Pulse vs. optimal stationary fishing: The Northern Stock of Hake

Abstract

Pulse …shing may be a global optimal strategy in multicohort …sheries. In this article we compare the pulse …shing solutions obtained by using global numerical methods with the analytical stationary optimal solution.This allows us to quantify the potential bene…ts associated with the use of periodic …shing in the Northern Stock of hake. Results show that: …rst, management plans based exclusively on traditional reference targets as F msy may drive …shery economic results far from the optimal; second, global optimal solutions would imply, in a cyclical manner, the closure of the …shery for some periods and third, second best stationary policies with stable employment only reduce optimal present value of discounted pro…t in a 2%.

Selectivity, Pulse Fishing and Endogenous Lifespan in Beverton-Holt Models

“…In an n age-class model, a periodic pulse with a length of L ≤ n such that F t+kL = ∞ ∀k ∈ Z and F j = 0 for any other period is a local optimum for problem (10) …”

“…It is worth mentioning that the qualifying conditions (11) are sufficient conditions to guarantee that the pulse satisfies the first order condition of the maximisation problem (10). Nevertheless, there may be cases in which the pulse does not satisfy the qualifying conditions but does satisfy the optimal conditions.…”

“…Nevertheless, there may be cases in which the pulse does not satisfy the qualifying conditions but does satisfy the optimal conditions. There is also a stationary solution, F t = F t+1 = F ss , that satisfies the first order condition of maximisation problem (10). As in the case of the 2-age model, the stationary solution can be expressed in terms of a Lerner rule.…”

“…6 We prove that this link also exists for age-structured fishery models. In order to find this link, we analyse the (non-)concavity properties of the objective function of problem (10). In particular, by focusing on the second order conditions, we are able to find sufficient conditions that guarantee that the stationary solution is not the optimal solution to problem (10).…”

“…The following proposition summarises this result. H corresponds to the order one minor in the Hessian matriz associated with the second order conditions of the maximisation problem (10). Notice that ∂ 2 y a ss /∂F 2 ss < 0 because the yield per unit of fish is a concave function.…”