Abstract
We present a bioeconomic fishery model with variable price based on supply and demand. The model considers three variables: resource biomass, fishing effort, and market price. Rapid price changes classify the fishery system as a slow–fast system. Two main cases arise: catastrophic equilibrium (CE) with overexploitation and fish extinction, and a sustainable fishery equilibrium. We aim to determine conditions for maximum sustainable yield by optimizing cost per unit of fishing effort. Additionally, we explore conditions to prevent extinction and restore sustainable fishing. Marine protected areas (MPAs) can restore fish stocks by destabilizing the CE and maintaining a stable positive equilibrium. A model incorporating an MPA and fish movement is proposed, suggesting a small carrying capacity-to-surface area ratio in the fishing zone. Optimal total catch can be achieved by selecting the appropriate MPA surface area.
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