A Bioeconomic Analysis of a Renewable Resource in the Presence of Illegal, Unreported and Unregulated Fishing

The issue of illegal, unreported and unregulated (IUU) fishing is of prime concern to fisheries in developing countries where the regulatory regimes are often weak. This study proposes a Gordon-Schaefer bioeconomic model with non-constant catchability and nonlinear cost to study the impact of IUU fishing on the stock size of a marine fishery in Ghana. The static equilibrium reference points of the model are established and discussed. Bifurcation analysis on the modified Schaefer model shows the existence of a transcritical bifurcation point were the model is structurally unstable. Pontryagin’s maximum principle is employed to investigate the necessary conditions of the model, and also established are the sufficiency conditions that guarantee the existence and uniqueness of the optimality system. The characterization of the optimal control gives rise to both the boundary and interior solutions, with the former indicating that the resource should be harvested if and only if the marginal revenue of harvest exceeds the marginal revenue of stock. Numerical simulations with empirical data on the Ghana sardinella are carried out to validate the theoretical results. It is shown that IUU fishing leads to excessive exploitation of the resource biomass to levels below 50% of the carrying capacity. This has the tendency of making the fishery unsustainable, with its concomitant loss of revenue to fishers.