A DYNAMIC THEORY OF FISHERIES INVESTMENT. Keywords: Fisheries investment, discounting, Clark-Munro rule, fisheries transition.

Transcription

1 FISHERIES AND AQUACULTURE Vol. V A Dynamic Theory of Fisheries Invesmen Ola Flaaen A DYNAMIC THEORY OF FISHERIES INVESTMENT Ola Flaaen Universiy of Tromsø, N937 Tromsø, Norway Keywords: Fisheries invesmen, discouning, ClarkMunro rule, fisheries ransiion. Conens 1. Fish Sock Invesmen 1.1. Discouning 2. Fish Socks as Capial 3. Longrun Opimal Sock Levels 4. Transiion o Longrun Opimum 5. Adjused Transiion Pahs Glossary Bibliography Biographical Skech Summary The aim of his chaper is o analyze in a simple way he issue of fish sock invesmen. The mahemaical prerequisies are a basic knowledge of calculus. Boh discree and coninuous ime frameworks are used. To fish down or o build up a fish sock akes ime, and ime is money for enerprises and consumers. The concep of discouning is inroduced and we analyze how a posiive discoun rae affecs he opimal long run sock level and harves, as well as he fishery in ransiion. A any poin in ime he resource manager has a choice beween depleing, rebuilding and equilibrium harvesing of he fish sock. These opions imply ha harves has o be eiher above, below or equal o he naural growh of he sock. To assure profiabiliy of an invesmen in a fish sock he presen value of posponing harves has o be greaer han he value of immediae harves. The ClarkMunro (1975) rule is derived wihou use of conrol heory and he longrun soluion of he sock level is presened and discussed graphically. In addiion o he bangbang ransiion, adjused ransiion pahs are discussed by use of maerial from FAO (1995) and OECD (2). 1. Fish Sock Invesmen To fish down or o build up a fish sock akes ime, and ime is money for enerprises and consumers. In his chaper we inroduce he concep of discouning and analyze how a posiive discoun rae affecs he opimal long run harves and sock level, as well as he fishery in ransiion. Boh discree and coninuous ime frameworks are used Discouning Oher chapers discuss resource ren in an open access and in a maximum economic yield fishery, and demonsrae ha open access implies dissipaion of he poenial resource ren due o excessive effor and oo low sock level. To change from open Encyclopedia of Life Suppor Sysems (EOLSS)

2 FISHERIES AND AQUACULTURE Vol. V A Dynamic Theory of Fisheries Invesmen Ola Flaaen access o maximum economic yield fishing necessiaes reduced effor and increased sock level. However, rebuilding a fish sock akes ime since he resource iself has a limied reproducive and growh capaciy. Rebuilding can only ake place if harvesing is reduced or sopped for some ime since harves has o be less han naural growh o generae growh in he sock. A any poin in ime he resource manager has he choice beween depleion, rebuilding and equilibrium harvesing of he fish sock. Depleion means ha harves is greaer han naural growh, and revenue is high in he shor run. However, his harves sraegy is no viable in he long run and will have o be changed afer some while o avoid economic losses. Rebuilding a fish sock means invesing he foregone harves, hus, revenue is reduced in he shor run wih he aim of geing more in reurn a a laer sage. In his case a par of he poenial ne revenue is invesed in he fish sock, he naural resource capial, o save for fuure purposes. For he resource owner, usually sociey, he quesion a any poin in ime is wheher o consume or inves. For an invesmen in he sock o be profiable, he reurn on his invesmen should be jus as good or beer han for oher invesmen projecs. A sum of money o be received in he fuure is no of he same value as he same sum of money received oday, since money could be deposied in he bank a a posiive ineres rae. Thus, he ineres rae plays an imporan role in he evaluaion of invesmen projecs as well as in comparison of he value of money a differen poins in ime. Before we proceed o sudying capial managemen of he resource sock, le us recapiulae he main connecions beween presen value and ineres rae in a discree and a coninuous ime conex. When invesing A dollars, for example as a bank deposi, a an annual ineres of i per cen, your capial will afer one year have grown o A (1+ i) and afer wo years he 2 value will be A (1+ i). In general, an invesmen of A dollars on hese condiions will afer years have he following value A A (1 i). = + (1) Solving Eq. (1) for A gives A A = (1 + i). (2) This shows he connecion beween he fuure and he presen value of money. dollars in years is worh A a he presen, herefore, A is called he presen value of A. I is easy o see from Eq. (2) ha he presen value of a given amoun of fuure money is lower he farher in he fuure i will be received and he higher he ineres is. For businesses and people invesing heir money, i is usually called he ineres rae or marke rae of ineres, whereas in economic analysis i is ofen called he social rae of A Encyclopedia of Life Suppor Sysems (EOLSS)

3 FISHERIES AND AQUACULTURE Vol. V A Dynamic Theory of Fisheries Invesmen Ola Flaaen discoun. The facor 1/(1+ i) = (1+ i) of (2) is he discoun facor, which has a value less han one for all posiive values of i and. For = he discoun facor equals one and i decreases for increased values of. This means ha money a he invesmen or loan poin in ime is no discouned, whereas all fuure money is. Noe ha he discoun facor approaches zero when goes o infiniy. This means ha money values in he very, very far fuure hardly have any value oday if hey are discouned. The presen value of a sream of fuure annual profi is he sum of he presen value of each of hem. For example, wih an annual ineres rae of 5 per cen he presen value of a profi of $1 a year for he nex five years, saring one year from now, is.952 $ $ $ $ $1 = $433. (Deliberaely, he auhor has made a misake for one of he discoun facors find his by use of your calculaor). Tradiionally, discree ime formulae as discussed above are commonly used in invesmen and economic analysis. This is due o he fac ha usually ineres is calculaed and firms repor economic resuls o owners and ax auhoriies on an annual basis. However, in principal he period lengh for ineres and presen value calculaions may be arbirarily chosen as long as he ineres rae is adjused accordingly. For use in populaion dynamics and naural resource economics i is ofen useful o calculae growh and decay on a coninuous ime basis using he insananeous annual rae of discoun, δ. The relaionship beween he discree ime annual ineres rae and he insananeous rae of ineres is δ (1 i) e, + = (3) where e = is he base of he naural sysem of logarihms. Figure 1 shows he connecion beween discoun facors for i=.1 and δ =.953 using discree and insananeous ime, respecively, on an annual basis. From (3) we derive, by aking he naural logarihm of boh sides, ln(1 + i) = δ. (4) For i=.1 we derive δ =.953 by using (4). For bank deposis, using he annual rae of ineres i, compound ineres is usually calculaed a he end of each year. However, using he insananeous rae of ineres δ implies ha ineres on ineres is calculaed on a coninuously basis hroughou he year. Tha is why δ is less han i he coninuous calculaed ineres on ineres compensaes for he lower value of he proper ineres rae (δ compared o i ). Noe ha his discussion is based on a ime sep of one year in he case of discree ime. If, however, we use a shorer ime sep, he difference beween i and δ, according o Eq. (4), will be smaller. In he exreme case when he ime sep approaches zero, he discree ime rae of ineres, i, will approach he coninuous ime rae of ineres, δ. As noed above formula (2) is for he discree ime case. Using coninuous ime he corresponding formula for compuaion of he presen value A of he fuure value a ime, A(), we ge Encyclopedia of Life Suppor Sysems (EOLSS)

4 FISHERIES AND AQUACULTURE Vol. V A Dynamic Theory of Fisheries Invesmen Ola Flaaen δ A A() e. = (5) Figure 1: Discoun facors for discree (bars) and coninuous (curve) ime, wih i=.1 and δ =.953. Wheher one should use discree or coninuous ime approach in economic analysis of invesmen is primarily a quesion of convenience. The formula (2) and (5) give he same resul as long as i and δ are in accordance wih (4). In heoreical analysis i seems ha he coninuous ime approach is he preferred one, whereas in empirical work discree ime calculaions are he mos common. The fac ha mos fish socks are assessed a regular ime inervals is a pracical argumen for using discree ime models in sudies of applied fisheries biology and fisheries economics. TO ACCESS ALL THE 18 PAGES OF THIS CHAPTER, Visi: hp:// Bibliography Clark, C.W., Mahemaical bioeconomics: he opimal managemen of renewable resources. 2. edn., 199, New York. John Wiley & Sons, A comprehensive key classical ex on fisheries economics for sudens wih a good background in mahemaics, including dynamic opimizaion. Encyclopedia of Life Suppor Sysems (EOLSS)

5 FISHERIES AND AQUACULTURE Vol. V A Dynamic Theory of Fisheries Invesmen Ola Flaaen Clark, C.W. and G.R. Munro, Economies of fishing and modern capial heory: a simplified approach, Journal of Environmenal Economics and Managemen, Vol. 2, 9216, This ofen quoed aricle analyses in a sringen form he invesmen issues in fisheries managemen. FAO, Code of Conduc for Responsible Fisheries. Food and Agriculure Organisaion of he Unied Naions, Rome, The inernaionally approved compromise ex on mos issues of fisheries managemen. OECD, Transiion o responsible fisheries economic and policy implicaions. Organisaion for Economic Cooperaion and Developmen, Paris, 2. A sudy by he OECD Fisheries Deparmen and Commiee on managemen and mismanagemen, based on he experience of more han weny fishing naions. Includes recommendaions on how member saes and oher fishing naions should proceed o achieve responsible fisheries. Sco A.D. and G.R. Munro, The economics of fisheries managemen, in Handbook of Naural Resources and Energy Economics, A.V. Kneese and J.L. Sweeney, eds. Elsevier Science Publishers. Berlin, A classical review aricle on fisheries economics and managemen, including resource capial and invesmens issues. Biographical Skech Dr. Ola Flaaen is a Professor of Resource Economics a he Norwegian College of Fishery Science, Universiy of Tromso, Norway (UiT). As he son of a fisherman and raised in a fishing village above he Arcic Circle he early in life go o know he pracical issues of he fishing indusry. He earned his MA in economics a he Universiy of Oslo and his Dr. Phil. in resource economics a he Universiy of Tromsø. In he was Head of he Fisheries Deparmen, he Organisaion for Economic Cooperaion and Developmen (OECD), Paris, and has spen sabbaical years a he Universiy of Briish Columbia, Canada and he Universiy of Porsmouh, UK. Previously he has worked for he Minisry of Fisheries, Oslo and he Regional Labour and Developmen Agency, Tromso. Currenly he is enjoying being an advisor o he economic componen of he join projec beween Nha Trang Universiy and hree Norwegian universiies, funded by he Governmen of Vienam and he Governmen of Norway hrough The Norwegian Agency for Developmen Cooperaion (NORAD). He is also he academic coordinaor of he NORAD suppored MSc program in Fisheries and aquaculure managemen and economics, NTU a join NTUUiT English augh program. He has published one book, book chapers, journal aricles, conference proceeding papers, and economic and policy repors, in boh English and Norwegian, wih some ranslaions o Russian and Vienamese. He has held eleced posiions naionally and inernaionally, including serving on he Execuive Commiee of he Inernaional Insiue for Fisheries Economics and Trade (IIFET). Encyclopedia of Life Suppor Sysems (EOLSS)