Optimal strategies for a fishery model applied to utility functions

• Main Authors: Carlos Camilo-Garay, R. Israel Ortega-Gutiérrez, Hugo Cruz-Suárez
• Format: Article
• Language: English
• Published: AIMS Press 2021-04-01
• Series: Mathematical Biosciences and Engineering
• Subjects: discounted markov decision processes; dynamic programming; fishery model; euler equation; fishery research; utility functions
• Online Access: http://www.aimspress.com/article/doi/10.3934/mbe.2021028http://www.aimspress.com/article/doi/10.3934/mbe.2021028

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.