = z qe x (3) and 5

7 h E = G( h, x, z ) = z γ 2 qx 1 γ 1 (4) whr F () and G() ar rspcivly h harvs and ffor funcions wih h random h variabls z and z ha can b inrprd as policy implmnaion rrors, rspcivly in h TAC and TAE conrols. W also spcify a sock dnsiy dpndn sochasic rowh funcion dfind as follows: x 1 x = + G( x, z ) h α x = zrx 1 h K (5) whr r is h inrinsic rowh ra, K is h carryin capaciy, and α rprsns h skwnss of h loisic rowh funcion G. Th chan in h biomass ovr a priod is h diffrnc bwn h harvs lvl and h random rowh in h sock. Th random variabl z rprsns unknown variabiliy in h rowh in h biomass. Objciv Funcion and Consrains For boh TAC and TAE conrols w assum h rulaor wishs o maximiz h discound n profis from fishin ovr an infini im horizon and ha h choic of which insrumn o us canno b chand. Our objciv is o compar h rlaiv bioloical and conomic payoffs undr various forms of uncrainy. Th rulaor s opimizaion problm is o maximz (6) subjc o consrains (7)-(9). max Ε β π (6) E or h = 0 subjc o 6

8 α x x+ 1 x = z rx 1 h K (7) x0 = x(0) (8) = i { h,, } i i z0 z (0) = (9) whr E is h mahmaical xpcaion opraor and β (0,1) is h im discoun facor. W dfin π as h n profi and π = phh ( ) ce, whr ph ( ) is h invrs dmand funcion and c is cos pr uni of ffor. In a TAC conrolld fishry h rulaor sks o s an opimal harvs quoa o maximiz discound n profis whil undr TAE conrol h rulaor ss h opimal ffor quoa. Th invrs dmand funcion is spcifid as ph 1/ δ, whr δ is h pric lasiciy of h dmand and p is a paramr. Thus, h oal rvnu and cos funcions ar, rspcivly, dfind as R = ph h and C = ce. 1/ δ Givn sric convxiy of h harvs funcion and concaviy of h ffor funcion i follows from Jnsn's inqualiy ha wih a ivn sock lvl ha x = x, * * * F E x Ε z <Ε F E x z and [ (,, Ε Gh x z)] < Gh (, x, Ε[ z]). 1 This rsul implis * h * h (,, [ ]) [ (,, )] ha, wih a fixd sock lvl, harvs conrol will yild a smallr cach and also a smallr ffor lvl on avra in a sochasic nvironmn. Howvr, h inqualiis do no always hold bcaus of h random variabl z ha varis h biomass ovr im. For xampl, assum ha F () is incrasin and G () is dcrasin funcion of h biomass and if x * > x%, hn * F E x Ε z >Ε F E x% z and Ε [ Gh (, x%, z)] > Gh (, x, Ε[ z]) can * h h (,, [ ]) [ (,, )] hold, rspcivly. Consqunly a modl ha accouns for uncrainy in h rowh funcion and how i chans h biomass ovr im will yild diffrn rsuls han a on-priod modl. Th dynamic rcursiv form of h problm dfind by (6)-(9) for TAE conrol aks h followin form: 7

9 γ1 γ2 ( β ) V ( x ) = max Ε p z qe x ce ) + ΕV ( x, z ) (10) h E 0 and for TAC conrol, 1 γ 1 h h V ( x) max ph c z h = Ε β V ( x 2 1, z 1) h 0 γ + Ε + + qx (11) Th soluion o h opimizaion problms in (10) and (11) yilds, rspcivly, h opimal ffor lvl and harvs lvl in ach priod. As a rsul of h random variabls h opimal lvls of ffor and harvs may no qual hir acual lvls. 3 Wsrn and Cnral Pacific Skipjack Fishry Th problm of insrumn choic is applid o h Wsrn and Cnral Pacific skipjack fishris. This is on of h world s lars wih simad oal harvs of approximaly 1.2 million mric ons pr yar (Lanly al. 2005). Th fish ar harvsd primarily from purs sin and pol and lonlin vssls. Th manamn of h fishry is ovrsn by h Wsrn and Cnral Pacific Fishris Commission (WCPFC) a rional fishris manamn oranizaion (Parris and Grafon 2005). Th WCPFC acs on bhalf of is mmbr naions ha includ coasal sas and disan war fishin naions and ss ma ruls for is mmbrs ha apply o boh h xclusiv conomic zons (EEZs) and h hih sas componns of h fishry. To addrss concrns ovr hihr han dsird lvls of fishin moraliy for yllowfin, and spcially biy una, mmbrs of h WCPFC hav ard o implmn a yp of TAE in h form of a ssl Day Schm (VDS) for hs spcis ha rsrics h numbr of days fishd o an avra ovr h priod. Alhouh fishin ffor for skipjack una is no dircly conrolld by h VDS i will also rula h skipjack fishry as biy and 8

10 yllowfin ar imporan bycachs. Th conomic and bioloical paramrs for our modl ar simad by usin annual im sris daa ( ) from h skipjack una purs sin fishris. Th ffor lvl is masurd by days a sa fishin and sarchin for fish. Dails of h simaion ar providd in Tabl 1 for boh h harvs funcion and h rowh funcion. For as of xposiion h carryin capaciy K is normalizd o uniy such ha h biomass x rprsns dnsiy rahr h acual wih of fish. Th pric lasiciy of dmand and h cos paramr ar obaind from Brinac al. (2000). Th pric lasiciy is s a δ = 1.55 and h cos paramr is s a c 1 = Thr is a lar variaion in h cos of purs sin fishris, and hus an alrnaiv cos paramr c 2 = 2.4 is also applid in h analysis. Th pric paramr is s a 50 o nsur h xisnc of a uniqu sady sa. Th bas cas rsuls ar drivd from h simad paramrs, and alrnaiv paramrs ar applid o invsia how h rlaiv fficincis bwn h wo insrumns chan. [Tabl 1 is abou hr] Th sochasic facors z and i i z ar spcifid as z = 1 + (2u 1) ε i {, = h,, }, whr u is uniformly discrizd wih 10 rids (a 10-sa Markov ransiion). Th rm ε drmins h siz of variaions in h harvs and ffor funcions and rowh funcion. I lis bwn 0 and 1, indicain from 0 pr cn o 100 pr cn variaions. W s ε = 0.01 (1 pr cn variaion) for small and ε = 0.05 (5 pr cn variaion) for lar uncrainy. An undrlyin assumpion in h uncrainy is ha h rsourc manars do no hav xac informaion of h variaion in h fish rowh and implmnaion of hir policis, bu hy do know abou h sourc of uncrainy (which variabls conain unprdicabl variaions) and hir disribuions (how lar h variaions would b). 4 Modl Rsuls 9

11 To solv h rcursiv problms in (10) and (11) numrically, h valu funcion iraion is uilizd wih vnly discrizd 200 sa spac rids. 2 This is implmnd usin a numrical mhod and wo xpcaion rms ar calculad. On is h xpcaion of h n rurns for h implmnaion uncrainy for all possibl combinaions of h sa variabls in h currn ( x ) and nx priod ( x + 1 ). Th ohr is h xpcd valu of h valu funcion for h rowh uncrainy. A ach iraion (updad from h prvious iraion), h opimal policy rul is drmind o maximiz h valu funcion for ach of h currn sas ( x 1 =Φ ( x, z )). Th valu funcion is irad unil a convrnc cririon is saisfid + ( V V < l+ 1 l 1 0 ). Usin informaion from h convrd valu funcion ( V rackin h Markov ransiions in z and * ) wih a ivn iniial sock and z, 50,000 ss of im sris ar simulad for h opimal policy rul, sock lvl, and conomic rurns for h TAC and TAE. Ths calculad valus ar rsricd o * 0 h K, * 0 E <, * 0 x * K and π <, 0 which imply ha hs variabls ar non-naiv and h harvs and biomass canno xcd h carryin capaciy. Th sady sa valus of h biomass, n profis, harvs and ffor lvls undr h drminisic cas, whr ε = 0 and ε = 0, ar prsnd in Tabl 2. 3 Wihou any sochasiciy in h rowh, and harvs-ffor funcions, boh h opimal n profis and fish sock lvl ar idnical for h TAC and TAE. This is bcaus undr prfc informaion, nforcmn and wihou any implmnaion rror, h fishry manar can opimally conrol h harvs and ffor lvl o maximiz h discound n profis by usin ihr insrumn. [Tabl 2 is abou hr] TAC vrsus TAE Conrol In ordr o drmin h suprioriy amon h wo fishris insrumns in a sochasic nvironmn, a rfrnc poin nds o b assind. This is bcaus h suprioriy bwn 10

12 h fishris insrumns may chan, dpndin on h diffrn ralizaions of uncrainis. Kompas, Ch and Grafon (in prss) us xpcd valus o compar TAC and TAE conrols. A problm wih hir approach, howvr, is ha a sinl valu of h xpcd valu of h oucoms (n profis and biomass) dos no provid a snsibl rfrnc poin o compar h wo insrumns. This is bcaus of h minimal diffrnc bwn h xpcd valus drivd from h wo conrol variabls. 4 W ovrcom his dficincy by consrucin a cumulaiv dnsiy funcion (CDF) of h oucoms avrad ovr 50 priods o capur h diffrnc in h wo insrumns. Th CDF dscribs h probabiliy disribuion of all possibl oucoms and for ach insrumn is drawn from h 50,000 simulaions. In ach CDF fiur h poin whr CDF = 0.5 rprsns h avra valu of h 50,000 simulaions, and hus i is h xpcd valu of h oucoms. Th inrscion of h wo funcions drivd from ach fishris insrumn rprsns h poin a which h oucoms from h wo insrumns ar idnical. If h inrscion is ihr blow or abov h poin whr CDF = 0.5 hn on of h insrumns is suprior o h ohr wih a hihr probabiliy in rms of h oucom masurs. Opimal Tim Pahs Fiur 1 prss h sampl opimal im pah for h harvs and ffor lvls undr wo diffrn scnarios 5. In h firs cas h rlaiv uncrainy in h rowh funcion is small rlaiv o h harvs-ffor funcion ( ε = 0.05 and ε = 0.01) whil in h scond h ohr hr is much mor uncrainy in h rowh funcion rlaiv o h harvs-ffor funcion ( ε = 0.01 and ε = 0.05 ). Th dod lin is h opimal im pah undr h drminisic nvironmn wih no uncrainy. Whn h uncrainy in h harvs and ffor funcions is rlaivly lar, h harvs lvl wih h TAE has a rar variaion han ha wih h TAC bu h variaion in h lvl of ffor is smallr han wih h TAC. This is bcaus h TAC dircly conrols h harvs lvl, whil h harvs in h TAE is indircly drmind by sin h opimal ffor quoa. Th fiur also shows ha h variaions in h 11

13 harvs and ffor lvls ar rar whn h uncrainy in h harvs-ffor funcion is rlaivly lar. [Fiur 1 is abou hr] Fiurs 2.1 and 2.2 illusra h rlaiv conomic payoffs bwn h wo insrumns chans accordin o h rlaiv siz of h uncrainy. If h uncrainy in h rowh funcion is small (Fiur 2.1: ε = 0.05 and ε = 0.01 ), h rlaiv conomic payoff favours h TAC. This is shown in Fiur 2.1 by h inrscion of h TAC and TAE CDFs a a poin rar han 0.5. By conras, if h uncrainy in rowh funcion is lar (Fiur 2.2: ε = 0.01 and ε = 0.05 ), h TAE has a hihr payoff han h TAC wih a hihr probabiliy as shown by h inrscion of h CDFs a a poin lss han 0.5. Th rar is h variaion in h harvs- ffor funcion hn h larr is h variaion in h harvs lvl wih a TAE conrol ha, in urn, conribus o ovr or undr fishin. On h ohr hand, h rar is h variaion in h biomass rowh funcion h larr is h rulaor s rror in prdicin h followin priod's sock lvl such ha TAC conrol is s a ihr a oo hih or oo low a lvl rducin is fficacy as a policy insrumn. [Fiur 2 is abou hr] Fiurs 3.1 and 3.2 provid a comparison bwn TAC and TAE conrols in rms of h avra biomass. In boh cass a TAC conrol dlivrs a hihr avra biomass. Th lar h variaion in h biomass rowh funcion rlaiv o h variaion in h harvs-ffor funcion h larr is h avra biomass associad wih TAC conrol compard o TAE conrol. This is bcaus wih a rlaivly hih ralizaion in h biomass a TAC conrol incrass h liklihood of harvsin lss han wha is opimal rlaiv o a TAE conrol. This mor han offss h cas of lowr han xpcd ralizaion in h biomass wih a TAC ha rsuls in rar han opimal fishin and rar ovrfishin han wih TAE conrol. As a rsul, h TAC mainains on avra a rar biomass han TAE conrol. 12

14 [Fiur 3 is abou hr] Snsiiviy Analysis: Sock Effc Th simad valu of h sock or biomass dpndncy paramr, γ 2, in h harvs funcion was no saisically sinifican diffrn from zro a h 5% lvl of sinificanc. Howvr, h sock ffc has bn shown o b imporan in som fishris so w assss h snsiiviy of h rsuls o chans in his paramr. 6 Fiurs 4 and 5 show how h rsuls chan whn hr is a wak link ( γ 2= 0.27) bwn h harvs and h biomass. Alhouh hr is no a subsanial chan in h rsuls, h inroducion of sock ffc favors TAE conrol vrsus TAC conrol in rms of n profis bcaus a smallr lvl of ffor is ndd o mainain h sam lvl of harvs. Givn a smallr lvl of ffor, hr is lss variaion in h harvs lvl in h TAE, and i is lss likly hr will b ovr or undr fishin. [Fiur 4 is abou hr] [Fiur 5 is abou hr] Snsiiviy Analysis: Pric Elasiciy of Dmand Th rar pric lasiciy of dmand, h mor rsponsiv is pric o chans in h oal harvs. To invsia how h pric lasiciy affcs h rsul, a larr valu of h pric lasiciy of dmand ( δ = 2.1) is applid. Th simulaion rsuls ar shown in Fiurs 6 and 7. Aain, h diffrnc o h bas-cas rsuls in Fiurs 2 and 3 is no lar. Howvr, F iur 6 dos show ha as h pric lasiciy incrass, h payoffs in rms of n profis incras for TAC vrsus TAE conrol. This is bcaus h mor rsponsiv is h pric o chan in h harvs h lss dsirabl is TAE conrol as i only indircly conrols h harvs. [Fiur 6 is abou hr] [Fiur 7 is abou hr] 13

15 Snsiiviy Analysis: Harvsin Coss An alrnaiv and subsanially smallr cos paramr ( c = 2.4 ) is applid o analyz how h rsuls alr wih chans in harvsin coss. Th simulaions ar prsnd in Fiurs 8 and 9. Th rsuls ar vry diffrn o Fiurs 2 and 3. As h cos paramr dcrass h cos of fishin bcoms lowr and h opimal harvs lvl incrass. A larr harvs, howvr, incrass h risk of ovrfishin and bcaus h TAE conrol only indircly limis h harvs i is opimal o hav a lowr lvl of fishin ffor o avoid such an oucom. By conras, h TAC conrol limis h harvs lvl dircly and hr is lss nd o compnsa wih lowr harvss if i can b conrolld dircly. Consqunly, h TAE is rlaivly favord in rms of h avra payoffs and nras a hihr biomass o h TAC rlaiv o h bas cas scnario. This findin conradics Hannsson and Sinshamn (1991) who find ha, as fishin cos dcrass, h consan ffor sray bcoms rlaivly lss profiabl han h consan cach manamn. Thir rsuls coms from h fac ha in a on priod modl wih a sricly convx cos funcion, h smallr is h fishin cos, h lss is h rlaiv fishin cos in h TAC. By conras, in our dynamic modl wih im varyin biomass, his rlaionship dos no always hold. For insanc, if h consan ffor sray consrvs a rar biomass, hn h fishin cos wih h TAC could b rar han ha wih h TAE. Thus, in our rsuls as fishin coss dcras, h TAE lvl is rducd as i only indircly conrols harvs and h probabiliy of ovrfishin incrass wih hihr opimal harvss. Consqunly, h harvs and ffor lvls wih h TAE bcom rlaivly smallr han hos wih h TAC ladin o hihr avra biomass and n profis rlaiv o TAC conrol. [Fiur 8 is abou hr] [Fiur 9 is abou hr] Snsiiviy Analysis: Pric Effc A similar rsul o h coss ffc is obaind wih a hihr pric of fish ( p = 100 ) bu wih h sam pric lasiciy of dmand. As h valu of a landd fish incrass, h opimal 14

16 harvs lvl riss. A a larr harvs h risk of ovrfishin bcoms rar and bcaus a TAE only conrols h harvs indircly, i is opimal o limi oal ffor mor han oal harvs. This is quivaln o a dcras in h cos paramr and favors TAE conrol rlaiv o TAC conrol in rms of avra n profis and h biomass. 5 Discussion [Fiur 10 is abou hr] [Fiur 11 is abou hr] W conribu o h liraur on insrumn choic by xaminin mulipl uncrainis in an acual fishry usin a dynamic modl and also provid a dcision makin framwork in h form of CDFs. Th approach offrs a subsanial improvmn ovr arlir work and nras addiional insihs. For insanc, Hannsson and Sinshamn (1991, p. 88), aru ha h mos imporan drminan as o which insrumn is prfrrd is h siz of h sock ffc in h harvs funcion. Our analysis suss ha ohr facors, such as h lvl of h coss and pric paramrs ar qually imporan in drminin h prfrrd insrumn. Danilsson (2002) provids h mos compl analyical s of rsuls rardin insrumn choic bu o obain his rsuls h was limid o xaminin h cas of only on form of uncrainy in ihr h biomass rowh funcion or in rms of cach pr uni of ffor, bu no boh. By mployin numrical mhods w ar abl o xamin mulipl uncrainis. Our findins suppor h rsuls of Danilsson (2002) and w also find ha modlin svral forms of uncrainy is rquird o mak adqua comparisons bwn h insrumns. Our approach has mos in common wih Kompas, Ch, and Grafon (in prss). Thy also us a dynamic modl and sima paramrs from h Norhrn Prawn fishry of Ausralia o compar TAC and TAE conrols. Thy do no, howvr, undr ak snsiiviy analysis in rms of cos and pric paramrs or h pric lasiciy of dmand, and rsric hmslvs o comparisons of xpcd valus and sandard dviaions in h biomass and n profis which is no an adqua mans of comparison. 15

17 Th principal manamn implicaions from our rsuls is ha TAC conrol nras widr risk boundaris for h avra biomass han dos TAE conrol. Howvr, a TAC has h advana ha i rsuls in a lowr variaion in boh biomass and n profis han a TAE. W also find hr ar radoffs bwn h harvs lvl and h risk of ovrfishin. If h rulaor ss a hih harvs lvl, ihr wih a TAC or TAE, h xpcd n profis will also incras for a ivn sufficin sock lvl. Howvr, hihr harvss incras h risk of ovrfishin and caus a lss hn opimal biomass lvl which lowrs fuur n profis. Harvsin lss oday also rducs h possibiliy of ovrfishin bu a h cos of n profis oday. Ovrall, our analysis provids a dcision framwork o balanc hihr xpcd n profis wih lowr xpcd biomass lvls, and o show how TAC and TAE conrols nra diffrn oucoms. Indd, a ky findin of our modlin is ha h larr is h harvs lvl hn h rar is h varianc in h n profis associad wih TAE vrsus TAC conrol, bu h hihr is h xpcd biomass. W fix h insrumn choic a h binnin priod and do no allow for a policy swich. Our rsuls imply, howvr, ha as coss and prics chan in a fishry h rlaiv prfrnc for a ivn mhod of conrol may chan. This suss h possibiliy ha a porfolio of insrumns could b applid o opimiz h manamn of fishris. In such a scnario, fishrs could b allocad boh shars in a TAE and a TAC. Only on of h insrumns would b bindin in any priod bu i would allow h opion o swich ino a diffrn policy rim as condiions in h fishry chand. For xampl, in h Easrn and Tuna Billfish fishry in Ausralia fishrs will b assind shars (dnominad in hooks) of a TAE binnin 1 January 2008, bu hy could subsqunly b allocad individual harvsin rihs as a shar of TAC conrol if such rihs wr assind in h sam raio as individual ffor shars. 16

18 6 Concludin Rmarks On of h mos difficul aspcs of manain fishris is o cop wih h inhrn uncrainis in sock-rcruimn and h harvs-ffor rlaionships. Dpndin on h rlaiv maniuds of h uncrainis in hs rlaionships and h pric and cos paramrs, manars can rad-off xpcd n profis and biomass lvls wih hir variabiliy. Usin paramr simas from on of h world s lars fishris, Wsrn and Cnral Pacific skipjack una, w analyz mulipl uncrainis and compar h us of a oal harvs conrol wih a oal ffor conrol. Usin a dcision framwork no prviously usd in his conx w compar h payoffs of h wo insrumns usin cumulaiv dnsiy funcions. A ky findin is ha nihr insrumn is always prfrrd in a world of uncrainy and ha rulaor s risk avrsion and wihin in rms of xpcd n profis vrsus biomass, and rad-offs in rms of xpcd valus and varianc drmin h insrumn choic. Our analysis also shows ha as harvsin coss dcras and h pric of fish riss h dsirabiliy of a oal ffor conrol incrass rlaiv o ha of a oal harvs conrol in rms of xpcd n profis and biomass. Ovrall, our rsuls provid a dcision and modllin framwork by rulaors o compar insrumns and o achiv dsird manamn oals. 17

19 Acknowldmn W ar raful o Quynh Nuyn, John C. Radcliff, Budy P. Rsosudarmo, and Marin Richardson for hir hlpful commns and susions on arlir vrsions of his papr. Commns from sminar paricipans, spcially from Jim McColl, Sphani McWhinni, and Mik Youn, a Souh Ausralian Branch of h Ausralian Ariculural and Rsourc Economics Sociy ar also rafully acknowldd. All rmainin rrors ar our own. 18

20 Rfrncs Brinac, M., H. Campbll, J. Hampon, and A. Hand Maximizin Rsourc Rn from h Wsrn and Cnral Pacific Tuna Fishris. Marin Rsourc Economics 15: Danilsson, A Efficincy of Cach and Effor Quoas in h Prsnc of Risk. Journal of Environmnal Economics and Manamn 43: Hannsson, R., and S. Sinshamn How o S Cach Quoas: Consan Effor or Consan Cach?. Journal of Environmnal Economics and Manamn 20: Judd, K Numrical Mhods in Economics. Cambrid: MIT Prss. Kompas, T., and T. Ch Economic Profi and Opimal Effor in h Wsrn and Cnral Pacific Tuna Fishris. Pacific Economic Bullin 21: Kompas, T., T. Ch, and R.Q. Grafon. in prss. Fishris Insrumn Choic undr Uncrainy. Land Economics (accpd for publicaion 14 Auus 2007). Lanly, A., J. Hampon, P. Williams and P. Lhody Th Wsrn and Cnral Pacific Tuna Fishry: 2003 Ovrviw and Saus of Socks. Ocanic Fishris Proramm, Tuna Fishris Assssmn Rpor No. 6, Scraria of h Pacific Communiy. Parris, H. and R.Q. Grafon. Tuna-ld Susainabl dvlopmn in h Pacific. Journal of Environmn and Dvlopmn 15(3): , Quiin, J How o S Cach Quoas: A No on h Suprioriy of Consan Effor Ruls. Journal of Environmnal Economics and Manamn 22: Wizman, M Prics vs. Quaniis. Th Rviw of Economic Sudis 41:

21 Appndix Th purpos of his appndix is o show ha whn h harvs lvl incrass from o h, h h0 1 prcna incras in h harvs lvl is rar han ha in h corrspondin ffor lvl. In ohr words, w wan o show ha % Δ h> % ΔE wih h = qe x and γ 1 γ h = qe x. γ 1 γ h h h Δ = = h h % h / γ1 1/ γ1 h1 h0 2 2 E1 E γ qx γ qx 1/ γ1 0 h % Δ E = = = 1 1 1/ γ 1 E h 0 h 0 0 γ 2 qx 1/ γ 1 Sinc 1/ γ 1< 1, h / h < ( h / h ) and % Δ h> % Δ E

22 Tabl 1 Esimaion rsuls of h rowh funcion and h harvs funcion Growh funcion Paramr Cofficin T raio r (0.154) α (0.396) Numbr of obs 30 R-squard 0.59 Harvs fucnion Paramr Cofficin T raio ln(q) (0.978) γ (0.082) γ (0.202) Numbr of obs 31 R-squard 0.91 P-valu (F-sa) No: Numbrs in parnhss ar sandard rrors. Tabl 2 Biomass, n profis, harvs and ffor a h sady sa undr a drminisic nvironmn Biomass N profis Harvs Effor TAC TAE

23 Fiur 1 Opimal sampl im pahs for h harvs and fish ffor undr sochasic nvironmn 1.1 Opimal sampl im pah for harvs ε = 0.01 ε = 0.05 ( and ) 1.2 Opimal sampl im pah for ffor ε = 0.01 ε = 0.05 ( and ) 1.3 Opimal sampl im pah for harvs ε = 0.05 ε = 0.01 ( and ) 1.4 Opimal sampl im pah for ffor ε = 0.05 ε = 0.01 ( and ) 22

24 Fiur 2 CDF of avra n profi wih diffrn siz of uncrainis ε = and ε = ε = 0.05 and ε = 0.01 Fiur 3 CDF of avra biomass wih diffrn siz of uncrainis ε = and ε = ε = 0.05 and ε =

25 Fiur 4 CDF of avra n profi wih a sock ffc in harvs and ffor funcions ε = and ε = ε = 0.05 and ε = 0.01 Fiur 5 CDF of avra biomass wih a sock ffc in harvs and ffor funcions ε = and ε = ε = 0.05 and ε =

26 Fiur 6 CDF of avra n profi wih pric lasiciy δ = 2.1 ε = and ε = ε = 0.05 and ε = 0.01 Fiur 7 CDF of avra biomass wih pric lasiciy δ = 2.1 ε = and ε = ε = 0.05 and ε =

27 Fiur 8 CDF of avra n profi wih cos paramr c = 2.4 ε = and ε = ε = 0.05 and ε = 0.01 Fiur 9 CDF of avra biomass wih cos paramr c = 2.4 ε = and ε = ε = 0.05 and ε =

28 Fiur 10 CDF of avra n profi wih pric paramr p = 100 ε = and ε = ε = 0.05 and ε = 0.01 Fiur 11 CDF of avra biomass wih pric paramr p = 100 ε = and ε = ε = 0.05 and ε =

29 End Nos: 1. Th paramr γ 1 is simad as γ 1= 1.37, hus h rsricion, 3.7 > δ > 1 is ncssary o nsur h sric concaviy of h profi funcion. Hnc, h harvs and ffor funcions ar, rspcivly, sricly convx and concav, and h rvnu and cos funcions ar concav wih rspc o h conrol variabls. 2. S Judd (1998) for furhr dails. 3. Th drminisic cas is providd o show ha a soluion xiss and ha h sysm is sabl and is no a bnchmark. 4. This findin is consisn wih h findins of Hannsson and Sinshamn (1991). 5. Th sam ralizaions in rms of h random variabls ar applid for boh TAC and TAE conrols. 6. For xampl, Kompas and Ch (2006) simad a harvs funcion ha shows h rlaionship bwn h harvs and biomass in hr of h una fishris in h Wsrn and Cnral Pacific. 28