Rent dissipation and efficient rationalization in for-hire recreational fishing

ARTICLE IN PRESS Journal of Environmental Economics and Management 58 (2009) 300–314

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Rent dissipation and efficient rationalization in for-hire recreational fishing Joshua K. Abbott a,, James E. Wilen b a b

School of Sustainability, Arizona State University, PO Box 875502, Tempe, AZ 85287-5502, USA Department of Agricultural and Resource Economics, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA

a r t i c l e i n f o

abstract

Article history: Received 31 August 2007 Available online 17 June 2009

Recreational fisheries are increasingly important in fisheries management; for some species, recreational take rivals or exceeds the amount harvested by commercial fishermen. Most recreational fisheries are regulated with gear restrictions, bag limits, and time/area closures, but there is increasing interest in the market-based solutions employed in commercial fisheries — this despite the lack of an adequate bioeconomic theory of the joint commercial/recreational aspects of many recreational fisheries. This paper integrates a detailed production specification with traditional bioeconomic tools in order to better understand the implications of rationalization schemes targeted at the charter sector. While confirming some of the qualitative conclusions of the commercial fisheries literature on open access and regulated open access our model also generates rich and novel predictions with respect to input choices, the number of vessels and congestion externalities. We devise a system of instruments that generate efficient outcomes and extensively discuss issues associated with their real-world implementation. & 2009 Elsevier Inc. All rights reserved.

Keywords: Recreational fisheries Rent dissipation Individual transferable quotas Bioeconomic modeling

1. Introduction A canvass of the resource economics literature of the last 30 years yields only a small number of applications of economic theory to the problems of recreational fishing, especially compared to the voluminous contributions to commercial fisheries over this same era.1 McConnell and Sutinen [21] pioneered the application of bioeconomic models in the recreational context with a simple model in which angler’s willingness to pay for a trip was solely a function of the quantity of trips and the harvest rate. They show the existence of a stock externality in free competition relative to the optimally managed system. Anderson [3] expands this framework by endogenizing the discard decisions of anglers and incorporating a mechanism for entry and exit of potentially heterogeneous fishery participants. Bishop and Samples [6] consider the issue of allocation of species that are shared between commercial and recreational fisheries. Homans and Ruliffson [14] examine the implications of minimum size limits for achieving management goals and improving fishing quality while Woodward and Griffin [31] take this analysis still further by considering the joint use of size and bag limits.

 Corresponding author. Fax: +1 480 965 8087.

E-mail addresses: [email protected] (J.K. Abbott), [email protected] (J.E. Wilen). By contrast, the empirical literature on recreational fisheries is voluminous. However, much of this literature has followed the broader recreation demand literature [23] in focusing on welfare estimates of regional fisheries or the static impacts of changes in natural amenities under existing institutions. Empirical models grounded in bioeconomic (dynamic) theory are scarce [20]. 1

0095-0696/$ - see front matter & 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2009.03.002

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This neglect may be linked to the virtual neglect of recreational fisheries by fisheries managers in the past. Until recently, recreational fisheries have typically gone largely unchecked while commercial fleets targeting the same species (for instance, the Gulf of Mexico red snapper fishery) have seen their ability to harvest the same species dramatically curtailed. This asymmetry may be justified when recreational takes are negligible for the purposes of stock management. However, it has become increasingly clear that recreational landings, while dwarfed by commercial landings at national and international scales are often substantial at regional scales or for particular species.2 This realization has driven regulators to employ a range of techniques aimed at reducing the mortality associated with angler-days with the more aggressive use of traditional restrictions such as bag limits and size limits being especially prominent. Economists have also entered the fray promoting innovative rights-based policy prescriptions that are grounded in the past successes of the management of commercial fisheries but with allowances for the unique contextual realities of the recreational case [16,28]. Despite the merits of these proposals, solutions grounded in the commercial experience may not be as immediately transferable as initially imagined. First, our understanding of the mechanisms of the rent dissipation process under open access is imperfect at best. Experience from the rationalization of commercial fisheries has yielded many surprises that demonstrate the inadequacies of simple single-index (i.e. effort) models in capturing the complexities of real-world rent dissipation [30]. Second, while the recreational sector may seem similar to commercial fisheries operations in many ways, there are key differences that may limit the simple transfer of knowledge and experience from commercial rationalization programs. These observations point toward the need for a more specialized theoretical foundation in order to predict the likely impacts of recreational fishery rationalization programs. As a first step, we develop a bioeconomic model of open access and optimal management for a for-hire recreational fishery.3 We restrict our attention to the for-hire sector for three reasons. First, charter and headboat trips account for a substantial part of total recreational fishing effort for some species and contribute significantly to many coastal economies [13].4 Second, due to their limited and known ports of origin and the clustering of multiple anglers on a single vessel, they are easier targets for regulation and are thus likely to be of importance in recreational fisheries policy making over the near horizon. Finally, as we demonstrate, the interaction of consumer preferences with the supply behavior of vessel owners creates the potential for an array of distortions and feedbacks with great relevance for fisheries policy. Our model builds upon the bioeconomic foundation of McConnell and Sutinen [21] and Anderson [2,3] by incorporating a realistic and flexible theory of the choice of inputs of the for-hire fishing firm. This methodological synthesis is unique, both in commercial and recreational fisheries applications.5 Integrating the supply and demand sides of the problem is necessary in order to examine the long-run distortions arising under open access in a manner that reflects feedbacks between angler preferences and the decisions of vessel owners. By comparing the unregulated fishery with the optimally managed case we discover a number of discrepancies. Along with the expected demonstration of excessive angler-days, catch and landings and insufficient biomass and social surplus in the unregulated fishery, we discover that vessel owners may face an incentive to carry too few anglers per trip in order to enhance the individual catch of anglers, thus leading to an excessive number of trips for a given level of trip demand. Second, we derive conditions that jointly determine the overall level of catch and non-catch aspects of quality associated with a trip and the mix of inputs that contribute to these metrics. Vessel owners fail to consider the dynamic external effects of investments in catch-enhancing inputs, leading to excessive fishing power per angler and potential under-investments in non-catch-related aspects of trip quality. Thirdly, we demonstrate that entry in a competitive fishery is likely to be excessive even in the absence of stock effect considerations, leading to excess capacity and underemployment in the sector. We then show how the incentive problems associated with open access can be addressed by three instruments—two targeted at fishing mortality (discards and landings) and another to prevent excessive entry—and conclude by discussing how these instruments may be practically implemented in realworld fisheries.

2 US recreational harvest of coastal species (excluding Alaska) was approximately 257 million pounds in 2006 compared to an equivalent estimate of over 4 billion pounds for commercial fisheries [24]. However, a number of important and highly exploited species have significant or dominant shares of recreational harvest (red drum, 100%; spotted seatrout, 98%; red snapper, 45%) [24]. Other species of commercial importance have substantial recreational shares of total harvests (summer flounder, 45%; Atlantic croaker, 32%) that compete for allocations [24]. Recreational fishing mortality figures especially highly for biologically depressed stocks; a recent study suggests that 23% of the landings of ‘‘populations of concern’’ (those that are either overfished or experiencing overfishing) are accounted for by recreational harvest [9]. This proportion exhibits significant regional variation—rising to 64% in the Gulf of Mexico. 3 The for-hire sector is composed of both charter and headboat vessels. A charter vessel is defined as a vessel for which a group of anglers pays a fixed rate for the exclusive use of the vessel for a trip whereas a headboat charges anglers individually for seats on the vessel. Our model applies to both types although we couch our analysis in terms of headboats. 4 Fifty-one percent of recreational red snapper landings in the Gulf of Mexico are attributable to the charter sector while 56% of recreational yellowfin tuna landings in the South Atlantic are harvested by charter vessels [22]. In general, large or highly mobile offshore species have relatively high shares of catch from charter vessels as compared to smaller, more sedentary inshore species. 5 Huang and Lee [15] develop a general model of commercial fishery production in a bioeconomic context. Empirical production economists have criticized the classic bioeconomic model [27] but there has been no attempt, to our knowledge, to reconcile the dynamic insights of the bioeconomic framework with a more subtle account of the choice of fishing inputs.

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2. A theory of for-hire recreational fishing under optimal management 2.1. Demand: angler preferences for trip attributes We begin by assuming that vessel owners supply fishing trips of a fixed and exogenous length—say a day.6 There is a population of identical anglers whose seasonal aggregated preferences for day trips conditional on their quality attributes are captured by a marginal benefit function: MB(D, H, L, S) where D is the number of angler-days of for-hire services demanded over the fishing season, H is the per angler-day catch of targeted fish, L is the amount of this catch that is landed and retained by anglers, and S is a measure of fishing trip quality that is unrelated to the quantity or disposition of catch. Note that anglers’ marginal willingness-to-pay for a day of fishing depends on both the quantity and quality of charter services consumed. Quality may be a function of the daily catch rate, the quantity of landings, and the non-catch aspects of trip quality, which include attributes such as the safety and general upkeep of the vessel and the devotion of labor toward non-catch related activities that enhance the experience of fishing (such as serving food or drink to passengers or filleting catch).7 This formulation incorporates the findings of the social science literature that finds non-consumptive aspects figure significantly in recreation demand [4,10,11]. We assume the marginal benefit function is continuous with respect to all variables and satisfies: MBD o0;

MBH 40;

MBS 40;

MBL ðD; H; 0; SÞ40;

MBjj o0;

j ¼ H; S; L

where subscripts indicate the first partial derivative with respect to the subscripted variable. The first condition ensures a downward-sloping demand function whereas the second and third state that the marginal willingness-to-pay for a day of fishing is strictly increasing in the quality aspects of the trip. We relax these assumptions for landings, however, as it is plausible that individuals may face satiation, and therefore make the minimal assumption that positive landings are a good for at least the first unit of consumption. The catch and non-catch aspects of trip quality are produced with multiple factors of production. We assume that pertrip harvest, H(X,zH,N), is a continuous, differentiable and increasing function of the current stock of the target species, X (HX40), and a Qx1 vector of capital and labor inputs selected by the vessel owner, zH, to enhance the skill of fishermen. For instance zH may include the use of additional fishing rods for each angler to increase catch per unit effort, investment in engine horsepower to allow faster access to productive fishing grounds and greater fishing time, the use of chum to attract certain species, or the allocation of crew time to education on fishing techniques and the baiting of gear. In agreement with conventional production theory, we assume that each of these inputs has a positive and diminishing marginal effect on per-angler harvest, ðHzH ðiÞ 40; HzH ðiÞzH ðiÞ o0 8i ¼ 1; . . . ; Q Þ. In addition to these purchased factors, we also assume that the number of anglers onboard a given vessel, N, has a negative and decreasing effect on per-angler harvest (HNo0, HNN40) which allows for a variety of possible intra-vessel congestion externalities (e.g. from entangled fishing lines). Non-catch quality, S(zS,N), is similarly dependent upon a Mx1 vector of inputs, zS, that may overlap with the zH. To account for the fact that some inputs that aid in the production of catch quality may actually reduce productive capacity for non-catch quality (and vice versa) we allow both ‘‘goods’’ and ‘‘bads’’ in the production relationship with sufficient curvature restrictions to ensure the overall concavity of the marginal benefit function with respect to all inputs. Note that all shared inputs are defined so that they are positive contributors to catch quality production. As with catch quality, we assume that non-catch quality is influenced by the number of passengers onboard a vessel in a negative and decreasing fashion to reflect negative attitudes toward crowding distinct from its impacts on catch.8 We assume S(zs,N) satisfies:9 SzS ðiÞ 40; SzS ðiÞzS ðiÞ o0 or SzS ðiÞ o0; SzS ðiÞzS ðiÞ o0 8i ¼ 1; . . . ; M; SN o0; SNN o0 . 2.2. Supply—industry input expenditures Given this structure of preferences and production relationships, we now consider the relationship between input choices and seasonal expenditures. We frame our analysis in terms of the seasonal vessel expenditure function instead of a 6 Charter and headboat trips vary in length according to the species; however, day trips are by far the most common offering, particularly along the Gulf Coast [29]. 7 Our assumption of identical preferences over catch, landings and non-catch quality can be relaxed by introducing a range of demand functions for various angler ‘‘types’’. While potentially illuminating, such an allowance would complicate the modeling by explicitly considering the discretecontinuous nature of recreational demand [3]. 8 Anglers may prefer the company of fellow anglers up to a point. For tractability we assume that preferences for ‘‘social’’ fishing are sufficiently weak to be negligible. 9 Our representation of catch and non-catch quality by production functions necessitates non-jointness restrictions on the transformation function. We divide inputs into one of two classes. The first are allocatable to the exclusive production of catch or non-catch quality (e.g., allocation of crew time between baiting hooks and serving anglers’ ‘‘creature comforts’’). Other inputs, while not allocatable, contribute in a non-rivalrous manner to both forms of quality. This is the case for aspects of vessel capital such as deck size whose usefulness in fostering catch (due to the dilution of congestion effects) does not detract or enhance its contribution toward non-catch quality. Common definitions of non-jointness encompass one or the other form of input but not both [17,18]. We invoke a form of ‘‘almost non-jointness’’ [19] that allows the specification of production functions where the only non-allocatable inputs are public in nature. Since we take a long-run view of input choice in this model (all inputs being variable), some common causes of jointness (e.g. allocatable fixed inputs [26]) are of no consequence here. Non-jointness does rule out certain technological interactions such as scope economies that may result if, for instance, perceptions of non-catch quality enhance the productivity of anglers.

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minimum cost function in order to derive explicit relationships for the choices of vessel inputs and the number of passengers that would only be implicit within a dual formulation—thus integrating theories of input ‘‘stuffing’’ within a bioeconomic framework. We assume that there are an endogenously determined number of identical vessels NV. Each of these vessels faces three classes of expenditures that are all variable at the temporal scale of decision making in our model: (1) those that vary according to the number of trips, (2) avoidable ‘‘trip-invariant’’ costs (costs that do not vary in the number of trips but are forgoable without exit) and (3) trip-invariant costs that are only avoidable by exiting the industry altogether (e.g. license fees, minimal vessel insurance, etc.), which we henceforth designate by C. The first category may include expenditures such as labor, fuel and use-dependent maintenance while the second includes expenditures on capital inputs.10 Inputs in each expenditure category are allowed to contribute to both catch and non-catch quality in a general fashion (i.e. they can belong to either/both zH or zS) although any one input is allocatable to only one expenditure category:     eðzH ; zS ; N; NumTripsÞ ¼ ðw0VN zVN ÞN þ w0V zV NumTrips þ ðw0FN zFN ÞN þ ðw0F zF Þ þ C, zj  ðzH [ zS Þ;

zj \ zi ¼ +;

[ zj ¼ ðzH [ zS Þ; j

i; j ¼ VN; V; FN; F;

iaj.

(1)

Note that seasonal expenditures are a function not only of inputs and their exogenous market prices (indicated by the vectors wj) but also of the number of trips taken in the season and the number of anglers per trip. Some fixed and tripvariable costs are allocatable on a per-angler basis and these are represented by zFN and zVN, respectively. For instance, a vessel owner may elect to allocate a given number of fishing rods per angler; this catch-augmenting input (a member of the vector zH) is housed in the vector zFN. Alternatively, crew time spent in training and baiting gear for each passenger is also captured in the zVN input vector.

2.3. The optimal for-hire recreational fishery Having established the nature of both costs and benefits, we now require an expression linking the behavior of anglers and vessel owners to the evolution of targeted biomass through time. We employ the following standard relationship: X_ ¼ gðXÞ  D ðfðHðX; zH ; NÞ  LÞ þ LÞ

(2)

where D* is the number of angler-days supplied per season and the term it is multiplied by is the fishing mortality per angler-day. f is a discard mortality parameter indicating the fraction of discarded catch per trip-day that dies before returning to the reproductive stock. The surplus growth function g(X) is assumed to be strictly concave with zero growth at zero biomass and at a positive carrying capacity stock level. The socially optimal outcome solves max

Z t

1 ds

e

Z

!

D

MBðD; HðX; zH ; NÞ; L; Sðzs ; NÞÞdD  N V eðzH ; zs ; N; NumTrips ds 0

(3)

D ; L; N; NV ; zq ; zs subject to (2), non-negativity constraints on the state and control variables and the following additional constraints: L  HðX; zH ; NÞ;

NumTrips  DMAX ;

NumTrips ¼

D NV N

(4)

The first constraint simply limits landings to an amount weakly less than individual harvest.11 The second constraint states that the number of trip-days taken by a vessel must not exceed the total number of fishing days in a season DMAX. Note, however, that NumTrips is not included as a separate control variable in our statement of the problem. The rationale is found in the third constraint of (4). Given the homogeneity of vessels in our model, both passengers and trips are spread evenly across the fleet. Combining this assumption with the endogenous number of vessels and anglers per trip as well as the constant variable cost of trips by a vessel yields the per-vessel trip count indicated in (4). The social planner chooses the time paths of fishing days, landings, angler density, the number of vessels and vessel inputs to maximize the discounted present value of the flows of seasonal social surplus. The constrained current value 10 Since many aspects of vessel capital are interpretable as heterogeneous bundles of valued characteristics (e.g. horsepower, fuel capacity, length, etc.), we adopt the language of hedonic pricing in our descriptions of capital inputs so that the rental rates for a characteristic are the first derivatives of the equilibrium bid function with respect to the quantity of that characteristic [25]. 11 Individual landings may exceed harvest if fishermen trade their catch with other passengers. In this case, the constraint could be modified to apply to the sum of individual landings and harvest on a trip. However, given identical preferences and skill across anglers, the individual and aggregate constraints are equivalent.

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Hamiltonian is Z D D Þ HCV ¼ MBðD; HðX; zH ; NÞ; L; SðzS ; NÞÞ dD  NV eðzH ; zS ; N; N VN 0     D . þ l gðXÞ  D ðfðHðX; zH ; NÞ  LÞ þ LÞ þ m1 ½HðX; zH ; NÞ  L þ m2 DMAX  NV N

(5)

2.3.1. Number of vessels Since NV does not enter the equation of motion and only affects net benefits through a linear positive effect on fixed costs, each vessel must be fully employed in every season in order to minimize these costs, so that the season-length constraint must strictly bind.12 Given that the second constraint in (4) must bind, a generalized version of the maximum principle [7, p. 152] states that a necessary condition for NV can be found by taking the partial derivative of (5) with respect to NV and setting it equal to zero, yielding: DMAX m . NV ¼  0 ðwFN zFN ÞN þ w0F zF þ C 2

(6)

Fixed costs are instrumental in determining the scale of the industry; the higher are fixed costs the lower the optimal number of vessels while an increase in the optimum angler density may lead to a decrease in the number of vessels due to fixed cost effects as well. Finally, the number of vessels is rising in the marginal valuation of an additional fishing day for the entire fleet. 2.3.2. Aggregate angler trip-days The necessary condition for the number of seasonal angler-days is    1 1 ¼ l fðHðX; zH ; NÞ  LÞ þ L . MBðD ; HðX; zH ; NÞ; L; Sðzs ; NÞÞ  ½ðw0VN zVN ÞN þ w0V zV   m2 N NV N

(7)

At an interior solution this condition states that the net marginal benefits from an additional angler-day are just offset at each point in time by the present value of the induced mortality. However, such an interior solution does not exist given the necessity of full vessel employment at the optimal solution. An increase in angler-days necessitates an increase in the number of vessels and a requisite increase in fixed costs. This is easily demonstrated by solving (6) for m2:

m2 ¼

 NV  0 ðwFN zFN ÞN þ w0F zF þ C DMAX

(8)

The benefit of an additional day of fishing lies in the reduction in capacity required to fill current demand. Therefore the third term in (7) reflects the increase in fixed costs from the investment required to accommodate an extra angler-day within the season-length constraint. 2.3.3. Landings per trip The necessary condition for angler landings is Z D MBL dD  m1 ¼ lD ð1  fÞ.

(9)

0

This condition implies that the net marginal benefits of additional landings must be offset by the full dynamic costs of the induced mortality. If discards experience full mortality (f ¼ 1) then there is no dynamic consequence to the allocation of catch and (9) becomes a static condition. If catch is insufficient to satiate anglers’ consumptive desires (m140) then all harvest is landed. 2.3.4. Anglers per vessel-trip The necessary condition for angler density is     Z D D D ½MBH HN þ MBS SN  dD  N V ðw0FN zFN Þ  ðw0V zV Þ þ ¼ lD fHN . m H þ m N 1 2 2 NV N NV N2 0 Substituting (8) into this condition (realizing that D =ðNV N 2 Þ ¼ DMAX =N) yields the following: Z D NV ½MBH HN þ MBS SN  dD þ ½ðw0V zV ÞDMAX þ ðw0F zF Þ þ C þ m1 HN ¼ lD fHN . N 0

(10)

(11)

12 The proof for this assertion is intuitive and arrived at by contradiction. The result follows from the lack of adjustment costs of entry/exit as well as the constant variable cost of trips. Given our ultimate concern for characterizing bioeconomic equilibria, omission of adjustment costs is immaterial as excess capacity cannot persist indefinitely with finite costs of adjustment.

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Note that the dynamic effect of an increase in angler density, the right-hand side of (11), is negative, implying a dynamic benefit from an increase in angler density due to its curbing effect on harvest efficiency and thus fishing mortality. This implies that intra-vessel congestion should be driven beyond the point where the marginal static return to society (the decrease in variable and fixed costs from a reduction in total vessel-trips and capacity less the loss of angler welfare from increased congestion) is set equal to zero. In the event that landings are constrained by harvest (i.e. m140) there is an additional near-term cost of increasing angler density due to the indirect effect on landings, driving the optimal solution toward an even lower density of anglers. In other words, ceteris paribus, a fishery characterized by anglers with strong retention preferences (e.g. high-quality food fish species) should have lower levels of angler congestion than a similar fishery characterized by weak retention preferences. 2.3.5. Vessel inputs In characterizing the necessary conditions for input optimality, we work at the maximum level of generality, assuming that an input affects both catch and non-catch quality. For the case of a variable input that (without loss of generality) is allocated on a per-angler basis an interior solution will satisfy: Z

D 

 MBH HzðiÞ þ MBS SzðiÞ dD  wVNðiÞ D þ m1 HzðiÞ ¼ lD fHzðiÞ

0

(12)

The current net marginal benefits from an increase in an input are balanced against the dynamic costs of the mortality due to increased catch effectiveness.13 Additionally, if landings are constrained by harvest (m140), then there is a further benefit to increasing factors that increase harvest as doing so also increases landings so that species for which preferences for landings are strong relative to the available harvest are likely to exhibit relatively high optimal levels of catchaugmenting capital. Factoring of (12) yields the following expression: "Z  # "Z  # D

0

D

MBH dD  lD f þ m1

HzðiÞ þ

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}w

H

SzðiÞ ¼ wVNðiÞ D .

MBS dD

0

(13)

|fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}w S

This equation mimics the standard profit maximization condition that the value of the marginal product of an input be equated to the marginal factor price, but with three key differences. First, our model works at the scale of the regional industry so that prices of outputs are not exogenous. Second, the production of catch and non-catch quality are conditional on a given (endogenous) level of trips so that the marginal benefits of quality change are measured with respect to shifts in the consumer demand function. Finally, wH and wS represent the optimal ‘‘prices’’ of catch and non-catch quality and therefore reflect the full dynamic implications of quality changes. Calculating (13) for another trip-variable factor j and forming the ratio of these conditions yields the following expression:

wH HzðiÞ þ wS SzðiÞ wVNðiÞ ¼ . wH HzðjÞ þ wS SzðjÞ wVNðjÞ

(14)

If inputs are exclusive contributors to either catch or non-catch quality, this equation reduces to the standard costminimizing tangency condition between the expenditure frontier and the marginal rate of technical substitution. More generally, (14) is identical in form to the condition generated by a cost minimization problem subject to dual quality constraints with non-joint production—only here the optimal prices of quality replace the Lagrange multipliers so that costs are minimized at the optimal quality levels. This finding demonstrates how the family of conditions embodied in (12) (where analogous conditions for non-trip-variable costs are easily obtained) jointly determine both the optimal quality levels and the cost-minimizing input combinations. Eq. (14) shows that the combination of inputs is determined by a mixture of two single-quality tangency conditions where the relative influence of catch or non-catch quality in influencing the mix of inputs is a product of their relative optimal marginal valuations. 2.3.6. Costate equation for biomass The costate equation for the dynamic optimization problem is

l_  dl ¼ 

Z

D

MBH HX dD  lðg 0 ðXÞ  D fHX Þ

(15)

0

Considering this equation at the steady state (l_ ¼ 0) yields the following solution:

lSS ¼

HX

R D 0

  MBH ðD; H X; zH ; N ; L; Sðzs ; NÞÞ dD  0 d  g ðXÞ þ D fHX

(16)

13 To ensure such interior solutions for all factors, we must supplement the properties of production functions with additional ‘‘Inada conditions’’ that all inputs are essential and have an infinite marginal product as the quantity of the input approaches zero.

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Several observations are warranted here. First, the capital value of the fish stock is, predictably, inversely related to the discount rate of the social planner. Second, if harvest rates have no impact on marginal benefits (MBH ¼ 0) or if increases in fish stock density have negligible effects on catch rates (HX ¼ 0) then an extra unit of stock has no long-run value and the user cost is zero. Third, the effect of a higher mortality rate of discards is to decrease the steady-state valuation of the fish stock due to the leakage of natural capital from the system.14 Having derived the necessary conditions for the optimal management of the fishery, we now contrast them with what we would expect in a perfectly competitive open access industry. 3. The open access recreational fishery 3.1. Equilibrium under open access In competitive equilibrium the market determines the number of fishing days and landings so as to maximize the sum of current consumer and producer surplus: Z D MBðD; HðX; zH ; NÞ; L; Sðzs ; NÞÞdD  N V eðzH ; zs ; N; NumTripsÞ max (17) 0 D ; L subject to the prior constraints on landings, the number of trips per vessel and the vessels’ choices of angler density, number of vessels and quality inputs. 3.1.1. Aggregate angler trip days under open access The first-order condition for D* is as follows: MBðD ; HðX; zH ; NÞ; L; Sðzs ; NÞÞ  ½ðw0VN zVN ÞN þ w0V zV 

 1 1 ¼0  m2 N NV N

(18)

This expression differs from (7) in that the full user cost of the mortality from additional angler-days is missing from the right-hand side. As a result, there will be excessive demand for days at sea by anglers in the competitive case relative to the social optimum.15 3.1.2. Landings per trip under open access The open access condition for L is Z D MBL dD  m1 ¼ 0.

(19)

0

Note that landings are determined without regard to the effects of the extra mortality on the future stock. Anglers either reach a satiation point in their consumptive use or are limited in their landings by the quantity of harvest. Therefore, the incentive to discard is excessive in a purely competitive system. The only exception occurs when there is full mortality of discards. In this case, all harvest is lost to the system regardless of whether it is retained and so statically optimal landings decisions are appropriate [5]. 3.1.3. Anglers per trip under open access The number of passengers per vessel and the factors of production are chosen by vessel owners and are driven to equilibrium values through competition in the market for fishing trips.16 Given that angler density influences both metrics of quality, vessel owners will seek to differentiate their services by altering the concentration of anglers on their vessel. In the absence of differentiated demand his competitors will respond in kind, leading to an iterative process of quality competition. The competitive market equilibrium arising as the limit of this process is implicitly defined by the following condition (again realizing that D =ðNV N2 Þ ¼ DMAX =N if m240):    Z D D DMAX ½MBH HN þ MBS SN  dD  N V ðw0FN zFN Þ  ðw0V zV Þ þ ¼ 0. (20) m H þ m N 1 2 N NV N2 0 In the case where landings are unconstrained, this condition says that competition drives angler density down to the point where the foregone increases in angler benefits and reduced N-variable fixed costs from a reduction in density are 14 The effect of the mortality parameter on the costate variable is analogous (although not perfectly equivalent) to the role of depreciation in the literature on investment. 15 In the event that vessels are fully employed in a competitive equilibrium (an unlikely event as we demonstrate), a fisherman desiring an extra day at sea would have to pay a discretely higher price than those immediately preceding him due to the necessity of covering the fixed costs of the marginal increase in vessel capital required to satisfy demand—thus the final term in (18). 16 We do not attempt to characterize the dynamic process of approaching such an equilibrium. A fully developed dynamic explanation of the path to equilibrium would likely entail the consideration of the adjustment costs of investment in fixed factors [8,12].

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just offset by the marginal costs of doing so, where these extra costs are incurred through an increase in the number of trips necessary to serve the available demand. In the event that landings are constrained by harvest, then a full accounting of the exploitable marginal benefits (i.e. the full marginal willingness to pay of anglers) of a decrease in density requires the third term in (20) to account for the value of increased landings. A comparison of (20) to (9) reveals that the competitive equilibrium fails to account for the dynamic implications of the choice variable. A decrease in N imparts a long-run cost due to its accelerating effect on per-angler mortality so that competitive equilibrium results in a smaller number of anglers per vessel than is optimal. This result is particularly telling given that open access competition typically encourages excessive congestion in commercial fisheries. While true for inter-vessel congestion (an arguably small effect for many recreational fisheries) congestion operates within a vessel in our model so that consumer preferences for congestion avoidance are relayed to vessel owners through market demand, driving this surprising result.

3.1.4. Attribute supply and input choice under open access The determination of quality-augmenting inputs under competition is arrived at via a similar sequential argument as made for angler density. The marginal condition that is satisfied in competitive equilibrium for a trip-variable, angler allocatable factor is: Z

D 

 MBH HzðiÞ þ MBS SzðiÞ dD  wVNðiÞ D þ m1 HzðiÞ ¼ 0.

0

(21)

This condition is identical to that in (12) except that decision making under unfettered competition fails to account for future mortality effects. Factoring (21) as in (13) reveals: "Z

#

D 0

MBH dD þ m1

HzðiÞ þ

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}wC

H

"Z

#

D

SzðiÞ ¼ wVNðiÞ D .

MBS dD 0

(22)

|fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}wC S

Note that the valuation of the marginal contribution of catch effectiveness to the ‘‘value of marginal product’’ is overstated relative to the optimal case (wCH 4wH ). The cost minimization tangency condition in (14) continues to hold, only now the relative preference given to catch quality in the quantity and composition of inputs is skewed toward excessive catch quality. In other words, equilibrium catch effectiveness will be too high under open access competition and some of the inputs that play a role in its production will see excessive use, although input costs will be minimized at the competitive levels of catch and non-catch quality. We now flesh out this insight for some simple cases. First, consider if catch quality is a function of a single exclusive input. Taking the ratio of conditions (13) and (22) we find: HzðiÞ HCzðiÞ

¼

wCq 41 ! zC ðiÞ4z ðiÞ wq

(23)

given the assumption of diminishing marginal productivity of inputs. Note, however, that this increase in catchaugmenting factors is not guaranteed to occur in general. When there are multiple catch-quality-exclusive inputs, the move from optimal management to competition may result in less of some inputs and more of others depending upon the nature of the catch quality production function although at least one input must exceed its optimal level. In the case where an input affects non-catch quality exclusively a comparison of (22) to (13) reveals that the valuation of non-catch quality under competition and optimal management is identical. There is, therefore, no direct incentive for the distorted use of this input. However, indirect distortions may propagate due to possible substitution effects between catch and non-catch quality in angler demand. For instance, if the two components of quality are substitutes, then the presence of excessive catch quality in pure competition will weaken demand for non-catch quality, lowering its equilibrium value and thus causing the use of at least one of its inputs to fall relative to the optimal input bundle. In the case where some inputs contribute to both catch and non-catch quality, the situation is much more complicated. With non-catch quality inputs, there will be a tendency to substitute away from exclusive inputs and towards inputs that pay a ‘‘double dividend’’ by contributing positively toward catch quality.17 This substitution is driven by the excessive price signal sent by the market for catch quality under perfect competition. The degree to which such behavior is seen in practice depends on the degree to which shared versus exclusive inputs are substitutable in consumer’s perceptions of non-catch quality, the relative prices of these classes of inputs and the difference between the optimal and competitive price of catch quality. 17 A corollary is that there will be over-investment in catch-influencing inputs that act as ‘‘bads’’ in the production of non-catch quality, particularly if the two quality metrics are highly substitutable to consumers and these inputs are not easily substituted in the production of catch quality. For instance, vessels may over-invest in noisy but powerful engines in order to increase fishing time yet diminishing the aesthetics of the trip in a way that reduces angler welfare.

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3.1.5. Number of vessels under open access The determination of the number of vessels in long-run competitive equilibrium is characterized by the elimination of all supranormal rents from the system. Mathematically MBðD ; HðX; zH ; NÞ; L; Sðzs ; NÞÞD  N V eðzH ; zs ; N; NumTripsÞ ¼ 0

(24)

Suppose that an optimally managed recreational fishery in steady state generates positive rents to the industry and then consider the deregulation of the system. Given that each vessel under optimal management was operating at full seasonal capacity beforehand, it follows that the number of vessels in the fishery will increase under the competitive open access scenario holding input choices and quantity demanded constant. Fixed costs, downward-sloping demand and diminishing returns to increases in quality inputs eventually exhaust excess rents, however, and entry stops when the headboat trip price (the equilibrium price per angler-day) equals the average total cost per angler-day. Note that there is no inherent mechanism to ensure vessels will be fully employed at the long-run equilibrium; indeed, it is likely that capital and labor will lie idle for some portion of the season. The lower the barriers to entry (i.e. the lower are unavoidable fixed costs) the greater will be the tendency of vessels to enter the fishery at a given price and thus the greater the amount of ‘‘idle capacity’’ within the system at equilibrium. It is important to note that the absolute number of vessels in open access equilibrium need not exceed that found in the optimal bioeconomic equilibrium. The investment in a higher long-run stock (with its catch-enhancing qualities) may sufficiently stimulate demand to overcome the demand-stunting effects of reductions in catch-augmenting inputs and the reduction in the number of trips required to service a given number of angler-days (given the incentive toward greater numbers of passengers per trip under optimal management) to actually increase the number of charter providers. Such an outcome is particularly likely under a scenario in which there is a strong harvest–stock linkage, where demand is strongly tied to catch of the species and the linkage between angler-days and fishing mortality is strong (either through high discard mortality or strong preferences toward landing catch). Notwithstanding this observation one finding is unequivocal: the number of vessels will be excessive under open access given the current demand, stock level and configuration of inputs. 3.2. Consequences of open access—summary Relative to optimal management, competition under open access will lead to excessive demand for fishing days. Vessel owners will take onboard too few passengers each trip and the number of vessels will exceed the optimal level and almost assuredly engage in too few trips per season. These vessels will be equipped with excessive catch-augmenting capital given their number of passengers so that the harvest effectiveness of individual anglers is too high. Distortionary spillovers from catch-augmenting inputs to non-catch quality inputs are likely although the nature of this interaction is ultimately an empirical matter. The proportion of catch landed will be too high (except where discards face full mortality) while the amount of landed catch will be further augmented by the distortions in the effectiveness of angler effort. The overall consequences of these distortions are a reduced equilibrium biomass level, lowered rents for vessel owners and reduced total social surplus compared to the optimally managed case.18 4. Optimal corrective policies 4.1. Input-targeted policies To mimic the necessary conditions of the efficient outcome in the steady state a policy or set of policies must explicitly or implicitly levy the following corrective taxes (where we have substituted out for D* using (4) and scaled taxes to logical units and levying periods):   tD ¼ lSS fðHðX SS ; zH ; NÞ  LÞ þ L ,

tL ¼ lSS ð1  fÞ, tN ¼ lSS N fHN , tzðiÞ ¼ lSS NDMAX fHzðiÞ ; 8i ¼ 1; :::; Q tNV ¼ MBðN V NDMAX ; HðX SS ; zH ; NÞ; L; SðzS ; NÞÞðNDMAX Þ  eðzH ; zS ; N; DMAX ; wÞ.

(25)

The first tax can be thought of as a ‘‘user fee’’ for access to for-hire recreational fishing and is presented at the resolution of an individual angler-day. The optimal tax on an angler-day reflects the full mortality impact of the trip including both 18 Interestingly, whether anglers are better off under rationalization is unclear a priori. Anglers do receive a greater number of days at sea and a preferred bundle of harvest inputs (although not necessarily a higher harvest rate) under open access. However, they also face lower stock levels which may outweigh these benefits. Furthermore, induced distortions in non-catch quality may tip the balance in favor of either regime without further restrictions on our model. In other words, it is far from certain that consumers of charter and headboat services would be better off under a rationalized fishery without some redistribution of the rents. This finding is of considerable potential importance for the political economy of the rationalization process.

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discards and landings. Note that the importance of harvest in determining tD declines for stocks with low discard mortality so that the intensive margin of fishing mortality dominates the tax on the extensive margin of choice. The tax on landings is denoted per angler-day and is proportional to the survivability of discards. If all catch dies regardless of its disposition (e.g. many deepwater fisheries) then no constraint on landings is warranted and the tax on angler-days collapses to a fee on harvest. The instrument for angler density is envisioned as a per-head subsidy administered at the trip level for each vessel. This subsidy increases at an increasing rate with optimal density, and goes to zero as the mortality of discards decreases. If there is no catch mortality apart from landings, there is no external dynamic implication to the choice of the number of anglers and the competitive market for angler-days internalizes remaining non-catch quality externalities. The taxes on catch-augmenting inputs are characterized as being levied on a seasonal basis per vessel. They increase the effectiveness of the factor in fostering catch and decline as the survivability of discards increases. Without the dynamic externality from excess fishing power, mortality is controllable through a single levy on landings and the market yields the proper configuration of fishing inputs in long-run bioeconomic equilibrium. The final tax is a seasonal levy per vessel that is designed to remove any rents available to the marginal entrant. This ‘‘permit fee’’ could also be administered through the selling or leasing of transferable rights to participate as a charter or headboat in the fishery. Note that the rationale for this instrument differs from that underlying the entry tax in the singleinput commercial fisheries literature where such a tax is justified on the grounds of correcting for the stock externality that leads to excess ‘‘effort’’. The previous taxes in (25) account for these dynamic externalities in a multidimensional sense. The tax on entry is necessitated by a form of rent dissipation that arises due to the lack of cross-firm coordination in entry behavior under an external capacity constraint (the number of available fishing days) and where vessels face declining average costs of trip production due to the presence of non-trip-variable costs. Without such a tax, there will likely be an excess burden of fixed costs in the industry. 4.2. Fishing mortality-targeted policies Although the conditions in (25) may suggest the necessity of imposing Q+4 corrective instruments to achieve optimal management, such is not the case. Consider the outcome of an open access market, with corrective taxes on landings, discards and the number of vessels: R D max 0 MBðD; HðX; zH ; NÞ; L; SðzS ; NÞÞ  tL L  tHL ðHðÞ  LÞ dD (26) N V eðzH ; zS ; N; NumTripsÞ  tNV NV ; D ; L; N; NV ; zq ; zs where the constraints in (4) are once again imposed. It is a simple exercise in algebraic substitution to demonstrate that each of the implicit tax conditions in (25) is satisfied as long as the fees are set as follows:

tL ¼ lSS tHL ¼ lSS f tNV ¼ MBðN V NDMAX ; HðX SS ; zH ; NÞ; L; SðzS ; NÞÞðNDMAX Þ  eðzH ; zS ; N; DMAX Þ.

(27)

Note that the Q+3 implicit taxes on inputs, angler density, landings and angler-days can be replaced with two instruments on the levels of discards and landings that account for their impacts on fishing mortality.19 By targeting discard mortality (i.e., harvest), a single properly calibrated instrument induces the optimal configuration of inputs while the intensive margin of fishing mortality is controlled by the landings tax. With catch quality properly set and the full cost of landings mortality assessed, the trip-making decisions of anglers are optimal as well. 5. Some practical considerations 5.1. Input-based versus output-based policies In the previous section, we showed that efficiency can be achieved by adopting an extensive ‘‘price-based’’ incentive system that taxes or subsidizes all relevant inputs in order to convey the correct signals to decision makers (both anglers and vessel owners) about their impacts on fishing mortality.20 We also showed how an equivalent outcome can be reached with a parsimonious policy that directly alters the price of the two principle determinants of fishing mortality, namely discards and landings. This mirrors a common finding in the environmental economics literature—that pollution can be 19 These instruments would not ensure an efficient outcome in the event that recreational species are also valued for non-consumptive reasons. In this case the theoretical solution is to augment the implicit or explicit taxes to reflect the marginal user cost arising exclusively from non-use values. In an ITQ setting this will likely require setting the quota level at a higher stock than otherwise if non-use values are monotonic in stock size. Marine protected areas may also be useful if there is societal preference for the preservation of ‘‘natural’’ areas from fishing effort. 20 The implication of (25) is not that all the listed taxes/subsidies be explicitly levied. Doing so would result in redundant ‘‘double taxation’’ in one case. Specifically, given a tax on landings and all of the inputs of the harvest function, a separate tax on fishing days is not needed. Nonetheless, Q+3 other inputs do require directed treatment.

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efficiently controlled by altering the prices of all inputs according to their marginal contribution to pollution, or by targeting pollution itself. If the harvest production function is fairly transparent, with relatively few inputs and little substitutability, then input taxes are feasible options. In general, however, it is likely that harvest production functions are complex, with multiple substitutable inputs. In these cases (as in the pollution literature) there appears to be a prima facie case for direct, mortality-based instruments given their relative simplicity and potentially lower transactions costs. However, as we discuss below, measuring this mortality is not necessarily straightforward, particularly in the case of partial survivability of discards. The conclusions concerning first- and second-best policies are therefore highly contingent upon characteristics of biology, technology, and angler behavior. 5.2. Controlling fishing-induced mortality One of our more important findings is that optimal policies hinge on the nature and magnitude of fishing-induced mortality. Mortality, in turn, depends upon the biological characteristics of the target species, aspects of the chosen gear, and angler preferences for catch and release fishing. Fisheries in which anglers prefer to land everything that they catch generate no differences between harvest and landings and hence may be managed with a dockside landings instrument. Likewise, fisheries with either very high or low survivability rates of discards may operate effectively under a single fishing mortality instrument despite catch and release behavior. For example, if discard mortality is zero, all fishing mortality can be accounted for at the dock. In contrast, if all discarded fish die, optimal policy requires monitoring and taxing all fish harvested, whether fish are landed or not. Cases with partial survivability are more complicated, requiring differentiated instruments that account for differential mortality. 5.3. Quantity-based instruments: ITQs in charter recreational fisheries So far we have limited our discussion to the case of taxes or price-based instruments despite the well-known duality between price- and quantity-based policies. There is a strong preference for individual transferable quotas over taxes in commercial fisheries policy design, and so it is likely that rationalization of commercial recreational fisheries in the future will follow a similar path.21 Designing a quota system that controls fishing-induced mortality creates potentially substantial challenges of monitoring and enforcement. At the extremes, monitoring may be straightforward. For example, if anglers land their entire catch or the mortality of discards is zero, monitoring and limiting landings at the dock, via either fish ticket systems, or combinations of logbooks and spot monitoring, suffices. A properly implemented ITQ system would first determine the total fishing mortality that is sustainable and then allocate tradable landings permits to maintain total mortality at that level. At the other extreme, if anglers release all fish caught, then the ITQ must target the mortality of these discards. A well-designed ITQ system for a pure catch and release fishery would determine sustainable mortality associated with the catch and allocate permits to catch in amounts that held mortality to the desired level. Monitoring catch is more difficult than monitoring landings since it must be done at sea, either through logbooks, spot monitoring, electronic surveillance, or onboard observers. Real-world cases are likely to reside between these extremes with both discards at sea and landings on the dock and with discards suffering substantial but partial mortality. An efficient quota system must monitor and limit the mortality associated with both discards and landings. There are multiple ways to design such a system. One is to determine the optimal amounts of both discards and landings and allocate separate permits in the corresponding amounts where the allocation for discards may exceed the goals for discard mortality due to partial survival of discards. Anglers (or vessel owners) would have to surrender discard quota for each fish caught and released, as well as landings quota for each fish landed on the dock. Such a policy places a substantial burden on regulators who, contingent on a total sustainable mortality level, must sufficiently ascertain angler preferences to optimally allocate this quota between discard and landings quotas. A second and perhaps more attractive option is a design that allocates quota to total mortality (i.e. ‘‘landings equivalents’’) and then requires discards to be covered by surrendering landings quota at a discount determined by the survival rate of discards. Thus, if discard mortality is 50%, a unit of catch and release fishing requires the surrender of a half unit of landings quota. This ‘‘mortality quota’’ design avoids the inherent difficulties in ex ante allocation of mortality between landings and discards, allowing the market to determine the relative amounts of total mortality allocated to either discards or landings. As our modeling demonstrates, an important characteristic of recreational fisheries is that the respective quantities of landings and discards are endogenous and hence influenced by policy design features that affect angler and vessel owner incentives. Consider, for example, a fishery in which there are no discards under existing management. It might be initially tempting to assume that discards can be ignored, and to proceed with a strictly landings-based quota system, but once anglers (or vessel owners) must pay for landings quota, they may be induced to discard and highgrade under the new quota 21 Our analysis of ITQ rationalization is necessarily brief. We consider this and other policy implementation issues in much greater detail in a related paper [1].

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system. Alternatively, an unregulated fishery with discards will likely see an increase in the discard rate with a mortality quota system since the cost of landing a caught fish always exceeds the cost of discarding it in such a system. Discarding and high-grading are partially behavioral, and hence subject to change under the new incentives generated by adoption of a recreational ITQ system. This means that the design of appropriate quota programs must anticipate and forecast potentially complicated interrelationships between biological, technological and behavioral factors in order to avoid unanticipated outcomes. 5.4. Perverse incentives under ITQs: data fouling and endogenous mortality A particularly vulnerable aspect of most ITQ systems with quotas on either total catch or discards (not merely recreational ITQs) is the incentive for anglers/vessels to either underreport their actual discards in a system where selfreported statistics are used for quota management purposes or to try to escape detection of discarding behavior when third-party enforcement measures are utilized—in either case estimates of discards are biased downward, jeopardizing the sustainable management of the fishery. The heart of the problem is that the very instrument that provides the proper incentive for anglers and vessel owners to internalize the stock externality in their choice of trips and input choices (the discard tax/quota) also provides a strong incentive for moral hazard so that the quantity of actual discards in the system exceeds the level that would be suggested by the discard quota price. Since species with high discard mortality rates will, ceteris paribus, command a higher quota price, the very species for which tight monitoring of discards is most necessary will also be the most prone to data fouling. Measures derived from commercial fisheries all have their strengths and weaknesses. Mandatory onboard observers would be quite costly and perhaps feasible for only the largest of headboats. Random audits and substantial penalties (e.g. license forfeiture) can foster truthful revelation but the standard of evidence necessary for such stiff penalties may be prohibitively high. Indeed, both theory and commercial fisheries experience suggests that the first-best will be elusive in fisheries with significant discard mortality rates; hybrid policies that balance the benefits of truthful revelation of discards against the distortions in the extensive and intensive margins of fishing mortality (while being mindful of transaction costs) may ultimately be necessary. While we have treated the mortality rate of discards as exogenous, this may not always be the case. Rather, mortality may be the result of vessel and angler-specific inputs such as the type of hooks used or whether the angler quickly discards a fish or retains his entire catch prior to discarding in order to highgrade. The first-best solution would require that vessel owners/anglers bear the full cost of their mortality-influencing decisions—requiring a scenario-specific trading ratio between landings and discard quota. A more plausible solution would be to set this trading ratio for particular vessels according to their voluntary adoption of verifiable technologies and procedures to minimize estimated discard mortality. Vessels would be certified into one of a discrete set of trading ratios and would be rewarded with ‘‘cleaner’’ certifications to the extent that they upgrade their mortality reducing practices. While definitely second-best, such a system has a number of positive aspects. First, regardless of whether anglers or vessel owners directly pay for discards, the system fosters efficient mortality-influencing choices on the part of the vessel owner (within the limits of the discrete classifications).22 Second, it is possible that the monitoring and enforcement costs of such a system would be relatively low. Third, the certification system can foster incentives for the development of new mortality reducing technologies that achieve better certifications. Finally, as a voluntary system, vessel owners can opt out of a higher certification level if it is not cost effective or if it imposes constraints on anglers that some anglers are willing to pay in excess of the differential mortality surcharge to avoid—ameliorating some of the welfare-stunting bluntness of technological mandates. 5.5. Who should hold quota in a recreational ITQ fishery? Should anglers or vessel owners be granted ITQs in a commercial recreational fishery managed by quotas? In a model of perfect competition, complete and symmetric information and zero monitoring costs, it does not matter for efficiency. If anglers hold quota and trade it among themselves, it will flow to anglers who value it the most. Those anglers will then contract for fishing trip services, inducing providers to supply trips with the desired characteristics at least cost. Anglers will bear the full costs of each trip, including service costs and the full cost of fishing mortality for both discards and landings. As a result, trip demand will not be excessive, and there will be no race to fish or distorted catch-augmenting input use. On the other hand, if vessel owners hold quota, they will pass the full price of quota to anglers in the form of a bundled price that includes costs of services provided and user costs of quota utilized. We thus should expect the market to generate a two-part pricing scheme where anglers pay the same ‘‘base’’ price for a trip with particular characteristics but different total prices depending upon how many fish each angler lands and discards. These prices, in turn, ensure that discard and landings mortality flow to those who value it the most and that both anglers and vessel owners employ the proper configuration of inputs.23 22 Since the certification and trading ratio is established at the vessel level, incentives for individual anglers will not be directly targeted by this system. However, the threat of losing their certification will encourage vessel operators to monitor anglers to the extent that constraints on angler behavior (e.g. restrictions on high-grading) are conditions of their certification. 23 It should be recalled from our conceptual modeling that, without another instrument limiting entry, there will be an excessive number of vessels in the fishery.

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In a less ideal world with significant transaction costs, it might be more efficient to allocate quota to the industry. The cost of establishing trading infrastructure among a limited number of vessel owners (who then potentially act as brokers of quota to passengers) is likely far lower than for a diffuse population of anglers. The long-run value of industry-held quota might induce collective investments in research, enhancement and enforcement activities that would not otherwise be encouraged if anglers held property rights. The case for vessel ownership of quota is not entirely clear, however. Limited numbers of vessels for some species/areas could raise concerns of market power. Also, high monitoring and enforcement costs may preclude the development of ‘‘pass through’’ quota markets to anglers. Instead vessels may charge a single price that capitalizes the surrendered discard and landings quota for the average angler. As a result, anglers would no longer bear the marginal cost of their mortality-influencing decisions aboard the vessel. Suffice it so say that this issue deserves more discussion and attention in future analyses of quota-based rationalization of recreational fisheries.

6. Conclusion The adoption of market-based rationalization programs in commercial fisheries has been met by a great deal of success. Rights-based systems such as ITQs give fishermen a stake in the health of the fishery, often reducing the adversarial nature of fisheries regulation and management and generating stewardship incentives among participants. A natural question is whether similar results could follow in the recreational context. In the absence of empirical experience, the alternative we pursue is to develop a conceptual structure with which to forecast the potential sources of rent dissipation in for-hire recreational fisheries and to gauge the likely consequences of various rationalization strategies. An important innovation in our approach is the detailed integration of the input decisions of the for-hire recreational sector within a traditional bioeconomic framework—an approach that is also unique in the commercial fisheries literature which is dominated by ‘‘single-index’’ models of decision making. Previous analyses of recreational fishing have focused on angler decision making without giving heed to the role of the suppliers of recreational trips, yet understanding this supply behavior is essential to discovering how welfare is dissipated and how various rationalization strategies influence incentives and the generation of social surplus. Importantly, we find that open access rent dissipation in the for-hire recreational sector operates in a manner subtly different from that in the commercial sector. In commercial fisheries, there is a direct link between harvest and revenue that drives each vessel owner to increase fishing capacity in the drive to increase their share of the aggregate catch. In the recreational sector, vessel owners instead produce a multidimensional recreational service for which harvest and landings are important yet partial drivers of recreational trip demand. Vessel owners do not simply purchase more catch-producing inputs as in the commercial sector; instead, they offer trips with various characteristics and prices, competing for anglers in the market who select among recreational providers according to utility maximization. It is the subtle interaction of angler preferences with open access competition among suppliers that leads to our predictions of rent dissipation, distorted inputs and excessive harvest and landings.24 Efficient rationalization requires that the full mortality from discards and landings be incorporated within the institutional design. When the proportion of discard mortality lies between zero and one, it is necessary to induce both anglers and vessel owners in the for-hire sector to correctly account for their respective roles in influencing total fishing mortality. An important result is that if both forms of mortality are appropriately priced, this induces efficient choices of all other fishing inputs, except the size of the fleet. A corollary is that with discard mortality, an efficient ITQ program must have transferable quota for both discards and landings. This problematic situation poses monitoring, measurement and enforcement difficulties that are yet to be solved in many long-standing commercial fisheries with significant discard mortality. Although we focus our attention on theoretically optimal policies in this paper, our framework is nevertheless useful in addressing the strengths and shortcomings of more limited second-best rationalization policies. For example, in lieu of the three-part tax (or quota) we have prescribed above, regulators could instead fix total angler-days and allow vessel owners to purchase the rights to service these angler-days in a quota market.25 Such an approach is easily monitored and enforced and is justified by the first condition in (25) that shows how a properly set quota is capable of providing efficient incentives for the total number of angler-days. However, if applied without regard to the discards or landings associated with individual trips, this policy will induce slippage in per-angler landings, catch-augmenting and (possibly) qualityaugmenting inputs, anglers per vessel and the equilibrium fleet size. Alternatively, many recreational fisheries are managed by ‘‘bag limits’’ which limit the number of fish an angler can retain on a trip. This policy is sensible when the mortality of discards is negligible and (with homogeneous landings preferences) may yield efficient incentives for discarding and the input decisions of vessel owners. However, when discard mortality is substantial, a bag limit is a poor instrument in that it targets a margin of behavior with little marginal effect on fishing mortality while providing only indirect and blunt influence on aspects of behavior that are more important to 24 Our approach has applicability in any recreational setting where use has a dynamic impact, access to the resource is gained through a commercial service provider and where property rights are imperfect (e.g. commercial providers of guided hunting, safaris, scuba diving, river rafting, and guided access to unique and pristine ecosystems). 25 A similar scheme has been in place in the New England commercial groundfish fisheries for several years to control fishing mortality.

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mortality (i.e. anglers’ choice of whether to fish and vessel owners’ investment behavior). The message of our modeling is that there are potentially many avenues for rent dissipation in recreational fisheries. Polices aimed at subsets of these margins generate perverse incentives with respect to unconstrained inputs, a lesson that has been repeatedly borne out (if not always heeded) for commercial fisheries as well.26 These observations only scratch the surface of the numerous issues involved in contemplating the rationalization of recreational sectors. The difficulties involved in managing ‘‘pure’’ recreational fisheries where a diffuse population of anglers pursues a range of species from numerous ports using mostly private inputs are well known, if not tractably solved [16,28]. Our finding of subtle yet important distinctions between the models of a generic mixed commercial/recreational fishery and their commercial counterparts suggests that economists need to devote greater attention to empirical research in recreational fisheries—not only in the estimation of recreational demand but in understanding the supply decisions of recreational service providers. This knowledge will be critical in the coming years as recreational fisheries increasingly become the ‘‘next frontier’’ for rights-based fisheries management.

Acknowledgments We thank Chris Costello, Vishwanie Maharaj, Kerry Smith, two anonymous referees, and participants in seminars at the IIFET 2008 Conference and the AAEA Annual Meetings for their helpful comments. We acknowledge funding from Environmental Defense. References [1] J.K. Abbott, J.E. Wilen, V. Maharaj, Designing ITQ programs for commercial recreational fishing, Marine Pol. 33 (2009) 766–774. [2] L.G. Anderson, The demand curve for recreational fishing with an application to stock enhancement activities, Land Econ. 59 (1983) 279–286. [3] L.G. Anderson, Toward a complete economic-theory of the utilization and management of recreational fisheries, J. Environ. Econ. Manage. 24 (1993) 272–295. [4] R. Arlinghaus, On the apparently striking disconnect between motivation and satisfaction in recreational fishing: the case of catch orientation of German anglers, N. Amer. J. Fish. Manage. 26 (2006) 592–605. [5] R. Arnason, On catch discarding in fisheries, Marine Res. Econ. 9 (1994) 189–207. [6] R.C. Bishop, K.C. Samples, Sport and commercial fishing conflicts—A theoretical-analysis, J. Environ. Econ. Manage. 7 (1980) 220–233. [7] M.R. Caputo, Foundations of Dynamic Economic Analysis: Optimal Control Theory and Applications, Cambridge University Press, New York, 2005. [8] C.W. Clark, F.H. Clarke, G.R. Munro, Optimal exploitation of renewable resource stocks—problems of irreversible investment, Econometrica 47 (1979) 25–47. [9] F.C. Coleman, W.F. Figueira, J.S. Ueland, L.B. Crowder, The impact of United States recreational fisheries on marine fish populations, Science 305 (2004) 1958–1960. [10] R.B. Ditton, D.A. Gill, C.L. MacGregor, Understanding the market for charter and headboat fishing, Marine Fish. Rev. 53 (1991) 19–26. [11] A.J. Fedler, R.B. Ditton, A framework for understanding the consumptive orientation of recreational fishermen, Environ. Manage. 10 (1986) 221–227. [12] J.R. Gould, Adjustment costs in the theory of investment of the firm, Rev. Econ. Stud. 35 (1968) 47–55. [13] S.M. Holland, A.J. Fedler, J.W. Milon, The operations and economics of the charter and headboat fleets of the Eastern Gulf of Mexico and South Atlantic Coasts, Technical Report for U.S. Department of Commerce: National Marine Fisheries Service, 1999, p. 337. [14] F. Homans, J. Ruliffson, The effects of minimum size limits on recreational fishing, Marine Res. Econ. 14 (1997) 1–14. [15] D.S. Huang, C.W. Lee, Toward a general model of fishery production, Southern Econ. J. 43 (1976) 846–854. [16] R.J. Johnston, D.S. Holland, V. Maharaj, T.W. Campson, Fish harvest tags: an alternative management approach for recreational fisheries in the U.S. Gulf of Mexico, Marine Pol. 31 (2007) 505–516. [17] U. Kohli, Non-joint technologies, Rev. Econ. Stud. 50 (1983) 209–219. [18] L.J. Lau, P. Yotopoul, Profit, supply, and factor demand functions, Amer. J. Agr. Econ. 54 (1972) 11–18. [19] J.R. Livernois, D.L. Ryan, Testing for non-jointness in oil and gas exploration—a variable profit function-approach, Int. Econ. Rev. 30 (1989) 479–504. [20] D.M. Massey, S.C. Newbold, B. Gentner, Valuing water quality changes using a bioeconomic model of a coastal recreational fishery, J. Environ. Econ. Manage. 52 (2006) 482–500. [21] K.E. McConnell, J.G. Sutinen, Bioeconomic models of marine recreational fishing, J. Environ. Econ. Manage. 6 (1979) 127–139. [22] NMFS, Personal Communication, Fisheries Statistics Division, 2008. [23] D.J. Phaneuf, V.K. Smith, Recreation demand models, in: K.G. Maler, J.R. Vincent, (Eds.), Handbook of Environmental Economics, Elsevier, Amsterdam, 2005, pp. 671–761. [24] E.S. Pritchard, Fisheries of the United States 2006, National Marine Fisheries Service, Silver Spring, 2006. [25] S. Rosen, Hedonic prices and implicit markets—product differentiation in pure competition, J. Polit. Economy 82 (1974) 34–55. [26] C.R. Shumway, R.D. Pope, E.K. Nash, Allocatable fixed inputs and jointness in agricultural production—implications for economic modeling, Amer. J. Agr. Econ. 66 (1984) 72–78. [27] D. Squires, Fishing effort-its testing, specification, and internal structure in fisheries economics and management, J. Environ. Econ. Manage. 14 (1987) 268–282. [28] J.G. Sutinen, R.J. Johnston, Angling management organizations: integrating the recreational sector into fishery management, Marine Pol. 27 (2003) 471–487.

26 We acknowledge that the partial equilibrium perspective of our analysis is potentially misleading when populations are harvested by both commercial and sports fishing anglers. Rationalizing only the commercial fishery component of a mixed fishery creates conflicts as value is created, raising the opportunity costs of recreational allocations. In principle, such concerns could be dealt with through an ITQ system that allowed trading across sectors. Similarly, rationalizing only the recreational component of a mixed fishery could amplify existing conflicts with commercial fisheries and create new conflicts with other recreational fisheries as anglers facing higher prices opt to intensify effort in unregulated fisheries.

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