The Construction of a Bioeconomic Model of the Indonesian Flying Fish Fishery

Transcription

1 Marine Resource Economics, Volume 0, pp /95 $ Prined in he U.S.A. All righs reserved. Copyrigh 995 Marine Resources Foundaion The Consrucion of a Bioeconomic Model of he Indonesian Flying Fish Fishery BUDY P. RESOSUDARMO Deparmen of Agriculural, Resource, and Managerial Economics Cornell Universiy and Indonesian Governmen Agency for he Assessmen and Applicaion of Technology Absrac The high price of flying fish eggs in Japan encourages Souh Sulawesi fishermen in Indonesia o harves increasing quaniies of eggs every year. Similarly, he increasing local demand for flying fish encourages Indonesian fishermen o use gill nes o cach more fish. As a consequence of his increasing quaniy of eggs harvesed and fish caugh, Indonesia has become concerned abou he overexploiaion of he flying fish populaion. Thus far policy suggesions concerning he managemen of he flying fish fishery have been based on a saic biological model, since he daa needed o consruc a dynamic bioeconomic model are very limied. This paper presens a mehod for consrucing a dynamic bioeconomic model of he Indonesian flying fish fishery wih very limied daa on he fish populaion. A calibraion echnique is developed o build he dynamic biological model. Key words bioeconomics, dynamic opimizaion, fishery managemen, resource economics. Inroducion For he people living on he souh coas of Sulawesi (Celebes) in Indonesia, he flying fish and heir eggs have been a delicacy for many years. Unil he early 970s, fishermen only caugh his fish by using a small-scale fishing echnique known as he pakkaja. Pakkajas are barrel-shaped baskes made of slender lenghs of spli bamboo ied ogeher wih wine woven from sugar palm leaves. In 968, he Japanese marke for flying fish eggs was developed. From 97 o 98, egg expors o Japan increased annually a an average rae of 30%. (Souh Sulawesi Fishery Agency 990). Paralleling his increase, he local price of flying fish eggs per kilogram increased subsanially. Zerner (987) noed ha he price of eggs per kilogram was approximaely $2.4 in 97, increasing o $0.50 in 985. In conras, he local price of he fish was $0.20 per kilogram in 973, and only $0.30 in 985. The high price of eggs encourages fishermen o cach more eggs each year for he Japanese marke. Alhough he ulimae aim is he eggs, he pakkajas require ha vas amouns of fish also are caugh. This increasing harves of eggs and fish has raised concerns of overexploiaion. A second issue concerns he gill nes ha Indonesian fishermen have used o cach flying fish since 973. Alhough he use of gill nes is less expensive han us- The auhor wishes o hank Bryce Allison Isham and wo anonymous referees for heir useful commens. They are no, however, responsible for any misakes in his paper. 357

2 358 Resosudarmo ing pakkajas, gill nes cach mosly immaure flying fish in effec, gill ne fishermen forgo he opporuniy o obain fish eggs. The uilizaion of gill nes herefore could lower he ne benefi for he flying fish fishery (Budihardjo and Nessa 982; Dwiponggo e al. 98; Zerner 987). Indonesian researchers have conduced several sudies o examine hese wo problems of overexploiaion and gill ne use. Dwiponggo e al. (98 and 982), applying a saic model of he flying fish fishery, esimaed ha he maximum susainable annual yields of he flying fish and heir eggs are approximaely 6,000 7,000 ons and 3850 ons, respecively. Budihardjo and Nessa (982) conduced a comparaive sudy on he echnical and economic aspecs of caching flying fish wih pakkajas and gill nes. They suggesed he prohibiion of gill nes during March and April, so gill ne fishermen could no cach immaure flying fish. None of he above papers uses a dynamic bioeconomic model as a base for is resuls. However, a dynamic model ha describes he biological characerisics of flying fish and he economic condiions of he fishery will produce more accurae resuls han a saic model, and provide a year-o-year opimal harves policy. The main difficuly in developing a dynamic bioeconomic model of he flying fish fishery is ha he daa on he flying fish populaion are very poor. Hence, he firs goal of his paper is o develop a bioeconomic model of he Indonesian flying fish using he very limied exising informaion abou he fish populaion. The paper will develop several reasonable assumpions and use a calibraion echnique. The second goal is o deermine he opimal harves policy for he flying fish. In addiion o researchers ineresed in he flying fish fishery, his paper is also useful for researchers who wan o develop a dynamic bioeconomic model of oher fisheries where daa on fish populaions are very limied. This caegory includes mos fisheries in developing counries. The Model Flying fish are fas-moving fish ha have a habi of leaping ou of he waer and flying over long disances. Around February hey migrae in a group from he norh par of Sulawesi ino he Makasar Srais (figure ). They swim in he Souh Sulawesi area from abou April hrough June, in concurrence wih heir spawning season. They hen coninue easward, some o he norh and ohers o he souh o he Banda Sea (Dwiponggo e al. 98). The fac ha he flying fish is a single cohor (Khokiaiwong 988) which lives for only eigheen monhs simplifies he biological model. Define X as he biomass level of he flying fish populaion a he beginning of he spawning season in year. Y is he amoun of flying fish, by weigh, caugh by gill nes in year. H is he amoun of flying fish, by weigh, caugh by pakkajas. E is he amoun of he eggs, by weigh, caugh by pakkajas. Le E = γh ; γ > 0 () In year, he amoun of fish no caugh by pakkajas and gill nes is X Y H. Hence, he biological model X + = T(X Y H ) (2) where T(.) is assumed o be a sricly concave and wice differeniable funcion of X, Y, and H.

3 The Indonesian Flying Fish: A Bioeconomic Model 359 Figure. Fishing Area of he Indonesian Flying Fish [in he shaded area souh of Sulawesi (Celebes) Island] Pakkajas cach he fish in heir spawning period, while gill nes cach immaure fish and fish in heir pos-spawning phase. Therefore, he fish caugh by pakkajas each year are hose no caugh by gill nes and vice versa, i.e. and Y = Y(X H, N ) (3) H = H(X Y, M ) (4) where N is number of gill nes used o cach flying fish in year, and M is number of pakkajas in year. By esimaing he wo equaions above, he cos of operaing gill nes and pakkajas can be shown as a funcion of he amoun of fish caugh by each mehod and he biomass of fish in he sea. CN(N ) = CN(X H, Y ) (5) CM(M ) = CM(X Y, H ) (6) where CN(.) is he cos of using gill nes, and CM(.) is he cos of using pakkajas. The above cos funcions are assumed o be perfecly malleable and sricly convex. As menioned earlier, Japan is he mos imporan marke for he eggs. Since Japan also impors flying fish eggs from oher counries, he model applies a priceaker assumpion o he price of Indonesian flying fish eggs. In conras, flying fish are sold only o local consumers, and he local marke is

4 360 Resosudarmo supplied only by he fish caugh in Souh Sulawesi waers. Thus, he amoun of fish caugh each year dicaes he price of he fish. Now, he problem of maximizing he presen value of he ne benefi o sociey from he flying fish fishery hroughou an infinie ime horizon can be summarized as a dynamic programming problem max ρ { Y, H} = 0 subjec o H + Y (, ) P(h + y )d(h + y ) + P R E CN(X H, Y ) CM X Y H 0 X + = T(X H Y ); = 0,... X 0 = X ini X s, H s, Y s 0 where P(h + y ) is he price of he fish in year as a linear funcion of he oal quaniy of flying fish caugh in year, P R is he price of he eggs, X ini is he iniial level of biomass (from he daa), and ρ is a discoun facor. The Search for he Biological Model Several funcions are commonly used as biological models. From hese funcions, choose a simple logisic growh funcion for he biological model of flying fish X + = A (X H Y ) X H Y (7) B If fish populaion daa are available each year, an economeric echnique can be used o esimae he equaion (7) above. However, he daa are no available. This paper will develop a calibraion mehod o search for he parameers A and B. Firs, choose any number for A and B. Second, simulae he relaion (7) hroughou several years. This paper simulaes he relaion (7) from 967 o 989. Third, yearly fish populaion resuling from his simulaion should saisfy several consrains ha represen he condiions of he flying fish fishery during he simulaion years. If no, choose anoher A and B. Before developing he consrains for he fish populaion, define a resricion for parameer A. If he fishing moraliy is equal o zero, he biological model is defined as X + = A X X (8) B Assume ha he flying fish will reach a sable seady-sae populaion. According o Leopunov s indirec mehod, he relaion (8) will have a sable seady-sae condiion, if he absolue value of X + / X is less han one. This relaionship is X + X = A AX 2 < (9) B Le X be he biomass level in he naural seady-sae condiion

5 The Indonesian Flying Fish: A Bioeconomic Model 36 Table Toal Annual Cach of Flying Fish and Eggs and he Esimaed Populaion in Souh Sulawesi Waers Lower Bound Upper Bound Annual Esimaed Esimaed Fish Cach Populaion Populaion Year (ons) (ons) (ons) 967 4,00 32, , n.a. 32, , n.a. 32, , n.a. 32, , n.a. 32, , n.a. 3, , n.a. 30, , n.a. 29, , ,98 28, , ,304 25, , ,988 20, , ,453 6, , ,75 8, , ,447 7, , ,447 6, , ,642 5, , ,300 5, , ,437 4, , ,2 3, , ,006 2, , ,967, , ,927, , ,83 0, , n.a. 0, , Source: Toal annual cach of flying fish are from Cushing (97) and he Souh Sulawesi Fishery Agency (990). X = AX X (0) B Subsiuing (0) ino (9), A should be beween and 3. Hence, define he firs consrain such ha A should be beween and 3. Now define several oher consrains represening he condiions of he fish populaion from 967 o 989. The second consrain is ha he fish populaion in 967 was he same as ha in 968. This consrain is based on he fac ha fishermen sared o expor flying fish eggs in 968. Before 968 fishermen only sold he fish and heir eggs o local markes. The prices were relaively low so no incenive exised for he fishermen o cach more fish or eggs. The Indonesian Direcorae General of Fisheries esimaed ha in 967 he amoun of flying fish caugh was approximaely 4,00 ons (Cushing 97). Thus, i can be assumed ha several years before and up o 968, he flying fish fishery reached a susainable yield and fish populaion. The hird consrain is ha from 968 o 974 he annual cach increased linearly. This assumpion is necessary since no daa on he annual fish cach during hese years exis (see able ).

6 362 Resosudarmo Table 2 Number of Pakkajas and Gill Nes Used o Cach Flying Fish in Souh Sulawesi Pakkaja CPUE of Gill Ne CPUE of Year (unis) Pakkaja (unis) Gill Ne 979 2, , , , , , , , , , , , , , ,89.765, , , Source: Souh Sulawesi Fishery Agency (990). The fourh consrain is ha he flying fish populaion in 97 was approximaely 32,000 ons. This figure is based on esimaions from several sudies. Cushing (97) measured he carbon conained in he Flores Sea. Based on Cushing s daa, Dwiponggo (982) esimaed ha he oal biomass level of all kinds of fish in he area was around 640,000 ons. He also esimaed ha flying fish consiued approximaely 5% of he oal fish in he area. The fifh consrain is ha he fish populaion in year + 4 mus be less han he populaion in year. Choosing a four-year difference allows he populaion o flucuae during four years. This consrain is based on indicaions ha he populaion of flying fish was decreasing afer 974. Firs, he daa for annual caches from 974 unil 989 show ha he maximum annual cach occurred in 976, and ha he annual caches decreased afer ha year (able ). Second, he daa for cach per uni effor (CPUE) of pakkajas and gill nes (able 2) show ha he caches per uni of effor for pakkajas and gill nes were almos consisenly decreasing afer 979. The sixh consrain is ha he fish populaion which enered Souh Sulawesi waers in 989 was a leas wice he amoun of fish caugh in ha year. This assumpion is based on hree facs. Firs, Souh Sulawesi waers consiue a relaively large area. Second, flying fish are fas-moving. Third, flying fish fishermen use relaively simple fishing echnology. Hence, i would have been difficul for he fishermen o harves more han half of he fish populaion in ha year. Noe ha he sixh consrain should be applied each year from 967 o 989. However, if his consrain is applied each year, he resul would be ha no soluion o A and B could be found. Hence, his consrain is only applied in 989, he las year of he simulaion. Afer defining all he consrains represening he condiions of flying fish during 967 and 989, he calibraion process can be conduced by randomly choosing A and B. Several combinaions of A and B saisfy all he consrains. Thus he range of A and B should be defined. Define an upper bound process as a process o find he highes possible fish populaion in 990. A lower bound process is a process o find he lowes possible fish populaion in 990. The process of searching for he parameers A and B can be convered o an opimizaion problem

7 The Indonesian Flying Fish: A Bioeconomic Model 363 Figure 2. Upper and Lower Bound Esimaed Fish Populaion max(min) X 990, for upper bound (lower bound) () subjec o X + = [A (X H Y )] A 3 X H Y, = B X 967 = X 968 X X +4, = X 989 2H 989 H s are given and X s, A, B 0 Noe ha o have a naural seady-sae condiion (wihou fishing moraliy), he firs consrain should no be binding. GAMS\MINOS opimizaion sofware is used o solve he above problem. The resul for he upper bound is ha A equals 2.76 and B equals 59, The resul for he lower bound is ha A equals 2.76 and B equals 59, I can be seen ha A is relaively sable a 2.76, while he range of B varies from 59, o 59, Figure 2 shows he esimaed flying fish populaion from 967 o 990 resuling from he wo opimizaions above (see also able ). Finally, he biomass raio beween eggs and fish caugh (γ) in equaion () above is based on he work by Nessa (978). He esimaed ha he biomass raio beween eggs and fish caugh by pakkajas was o 0.

8 364 Resosudarmo Esimaion of he Cos and Benefi Funcions The ideal way o esimae cos and benefi funcions is by simulaneously esimaing he supply and demand curves. This echnique requires a rigorous mahemaical applicaion o overcome he problems caused by muliple markes and nonlinear funcions. Hence, each funcion will be esimaed separaely, alhough his mehod migh generae less accurae esimaions. To find he cos funcions, equaions (3) and (4) should be esimaed firs. One problem in esimaing hese relaions is he unavailabiliy of daa on flying fish caugh separaely by pakkajas and gill nes. Insead, daa exis on he oal quaniy of fish caugh using boh ypes of equipmen collecively. Daa are also available on he quaniy of eggs harvesed using pakkajas. A second problem is ha, for gill nes, he only daa available are he oal number of gill nes used each year. This number does no represen he real effor of gill nes in he flying fish fishery, since gill nes are used o cach oher fish besides flying fish. To overcome he firs problem, his paper uses he daa on he eggs and he raio beween fish and eggs caugh wih pakkajas esimaed by Nessa (978). Thus he quaniy of fish caugh by pakkajas can be esimaed. For he second problem, his sudy uses an esimae of around 5% of he oal quaniy of gill nes used each year o cach flying fish (Budihardjo and Nessa 982), as in able 2. This paper uses exponenial producion funcions o represen relaions (3) and (4) since he reduced forms of hese funcions are simple and easy o esimae. The funcions are as follows and Y = (X H ) H = (X Y ) e qnn ( ) (2) e q M M ( ) (3) Appendix A describes he procedure and resuls of esimaing equaions (2) and (3). Budihardjo and Nessa (982) esimaed ha he annual coss for a uni of pakkaja and for a uni of gill ne are around Rp.,50,435 and Rp.,0,305, respecively. Hence, he oal cos funcions for pakkajas and gill nes, respecively, can be shown as below Subsiuing (2) ino (4) and (3) ino (5) produces CN =,0,305 N (4) CM =,50,435 M (5) CN = CM =, 0, 305 X H ln (6) q X H Y N, 50, 435 X Y ln (7) q X Y H M The nex sep is o find he benefi funcion. The price of eggs is assumed consan a Rp. 0,500 per kilogram of eggs (Zerner 987), while he price of he fish is assumed o be a funcion of he oal amoun of flying fish caugh and he welfare of he people in Souh Sulawesi (an inverse demand funcion). The variables used o

9 The Indonesian Flying Fish: A Bioeconomic Model 365 Table 3 Ex-vessel Nominal Price of Flying Fish, Indonesian GNP, and Populaion Price of Indonesian Indonesian Flying Fish GNP Populaion Year (Rp per kg) (Rp 0 9 ) (0 6 ) , , , , , , , , , , , , Source: Direcorae General of Indonesian Fishery (987) and Inernaional Financial Saisics Yearbook 990. represen he welfare of people in Souh Sulawesi are he Indonesian GNP and he oal Indonesian populaion (able 3). Afer esimaing he inverse demand funcion (see appendix B), assume ha GNP is consan a 02,000 billion rupiahs and he populaion of Indonesia is consan a 70 million people. The final resul is P = α + β(h + Y ) (8) where α = 429,70, and β = 7.44 The benefi funcion ha describes he oal benefis o sociey from he fish and heir eggs is B = H + Y α + β(h + y )d(h + y ) + 0.P R H (9) 0 where P R = 0,500,000 (Rp/on), and 0. = he average raio beween he amoun of he eggs harvesed and fish caugh wih a uni of pakkaja. Opimal Managemen In his secion, he paper subsiues he esimaed forms of he cos, benefi, and biological funcions in he previous secions ino he maximizaion problem in he bioeconomic model. This model can be wrien as H + Y max ρ { Y, H} = 0 0 [α + β(h + y )]d(h + y ) + 0.P R H (20), 0, 305 X ln,, H X Y ln qn X H Y qm X Y H

10 366 Resosudarmo Figure 3. Opimal Harves Policy (no gill ne is allowed o cach flying fish during he spawning season) subjec o X + = A(X H Y ) X H Y, = 0,... B X 0 = X 990 where ρ = 0.89 since he discoun rae is assumed o be approximaely 2% per year. The esimaed fish populaion in 990 is used as he iniial condiion. The maximizaion problem above is solved using GAMS/MINOS opimizaion sofware. Appendix C oulines he deailed procedure used o solve he problem (20) above. Figure 3 shows he opimal harves policy during he hireen-year ime horizon. No gill ne is allowed o cach flying fish during he spawning season in Souh Sulawesi waers, and a year s delay in harvesing he fish is suggesed. The presen values of he oal ne benefi from he flying fish fishery hroughou he hireen-year ime horizon are 58 billion rupiahs and 59 billion rupiahs, using he lower and he upper bound fish populaion daa, respecively. The wo opimal harves policies in figure 3 can be inerpreed as a range of he opimal harves. Figure 4 shows he opimal pah of he fish populaion. In boh scenarios, he fish populaion is expeced o be in a seady-sae condiion by year en. Figure 5 shows he opimal harves policies if he discoun facor (ρ) equals 0.8 and, or he discoun rae is assumed o be approximaely 24% and 0%, respecively. I can be seen ha he suggesions o implemen a one-year delay in harvesing he fish and o ban he use of gill nes are relaively sable.

11 The Indonesian Flying Fish: A Bioeconomic Model 367 Figure 4. Fish Populaion During he Opimal Harves Policy Discussion This paper shows ha a calibraion mehod can be used o build a dynamic biological model when populaion daa are very limied. This paper also demonsraes he procedure o deermine he annual opimal harves amoun of flying fish and heir eggs. Wih a dynamic model, i can be seen how long and by how much people should reduce heir harves so ha hey can enjoy a larger ne benefi from he fishery. This informaion canno be found in a saic model. Two imporan poins deserve menion in using he calibraion mehod in his paper. The firs poin is he choice of he funcional form o represen he biological model. One should apply several funcional forms and observe he esimaed fish populaion and he projeced opimal managemen policy resuling from each funcional form. From he esimaed populaion and he projeced opimal policy, one should decide which funcional form(s) is (are) reasonable. For example, in he case of Indonesian flying fish, one should eliminae any funcional form which esimaes a relaively seady fish populaion from 967 o 989. One should also eliminae any funcional form which projecs an exremely high ne benefi from he fishery. This paper used a logisic funcion since oher funcions were no be able o generae resuls for A and B in he opimizaion problem (). The second poin is he consrain assumpions. If he consrains reflec he real world, hen i can be argued ha he resuls from he calibraion should be close o X + = A + BX and X + = A X B

12 368 Resosudarmo Figure 5. Opimal Harves Policy When ρ Equals 0.8 and (no gill ne is allowed o cach flying fish during he spawning season) he resuls from he rue relaionships. Imposing consrains ha are oo srong, however, can creae an unreasonable soluion. The same siuaion migh occur if he consrains are oo weak. For example, if he fourh consrain in he opimizaion problem () is X X +, no soluion exiss for ha problem. Omiing his fourh consrain could resul in a seady fish populaion from 967 o 989. The opimal soluion resuling from he bioeconomic model in his paper suggess delaying he harves of he fish and heir eggs for one year and, afer ha year, slowly increasing he quaniy harvesed. This paper also recommends ha fishermen do no use gill nes during he spawning season. In inerpreing he laer recommendaion, one should remember wo poins. The firs poin is he assumpion in his model ha gill nes cach pre-spawning fish if hey are used during he spawning season. The second poin is ha flying fish are a single cohor. Pos-spawning fish will no reurn nex year during he spawning season. Therefore, he correc inerpreaion of he resuls in his paper is ha gill nes should no be used o cach pre-spawning fish, bu hey should (could) be used o cach pos-spawning fish. In pracical erms, fishermen should use gill nes afer he spawning season in he easern par of Souh Sulawesi waers. One should also noe ha since pakkajas canno be used o cach pos-spawning fish, gill nes are he only ool o cach hese fish. The benefi of having pos-spawning fish in he sea is essenially zero in his model, i.e. pos-spawning fish conribue nohing o nex year s new recruimen process. Hence, he opimal amoun of pos-spawning fish caugh by gill nes occurs where he marginal cos of caching ha las uni of fish equals he price of ha uni of fish. The opimal soluion, however, should be appropriaely qualified. Firs, he model does no ake ino accoun he possibiliy ha sopping he harves for one

13 The Indonesian Flying Fish: A Bioeconomic Model 369 year migh adversely affec he esablished markeing and disribuion infrasrucure. To avoid his poenially negaive impac, one could add anoher consrain o he bioeconomic model no o reduce he harves more han, for example, 50% or 67% from he previous year s harves. Second, he model assumes ha here are no echnological improvemens in fishing in he fuure ime. This srong assumpion is made because developing a model wih uncerainy abou fuure condiions is very difficul. Hence, i is recommended o recalculae he model as significan new informaion occurs. Third, he model does no ake ino accoun he possibiliy ha implemening he opimal soluion migh induce an undesirable redisribuion of income beween pakkaja fishermen and gill ne fishermen. Specifically, while his opimal soluion benefis pakkaja fishermen, i migh adversely affec he incomes of gill ne fishermen; under he opimal soluion, no gill ne is allowed o cach flying fish during he spawning season. Thus, who can use he pakkaja and who can only use he gill ne is a criical issue. Alhough his issue beyond he scope of his paper, i cerainly should be addressed in he fuure. In he Indonesian flying fish fishery, policy recommendaions o address resource exploiaion issues are difficul o deermine. When an urgen need exiss for such a recommendaion, he resuls from he calibraion mehod and model presened in his paper can be of value. Appendix A. Esimaion of he Producion Funcion Using an exponenial producion funcion, he relaionships beween cach and effor in he flying fish fishery are and Y = (X H )( e q N N ) (A) H = (X Y )( e q M M ) (A2) To find he reduced form, manipulae (A) and (A2) o become Y + H X X H H + Y X X Y = e q N N (A3) = e q M M (A4) Then, divide (A4) by (A3) ln X H = q M M + q N N X Y (A5) The resuls of esimaing he relaion (A5) are:. Using he lower bound daa for fish populaion

14 370 Resosudarmo ln X H = M N X Y ( 47. ) ( 696. ) 2. Using he upper bound daa for fish populaion R 2 = 0.69 D-W saisics = 2.09 ln X H = M N X Y ( 435. ) ( 653. ) R 2 = 0.65 D-W saisics = 2.22 where R 2 is no a valid measure of fi when he inercep is suppressed. The Cobb-Douglas producion funcion is no chosen in his paper since i canno provide a reduced form ha is boh easy o esimae and give he coefficiens of he original formulas. Appendix B. Esimaion of he Benefi Funcion A linear inverse demand funcion is chosen in his paper. The main reasons for choosing he linear funcion is ha i is very simple. A simple formula is needed o reduce he complexiy of he dynamic opimizaion problem as in equaion (20). The resul of he esimaion is P = 338, ( Y + H) ( 538. ) ( 34. ) ( 229. ) GNP CAPITA (B) R 2 = 0.86 D-W saisics = 2.0 Appendix C. Opimal Managemen of Flying Fish The Lagrangian formulaion of he dynamic opimizaion problem (20) is L = H ρ + Y = 0 0, 0, 305 ln q N α + β(h + y )d(h + y ) + 0.P R H X H X H Y + ρλ, 50, 435 ln q M [ AX ( H Y) X Y X Y H (C) X H Y X ] B γ 0 (X 990 X 0 ) The Kuhn-Tucker firs-order necessary condiions are L X, 50, 435 H, 0, 305 Y = + q ( X Y )( X Y H ) q ( X H )( X H Y ) M N (C2)

15 The Indonesian Flying Fish: A Bioeconomic Model 37 + ρλ A A X H Y + 2 λ 0 B, 50, 435 H, 0, 305 Y + q ( X Y )( X Y H ) q ( X H )( X H Y ) (C3) M N + ρλ A A X H Y + 2 λ X = 0 B L H = α + β( H + Y ) Y +. P,, R q ( X H )( X H Y ), 50, 435 q X Y H M N A 2A X H Y + ρλ B (C4) α + β( + ) +.,, Y H Y 0PR qn ( X H )( X H Y ), 50, 435 q X Y H M A 2A X H Y + ρλ + + H 0 B = (C5) L Y = α + β( H + Y ),, H q ( X + Y )( X + Y H ), 0, 305 q X H Y N M A 2A X H Y + ρλ B (C6) α + β( + ),, H H Y q ( X Y )( X Y H M ), 0, 305 q X H Y N A 2A X H Y + ρλ + + Y 0 B = (C7) X H Y AX ( H Y ) X + ρλ + = 0 B (C8) [ X X ] λ = (C9) Noe ha he objecive funcion (20) and all he consrains are sricly concave and wice differeniable funcions of X, Y, and H. The firs sep in solving he problem above is o find he long-run opimal seady-sae condiion. In his condiion, he annual biomass in he sea and he annual quaniy of fish caugh are he same. Hence, he opimal long-run seady-sae condiion can be found by dropping he

16 372 Resosudarmo ime noaion () in equaions (C2)-(C9) and hen solving hose relaions. The second sep is o change he ime horizon o a finie ime horizon T. An addiional consrain ha mus be added is ha in year T he populaion is already a he seady-sae condiion. Then solve he equaions (C2)-(C9) for he T-year ime horizon. If he fish populaion is already sable a he seady-sae condiion several years before year T, his pah is he soluion o problem (20). However, if he populaion has no reached he seady-sae condiion in year T, increase T. References Ali, S.A. 98. Kebiasaan Makanan, Pemijahan, Hubungan Bera Panjang dan Fakor Kondisi Ikan Terbang, Cypsilurus Oxycephalus (Bleeker) di Lau Flores, Sulawesi Selaan. Tesis Sarjana, Universias Hasanuddin, Ujung Pandang, Indonesia. Budihardjo, and M.N. Nessa Analisa Tingka Produkivias dan Pendapaan Usaha Penangkapan Ikan Terbang dengan Pakkaja dan Gill Ne Sera Sisem Pemasarannya. Laporan Peneliian Perikanan Lau, pp. 9. Conrad, J.M. 99. A Bioeconomic Model of he Pacific Whiing. Deparmen of Agriculural Economics Working Paper No. 90-4, Cornell Universiy. Cushing, D.H. 97. Survey of Resources in he Indian Ocean and Indonesian Area. FAO, Roma, Ialy. Dwiponggo, A Pengkajian Sumber Daya Perikanan dan Tingka Pengusahaannya di Perairan Sulawesi Selaan. Laporan Peneliian Perikanan Lau, 8. Dwiponggo, A., T. Sujasani, and S. Nurhakim. 98. Pengkajian Poensi dan Tingka Pengusahaan Perikanan Torani di Perairan Sulawesi Selaan. Seminar Ikan Torani, Ujung Pandang, Indonesia. Kennedy, J.O.S Dynamic Programming: Applicaions o Agriculure and Naural Resources. New York: Elsevier Applied Science Publishers. Khokiaiwong, S Seasonal Abundance and Reproducion of he Flying Fish Hirundichhys Affinis and Parexocoeus Brachyperus Near Barbados. Maser s hesis, McGill Universiy, Canada. Luenberger, D.G Inroducion o Dynamic Sysems: Theory, Models and Applicaions. New York: John Wiley & Sons. Nari, B Sudi Tenang Beberapa Parameer Dinamika Populasi dan Tingka Eksploiasi Ikan Terbang (Cypsilurus spp.) di Perairan Kabupaen Takalar. Tesis Sarjana, Universias Hasanuddin, Ujung Pandang, Indonesia. Nessa, M.N Perikanan Ikan Terbang Diinjau Dari Aspek Penangkapan dan Sosial Ekonomi. Simposium Modernisasi Perikanan Rakya. Jakara, June, SMPS/78 No. P28. Nessa, M.N., H. Sugondo, I. Andrias, and A. Raneondok Sudi Pendahuluan Terhadap Perikanan Ikan Terbang di Sela Makasar. Sub. Proyek PIP, UNHAS, ah., Sulawesi Selaan. Souh Sulawesi Fishery Agency Annual Saisics. Dep. Peranian, Souh Sulawesi, Indonesia. Zerner, C The Flying Fishermen of Mandar. Culural Survival Quarerly (2):822.