• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.527-543
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• 2024

In the realm of differential games and bioeconomic modeling, where intricate systems and multifaceted interactions abound, we explore the precision and efficiency of the Chebyshev Tau method (CTM). We begin with the Weierstrass Approximation Theorem, employing Chebyshev polynomials to pave the way for solving intricate bioeconomic differential games. Our case study revolves around a three-player bioeconomic differential game, unveiling a unique open-loop Nash equilibrium using Hamiltonians and the FilippovCesari existence theorem. We then transition to numerical implementation, employing CTM to resolve a Three-Point Boundary Value Problem (TPBVP) with varying degrees of approximation.

• Journal of Navigation and Port Research
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• v.36 no.9
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• pp.741-751
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• 2012

This article analyzes the interdependency between nonrenewable marine sand resources and renewable fishery resources by the developed dynamic bioeconomic model. The developed bioeconomic model is applied to a case study of efficient sustainable management for marine sand mining, which adversely affects a valuable blue crab fishery and its habitat in Korea. The socially-efficient extraction plan for marine sand and the time-variant environmental external costs to society in terms of diminished harvest rate of blue crab are determined. To take into account long-term effects from destroyed fishery habitat, a Beverton-Holt age structure model is integrated into the bioeconomic model. The illustrative results reveal that the efficient sand extraction plan is dynamically constrained by the stock size of the blue crab fishery over time. Thus, the dynamic environmental external cost is more realistic resource policy option than the classical fixed external cost for determining socially optimal extraction plans. Additionally, the economic value of bottom habitat, which supports the on- and off-site commercial blue crab fishery is estimated. The empirical results are interpreted with emphasis on guidelines for management policy for marine sand mining.

• Ocean and Polar Research
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• v.25 no.4
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• pp.483-491
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• 2003

Since the red grouper was declared overfished, the Gulf of Mexico Fishery Management Council must prepare a rebuilding plan considering the following alternative management policies: a Total Allowable Catch (TAC), 5-month season closure, 1800-pound trip limit, and a 50-fathom longline boundary. This study was aimed at evaluating the effects of proposed policies for rebuilding the red grouper stock in a 10-year period by developing a bioeconomic model. Under the assumption that the recreation sector was held to its share of TAC (24% of the total quota), the target stock biomass goal was attained in all policies. The NPV was the largest in the 5-month season closure policy if the output price did not fall. There were distributional effects on the different components of the fleets in the 1800-pound trip limit and the 50-fathom longline boundary policy.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.127-142
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• 1999

This paper develops a methematical model for growth and exploitation of a schooling fish species using a realistic catch-rate function and imposing a tax on the catch to control harvesting. Fishing effort is assumed to depend on the net revenue. The steady states of the system are determined and their local and global stabil-ity are discussed. Taking the tax as a control variable; the optimal harvest policy is formulated and solved as a control problem. The results are illustrated with the help of a numerical example.

• Journal of Fisheries and Marine Sciences Education
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• v.16 no.1
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• pp.84-98
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• 2004

Due to a publicly owned resources, the overexploitation of the fisheries resources can result in externalities in the form of reduced future levels of yield. These problems can be theoretically improved through effective management of the fishery. The paper illustrates maximum sustainable yield(MSY), maximum economic yield(MEY) and F0.1 level of fishing mortality as the concept of optimal yield, and it theoretically shows that MSY is more appropriate for the optimal yield than MEY where prices increase even though MEY achieves the maximization of economic rent in a fishery assuming constant prices. And the paper presents several fisheries management tools and policies such as input controls, output controls and taxes. As the traditional approach to fishery management, input controls involve restrictions on the physical inputs into the production process(e.g. capital, time or technology) and output controls involve limits on the quantity of fish that can be landed. To introduce user cost into the harvest decisions of rent-seeking fishers, taxation, as a bioeconomic management policy of the fisheries, directly addresses the problems associated with the resource being unpriced. As most fisheries management plans, however, have increasing fisher income as an objective, taxes have not been introduced into any fisheries management policies despite their theoretical attraction.

• The Journal of Fisheries Business Administration
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• v.46 no.1
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• pp.29-39
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• 2015

This study aimed to evaluate the TAC policy and to examine the effective annual TAC quota in the sandfish stock rebuilding plan using a bioeconomic modelling method. In the analysis, first, a sandfish bioeconomic model was developed by combining a sandfish stock population model and economic models by fishery and second, achieving stock rebuilding targets and changes of fishing revenues by the level of annual TAC quota were examined. Model results indicated that the TAC 1,500ton policy would have the greatest impact on the increase of sandfish stock biomass comparing to the status quo and other TAC policies. In addition, it was evaluated that the total fishing revenues of coastal gillnet and danish seine fisheries could be increased the most in the TAC 2,500ton policy. In both cases of TAC 3,500ton and 4,000ton, the fishing revenues of both fisheries were inversely reduced due to the decrease of catch by coastal gillnet and the decline of market prices by danish seine's excessive catch. Furthermore, they would have a negative impact on sandfish stock biomass.

• The Journal of Fisheries Business Administration
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• v.35 no.1
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• pp.1-22
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• 2004

Since the red grouper stock was initially declared to be overfished by the NMFS in September 2002, the Gulf of Mexico Fishery Management Council must prepare for the red grouper rebuilding plan considering the following alternative management policies: Total Allowable Catch(TAC), 5 - month season closure, 1800 - pound trip limit, and 50 - fathom longline boundary. The first concern the Council has is to evaluate the effects of recommended policies and the second is to analyze the impact of management policies on yellow edge grouper. This is because the fleets harvest red grouper also catch yellowedge grouper, the regulations on red grouper are likely to allow fishing effort to be distributed into yellowedge grouper. Therefore, this study is aimed at evaluating the biological and economic effects of management policies considering simultaneously the impact of red grouper regulations on yellow edge grouper by developing a combined red grouper and yellowedge grouper bioeconomic model. The overall results indicate that management policies for red grouper would adversely affect the yellowedge grouper stock if yellowedge grouper is not protected by its regulations. The TAC policy has the most serious impact on the yellowedge grouper stock, while the 1800 - pound trip limit policy minimizes the reduction in the yellowedge grouper stock. However, the target stock size of red grouper is achieved as well as the largest net present value of returns is gained in the TAC policy.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.219-231
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• 2003

This paper aims to study the problem of combined harvesting of a system involving one predator and two prey species fishery in which the predator feeds more intensively on the more abundant species. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equiblibrium case by using Pontryagin's Maximum principle. Dynamic optimization of the harvest policy is also discussed by taking E(t), the combined harvest effort, as a dynamic variable. Biological and bioeconomic interpretations of the results associated with the optimal equilibirum solution are explained. The significance of the constraints required for the existence of an optimal singular control are also given.

• Environmental and Resource Economics Review
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• v.12 no.4
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• pp.663-686
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• 2003

This study is aimed at analyzing the effectiveness of TAC policy using a bioeconomic model. A surplus-production model is used as a population dynamic model, from which the yellowedge grouper is estimated to be overfished. As a result, a 10-year rebuilding plan using the TAC policy is established. According to the result of model, under the well-enforced system, the target stock biomass is achieved during the rebuilding period. Especially, in order to accomplish the target stock biomass, the annual quota should be allocated much less than 342 tons that NMFS recommended. The NPV over a 25-year under the TAC policy Is predicted to be less than under the status quo. The economic gains under the variable-catch TAC policy is less than under the constant-catch TAC policy as the interest rate decreases, while the NPV under the constant-catch is greater than under the variable-catch TAC policy when the interest rate is high.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.57 no.2
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• pp.173-184
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• 2021

In this study, internationally widely utilized bioeconomic models were used to make a comparison and analyze the effectiveness of red snow crab fisheries management measures. As a specific effect analysis, biological and economic effects of both total allowable catch (TAC) and effort reduction management measures were analyzed simultaneously. Model results showed that the red snow crab biomass would be decreased from 106,000 tons to 73,076 tons after ten years when the TAC is set to and maintained at the current level of 26,000 tons. The amount of biomass would be increased to 125,316 tons when the level of TAC is set to 22,000 tons. In cases of reduced fishing efforts, a 30% decrease from the current level would result in greater biomass and NPV would be also estimated at the highest level. In addition, a sensitivity analysis by market price was conducted to analyze the minimum TAC level of the red snow crab offshore pot fishery. Results showed that the minimum TAC level would be 8,210 tons when the market price increased by 30% and it would be also 15,247 tons when the market price decreased by 30%. Furthermore, results of the sensitivity analysis by fishing cost showed that the minimum TAC level was analyzed to be 13,857 tons when the fishing cost increased by 30% from the current level.