Reconciling Economic and Biological Modeling of Migratory Fish Stocks: Optimal Management of the Atlantic Salmon Fishery in the Baltic Sea

Transcription

1 MTT Discussion Paprs Rconciling Economic and Biological Modling of Migraory Fish Socks: Opimal Managmn of h Alanic Salmon Fishry in h Balic Sa Kulmala, S., Laukkann, M. & Michilsns, C.

2 MTT Discussion Paprs Rconciling Economic and Biological Modling of Migraory Fish Socks: Opimal Managmn of h Alanic Salmon Fishry in h Balic Sa Kulmala Soil 1,, Laukkann Maria 3, Michilsns Cahrin Absrac Th papr pus forward a modl of h Alanic salmon fishry in h Balic Sa ha ingras h salin biological and conomic characrisics of migraory fish socks. Dsignd o b compaibl wih h framwork usd for acual sock assssmns, h modl accouns for agsrucurd populaion dynamics, h sasonal harvs and comping harvsing by commrcial and rcraional fishrmn. I is calibrad using daa and paramr simas for h Simojoki Rivr sock. Th socially opimal policy for maximizing discound n bnfis from h fishry wihin an uncrain nvironmn is drmind using a dynamic programming approach and numrical soluion mhod. Our rsuls indica ha subsanial conomic bnfis could b ralizd undr opimal managmn wihou compromising sock susainabiliy. Ky words: bioconomic modling, uncrainy, ag-srucurd populaion dynamics, opimal rsourc managmn, ingrad biological and conomic modling, Alanic salmon 1 Dp. of Economics and Managmn, P.O. Box 7, Univ. of Hlsinki, Finland Finnish Gam and Fishris Rsarch Insiu, P.O.Box, Hlsinki,Finland 3 MTT Agrifood Rsarch Finland, Luunanini 13, Hlsinki, Finland. Copyrigh 006 by Kulmala Soil, Maria Laukkann, Michilsns Cahrin. All righs rsrvd. Radrs may mak vrbaim copis of his documn for non-commrcial purposs by any mans, providd ha his copyrigh noic appars on all such copis.

3 1. Inroducion Th managmn of salmon and ohr migraory spcis is complicad by h dispara inrss of h fishris ha harvs h fish a hir diffrn lif sags and by h complxiy of sock dynamics. Th managmn of h fishry for Alanic salmon (Salmo salar) in h Balic Sa has mphasizd biological objcivs, and pas managmn ffors hav drawn had criicism from h fishing indusry. Dspi rgulaion basd on sock consrvaion goals, wild salmon socks hav dclind ovr im. An aciv policy dba has sprung up in h Nordic counris du o h low profiabiliy of commrcial salmon fishris and h high saus of salmon for anglrs. Sciniss, fishrmn, nvironmnaliss and adminisraors alik hav calld for h procion of wild salmon socks. Th Rgional Council of Lapland has sablishd a Salmon Fund, which aims a sling h ongoing dispu ovr harvs allocaion bwn profssional and rcraional fishrmn. Th Inrnaional Balic Sa Fishry Commission has launchd h Salmon Acion Plan , a program dsignd o nhanc wild salmon populaions and incras salmon cachs. Rsoring salmon socks and improving h profiabiliy of h salmon harvs rquirs ha boh h cological and conomic characrisics of h fishry b akn ino considraion. To b scinifically sound, managmn prscripions mus xplicily accoun for h conflicing inrss of h diffrn usr groups as wll as h cological complxiy and uncrainy inhrn in salmon sock dynamics. Alhough h Europan Commission has mphasizd h socio-conomic aspcs of fishris managmn (Europan Commission, 001), managmn auhoriis in h Balic Sa rgion hav primarily rlid on managmn advic from naural sciniss. On rason why h conomic poin of viw has rmaind undrrprsnd in managmn dcisions may li in h highly simplifid populaion modls gnrally usd in conomic analyss. If h undrlying biological modl is lmnary, managmn guidlins proposd by conomiss ar asily dismissd by naural sciniss and managmn auhoriis. Th objciv of his sudy is o dvlop ools for producing conomically and biologically sound managmn guidlins by consrucing an conomic opimizaion modl ha accommodas h complxiy of h biological modling of rsourc sock dynamics. To his nd, w consruc a bioconomic modl of h fishry for Alanic salmon in h Balic Sa. Th modl aks ino accoun h migraion parns of salmon, ag-srucurd sock dynamics and rproducion 3

4 uncrainy 1, as wll as h diffrn conomic and biological characrisics of h svral fishris ha arg salmon. Th bioconomic modl rconcils h conomic modling of salmon fishris in h Balic Sa wih h sock assssmn modls currnly usd as h basis for managmn advic (s,.g., ICES, 005). W apply h modl o dvlop opimal policy prscripions for managing h salmon fishris in h Balic Sa. In ordr o conribu o h ongoing policy dba, h modl is calibrad wih daa for h Simojoki salmon sock, whos naiv rivr is locad in h norhrn Balic Sa. Earlir sudis addrssing harvs allocaion bwn diffrn usr groups arging a migraory spcis hav collapsd h sock dynamics ino simpl biomass modls (Charls and Rd, 1985; Cook and McGaw, 1996; Laukkann, 001). Economic analyss accouning for uncrainy hav also gnrally rsord o such modls (Rd 1974, 1978, 1979; Clark and Kirkwood, 1986, Shi al., 005). Bjørndal al. (004) sudid h Norwgian spring-spawning hrring fishry using an ag-srucurd modl wih rcruimn uncrainy bu rlid on simulaions o compar alrnaiv managmn sragis. Th prsn papr xnds h squnial harvs modls prsnd by Charls and Rd (1985) and Laukkann (001, 003). I combins an xplici analysis of squnial harvsing by comping usr groups, an ag-srucurd populaion modl and an accoun of h uncrainy in h rlaionship bwn h sock siz and h corrsponding rcruimn. Dynamic programming and a numrical soluion mhod ar usd o driv opimal managmn prscripions. Th papr is srucurd as follows. Th scion o follow prsns h biological, conomic and insiuional characrisics of h Balic Salmon fishry. Scion hr dscribs h populaion dynamic modl and dfins h conomic bnfis of h salmon harvs. Scion four formulas h dcision problm ha h fishry managr facs. In scion fiv, w calibra h modl. Scion six discusss h opimal harvs policy and scion svn concluds h papr wih a summary of h insighs gaind in h sudy. 1 Du o h M74-syndrom, a rproducion disordr of salmon ha causs clos o 100 % moraliy in h juvnil phas, rcruimn uncrainy is h principal sourc of salmon populaion flucuaions in h Balic Sa (s,.g., Karlsson and Karlsröm, 1994). 4

5 . Th Salmon Fishry in h Balic Sa In h Balic Sa rgion, juvnil salmon usually spnd hr yars in rivrs, afr which hy migra ino h Balic Main Basin in h springim. Adul salmon hn spnd 1 o 4 yars fding a sa bfor hy sar h migraion back o hir naal rivrs in h arly summr o spawn (s.g. Karlsson and Karslsröm, 1994). Th focus of his sudy is h fishry xploiing salmon whos naiv rivrs ar in h Norhrn Balic Sa ara. Th fishry opras in h Gulf of Bohnia and h Balic Main Basin (Figur 1.) Characrisic of h fishry is h squnial harvsing of migraing fish. Th squnial fishris diffr in rms of gar, cachabiliy, fishing coss, and h pric obaind for hir cach. Th commrcial offshor fishris us drifns and longlins o harvs salmon fding in h main basin. Hisorically, mos of h commrcial salmon cach has bn harvsd by h coasal fishris in h Gulf of Bohnia, which ak maur salmon migraing o hir naiv rivrs during h arly summr (Jun and July) using drifns and rapns. In h rivrs, h fish ar harvsd by rcraional fishrmn, wih angling bing h only form of fishing prmid. Th currn inrnaional salmon fishry rgulaions ar basd on oal allowabl cach and chnical managmn masurs such as minimum landing siz, minimum drifn msh siz, and minimum hook siz. In addiion, ach Balic Sa naion has is own rgulaory masurs. As of 008, EU fishry rgulaions will ban h us of drifns. [Figur 1 abou hr] 3. Bioconomic Modl Our bioconomic modl ncompasss h fiv fishris harvsing h salmon socks from h Norhrn Balic Sa ara: h coasal drifn fishry (cdn), h coasal rapn fishry (cn), h rivr fishry (ri), h offshor drifn fishry (odn) and h offshor longlin fishry (oll). Figur illusras h srucur of h fishry. In our modl, a yar bgins in May, which is whn smols migra from hir naal rivr o h Balic Main Basin and join h fding adul populaion. For h sak of racabiliy, h modl assums ha h diffrn fishris ak plac squnially. Th coasal harvs occurs in h arly summr, whn maur salmon sar hir spawning migraion norh owards hir naal rivrs. Th coasal drifn fishry harvss h migraing salmon in Jun, and h coasal rapn fishry h surviving salmon onc hy arriv in h Gulf of Bohnia in July. Th salmon surviving boh coasal fishris ar harvsd by h rcraional rivr fishry in Augus, whn hy rach hir hom rivr. Salmon ha surviv h 5

6 rivr fishry rproduc. Th immaur salmon ha rmain in h Balic Main Basin in h spring o fd ar harvsd by h offshor fishry in h fall. Th offshor drifn fishry aks plac in Ocobr, h offshor longlin fishry in Dcmbr. [Figur abou hr] 3.1 Populaion Dynamics W considr a discr im and ag-srucurd modl of populaion dynamics ha follows h lif cycl of salmon. Our modl aks ino accoun h following ag groups: ggs, fry, parr, smols, on-sa-winr and wo-sa-winr salmon. Th on-sa-winr ag group is furhr dividd ino wo lif sags - immaur salmon which rmain in h Balic Main Basin o fd and grils which maur and sar hir spawning migraion. W assum hr ha all wo-sawinr salmon maur. Th coasal drifn, coasal rapn and rivr fishris harvs boh grils and wo-sa-winr salmon whil h offshor drifn and longlin fishris arg immaur on-sa-winr salmon. Th populaion dynamics modl for h salmon sock is h sam as h on proposd by Michilsns al. (006) and implmnd wihin h Inrnaional Council for h Exploraion of h Sa (ICES) working group for h assssmn of Alanic salmon wihin h Balic Sa (ICES 005), wih h xcpion ha h modl only accouns for h wo mos abundan yps of maur salmon i.. grils and SW salmon. Th srucur of h salmon populaion can b summarizd in a sa vcor, S, { s, s s } S 1,,,..., 6,, which racs h siz of ach ag group. Th sa of h salmon sock in priod dpnds on h sa of h sock and h fishing ffor in priod -1. Th fishing ffors cdn cn ri odn oll of h fiv fishris ar summarizd in vcor, {,,,, } changs from on fishing sason o h nx follow S G( S ), = 1 1. Thus, h sa, wih h sa ransiion funcions dfining s ( a, = g a S 1, 1. Indx a indicas h ag group, a { 1,..., 6}, and G { g, g g 6} 1,..., ) is h vcor of sa ransiion quaions. Th lmns of h sa vcor S and h sa ransiion vcor G {} ar dscribd in Tabl 1. Appndix A dscribs h populaion modl in mor dail. Th noaion is as follows: r s is sx raio and f avrag fcundiy, m is h insananous naural moraliy ra, and f q l is h 6

7 cachabiliy cofficin of lif sag l by fishry f. Th harvsd lif sags - grils, immaur on-sa-winr salmon and wo-sa-winr salmon - ar subscripd by gr, 1 and. Furhr, θ ar indpndn and idnically disribud random shocks on rcruimn, α and β ar h w r rcruimn paramrs, and ar h pos-smol moraliis for wild and rard m p sm m p sm salmon, I is h numbr of sockd smols, and L is h mauraion ra of on-sa-winr salmon. [Tabl 1 abou hr] 3. Economic Modl This scion dscribs h cachs and annual n conomic bnfis o ach of h fiv fishris. Cach pric, fishing coss and cachabiliy may vary bwn h fishris, as hy opra a diffrn ims of h yar, cach salmon of diffring siz and us diffrn quipmn. Th cach wigh of salmon also varis according o lif sag. Throughou h modl, f f ( ) q l p f is h pric of salmon in fishry f and c f h cos of fishing ffor in h fishry. Th harvs ra of lif sag l by fishry f is givn by 1, and h cach wigh of lif sag l is dnod by. W l Th coasal drifn fishry harvss grils and wo-sa-winr salmon. Th numbrs of grils and m / 1 m /1 wo-sa-winr salmon availabl o h fishry ar givn by Ls and s. Th profis of h coasal drifn fishry, π cdn,, ar 5, 6, π cdn cdn q cdn cdn m q gr cdn = / 1 pcdn Ls Wgr + 1 s 1, 5, 6, W c cdn cdn. (1) Th coasal rapn fishry harvss spawnrs afr h coasal drifn fishry. Th numbrs of grils and wo-sa-winr salmon ha rach coasal rapns ar m / 6 Ls 5, cdn cdn q gr and s m / 6 q cdn 6, cdn π cn,. Th profis of h fishry can b calculad using h following quaion: π cdn cdn cn cn q cdn cdn q cn cn m q gr q gr cn = / 6 pcn Ls Wgr +, 5, 1 s6, 1 W c cn cn. () 7

8 Th rivr harvs is akn by rcraional anglrs. Th numbrs of grils and wo-sa-winr cdn cdn cn cn salmon raching h rivr fishry ar givn by gr gr cdn cdn cn cn m / 4 q q m / 4 q Ls and q s. For h sak of racabiliy, w assum ha h n social bnfis from h rcraional rivr fishry ar quadraic in h rivr harvs; i.., 5, 6, NB ( H ), = kh v (3) ri, ri, ri, whr H Ls ri ri cdn cdn cn cn ri ri qgr + 1 q q q W s 6, gr W cdn cdn cn cn = m / 4 qgr qgr, 5, ri 1 h priod harvs of h rivr fishry and k and v ar paramrs of h n bnfi funcion. is Th offshor fishris harvs only h salmon fding in h Balic Main Basin. Th numbr of on-sa-winr salmon availabl in h main basin in Ocobr is supplid by profis of h offshor drifn fishry ar ( 1 L) s 5 / 1m 5,. Th π odn odn odn m q = 5 / 1 1, podn 1 1 odn ( L) s W c 5, 1 odn. (4) Finally, wih h numbr of salmon availabl for harvs givn by 7m / 1 odn odn q1 ( 1 L) s5,, h profis of h offshor longlin fishry, which harvss on-sa-winr salmon afr h offshor drifn fishry, ar π oll odn odn q oll oll m q = 7 / 1 1 1, poll 1 1 oll ( L) s W c 5, 1 oll. (5) Thrfor, h oal annual n conomic gain π for h Norhrn Balic salmon fishry is π + π cdn, + π cn, + NB ri, + π odn, π oll, = (6) 8

9 4. Th Opimizaion Problm Equaions (1) o (5) illusra h inrdpndnc of h squnial fishris. Th harvs of ach fishry affcs h profis of h nx and rducs h fuur salmon sock. Th opimal harvs sragy would balanc h marginal profis of ach fishry o qual h rvnus forgon in h nx fishry in h squnc in h currn sason and in h fuur. Th objciv of h fishry managr is o maximiz h discound n bnfis from h salmon fishry hrough h opimal choic of fishing ffor for h fiv squnial fishris. In h bginning of vry sason, h managr obsrvs h siz of h salmon sock S and hn chooss h opimal vcor of fishing cdn cn ri odn oll ffors, whr {,,,, } as a whol, (. Th n conomic bnfis for h fishry π S, ), dpnd on sa of h salmon sock S and h fishing ffors. Th salmon sock volvs from on priod o h nx according o h sa ransiion quaions S = G( S, 1 1 ) prsnd in Tabl 1. This is a conrolld Markov procss. Th n bnfis of h fiv fishris arging salmon ar givn by quaions (1) o (5). Th fishry managr sks a squnc of fishing policis, {}, which prscribs h ffors ha in a givn sa and priod will maximiz h xpcd n prsn valu of h currn and fuur harvs ovr an infini im horizon T. = ( S ) Bllman s (1957) principl of opimaliy implis ha h opimal policy mus saisfy h funcional quaion V ( S ) = max { π ( S, ) + δe [ V ( G( S,, θ ))]}, (7) θ ( S ) whr V is h valu funcion,δ is h discoun facor, and h rcruimn shocks θ. Th rward funcion ( S, ) E θ is h xpcaion opraor ovr π is boundd. Whr h valu of δ is lss han on, h mapping undrlying h Bllman quaion is a srong conracion on h spac of boundd coninuous funcions and hus, by h Conracion Mapping Thorm, will possss a uniqu soluion. 9

10 W solvd h dynamic program numrically using h collocaion mhod. This chniqu involvs wriing h valu funcion approximan as a linar combinaion of n known basis funcions φ 1, φ,, φ n whos cofficins c 1, c,, c n ar drmind by h quaion V ( S) n c j φ ( S) j= 1 j (8) Th cofficins c 1, c,, c n ar dfind by rquiring h valu funcion approximan o saisfy h Bllman quaion in (0) a a fini s of collocaion nods. Th soluion was implmnd using h CompEcon Toolbox for Malab. Th Malab cod is availabl from h auhors upon * rqus. Th soluion producs policy funcions for ( S) currn sa o h opimal harvs policy. ha provid a mapping from h Th soluion o h problm can b characrizd by h firs-ordr quilibrium condiions known as Eulr condiions. Th rlvan Eulr condiions in h prsn cas can b drivd by applying h Karush-Kuhn-Tuckr and Envlop Thorms o h opimizaion problm in (7). Th ffor lvls ar boundd from blow by zro. Th Eulr quaions ak h form and S ( S ) δe [ λ( G( S,, θ )) G ] τ π θ =, (9) + ( S ) + δe [ λ( G( S,, θ )) G ] λ( S ) π θ =,, (10) S λ is h shadow valu of h rsourc. Hr, π, π, G and dno h S GS whr ( S ) V ( S) parial drivas. Th ffors and τ mus saisfy h complmnary condiion 0 and 0 τ = 0. (11) i > i Th CompEcon Toobox is a library of MATLAB funcions for numrically solving a variy of problms in conomics and financ ha was dvlopd o accompany Miranda and Facklr (00). Th library is downloadabl a hp://www4.ncsu.du/~pfacklr/compcon/oolbox.hml. 10

11 Hr, τ is a 1 d vcor whos ih lmn, τ i, masurs h currn and xpcd fuur rward from a marginal incras in h ih acion variabl i. If i > 0, τ i mus b zro; ohrwis rwards could b incrasd by dcrasing i. 5. Calibraion W calibra h modl by using paramr simas for h salmon sock in h Simojoki Rivr. In kping wih h currn salmon managmn advic and h undrlying paramr simas, w masur fishing ffor in rms of gardays (s,.g., ICES, 005). Thus, our conrol variabls ar h opimal numbr of gardays for ach fishry. A garday is dfind as unis of gar ims numbr of fishing days. As ach fishry uss diffrn gar, h dfiniion of a garday diffrs accordingly: for h offshor and coasal drifn fishris, a garday is h numbr of ns ims h numbr of fishing days; for h coasal rapn fishry i is h numbr of rapns ims h numbr of fishing days; for h offshor longlin fishry i is h numbr of hooks ims h numbr of fishing days; and for h rivr fishry, a garday is qual o an angling day. Tabl displays h biological paramrs of h Simojoki salmon sock. Th paramr simas ar basd on h assssmns currnly usd by h corrsponding ICES working group (ICES, 005). Following Michilsns and McAllisr (004), h rcruimn shocks θ ar z assumd o follow a lognormal disribuion. Th rcruimn rrors ar hus dfind as θ =, whr h procss rrors ar normally disribud wih man µ and sandard dviaion σ. z [Tabl abou hr] Tabl 3 prsns h conomic paramrs. W obaind h fishing cos daa by inrviwing fishrmn. Th cos simas accoun for h variabl coss: gar pric, gar mainnanc, vssl mainnanc, ful and labor coss. Th coss diffr du o h diffrncs in h quipmn and chniqus usd in h fiv fishris. Th pric paramrs wr obaind from official Finnish saisics (FGFRI, 004) and h saisics producd by h Danish Fishris Dircora (Anon., 004). W assum hr ha h small-scal cachs of salmon naiv o Simojoki do no affc h mark pric of salmon. According o Sälä al. (00), salmon prics in Finland ar 11

12 drmind mainly by h impors of Norwgian salmon. Th pric diffrncs rflc sasonal variaion in h volum and qualiy of h salmon harvs as a whol. Th n bnfis of h rcraional harvs in h Simojoki hav bn simad basd on rsuls of a coningn valuaion sudy (Parkkila (005)) ascraining h willingnss o pay (WTP) for sock improvmns ha would doubl h xpcd cach pr angling day in h rivr from is 003 lvl of 0.35 kg o 0.70 kg. Th simad WTP among anglrs for a sock improvmn ha would doubl h cach was 8.50 uros pr angling day in addiion o h currn xpns of 1 uros a day. W assumd a linar marginal WTP for rcraional harvs, fi h associad curv o h simad WTP valus o obain individual n bnfis, and hn aggrgad across h approxima anglr populaion of 900 anglrs o obain a masur of h social n bnfis of h rcraional harvs. [Tabl 3 abou hr] 6. Rsuls Th dynamic bhavior of h modl was sudid using a Mon Carlo simulaion. Th simulaion gnrad 10,000 sa and policy pahs using as inpu h opimal ffor lvls = ( S ) dfind as h soluion o h dynamic program in (7). Th currn sock simas wr usd as h iniial sa. Figur 3 prsns h mans and 90 % probabiliy inrvals for opimal fishing ffor in h coasal rapn and rivr fishris. Undr h opimal policy, only h coasal rapn fishry and h rivr fishry would rmain aciv; h rsul holds for all sa configuraions producd by h simulaion. Th fac ha h coasal rapn fishry would coninu o harvs undr h opimal harvs policy whil h ohr commrcial fishris would no dspi highr prics and lowr uni coss - is xplaind by h diffrncs in h cachabiliis. Th cachabiliis of h argd lif sags by rapn fishry ar markdly highr han hos by h ohr commrcial fishris, which suffics o compnsa for h highr uni coss and lowr pric. Figur 4 shows h mans and 90 % probabiliy inrvals for h n bnfis o h wo aciv fishris. Th variaion in h coasal rapn fishry s ffor and n bnfis is considrabl, whras h rivr fishry s ffor and n bnfis rmain sabl. Whn low sock lvls ar obsrvd, h coasal rapn fishry rducs is harvs o h bnfi of h rivr fishry, which is abl o harvs from a rlaivly sabl sock of salmon. Th rsul follows from h diffrn characr of commrcial and rcraional fishing, which is manifsd in h 1

13 curvaur of h n bnfi funcions: h marginal n bnfi of harvsing is consan in h rapn fishry bu dcrass in h rivr fishry. Figur 5 prsns h man and 90 % probabiliy inrval for smol-sag salmon undr h opimal policy. Th xpcd numbr of smols convrgs o nar 75,000, som 0,000 mor han h xpcaion if h fishry mainaind is currn fl configuraion and ffor lvls. [Figur 3 abou hr] [Figur 4 abou hr] [Figur 5 abou hr] Th rsuls ar in lin wih h forhcoming changs in h EU Common Fishris Policy, which will prohibi drifn harvsing. Th finding ha hr of h four commrcial fishris sudid - h coasal drifn, h offshor drifn and h offshor longlin should b xcludd from harvsing is robus o changs in h ky conomic and biological paramrs. W conducd a snsiiviy analysis o sudy h ffc of such changs on h opimal policy. Th paramrs drmining h rlaiv prformanc of h commrcial fishris ar h cach pric, uni cos of fishing ffor, and cach pr uni of ffor. Whr h conomic paramrs wr concrnd, our snsiiviy analysis focusd on h coss and n bnfis of h rivr fishry, for which daa ar spars compard o pric and cach pr uni of ffor daa. W limid h analysis o h sady sa of h crainy-quivaln problm obaind by fixing h rcruimn shock a is man. Tabl 4 displays h crainy-quivaln sady sa and h rsuls of h snsiiviy analysis. Th opimal ffor lvls in h crainy-quivaln sady sa compud a h bas cas paramrs ar 50,408 gardays for h coasal rapn fishry and 4093 angling days for h rivr fishry. Th corrsponding harvs lvls ar approximaly 43,000 kg and 3700 kg. Th coasal rapn harvs in h crainy-quivaln sady sa is slighly smallr han h currn cach of h coasal fishris as a whol, which is 63,600 kg (prsonal communicaion, Marjaliisa Koljonn, Finnish Gam and Fishris Rsarch Insiu). In conras, h simad rcraional harvs is clos o svn ims h prsn harvs of 560 kg (prsonal communicaion, Erkki Jokikokko, Finnish Gam and Fishris Rsarch Insiu). Th cos savings from closing down h lss fficin fishris and h subsanial incras in h rcraional harvs would produc social n bnfis subsanially abov hos ralizd a prsn: in h crainy-quivaln sady 13

14 sa, h annual n bnfis of h Simojoki salmon sock ar nar 137,000 uros, as opposd o h currn n bnfis of approximaly 80,000 uros. Ohr hings bing qual, h uni cos of fishing ffor in h coasal rapn fishry would hav o b 80 % highr han h currn sima for h coasal drifn fishry o b includd in h opimal policy (Tabl 4). Furhr incrass in coss for h coasal rapn fishry would only shif cachs bwn h coasal fishris and h rivr fishry: a h currn simas of offshor uni coss, h offshor fishris rmain xcludd from h harvs rgardlss of h coasal fishris uni coss. If insad h uni cos of h offshor drifn fishry wr 89 % blow h currn sima, boh coasal fishris would b xcludd from h opimal policy and rplacd by h offshor drifn fishry. Similarly, a uni cos 95 % blow h currn sima for h offshor longlin fishry would mak ha fishry h only aciv commrcial on. On balanc, h rsuls appar robus o changs in h cos paramrs. As ful is h mos imporan opraing cos in fishing, a dcras in fishing coss is unlikly. An incras in h coss of rapn fishing is a mor likly scnario, sinc h incrasing sal populaion in h Balic Sa may forc salmon fishrmn o swich o sal-saf ns. [Tabl 4 abou hr] Figur 6 illusras h ffc of h fishris rlaiv coss on h opimal fishry configuraion. Th lf-hand sid shows h cas whr h coss of h offshor drifn and longlin fishris and n bnfis of h rivr fishry rmain a hir currn lvl whil h coss of h coasal drifn and rapn fishris vary. Th offshor drifn and rapn fishris harvs oghr wih h rivr fishry only for a narrow rang of coss. Th righ-hand sid dpics h cas whr h coasal fishris coss and h n bnfis of h rivr fishry rmain a hir currn lvl whil h offshor drifn and longlin coss chang. A significan dcras in fishing coss would b rquird in boh offshor fishris for hm o b includd in h opimal harvs policy. Again, h wo offshor fishris coxis only for a narrow cos rang. Th ffc of coss on h opimal fishry configuraion is id o h cachabiliis by h fishris. Th coss of offshor longlin fishing would hav o fall roughly on ordr of magniud blow hos of offshor drifn fishing o compnsa for h diffrnc in h cachabiliis by h fishris and allow boh o coninu harvsing. Th ffc is similar in h cas of h coasal fishris. 14

15 [Figur 6 abou hr] Changs in h marginal WTP for a rcraional harvs and in h biological paramrs rsuld only in a shif of harvs bwn h coasal rapn fishry and h rivr fishry; h opimal fishry configuraion rmaind unchangd (Tabl 4). Shifs in h marginal WTP of up o 0% downward or upward, as wll as similar rlaiv changs in h slop, mainaind h opimal fishry configuraion of coasal rapns and rivr fishry only. As on would xpc, an upward shif in h marginal WTP allocas mor harvs o h rcraional rivr fishry and dcrass h profis of h coasal rapn fishry. Th opimal fishry configuraion also rmains unalrd irrspciv of changs in h mauraion ra, h sockings and h pos-smol moraliy (Tabl 4). Dcrasing h mauraion ra o 0.1 from h currn sima of 0.15 did no affc h numbr of aciv fishris. Th ffor, cach and profis of h rapn fishry all incrasd slighly whil h oucom for h rivr fishry rmaind ssnially unchangd. Wihou offshor fishris, h smallr availabiliy of grils would b compnsad for by an incrasd numbr of wo-sa-winr salmon availabl o h rapn and rivr fishris. Th rapn fishry, which is h firs o harvs homing fish, would rap h bnfis of an incrasd numbr of h largr wo-sa-winr salmon. As a dcras in h mauraion ra incrass h numbr of salmon ha ar availabl o h offshor fishris (quaions 4 and 5), h assumpion ha h offshor fishris harvs only on-sawinr salmon whil h ohr hr fishris harvs boh on- and wo-sa-winr salmon canno b considrd crucial for h xclusion of h offshor fishris in h opimal policy. Kallio-Nybrg al. (004) propos highr pos-smol moraliy ras for wild and rard salmon han hos usd in h ICES sock assssmns. Alhough pos-smol moraliy is h principal biological paramr affcing salmon sock sizs afr rproducion, an incras in pos-smol moraliy ras did no affc h opimal policy wih rgard o h numbr of aciv fishris. I did, howvr, rsul in a significan dcras in h ffor, cach and profis in h coasal rapn fishry. Th highr pos-smol moraliis rsul in a clos o 60 % dcras in h opimal harvs o h rapn and rivr fishris as a whol. A low sock lvls h marginal bnfi of addiional ffor falls mor rapidly in h coasal rapn fishry han in h rivr fishry, whr h cachabiliy of wo-sa-winr salmon is markdly highr han in h coasal rapn fishry, and whr h marginal bnfi of addiional harvs is rlaivly high a low harvs lvls. 15

16 W also sudid h snsiiviy of h opimal policy o h numbr of sockd smols (Tabl 4). In h priod , h avrag numbr of sockd smols in h Simojoki was approximaly 80,000 (Erkinaro al., 003), which is significanly highr han h currn numbr of 000. Incrasing h numbr of rard smols did no affc h opimal policy in rms of aciv fishris. Th ffc on ffors and cachs is h opposi of ha brough abou by an incras in pos-smol moraliis: h opimal ffors, cachs and profis of h coasal rapn fishry now incras somwha whil hos of h rivr fishry rmain virually consan. A issu hr again ar h diffrn cachabiliis and dcrasing vrsus consan marginal bnfis of harvsing in h rivr and coasal rapn fishris. Highr ffor and cachs ar now rquird in h coasal rapn fishry o balanc h marginal n bnfis o qual hos in h rivr fishry. 7. Conclusion This papr provids a bioconomic modl of h fishry for Alanic salmon in h Balic Sa ha is compaibl wih h sock assssmn modls currnly usd o produc managmn advic. I hus bridgs h gap bwn conomic and biological modls. Th sudy xnds h bioconomic liraur on h opimal managmn of salmon by considring an ag-srucurd modl of populaion dynamics and squnial harvs by mulipl fishris wih diffrn conomic characrisics and impacs on h sock. Th papr oulins a framwork for numrically drmining h opimal harvs policy for ach fishry. Using daa calibrad for h Simojoki salmon sock, h modl has bn applid o solv for h opimal harvsing policy and h opimal allocaion of harvs bwn h fiv fishris harvsing salmon from h Norhrn Balic Sa ara. Uncrainy was includd in h modl in h form of rcruimn flucuaions, which ar h principal sourc of salmon populaion uncrainy in h Balic Sa. In h cas of a risk- nural fishry managr, h opimal policy dpnds xclusivly on h man of h rcruimn shock. Whn h man shock is on, h opimal policy for ach sa producd by h sochasic modl coincids wih h opimal policy producd by h drminisic modl, in which h rcruimn 16

17 shock is fixd a is man. 3 Whil h opimal policy in ach sa is similar o ha indicad by h drminisic modl, accouning for rcruimn uncrainy yilds insigh ino h volailiy ha h procss may xhibi and is ffc on h opimal fishry configuraion. Th rsul ha h coasal and offshor drifn fishris and h offshor longlin fishry should b xcludd from harvsing is robus o variaion in h populaion siz: h fishris wr xcludd vrywhr along h simulad sa pahs, vn whn vry larg shocks wr ralizd and h harvsabl populaion was abundan. Th rsuls suppor fuur fishry policy changs which will ban drifn fishris in h Balic Sa. Howvr, h mpirical analysis prsnd hr is confind o h Simojoki salmon sock, and h rsuls on h opimal fishry configuraion and harvs allocaion canno b gnralizd as such o ohr Balic salmon fishris. To obain conomically opimal managmn advic for h Balic as a whol, h framwork providd hr should b xndd o considr mulipl coxising socks, and h daa ndd for mpirical analysis should b gahrd for all Balic salmon fishris. Th currn guidlins for managing Balic salmon ignor h conomic aspcs of h fishry (ICES, 005). Th snsiiviy analysis carrid ou hr undrlins h imporanc of conomic informaion for fishris managmn. In h squnial fishry modl, rlaiv changs in h fishing coss affc h opimal fishry configuraion, whras changs in h biological paramrs only alr h allocaion of h harvs bwn h aciv fishris. Collcing rprsnaiv fishing cos daa for all h Balic salmon fishris is ssnial for producing managmn rcommndaions ha accoun for conomic considraions. Furhr rsarch on h valu of rcraional fishris in h Balic salmon rivrs is also ndd. Finally, our focus hr has bn on opimal harvs policy undr h assumpion ha h Balic salmon fishry is managd by a singl auhoriy. A worhwhil xnsion would b ransboundary coopraion o susain h opimal policy, for hr ar a numbr of counris ha harvs salmon in h Balic Main Basin. 3 In modls wih boh rcruimn uncrainy and uncrainy driving from sock masurmns or policy implmnaion, h harvs policy producd by h sochasic modl is mor consrvaiv han ha producd by h corrsponding drminisic modl. S,.g., Clark and Kirkwood (1986) and Shi al. (005). 17

18 Acknowldgmns This rsarch was a par of h Acadmy of Finland s Balic Sa Rsarch Program BIREME and parly fundd by h Acadmy and h Finish Minisry of Agriculur and Forsry. W would lik o hank h parnrs of h projc nild Th Balic Salmon Acion Plan in h Bohnian Bay Rivrs: Inrdisciplinary Modlling of h Evolving Salmon Sock and Socio- Economic Aspcs. W also hank Marko Lindroos, Jon Olaf Olaussn and Ragnar Arnason for hir insighful commns on an arlir vrsion of his papr. 18

19 Rfrncs Anon., 004. Yarbook of Fishry Saisics 003. Danish Fishris Dircora. Minisry of Food, Agriculur and Fishris. Bllman, R.E., Dynamic Programming. Princon, NJ: Princon Univrsiy Prss. Bjørndal, T., Gordon, D. V., Kaiala, V., Lindroos, M., 004. Inrnaional Managmn Sragis for a Sraddling Fish Sock: A Bio-Economic Simulaion Modl of h Norwgian Spring-Spawning Hrring Fishry. Environmnal and Rsourc Economics 9, Brown, C., Laland, K., 001. Social Larning and Lif Skills Training for Hachry-Rard Fish. J. Fish Biol 59, Charls, A. T., Rd, W. J., A Bioconomic Analysis of Squnial Fishris: Compiion, Coxisnc, and Opimal Harvs Allocaion bwn Inshor and Offshor Fls. Canadian Journal of Fishris and Aquaic Scincs 4, Clark, C. W., Kirkwood, G. P., On Uncrain Rnwabl Rsourc Socks: Opimal Harvs Policis and h Valu of Sock Survys. Journal of Environmnal Economics and Managmn 13, Cook, B. A., McGaw, R. L., Spor and Commrcial Fishing Allocaion for h Alanic Salmon Fishris of h Miramichi Rivr. Canadian Journal of Agriculural Economics 44, Dacon, R. T., Brookshir, D. S., Fishr, A. C., Kns, A. V. Kolsad, C. D., Scrogin, D., Smih, K. V., Ward, M., Wiln, J., Rsarch Trnds and Opporuniis in Environmnal and Naural Rsourc Economics. Environmnal and Rsourc Economics 11 (3-4), Erkinaro, J., Mäki-Päys, A., Jununn, K., Romakkanimi, A., Jokikokko, E., Ikonn, E., Huhmarnimi, A., 003. Th Balic Salmon Acion Plan in Finland, Kalaukimuksia, 186. Finnish Gam and Fishris Rsarch Insiu. (in Finnish) Europan Commission, 001. Grn Papr. On h Fuur of Common Fishris Policy. Commission of h Europan Communiis. COM (001) 135 final. pp. 41. Finnish Gam and Fishris Rsarch Insiu (FGFRI), 004. Producr Prics for Fish 003. Agriculur, Forsry and Fishry 004: 54. ICES, 005. Rpor of h Working Group of h Assssmn of Balic Salmon and Trou. ICES, Hlsinki. 19

20 Jokikokko, E., Kallio-Nybrg, I., Juila, E., 004. Th iming, sx and ag composiion of h wild and rard Alanic salmon ascnding h Simojoki rivr, norhrn Finland. Journal of Applid Ichhyology 0, Kallio-Nybrg, I., Juila, E., Salmonimi, I., Jokikokko, E., 004. Associaion bwn nvironmnal facors, smol siz and h survival of wild and rard Alanic salmon from h Simojoki rivr in h Balic Sa. J. Fish. Biol. 65, Karlsson, L., Karlsröm, Ö., Th Balic salmon (Salmo salar L.): is hisory, prsn siuaion and fuur. Dana 10, Laukkann, M., 001. A Bioconomic Analysis of h Norhrn Balic Salmon Fishry: Coxisnc Vrsus Exclusion of Comping Squnial Fishris. Environmnal and Rsourc Economics 18, Laukkann, M., 003. Coopraiv and Non-Coopraiv Harvsing in a Sochasic Squnial Fishry. Journal of Environmnal Economics and Managmn 45, Michilsns, C. G. J., McAllisr, M. K., 004. A Baysian hirarchical analysis of sock-rcrui daa: quanifying srucural and paramr uncrainis. Canadian Journal of Fishris and Aquaic Scincs 61, Michilsns, C. G. J., McAllisr, M. K., Kuikka, S., Pakarinn, T., Karlsson, L., Romakkanimi, A., Prä, I. and Mänynimi, S. 006, A Baysian sa-spac mark-rcapur modl o sima xploiaion ras in mixd-sock fishris. Canadian Journal of Fishris and Aquaic Scincs 63, Miranda, M. and Facklr, P, 00. Applid Compuaional Economics and Financ, MIT prss. Parkkila, K., 005. Esimaing h willingnss o pay for cach improvmns in h rivr Simojoki. Masr s hsis, Dparmn of Managmn, Univrsiy of Hlsinki. Rd, W. J., A Sochasic Modl for h Economic Managmn of a Rnwabl Animal Rsourc. Mahmaical Bioscincs, Rd, W. J., Th Sady Sa of a Sochasic Harvsing Modl. Mahmaical Bioscincs 41, Rd, W. J., Opimal Escapmn Lvls in Sochasic and Drminisic Harvsing Modls. Journal of Environmnal Economics and Managmn 6, Shi, G., Cosllo, C., Fishr, A., Hanmann M., Karp., L., 005. Fishry Managmn undr Mulipl Uncrainy. Journal of Environmnal Economics and Managmn 50,

21 Sälä, J., Mickwiz, P., Virann J., Honkann A., Saarni, K., 00. Th ffc of rad libraion on h salmon mark in Finland. In: Fishris in h Global Economy Procdings of h Elvnh Binnial Confrnc of h Inrnaional Insiu of Fishris Economics and Trad. Augus 19-, 00. Wllingon, Nw Zaland. Inrnaional Insiu of Fishris Economics and Trad. IIFET, CD-ROM. 1

22 Appndix A. Populaion Dynamics. Th appndix dscribs h populaion dynamics by ag group. Th ggs hach in h spring. Afr haching, i aks a salmon approximaly hr and a half yars o squnially dvlop ino fry (s ), parr (s 3 ) and finally rach h smol sag (s 4 ). Th rlaionship bwn h numbr of ggs and h numbr of smols can b summarizd by a Bvron-Hol sock-rcruimn funcion (s,.g., Michilsns and McAllisr, 004). Fry (s ) and parr (s 3 ) ar usd as accouning variabls in h our modl: s 3, = s1,. Th numbr of wild smols in May of yar is hrfor givn by s 4, s = θ. (A1) 3, 1 α + βs3, 1 Th salmon sock is safguardd hrough socking of juvnils. W assum ha h rproducion funcion and associad paramrs ar h sam for wild and rard salmon. Th numbr of onsa-winr salmon in May of yar is givn by s 5, w mp sm = s4, 1 + I 1 m r p sm. (A) Th populaion dynamics of rard salmon ar similar o hos of wild salmon xcp ha h rard salmon nr h sysm hrough socking. Th naural moraliy during h firs yar ha salmon spnd a sa (pos-smol moraliy) is also highr for rard salmon han for wild salmon (Brown and Laland, 001). Th maur on-sa-winr salmon, grils, sar hir spawning migraion. Th numbr of grils availabl o h coasal drifn fishry in Jun of yar is givn by N cdn gr, m /1 = L s5,. (A3) Th numbr of grils ha ar availabl o coasal rapns in July of yar is dfind by N cn gr, = N cdn gr, q cdn cdn gr m /1. (A4)

23 Th numbr of grils ha rach h rivr fishry in Augus of yar is givn by N ri gr, = N cn gr, q cn cn gr m /1. (A5) W assum ha grils, which ar prdominanly mals (Jokikokko al., 004), di naurally if hy ar no caugh in h rivr fishry. Thus, hy do no rproduc in our modl. Th numbr of immaur on-sa-winr salmon availabl o h offshor drifn fishry in Ocobr of yar is givn by N odn 5m /1 1 sw, = (1 L) s5,. (A6) Th numbr of on-sa-winr salmon raching h offshor longlin fishry in Dcmbr of yar is givn by h quaion N oll 1 sw, odn odn odn q 1 m / 6 N 1 sw, =. (A7) Th numbr of wo-sa-winr salmon in May quals h numbr of on-sa-winr salmon surviving h offshor longlin fishry, minus naural moraliy: odn odn q oll oll m q 1 1 s (1 L) s 6, 5, = (A8) Th numbr of wo-sa-winr salmon availabl o h coasal drifn fishry in Jun of yar is givn by quaion cdn m /1 N sw, s6, =. (A9) Th numbr of wo-sa-winr salmon availabl o h coasal rapn fishry is givn by 3

24 N cn sw, cdn cdn cdn q m /1 N sw, =. (A10) Th numbr of wo-sa-winr salmon raching h rivr fishry is N ri sw, = N cn sw, q cn cn m /1. (A11) Finally, h numbr of spawning salmon (SSN) is givn by SSN = N ri sw, q ri ri m / 6. (A1) By assumpion all salmon di spawning. Th numbr of ggs producd is givn by N = SSN r f w g, s. (A13) 4

25 Tabl 1.Th lmns of h sa vcor S and ransiion vcor S G( S ), = 1 1 Ag group Sa variabl Sa ransiion quaion ( S ) a as funcion of Egg s 1, ( S ) Fry s, g ( ) S 1, 1 = s1, 1 Parr s 3, g ( ) 3 S 1, 1 = s, 1 S1 and 1 g for ag group a, 1 1 q cdn cdn q cn cn 5m / 1 g, = r f s s 6, 1 Smol s 4, g ( S ) θ s ( α + β s ) 4 1, 1 = 3, 1 / 3, 1 w On-sa-winr salmon s 5, m sm g ( ) 5 S 1, 1 = s4, 1 Two-sa-winr salmon s 6, ( S, ) = ( L) r sm m P p + 1 odn odn oll oll m q1 q1 g s5, 1 I q ri ri 5

26 Tabl. Biological paramrs (from ICES 005). Symbol Dfiniion Valu Uni r sx raio 0.5 mals and fmals s f fcundiy 10,000 ggs/fmal m insananous adul naural moraliy 0.18 yar -1 cdn q cachabiliy of wo-sa-winr salmon by cdn fishry gardays -1 cn q cachabiliy of wo-sa-winr salmon by cn fishry gardays -1 ri q cachabiliy of wo-sa-winr salmon by ri fishry.1-5 gardays -1 odn q 1 cachabiliy of on-sa-winr salmon by odn fishry gardays -1 oll q 1 cachabiliy of on-sa-winr salmon by oll fishry gardays -1 cdn q gr cachabiliy of grils by cdn fishry gardays -1 cn q gr cachabiliy of grils by cn fishry gardays -1 ri q gr cachabiliy of grils by ri fishry.0-5 gardays -1 α paramr of rcruimn funcion 105 β paramr of rcruimn funcion I sockings 000 numbr of smols w m pos-smol moraliy of wild salmon 1.67 yar -1 p sm m pos-smol moraliy of rard salmon. yar -1 r p sm L mauraion ra for on-sa-winr salmon 0.15 W cach wigh for grils 0.97 Kg gr W 1 cach wigh for on-sa-winr salmon 3.95 Kg W cach wigh for wo-sa-winr salmon 8.65 Kg µ man of procss rror z 0 σ sandard dviaion of procss rror Z

27 Tabl 3. Economic paramrs Abbrviaion Dfiniion Valu Uni c cdn uni cos of coasal drifn fishry 0.03 /garday c cn uni cos of coasal rapn fishry 0.97 /garday c odn uni cos of offshor drifn fishry 0.05 /garday c oll uni cos of offshor longlin fishry 0.03 /garday p pric for coasal drifn fishry /kg cdn p pric for coasal rapn fishry.5 /kg cn p pric for offshor drifn fishry /kg odn p pric for offshor longlin fishry /kg oll k paramr of rivr n bnfi funcion 39.3 v paramr of rivr n bnfi funcion Pric of salmon in h Åland Islands in Jun 003 (FGFRI, 004). Th avrag producr pric of salmon in h Bohnian Sa and h Bohnian Bay in July 003 (FGFRI, 004). 3 Avrag pric of salmon landd in Dnmark in h yar 003 (Anon., 004). In winr in paricular, h Finnish offshor harvs is landd primarily in Dnmark. 7

28 Tabl 4. Opimal policy and snsiiviy analysis Fishry Bas cas 80 % incras CTN coss 89 % dcras in ODN coss 95 % dcras in OLL coss Effor (gardays) Cach (kg) N bnfis (EUR) Effor (gardays) Cac h (kg) N bnfis (EUR) Effor (gardays) Cach (kg) N bnfis (EUR) Effor (gardays) Cach (kg) N bnfis (EUR) CDN CTN RI ODN OLL Fishry sockd smols Incrasd pos-smol moraliis: w r m =., =. 8 Effor (gardays) Cach (kg) N bnfis (EUR) psm Effor (gardays) Cach (kg) m p sm N bnfis (EUR) Lowr mauraion ra: L=0.1 Effor (gardays) Cach (kg) N bnfis (EUR) CDN CTN RI ODN OLL Fishry CDN CTN 0 % incras in h inrcp of marginal WTP for rcraional harvs Effor (gardays) Cach (kg) N bnfis (EUR) 0 % dcras in h inrcp of marginal WTP for rcraional harvs Effor (gardays) Cach (kg) N bnfis (EUR) 0 % incras in h slop of marginal WTP for rcraional harvs Effor (gardays) Cach (kg) N bnfis (EUR) 0 % dcras in h slop of marginal WTP for rcraional harvs Effor (gardays) Cach (kg) N bnfis (EUR) RI ODN OLL

29 Figur 1. Migraion rous of h salmon socks from h Norhrn Balic Sa. Salmon ar harvsd during fding and spawning migraions in h Balic Main Basin, h Gulf of Bohnia and rivrs. 5º Russia Alanic Ocan Norway Swdn Gulf of Bohnia Finland 60º Esonia Dnmark Balic Sa Balic Main Basin Lihuania Lavia km 9

30 Figur. Srucur of h salmon fishry in h Balic Sa, following Michilsns al. (006). Th coasal drifn, coasal rapn and rivr fishris harvs spawning salmon.th offshor drifn and longlin fishris harvs immaur salmon ha rmain in h Balic Main Basin o fd. Gulf of Bohnia Harvs of spawning salmon N=abundanc of salmon C=cach ODN=offshor drifn fishry OLL=offshor longlin fishry CDN=coasal drifn fishry CTN=coasal rapn fishry RI=rivr fishry SSN=spawnrs C CDN C CTN C RI N Jun N July N Augus SSN N April N May N ocobr N Dcmbr C ODN C OLL Main Basin Harvs of fding salmon Yar Yar +1 30

31 Figur 3. Mans and 90 % probabiliy inrvals for fishing ffors in (a) h coasal rapn and (b) rivr fishris for a 50-yar simulaion priod. 1 x Gardays h prcnil man 5h prcnil Angling days Yar (a) Yar (b) 31

32 Figur 4. Mans and 90 % probabiliy inrvals for (a) h n bnfis o h coasal rapn and (b) rivr fishris for a 50-yar simulaion priod..5 x h prcnil man 5h prcnil 7.9 x EUR EUR Yar (a) Yar (b) 3

33 Figur 5. Man and 90 % probabiliy inrval for smol-sag salmon for a 50-yar simulaion priod. Th iniial sa corrsponds o h currn sock simas. 16 x h prcnil man 5h prcnil 1 Smol abundanc Yar 33

34 Figur 6. Opimal fishry configuraion as a funcion of fishris uni coss. c cn / c oll / CDN, RI CDN, CTN, RI RI 0,003 0,00 RI, ODN, OLL RI, ODN RI, CTN 1 CTN, RI 0,001 RI, OLL 0,0 0,04 0,06 0,08 c cdn / 0,0 0,04 0,06 0,08 c odn / 34

35 MTT Discussion Paprs ISSN