A mathematical model of a fishery with variable market price : sustainable fishery/over-exploitation

We present a mathematical bioeconomic model of a fishery with a variable price. The model describes the time evolution of the resource, the fishing effort and the price which is assumed to vary with respect to supply and demand. The supply is the instantaneous catch while the demand function is assumed to be a monotone decreasing function of price. We show that a generic market price equation (MPE) can be derived and has to be solved to calculate non trivial equilibria of the model. This MPE can have 1, 2 or 3 equilibria. We perform the analysis of local and global stability of equilibria. The MPE is extended to two cases: an age-structured fish population and a fishery with storage of the resource

A model of a multi-site fishery with variable price : from over-exploitation to sustainable fisheries

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fishes and boats movements between the different it sites, fishing effort and price that varies with respect to supply and demand. We suppose that boats and fishes movements as well as prices variations occur at a fast time scale. NW use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model. We show that the aggregated model can have I, 2 or 3 non trivial equilibria. We show that a variation of the total number of sites can induce a switch from over-exploitation to sustainable fisheries