Management of interacting species: regulation under nonlinearities and hysteresis

We consider the optimal regulation of an open access fishery when biomass dynamics are combined with fishing effort dynamics. The interaction of inelastic demand and backward bending nature of the ecological supply curve introduce nonlinearities that could lead to multiple bionomic equilibria and hysteresis effects. We obtain convergence results for general bionomic models and indicate cases where hysteretic regulation failure could be a problem when economic dynamics are slow enough relative to biological dynamics. We show that when biological dynamics are slow enough relative to the economic dynamics, the social optimum can be achieved by a time dependent landing fee.