Primal and dual approaches to fishing capacity: The impact of the convexity assumption

Application of primal non-parametric approaches to estimation of fishing capacity provides useful disaggregated information about fishing firm’s capacities utilizations. A potentially
serious issue is that the estimated capacity utilization rates can be relatively low. This may call for reductions in the fishing fleet that are political impossible to defend. In this paper two
modifications of the traditional approach are explored. First, non-convex technologies are introduced and it is shown how the primal non-parametric approach leads to different capacity
utilization rates. Then capacity utilization measures using cost functions are specified for both convex and non-convex technologies. It is illustrated how the convexity assumption impacts
capacity utilization rates and how this dual approach differs from the primal approach. Second, the effect of utilizing these different convex versus non-convex capacity utilization rates in the
short-run Johansen industry production model is explored in terms of the resulting policy conclusions. This model has been used to formulate realistic plans to implement fishery policies
(decommissioning schemes, zone and time restrictions, etc). Empirically, we illustrate these capacity measures on the Pacific albacore tuna fishery to document the impact of convexity.