Reconciling economic and biological modeling of migratory fish stocks: Optimal management of the Atlantic salmon fishery in the Baltic Sea

The paper puts forward a model of the Atlantic salmon fishery in the Baltic Sea that integrates the salient biological and economic characteristics of migratory fish stocks. Designed to be compatible with the framework used for actual stock assessments, the model accounts for age-structured population dynamics, the seasonal harvest and competing harvesting by commercial and recreational fishermen. It is parameterized for the Simojoki River stock. The socially optimal policy for maximizing discounted net benefits from the fishery within an uncertain environment is determined using a dynamic programming approach and numerical solution method. Our results indicate that substantial economic benefits could be realized under optimal management without compromising stock sustainability.     

Parameter Uncertainty in CGE Modeling of the Environmental Impacts of Economic Policies

Political and economic factors usually determine the harvest sharesallotted to heterogeneous fisher groups harvesting upon the same fishstock. Given that the fishers harvest upon different segments of a fishstock with, for instance, cannibalistic tendencies, the shares allottedmay have considerable effect upon the well-being of the stock and theeconomics of the fishery. This paper analyses an existing allocationrule defining harvest shares allotted to two vessel groups (trawlers andcoastal vessels) in the Norwegian cod fishery. We apply a model with twointeracting age groups within a single fish stock, where the interactionhas both biological and economic implications. Requiring a first bestapproach to an optimal stock size results in no harvest in the firstyears studied. In order to ensure harvest amounts close to the historicharvest, we design a second best model giving optimal biological sharesin the build-up phase of the stock, and bioeconomic optimal shares atthe optimum fish stock level. The second best model recommends that foran increasing stock size the trawlers should obtain decreasing shares.We find that the actual allocation rule functions in a manner oppositeto the second best model, since this rule allocates an increasing shareto the trawlers for an increasing stock size.     

Cannibalism and the Optimal Sharing of the North-East Atlantic Cod Stock: a Bioeconomic Model

This paper shows how intra-stock relations such as cannibalism and growth enhancement, determine the economically optimal sharing of a fish resource between heterogeneous harvesting agents. The sharing of resources between different vessel groups is often left for political decision making. Nonetheless, such decisions may have both biological and economic consequences. This becomes quite clear when different harvesting groups exploit different sections (age groups) of a stock that has intra-stock interactions in the form of cannibalism. A two-agent bioeconomic model with cannibalism is developed and used to determine (i) optimal annual harvest sizes (TACs) for cod, and (ii) the optimal proportion of the TAC that should be harvested by the different vessel groups in the fishery. Applying biological and economic data in a numerical procedure, and comparing the results obtained to previous studies, it is shown that intra-stock interactions such as the presence of cannibalism has a significant impact on who should take what proportion of the TAC, and hence, the standing stock size and discounted economic rent achievable. In contrast to other studies, we find that the optimal harvest requires that both trawlers and coastal vessels should harvest the fish resource. In addition, the results indicate that, from a bioeconomic perspective, the existing trawler fleet’s harvest share in the cod fishery is too high. This revised version was published online in August 2006 with corrections to the Cover Date.     

Increasing returns and cycles in fishing

We consider optimal fishery management under the assumption of increasing returns that is supported by previous empirical evidence. We improve the tractability and realism of the previous approaches by introducing flow adjustment costs on changes in harvest rate. Our framework is the first to provide a link between stable limit cycle policies and increasing returns in harvesting. The type of the harvest policy depends on flow adjustment costs: for relatively costly adjustments the usual steady state harvest policy is conceivable, whereas for relatively cheap adjustments the harvest policy is cyclical. We also show a connection between chattering control policies and limit cycles, which helps us to develop a clear economic meaning for cyclical harvesting.     

Optimal fishery harvesting rules under uncertainty

This paper derives the optimal fishery harvest policy in a real-option model with a stochastic logistic growth process, harvest-sensitive output price, and both fixed and variable harvesting costs. The policy specifies the harvest trigger and harvest size, while outputs from the model include the value of the fishery and the risk of extinction. The optimal policy is illustrated with data from the Pacific Halibut Fishery. For this particular case, the optimal policy recommends harvesting when the fish stock rises to about three-quarters the environmental carrying capacity, and the amount harvested should be approximately a quarter of the prevailing stock. This harvesting policy maximizes the value of the fishery, and importantly, the resulting risk of extinction is negligible. We also carry out some sensitivity analysis to see how the optimal policy (and the resulting fishery value and risk of extinction) change when the input parameters are varied, particularly the ecological parameters intrinsic growth rate and volatility of the stock, and also the economic parameters that have been ignored in previous papers (price sensitivity and fixed cost). If the optimal policy is followed, the risk of extinction will be negligible, except for very low growth rate and high volatility.     

Boundary conditions for the sustainable use of major fish stocks in the Baltic Sea

The history of the management of Baltic fishery resources suggests that both biological and non-biological factors influence management decisions and that both types of information are essential for management which promotes sustainability. There is a direct link between the exploitation level and the risks for fishing as an economic activity due to fluctuations in the resource. This paper analyses the sustainability of the present catch levels of major Baltic fish stocks. By examining the rate of fishing mortality and recruitment variability, the possibility of sustaining present catch levels can be investigated. Current catch levels of Baltic cod and some salmon stocks are not sustainable whereas sprat and herring catches are. High rates of fishing mortality of cod and salmon may endanger stocks if a drop in the recruitment causes an increase of the fishing mortality rates in order to sustain short-term catches. By analysing the trade off between exploitation level and risk of stock decline, managers can obtain a basis for quota negotiations.     

Measuring potential profits in a bioeconomic model of the mixed demersal fishery in the North Sea

This paper measures for potential profit in the North Sea mixed demersal fishery for cod, haddock and whiting. Dynamic bioeconomic models for three UK fisheries are developed, incorporating both population dynamics and economic structure. Actual profit in 2006, for the three UK fleets included in the analysis, is estimated at ??10.3?million. If the TAC remains unchanged but vessels are allowed to harvest at near efficient levels with fleet size reduced accordingly, potential profit is measured at ??34.5?million. If demersal stocks are allowed to recover to near optimal levels potential UK profit exceeds ??185?million. This indicates substantial profit dissipation due to overcapacity and stock depletion in the fishery. The results of the paper should be of policy interest and will add to the empirical literature on resource profits in mixed demersal fisheries.     

Optimal Management Under Institutional Constraints: Determining a Total Allowable Catch for Different Fleet Segments in the Northeast Arctic Cod Fishery

Many real world fisheries have an individual vessel quota system with restrictions on transferability of quota or entrance of new vessels into the fishery. While the standard economic reasoning is that these institutional constraints lead to welfare losses, the size of those losses and optimal second-best policies are usually unknown. We develop a dynamic bioeconomic model, in which a scientific body provides an optimal TAC given restrictions on (i) transferability between vessel segments and (ii) entrance of new vessels. Further, we also quantify welfare losses arising from not maximizing economic welfare, but physical yield—which is actually the case in many fisheries. We apply the model to the Northeast Arctic cod fishery, and estimate not only the cost and harvesting functions of the various vessel types, but also the parameters of the biological model as well as those of the demand function. This allows us to determine optimal second-best policies and quantify corresponding welfare effects for our case study fishery.     

Does the Optimal Size of a Fish Stock Increase with Environmental Uncertainties?

We analyze the effect of environmental uncertainties on optimal fishery management in a bio-economic fishery model. Unlike most of the literature on resource economics, but in line with ecological models, we allow the different biological processes of survival and recruitment to be affected differently by environmental uncertainties. We show that the overall effect of uncertainty on the optimal size of a fish stock is ambiguous, depending on the prudence of the value function. For the case of a risk-neutral fishery manager, the overall effect depends on the relative magnitude of two opposing effects, the ‘convex-cost effect’ and the ‘gambling effect’. We apply the analysis to the Baltic cod and the North Sea herring fisheries, concluding that for risk neutral agents the net effect of environmental uncertainties on the optimal size of these fish stocks is negative, albeit small in absolute value. Under risk aversion, the effect on optimal stock size is positive for sufficiently high coefficients of constant relative risk aversion.     

Economies of scale and the optimality of rotational dynamics in forestry

Forest harvesting is traditionally analyzed in terms of the Faustmann rotation model. This paper considers the identification of optimal forest harvest regimes using jump controls. This approach enables the structural assumptions of clear-cut technology and identical cycles in perpetuity which are imposed in a Faustmann model to be relaxed. Jump control models permit investigation of the biological and economic conditions which favour continuous growth management regimes as opposed to clear-cut harvest regimes. A numerical solution approach to the jump control model is presented. The link between the harvest cost function and the optimal biomass path is analyzed. Economies of scale are shown to generate rotational harvest as optimal policies.      

Shared renewable resources and gains from trade under technology standards

Using a two‐country, two‐good model of international trade, we examine gains from trade and strategic interaction in resource management among countries that share renewable resources such as fishery stocks. Two goods are a resource good, which is the harvest of the shared stock, and some other good that may be thought of as manufactures. The productivity of the resource good depends on harvesting technology and the stock level. This paper focuses on technology standards (e.g., restrictions on fishing gears, vessels, areas, and time) over other methods for resource management because they are most commonly implemented in fisheries. Technology standards are modeled as a restriction on the harvesting technology; that is, under strict technology standards, firms exploit resources as if they are using inferior harvesting technology. We show that an opening up of trade may reduce the shared stock and cause steady‐state utility to decrease in a resource‐good importing country and increase in a resource‐good exporting country. Strikingly, when the shared stock is in jeopardy (a high demand for the harvest), steady‐state harvest is maximized after an opening up of trade by what we call multilateral resource management in this paper and both countries gain from trade.     

Predators in the market: implications of market interaction on optimal resource management

A two-species bioeconomic model is analyzed, but in contrast to most similar models, there is no biological interaction between the species, only economic. The interaction takes place in the market where the quantity of either species may affect the price of the other. The effects of cross-price elasticities on the optimal steady state and on the optimal paths in the sole-owner case are investigated both analytically (steady states) and numerically (optimal paths). First, it is shown that if the harvest of one species has impact on the price of another species, then this has a positive effect on its steady-state stock. The effect increases with the stock-elasticity in the cost function. Further, in the case of linear demand functions, the steady state outcome depends solely on the sum of the cross-price parameters and not their individual values. Secondly, in the investigation of optimal paths, it is shown that if the harvest of one species has impact on the price of the other, optimal trajectories reach steady state faster for itself and slower for the other species. Further, when cross-price elasticities are sufficiently high, the paths go from being monotonic to feature over- or undershooting.     

Portfolio Fishing

The optimal fishing pattern in a multi-cohort fishery is determined using risk theory.Portfolio theory becomes applicable by treating different age groups of fish as different assets. A possibility set is derived using data on Icelandic cod fisheries. In the presence of risk aversion, it is shown that the abrupt behavior found in deterministic models is changed towards a smoother fishing pattern. The historical selection pattern for the Icelandic cod stock is shown to be near optimal using a maximal effort-type cost function, but historical levels of effort are inefficient and lead to less profit and greater fluctuations than implied by profit or utility maximization.     

Non-consumptive values and optimal marine reserve switching

A bioeconomic model is constructed to analyze spatial harvesting and the effects of marine reserve “switching” between a “no-take” area and a harvested area while accounting for both harvesting/consumptive and also non-consumptive values of the fishery. Using estimated parameters from the red throat emperor fishery from the Great Barrier Reef, simulations show that an optimal switching strategy can be preferred to a fixed reserve regime, but is dependent on spillovers from reserves to harvested areas, the nature of shocks to the environment, the size of the non-consumptive values and how they change with the biomass, and the sensitivity of profits to the harvest and biomass. Importantly, the results show that how non-consumptive values change with the size of the fishery substantially affects both the returns from switching and the optimal closure time.     

Optimal control of a multi-cohort fishery

Models of optimal renewable resource exploitation typically assume an equation for total population growth over time irrespective of the age distribution of the stock. By means of the theory of parametric optimal control, this paper outlines a model of a fishery with population varying in both age and time. Instead of an optimal steady-state harvest we derive an optimal harvest age distribution with lower utilization of younger members of the population.     

Variable unit costs in an output-regulated industry: The Fishery

Departing from general cost theory of the firm and bioeconomic theory of the fishery, this study contributes with an empirical examination of how variable unit costs in a Norwegian demersal and pelagic fishery depend on output and the fish stock. The identification of the separate effects that the two factors have on costs is not common in the literature. Three Norwegian fleets fishing Norwegian spring spawning herring (Clupea Harengus) and five Norwegian fleets fishing Northeast Arctic cod (Gadus Morhua) are evaluated. The findings indicate that variable unit costs fall in output in both fisheries. The results also show that variable unit costs fall in fish stock in the demersal fishery, but with a stock elasticity of variable unit costs in absolute terms significantly less than 1. These results are of relevance to a manager seeking the optimal harvest rule and to understand fishermen's incentives when individual vessel quotas are reduced.     

Spare the Young Fish: Optimal Harvesting Policies for North-East Arctic Cod

The North-East Arctic cod (Gadus morhua) fishery, as most other commercial fisheries, is wasting the larger part of its potential. Examining a detailed multi-cohort, multi-gear bioeconomic model, we show that the cause is rather a too small mesh size than excessive effort. Although internationally and nationally managed by quota allocations and regulations, the current exploitation pattern implies that essentially the wrong fish are targeted. Catching older and heavier fish could double the fishery’s Net-Present-Value. This increases harvested biomass while it reduces the number of fish removed from the ocean, highlighting the importance of age- and gear-specific modeling. Moreover, optimal harvesting policies would also lead to a much more robust and abundant cod stock.     

Cooperative and non-cooperative management of the Northeast Atlantic cod fishery

The fishery for Northeast Atlantic cod (Gadus morhua) in the Barents Sea is one of the most valuable fisheries in the North Atlantic. After the introduction of Extended Fisheries Jurisdiction, cod is a shared stock between Norway and Russia. Overfishing of quotas has been a concern for a number of years. The purpose of this article is to analyse cooperative and non-cooperative management of the Northeast Atlantic cod fishery. This will be done in a game theoretic context, based on different assumptions regarding important variables such as cost of effort and initial stock size. The game theoretic analysis will be based on an empirical bioeconomic model developed and estimated by Hannesson (Mar Policy 31:698–705, 2007; J Bioecon forthcoming). The case of cooperative management is analysed for different cost parameters and starting values of the stock. An interesting result is that the optimal policy gives rise to pulse fishing. As this involves effort (and harvests) varying from year to year, potentially imposing substantial social costs on the industry in years when the fishery is closed, a policy of constant effort is also considered. Finally, non-cooperative management is analysed.     

An Enforcement-Coalition Model: Fishermen and Authorities Forming Coalitions

The paper sets up a four-stage enforcement model of fish quotas. The purpose of the paper is to show how the level of enforcement set by the authorities affects the way fishermen form coalitions. We show that a high level of control effort yields less co-operation among fishermen, while in the case of low control effort, coalitions are somewhat self-enforcing. The paper further discusses how the optimal enforcement level changes when the coalition formation among authorities changes: centralised, partly centralised and decentralised authorities. We show that decentralised authorities set a lower level of control effort compared to the centralised authorities. The theoretical results are illustrated by simulations of the Baltic Sea cod fishery.The authors acknowledge valuable comments and suggestions from Frank Jensen and Niels Vestergaard.