Optimal strategies for a fishery model applied to utility functions

Carlos Camilo-Garay; R. Israel Ortega-Gutiérrez; Hugo Cruz-Suárez; Carlos Camilo-Garay; R. Israel Ortega-Gutiérrez; Hugo Cruz-Suárez

doi:10.3934/mbe.2021028

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 518-529. doi: 10.3934/mbe.2021028

Previous Article Next Article

Research article

Optimal strategies for a fishery model applied to utility functions

Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y Río Verde, Col. San Manuel, Ciudad Universitaria, Puebla, Pue 72570, México

Received: 05 September 2020 Accepted: 22 November 2020 Published: 11 December 2020

This work examines aquaculture-related activities in the commercial exploitation of fish reproduction. Fisheries' problem of maximizing utility is modeled for the state of Puebla, Mexico, to determine optimal fish production. The problem of maximizing utility subject to the fish production function is solved using an approach based on Euler's equation. The theoretical results are then applied, using data on aquaculture production and tilapia sales prices in the state of Puebla, Mexico. A logarithmic regression is used to approximate the utility function. The optimal fishing production and utility functions are thus explicitly obtained. Furthermore, this work shows how to obtain greater profits from the amount of fish that can be extracted without reducing the fish population.
- discounted Markov decision processes,
- dynamic programming,
- fishery model,
- Euler equation,
- fishery research,
- utility functions
Citation: Carlos Camilo-Garay, R. Israel Ortega-Gutiérrez, Hugo Cruz-Suárez. Optimal strategies for a fishery model applied to utility functions[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 518-529. doi: 10.3934/mbe.2021028

Related Papers:

Abstract

This work examines aquaculture-related activities in the commercial exploitation of fish reproduction. Fisheries' problem of maximizing utility is modeled for the state of Puebla, Mexico, to determine optimal fish production. The problem of maximizing utility subject to the fish production function is solved using an approach based on Euler's equation. The theoretical results are then applied, using data on aquaculture production and tilapia sales prices in the state of Puebla, Mexico. A logarithmic regression is used to approximate the utility function. The optimal fishing production and utility functions are thus explicitly obtained. Furthermore, this work shows how to obtain greater profits from the amount of fish that can be extracted without reducing the fish population.

References

[1]	D. Ngom, A. Iggidir, A. Guiro, A. Ouahbi, An observer for a nonlinear age-structured model of a harvested fish population, Math. Biosci. Eng., 5 (2008), 337–354. doi: 10.3934/mbe.2008.5.337
[2]	D. P. Bertsekas, Dynamic Programming and Stochastic Control, 1^st edition, Academic Press, New York, 1976.
[3]	O. Hernández-Lerma, J. B. Lasserre, Discrete-Time Markov Control Processes: Basic Optimality Criteria, 1^st edition, Springer-Verlag, New York, 1996.
[4]	M. L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic, 1^st edition, Wiley-Interscience, California, 2005.
[5]	B. Liao, Q. Liu, X. Wang, K. Zhang, J. Zhang, K. H. Memon, M. A. Kalhoro, Asymptotic behaviour of the n-species stochastic Gilpin-Ayala Cooperative model, Stoch. Environ. Res. Risk Assess, 30 (2015), 39-45.
[6]	B. Liao, X. Shan, C. Zhou, Y. Han, Y. Chen, Q. Liu, A dynamic energy budget–integral projection model (DEB-IPM) to predict population-level dynamics based on individual data: A case study using the small and rapidly reproducing species engraulis japonicus, Mar. Freshwater Res., 71 (2019), 461–468.
[7]	D. Levhari, L. J. Mirman, The great fish war: An example using a dynamic Cournot-Nash solution, Bell J. Econ., 11 (1980), 322–334. doi: 10.2307/3003416
[8]	L. J. Mirman, Dynamic models of fishing: A heuristic approach, Control Theory Math. Econ., (1979), 39–73.
[9]	H. Cruz-Suárez, R. Montes-de-Oca, An envelope theorem and some applications to discounted Markov decision processes, Math. Methods Oper. Res., 67 (2008), 299–321. doi: 10.1007/s00186-007-0155-z
[10]	Y. K. Kwan, G. C. Chow, Estimating economic effects of political povements in China, J. Comp. Econ., 23 (1996), 192–208. doi: 10.1006/jcec.1996.0054
[11]	Información Estadística por Especie y Entidad. March 10th, 2020, de Gobierno de México Sitio web, CONAPESCA. (2006-2014). https://www.conapesca.gob.mx/wb/cona/informacion_estadistica_por_especie_y_entidad
[12]	H. Cruz-Suárez, R. Montes-de-Oca, G. Zacarías, A consumption-investment problem modelled as a discounted Markov decision process, Kybernetika (Prague), 67 (2011), 909–929.
[13]	A. de la Fuente, Mathematical Methods and Models for Economists, 1^st edition, Cambridge University Press, 2000.
[14]	J. L. Troutman, Variational calculus and optimal control: optimization with elementary convexity, 2^nd edition, Springer Science and Business Media, 2012.
[15]	H. Cruz-Suárez, R. Montes-de-Oca, Discounted Markov control processes induced by deterministic systems, Kybernetika, 42(6) (2006), 647–664.
[16]	H. Cruz-Suárez, G. Zacarías-Espinoza, V. Vázquez-Guevara, A version of the Euler equation in discounted Markov decision processes, J. Appl. Math., (2012), 1–16.
[17]	A. Jaskiewicz, A. S. Nowak, Discounted dynamic programming with unbounded returns: Application to economic models, J. Math. Anal. Appl., 378 (2011), 450–462. doi: 10.1016/j.jmaa.2010.08.073

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)