Quota setting and enforcement choice in a shared fishery

Transcription

1 Quota settng and enforcement choce n a shared fshery Aaron Hatcher, Unversty of Portsmouth, UK and Lnda Nøstbakken, Unversty of Alberta, Canada Abstract We consder the explotaton of a transboundary (shared stock) fshery whch s managed by means of natonal quotas determned as agreed shares of a total allowable catch (TAC). Gven ts annual quota allocaton, each country maxmses current perod benefts whle choosng a level of costly enforcement effort wth whch to secure what t consders to be an acceptable degree of quota complance by ts fshng fleet. We compare ths level of enforcement wth the socally optmal level, gven the agreed quotas. We also explore the optmal soluton to the settng of quotas n addton to enforcement levels. We go on to consder the TAC a socal planner would choose n order to maxmse the total value of the fshery, gven the agreed quota shares and each country s enforcement preferences. Fnally, we model the ncentves for countres to seek a hgher TAC than that proposed durng nternatonal negotatons. JEL classfcaton: Q22, Q28, Q57 Keywords: shared fsh stocks; transboundary resources; enforcement; complance; quota management 1

2 1. Introducton The problem of the cooperatve (or ndeed non-cooperatve) management of shared renewable resources, such as transboundary fsh stocks, has receved a consderable amount of attenton n the lterature, prmarly from a game theoretc perspectve (see, for example, Katala 1986, Katala and Lndroos 2007, Lndroos 2008, Munro 2009 and Hannesson 2011). In general, analyss has focused on the determnaton of optmal harvest shares and the possbltes for cooperatve agreement on harvests by partcpatng countres. In common wth most theoretcal models of fshery explotaton, ether harvest tself or harvest as a functon of fshng effort s taken as the control varable. In practce, however, natonal admnstratons are only able to control harvest ndrectly, by ntroducng management measures (such as quotas) and then expendng enforcement effort n order to acheve a degree of complance by ther fshng ndustres. Gven that enforcement s costly, and hence there s a socal cost to controllng harvest, the need for enforcement mples second best solutons n whch optmal harvests dffer from those whch would hold were enforcement perfect and costless. 1 It s also apparent that, n the case of many shared fsh stocks (for example, those wthn the EEZs of the European Unon), nternatonal agreements do exst on harvest shares, at least n prncple. Once such agreements are reached, moreover, they tend to endure, snce they are poltcally costly to renegotate. 2 The fundamental problems for resource management n such cases are, frstly, the settng of an approprate total harvest or total 1 Ths mrrors, but s not dentcal wth, the observaton that perfect regulatory enforcement s unlkely to be optmal f enforcement s costly (Sutnen and Andersen 1985). 2 A good example s provded by the Atlantc and North Sea fsheres of the EU. Fxed TAC shares were agreed 2

3 allowable catch (TAC) - usually on an annual bass - to be dvded amongst partcpatng countres as natonal quotas, and secondly, complance wth those quotas by natonal fshng fleets, whch depends upon countres ndvdual enforcement efforts. These realworld problems are the focus of ths paper. To llustrate the problems, we have n mnd a fshery such as the Northeast Atlantc cod fshery, whch s shared between Norway and Russa and whch has rased sgnfcant enforcement ssues over the years (see Sumala 1997 and Hannesson 2007). In the paper we model the explotaton of a shared (transboundary) fsh stock by two countres whch have prevously reached agreement on ther percentage shares of an annual TAC. Once the TAC s determned, therefore, each country s quota s fxed and the problem for the country s then to choose a level of costly enforcement effort to apply to ts fleet n order to maxmse natonal economc benefts whle securng an acceptable degree of complance wth the quota. Gven the natonal quota and the level of enforcement, the fleets then respond ratonally wth a prvately optmal harvest level. We assume, however, that the country knows ths harvest response functon when t chooses a level of enforcement effort and hence harvest and enforcement are jontly determned. We compare the countres enforcement choces wth the socally eff cent levels of enforcement, gven the quotas n force. As an asde, we also consder the potental problem for a socal planner of settng optmal quotas, as well as enforcement levels, n order to maxmse the total value of the fshery. Ths rases the nterestng queston of why quotas are not much lower n 1983 after years of dff cult negotatons (see Holden and Garrod 1994). Snce then, the shares have remaned more or less constant (accordng to the so-called prncple of relatve stablty ) as no member state has wanted to reopen the negotatons. A notable excepton s the Northeast Atlantc mackerel fshery, whch s shared between the EU, Norway and Iceland. In ths case, all partes agree on the ICES-recommended TAC, but there s dsagreement over quota shares. 3

4 than they actually are n practce, snce, n the absence of a cost to settng low quotas, wth a non-complant fleet the most eff cent way of achevng any gven level of harvest s to set a very low quota and relax enforcement. We then consder the eff cent TAC for the fshery as a whole, gven the agreed bass for quota shares and the best-response enforcement and harvest choces of the partcpatng countres admnstratons and ther fshng fleets. Fnally, we examne the ncentves for countres to seek ncreases n the TAC durng the annual decson-makng process n whch a recommended TAC must be agreed upon by partcpant countres. The paper extends and augments some of the analyss n an earler paper by Beard and Nøstbakken (2010), whch had as ts prmary focus a dynamc game n enforcement between the two countres. The present paper models natonal enforcement choces as compettve (no strategc nteracton) and focuses on the problem of TAC settng wth fxed quota shares. The paper s structured as follows. In the secton that follows we frst develop the ndustry harvest model and then examne the eff cent and myopc enforcement choces of the countres, gven ther TAC shares. In Secton 3 we look at the determnaton of the eff cent TAC for a fshery managed by means of natonal quotas and then consder the ncentves for countres to bd up a recommended TAC durng annual negotatons. A fnal secton concludes. 4

5 2. Model and prelmnares 2.1 The ndustry s harvest response functon We begn by modellng the harvest response (reacton functon) of the ndustry n Country to the agreed natonal quota (TAC share) and the natonal level of enforcement effort. Here, followng Beard and Nøstbakken (2010), enforcement effort s normalsed to the probablty that a partcular frm s nspected and fned for landng over-quota fsh (whch mples an underlyng lnear relatonshp between enforcement effort and the probablty of nspecton and sancton). For smplcty, and to abstract from the ssue of allocatve eff cency at the natonal level, we represent the ndustry n each country by a sngle (prce-takng) frm. The frm seeks to maxmse (expected) per perod profts as max h E (π (h ; φ, q, x)) ph c (h ; x) φ f (h ; q ), (1) where h s the harvest, p s the (exogenous) market prce, c ( ) are (mnmsed) harvestng costs, x s the stock sze (whch the frm takes as gven n the short run), φ 0, 1 s enforcement effort (probablty of detecton), f s a monetary fne and q s the quota. To be specfc, let E (π ( )) ph c 2x h2 φ f h q q, (2) where c s a harvestng cost parameter and f s a fne rate. Note that here the expected penalty for landng over-quota fsh s a lnear functon of the relatve quota volaton. Ths ensures that the frm s optmal per perod harvest s dependent upon the sze of the quota q. Otherwse, the model arguably represents a vessel operatng under a management system based upon taxes, rather than quotas. 3 The necessary frst order condton for an 3 We could, alternatvely, have an expected penalty whch s a non-lnear functon of the level volaton h q, 5

6 (expected) proft-maxmsng level of harvest s p c x h φ f q = 0 (3) and we can then fnd the ndustry s optmal harvest response to the country s choce of φ (gven a quota q ) as h (φ ; q, x) = x f p φ c. (4) q Here, we assume that h > q and hence φ f /q > 0,.e., that the quota s less than the ndustry s capacty output and that there s non-complance. Capacty output h s thus defned where φ f /q = 0 and hence h = x c p. (5) From (4) we can see that, as would be expected, the ndustry s optmal harvest response h ( ) s ncreasng n the stock sze, the market prce and the sze of the quota and decreasng n harvest costs, enforcement effort and the fne rate. Note, n partcular, that and h ( ) φ h ( ) q = xf c q < 0 (6) = φ xf c q 2 > 0. (7) We can also see that (7) s decreasng n q. All else equal, ncreases n the quota result n ncreasngly smaller ncrements n the ndustry s harvest level as we approach ts capacty output h. but the functonal form used here s less cumbersome. Hatcher (2005, 2012) consders the ntuton for relatve volaton arguments n expected penalty functons and examnes the mplcatons for modellng quota complance n natural resource ndustres. 6

7 2.2 Eff cent enforcement Before proceedng to examne the ndvdual countres (myopc) enforcement choces, we frstly consder, as a benchmark, the optmal level of enforcement for each country f a socal planner were responsble for the decson, gven an agreed annual quota par q, = 1, 2. We assume that the socal planner s objectve s to employ enforcement effort n both countres so as to maxmse the total dscounted flow of ndustry harvestng profts (ncludng any fnes, snce these are smply transfers) less the costs of enforcement, subject to the (known) ndustry harvest responses and the dynamcs of the stock. Omttng tme arguments for clarty, the planner s objectve functonal s max φ 0 e rt { 2 =1 s.t. π (h ( )) + φ f ( ) ω (φ ) ẋ = g (x) } dt 2 h ( ), (8) where ω (φ ) s the cost of enforcement n Country, g (x) s the natural growth functon for the stock and r s an approprate nterest rate. Lettng ω (φ ) ω, a (constant) margnal cost of enforcement, the correspondng (current value) Hamltonan s 2 H c ( ) ph c 2 2x h 2 ω φ + λ g (x) h, (9) =1 where λ s the Lagrange multpler on the stock constrant. 4 The necessary condtons for =1 maxmsng the Hamltonan wth respect to φ are H c φ p c x h λ h φ ω = 0, = 1, 2. (10) =1 Substtutng for h and h φ usng (4) and (6), we obtan the eff cent level of enforcement 4 By specfyng constant harvestng cost parameters c, we make the mplct assumpton that ndustry capacty n each country remans fxed. A socal planner amng to maxmse the economc value of the fshery would choose a combned level of capacty (captal) that s optmal for the TAC, but we gnore ths possblty here. 7

8 effort for Country as φ = q λ c q ω, (11) f xf where a postve level of enforcement mples λ > ω c q /xf. Rearrangng (10), we can observe that λ = p c x h ω, = 1, 2, (12) h φ where ω /h φ = ω c q /xf. Thus, the eff cent level of enforcement results n a shadow prce for the stock whch s greater than the margnal proft from harvestng n Country. The wedge that s drven between margnal proft and the shadow prce s due to the (margnal) cost of enforcement, or, more accurately, the margnal reducton n the cost of controllng the harvest through enforcement. Ths, notce, s ncreasng n the sze of the quota q. Ths s because, all else equal, n order to acheve any gven harvest level, a larger quota mples a smaller volaton whch s more costly to attan n terms of enforcement effort. We can also see from (12) that f the margnal cost of enforcement effort ω s hgher n one country than n the other, then, all else equal, margnal proft must be smaller n that country and hence the level of harvest greater. Thus, for a gven quota par, enforcement effort, when allocated optmally, s concentrated n the country where t s least costly to deploy. For completeness, the correspondng stock condton s 2 λ rλ = Hx c p c x h λ h x + c 2x 2 h 2 λ g x, (13) =1 8

9 where h x = 1 c p φ f > 0. (14) q If a steady state exsts (ẋ = λ = 0), then gven a parametersaton for g (x) we can, n prncple, solve for λ and fnd the optmal stock sze x and the optmal enforcement levels φ. 2.3 Eff cent enforcement and quota settng Although we have taken them as gven, n prncple we should also be able to maxmse the value of the fshery wth respect to the natonal quotas q, = 1, 2. If we re-wrte the Hamltonan as H c ( ) 2 =1 ph c 2x h 2 ω φ ψ q q + λ g (x) 2 =1 h, (15) where ψ s some transactonal (let us assume, poltcal) cost assocated wth settng the sze of the quota for Country below some arbtrary level q, we can fnd the optmal quota condtons H c q Substtutng for h q usng (7), these condtons mply p c x h λ h q + ψ = 0, = 1, 2. (16) λ = p c c q x h 2 + ψ φ, = 1, 2. (17) xf Comparng (17) wth (12), t s apparent that for an eff cent soluton to exst wth respect to both φ and q, we must have φ q = ψ ω > 0, (18) and hence ψ > 0. For a meanngful soluton to (8) whch ncludes quota settng, therefore, t must be costly for a country to reduce ts quota (to below some predetermned level). 9

10 Otherwse, we can see from lookng back at equaton (4) that any gven level of harvest could always be acheved at least cost by reducng both enforcement effort and the sze of the quota. Ths may appear odd, but s qute ratonal. Settng a low quota and then relaxng enforcement to allow a relatvely large volaton s always the least-cost means of achevng a gven level of catch, provded t s not costly to reduce the sze of the quota. Hence the need for the ncluson of the cost term ψ q q. Expresson (18) then dentfes the optmal rato between the quota and the level of enforcement for gven enforcement costs and the (poltcal) cost of reducng the quota. 2.4 Country-specfc (myopc) enforcement When each country s unlaterally decdng upon a level of enforcement effort, concern about the long term value of the stock s, we assume, effectvely relegated to the nternatonal TAC settng process (see Secton 3). Once an annual quota par q, = 1, 2, has been agreed, each country behaves myopcally and maxmses only current perod socal benefts. Nevertheless, we assume that each country has some concern for adherng to ts agreed quota, whch we represent by a socal cost attached to over-quota harvestng by ts fleet. Gven ths, the country s objectve functon s max φ SB π (h ( )) + φ f ( ) δ (h ( ) ; q ) ω (φ ), (19) where δ ( ) s a socal damage (or dsutlty) functon for exceedng the quota (measured n monetary unts for convenence). In specfc form, we can wrte the country s problem as max φ SB ph ( ) c 2x h ( ) 2 δ h ( ) q ω φ. (20) 10

11 The frst order condton for the optmal level of enforcement effort φ s then p c x h δ h φ ω = 0. (21) Substtutng for h and h φ usng (4) and (6) and rearrangng, we obtan φ = q c q δ ω, (22) f xf whch we can see s exactly analogous to (11). Here, though, snce δ s a parameter, the nterpretaton s that a postve level of enforcement effort requres that δ > ω c q /xf = ω /h φ,.e., the margnal socal cost of over-quota landngs must exceed the (savng n) enforcement costs of a margnal ncrease n the over-quota catch. Otherwse, the country wll not undertake any costly enforcement. For a gven par of quotas q, an eff cent level of enforcement would, as we mght expect, result from δ = λ n each country. If a country cares too lttle about over-quota catches, the total level of enforcement wll be sub-optmal and the total level of harvest wll be excessve. On the other hand, we also have the perverse possblty that, f a country cares too much about over-quota landngs, t wll employ too much costly enforcement effort compared to the eff cent level. Clearly, though, what consttutes too much or too lttle enforcement, relatve to the socal optmum, depends upon the magntude of the quotas set. If, for example, the quotas are very low, then the optmal amount of enforcement would be less than f the quotas were set at a hgher level. In ths case a lower value of δ would be approprate. On the other hand, for a gven value of δ, the mpact of alterng the sze of the quota s ambguous (see below). We can see from (22) that, all else equal, Country s choce of enforcement effort φ s ncreasng n ts dsutlty rate for over-quota catches δ and decreasng n the cost 11

12 of enforcement ω. 5 Note that a standard result from enforcement models s that less enforcement effort s requred n order to acheve a target level of harvest f the fne s ncreased. Here, though, because there are socal benefts as well as costs to volaton, the net mpact of alterng the fne rate f on the optmal level of enforcement s ambguous. Increasng the fne, all else equal, ncreases the effectveness of enforcement n reducng (over-quota) harvest, but whle ths reduces the dsutlty from over-quota catches, t also reduces ndustry profts. From φ f = q f 2 c q 2ω δ 0, (23) xf we can see that f δ > 2ω c q /f x then ncreasng the fne reduces the optmal level of enforcement effort. If ncreasng the fne reduces the socal costs of harvestng more than the benefts, we would expect enforcement effort to be relaxed. Conversely, f ncreasng the fne reduces the benefts of harvestng more than the socal costs, we would expect enforcement to be ncreased. The mpact of a change n the sze of the quota s smlarly ambguous: from φ = 1 c q δ 2ω 0, (24) q f xf t s apparent that φ / q takes the opposte sgn to φ / f. If δ s relatvely large, reflectng a greater desre by the country to lmt over-quota catches, t s more lkely that φ / q wll be postve, so that an ncrease n the quota wll be matched by an ncrease n enforcement effort. 5 If we were to recast the problem of myopc enforcement n a game theoretc framework, t would seem ntutve to model each country s δ as a functon of the other country s (observed) level of enforcement φ. It s not dff cult to see that ths would result n non-cooperatve behavour (see Hannesson 2007). 12

13 3. Settng the total allowable catch (TAC) Havng establshed the enforcement effort response of each country to a natonal quota, gven the harvest response of ts fshng ndustry, we now turn to the problem of settng a TAC when the shares of the TAC used n determnng natonal quotas are fxed. We frstly examne the determnaton of the socally optmal TAC, before consderng the ncentves for countres to bd up a (proposed) TAC durng the TAC negotaton process. 3.1 Optmal TAC settng wth fxed quota shares To establsh the benchmark result, we let an omnscent central planner set an annual TAC Q for the fshery whch translates nto natonal quotas q γ Q for the two countres, where γ 1 + γ 2 = 1 are the TAC shares that have prevously been agreed. Usng (22) and (4), we can rewrte the ndvdual countres enforcement choces as φ (Q; x) = γ Q c γ δ ω Q, = 1, 2, (25) f xf gven ther ndustres harvest response functons h (φ ; x) = x p φ (Q) f, c γ Q = 1, 2. (26) Substtutng (25) nto (26) and rearrangng, we obtan an expresson for ndustry harvest as a functon of Q (gven x) as h (φ (Q) ; x) = x c p δ + γ Q ω f, = 1, 2, (27) where, recall, we assume that h > h ( ) > γ Q. Note that here h δ = x c < 0 (28) 13

14 and h Q = γ ω > 0. (29) f Snce the country s smultaneously choosng a (prvately) optmal level of enforcement effort n response to changes n ts quota, ndustry harvest s now a lnear functon of the TAC and hence the natonal quota. Omttng tme arguments as before, the planner s objectve functonal s max Q 0 e rt { 2 =1 s.t. ph ( ) c } 2x h ( ) 2 ω φ ( ) dt ẋ = g (x) and the correspondng (current value) Hamltonan s 2 H c ( ) ph ( ) c 2x h ( ) 2 ω φ ( ) + λ g (x) =1 =1 2 h ( ) (30) =1 2 h ( ). (31) The frst order condton for a maxmsng choce of Q s 2 HQ c p c h x h ( ) λ ( ) Q ω φ ( ) = 0. (32) Q Substtutng for h ( ) and h ( ) / Q usng (27) and (29), together wth φ ( ) Q = γ c γ δ 2ω Q 0, (33) f xf (whch, recall, we cannot unambguously sgn) after some rearrangement we obtan 2 γ ω γ f Q ω c λ = 0. (34) xf Ths mples λ = 1 x Q =1 2 =1 ω2 c γ 2 f 2 2 =1 ω γ Q = xλ f 2 =1 ω2 =1 2 =1 ω γ f c γ 2. (35) If the natonal quotas q γ Q are allocatvely eff cent, however, t s relatvely straght- f 2 14

15 forward to show that n (34) we wll have λ = γ Q ω c xf Q = 1 γ λ xf ω c, = 1, 2. (36) We can see from (32) that ths s equvalent to λ = p c x h ( ) ω φ ( ) Q / h ( ), = 1, 2, (37) Q whch shows more clearly that, at the optmum, the shadow prce of the stock equates wth margnal proft less the margnal cost of controllng harvest ndrectly by means of adjustments n the TAC. Whle we can rearrange (32) to aff rm that here p c x h ( ) = δ γ Q ω c xf > 0, (38) whch recalls (22), note that we cannot unambguously sgn the second term on the RHS of (37). If the quota shares are such that the TAC s not eff cently allocated (whch, n practce, s lkely to be the case), equaton (34) wll hold wth γ Q ω c xf < λ < γ j Q ω jc j xf j, j. (39) Here, the TAC share to Country s too small and the share to Country j too large, gven the costs of fshng, enforcement costs and the fne rate pertanng n each country. If t were poltcally feasble, of course, we could adjust the shares γ and γ j so that the nequaltes dsappear and the TAC s eff cently allocated. The correspondng stock condton n ths case s 2 λ rλ = Hx c π x ω φ x λh x λg x, (40) =1 15

16 where and π x p c h x h ( ) ( ) + c x 2x 2 h ( ) 2 (41) φ x φ ( ) x. (42) Agan, f a steady state exsts, then gven the parameters of g (x) we can, n prncple, solve for λ and fnd the optmal stock sze x and the optmal TAC Q. 3.2 TAC set by poltcal negotaton Consder a recommended TAC Q, establshed ether as the result of a stock assessment and scentfc advce or based upon past levels of explotaton. 6 We assume that the ncentve for each country to try to negotate a hgher TAC depends upon the (expected) ncrease n ndustry profts (net of any fne payments), less the assocated enforcement costs, together wth a poltcal cost ncurred for ncreasng the TAC by appearng to be ant-conservatonst. As wth δ ( ), the subjectve cost of exceedng the quota, ths could nclude damage to nternatonal reputaton, as well as an nternal cost. For smplcty, we agan assume that ths can be represented by a monetary cost, whch we wll denote ( ρ Q; Q). To be specfc, let ρ ( ) be a non-lnearly ncreasng functon of Q, wth ρ ( ) 1 2 ρ Q Q 2 ρ ( ) Q = ρ Q Q. (43) Thus, usng (20), we have a margnal (net) socal beneft functon for Country as SB Q p c h x h Q h δ Q γ φ ( ) ω Q ρ Q Q. (44) 6 In the Northeast Atlantc, scentfc advce on fsheres s provded by ICES (the Internatonal Councl for the Exploraton of the Sea). In the case of EU fsheres, ICES advce s used by the European Commsson to propose TACs whch must then be agreed by the Fsheres Councl, comprsng the fsheres mnsters of all EU member states. Proposed TACs are ether advsory - based on stock assessments - or precautonary - based only upon hstorc landngs. 16

17 After substtutng wth (27), (29) and (33), ths expresson can be rearranged to yeld SB Q = γ γ Q c ω ρ xf 2 Q Q. (45) Note that both terms on the RHS are postve and lnearly ncreasng n Q. Straghtforwardly, the ncentve for Country to press for an ncrease n the TAC s exhausted when γ γ Q c ω 2 xf = ρ Q Q. (46) Rearrangng (46), we can fnd the (myopcally) optmal negotated TAC ˆQ Country as ˆQ = > Q for γ + ρ Q ρ γ 2 c ω 2, (47) whch s decreasng n the socal cost parameter ρ, but s ncreasng n the TAC share γ. Thus, all else equal, countres whch care less about the poltcal mpacts wll seek to establsh a hgher TAC (by constructon), but so wll those wth larger quota shares. Smlarly, all else equal, larger TACs wll be sought by countres wth hgher fshng costs and hgher enforcement costs. The fndng that countres wth larger TAC shares wll seek a hgher TAC may seem surprsng, but s smply due to the greater margnal economc benefts that they accrue, all else equal, from a margnal change n the TAC. We could, of course, assume that ths mght be offset by those countres havng a greater stake n the sustanablty of the resource and hence a larger value of ρ. xf 2 Complete agreement on the TAC to be set would, we assume, requre ˆQ = ˆQ j for Countres and j. If, however, we have ˆQ > ˆQ j γ + ρ Q ρ γ 2 c ω 2 xf 2 > γ j + ρ j Q c ρ j γ 2 j ω 2, (48) j j xf 2 j 17

18 whch seems lkely, then an agreed TAC s mpossble. Ether there must be an external arbter to mpose a decson, or, gven that the γ are assumed fxed, agreement requres countres to change ther preferences for sustanablty, whch mples changng ther values of ρ. 4. Concluson We have modelled the explotaton of a shared fsh stock by two countres wth fxed TAC shares. Gven the harvest response functon of ts fshng ndustry, for a gven TAC share each country chooses a level of costly enforcement effort n order to maxmse current perod economc benefts whle securng what t regards as an acceptable degree of complance wth the natonal quota. We compared the countres myopc enforcement choces wth the socally eff cent levels of enforcement, gven the quotas n force. Optmal enforcement only results f each country perceves a cost to over-quota landngs whch equates wth the shadow prce of the stock under optmal management. Otherwse, we have the nterestng possblty that a country wll expend too much enforcement effort, as well as the possblty of too lttle. In passng, we consdered the problem for a socal planner of settng optmal quotas, as well as enforcement levels, n order to maxmse the total value of the fshery gven fxed quota shares and ndustry capactes. Ths presents a straghtforward optmsaton problem whch, however, can only yeld an nteror soluton f quotas are costly to set at low levels. In the absence of a cost to settng low quotas, wth a non-complant fleet the most eff cent way of achevng any gven level of harvest s always to set a (vanshngly) 18

19 low quota and relax enforcement to very low levels. Ths s a ratonal soluton whch (perhaps for obvous reasons) s never observed n practce. Solvng the best-response enforcement and harvest choces of the partcpatng countres admnstratons and ther fshng fleets n order to endogense enforcement, so that we can express harvest drectly as a functon of the TAC, we then consdered the eff cent TAC for the fshery as a whole. We llustrated the sgnfcance of the TAC shares n determnng the eff cency of the TAC allocaton under optmal management. Fnally, we developed a model to examne the ncentves for countres to seek ncreases n the TAC above a level recommended durng the annual TAC negotatons. In our model, the only brake on seekng a hgher TAC s provded by a socal cost to the appearance of beng ant-conservatonst. Unless we assume that countres wth a larger TAC share actvely care more about the sustanablty of the resource, then these countres wll always press for a hgher TAC. 5. References Beard, R., and L. Nøstbakken (2010). Mult-jursdcton quota enforcement for transboundary renewable resources. SNF Workng Paper No. 28/10. Bergen: SNF. Hannesson, R., (2007). Cheatng about the cod. Marne Polcy 31: Hannesson, R., (2011). Game theory and fsheres. Annual Revew of Resource Economcs 3:

20 Hatcher, A., (2005). Non-complance and the quota prce n an ITQ fshery. Journal of Envronmental Economcs and Management 49: Hatcher, A., (2012). Market power and complance wth output quotas. Resource and Energy Economcs 34: Holden, M., and D. Garrod (1994). The Common Fsheres Polcy. Oxford: Blackwell (Fshng News Books). Katala, V., (1986). Game theory models of fsheres management: A survey. In: Dynamc Games and Applcatons n Economcs. Berln: Sprnger. Katala, V., and M. Lndroos (2007). Game theoretc applcatons to fsheres. In: A. Wentraub, ed., Handbook of Operatons Research n Natural Resources. Berln: Sprnger. Lndroos, M., (2008). Coaltons n nternatonal fsheres management. Natural Resource Modelng 21: Munro, G., (2009). Game theory and the development of resource management polcy: the case of nternatonal fsheres. Envronment and Development Economcs 14: Sumala, U. R., (1997). Cooperatve and non-cooperatve explotaton of the Arcto- Norwegan cod stock n the Barents Sea. Envronmental and Resource Economcs 10:

21 Sutnen, J. G., and P. Andersen (1985). The economcs of fsheres law enforcement. Land Economcs 61: