Rational taxation in an open access fishery model

TL;DR

This paper models fishery management with multiple agents, showing that a proportional tax based on the resource's marginal value can incentivize cooperative behavior, stabilizing fish biomass at an optimal level.

Contribution

It introduces a taxation scheme based on the resource's marginal value to promote cooperative harvesting in an open access fishery model.

Findings

Proportional tax can induce near-optimal cooperative harvesting behavior.

The value function for the cooperative problem is strictly concave and differentiable.

The scheme stabilizes fish biomass at the golden rule level.

Abstract

We consider a model of fishery management, where $n$ agents exploit a single population with strictly concave continuously differentiable growth function of Verhulst type. If the agent actions are coordinated and directed towards the maximization of the discounted cooperative revenue, then the biomass stabilizes at the level, defined by the well known "golden rule". We show that for independent myopic harvesting agents such optimal (or $\varepsilon$-optimal) cooperative behavior can be stimulated by the proportional tax, depending on the resource stock, and equal to the marginal value function of the cooperative problem. To implement this taxation scheme we prove that the mentioned value function is strictly concave and continuously differentiable, although the instantaneous individual revenues may be neither concave nor differentiable.