In this work, we present and analyze a fishery model with a price variation. We take into account the evolution in time of the fish biomass and the harvesting effort, while the price of fish is dependent on supply and demand. Assuming that the price variation occurs at a fast time scale. We assume that the stock and the effort evolution follow a slow time scale. Considering the different time scales, the model is reduced to a 2D model. We analyze the obtained model, and depending on the value of a parameter, there are two main cases that can arise: a fish exclusion case and a sustainable fishery. To avoid Fish Extinction we introduce a control parameter and we study the impact of the number of sites on the catch that allow the undesirable case to be avoided.
- Auger P., Mchich R., Raïssi N., Kooi B. Effects of market price on the dynamics of a spatial fishery model: Over-exploited fishery/traditional fishery. Ecological Complexity. 7 (1), 13–20 (2010).
- Gordon H. S. The economic theory of a common-property ressource: the fishery. Journal of Political Economy. 62 (2), 124–142 (1954).
- Smith V. L. On models of commercial fishing. Journal of Political Economy. 77 (2), 181–198 (1969).
- Clark C. W. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Wiley, New York (1990).
- Charouki N., Raïssi N., Auger P., Mchich R., Atmani H. A management oriented competitive model with two time scales: The case of sardine fishery along the Atlantic coast between Cantin Cape and Blanc Cape. Ecological Modelling. 222 (4), 1253–1261 (2011).
- Mchich R., Auger P., Brochier T., Brehmer P. Interactions Between the Cross-Shore Structure of Small Pelagic Fish Population, Offshore Industrial Fisheries and Near Shore Artisanal Fisheries: A Mathematical Approach. Acta Biotheoretica. 64, 479–493 (2016).
- Barbier E. B., Strand I., Sathirathai S. Do open access conditions affect the valuation of an externality? Estimating the welfare effects of mangrove-fishery linkages. Environmental and Resource Economics. 21, 343–365 (2002).
- Smith V. L. Economics of production from natural resources. The American Economic Review. 58 (3), 409–431 (1968).
- Ly S., Balde M., Mansal F., Nguyen-Huu T., Auger P. A Model of a Multi-Site Fishery with Variable Price: from Over-Exploitation to Sustainable Fisheries. Mathematical Modelling of Natural Phenomena. 8 (6), 130–142 (2014).
- Ly S., Auger P., Balde M. A bioeconomic model of a multi-site fishery with nonlinear demand function: number of sites optimizing the total catch. Acta Biotheoretica. 62 (3), 371–384 (2014).
- LaFrance J. T. Linear demand functions in theory and practice. Journal of Economic Theory. 37 (1), 147–166 (1985).
- Brochier T., Auger P., Thiao D., Bah A., Ly S., Nguyen-Huu T., Brehmer P. Can overexploited fisheries recover by self-organization? Reallocation of fishing effort as an emergent form of governance. Marine Policy. 95, 46–56 (2018).
- Nobuyuki Y., Masahiko A., Atsushi T., Yoshihito S. Application of a bioeconomics model to examine sustainability of fishery resources in the global market: the case of octopus resource in Morocco. Fisheries Science. 75 (1), 43–46 (2009).
- Report on the state of fish stocks in Morocco. INRH, 146–165 (2016).
- Report on the state of fish stocks in Morocco. INRH, 118–136 (2017).
- Report on the state of fish stocks in Morocco. INRH, 33–37 (2018).