A Model of Regulated Open Access Resource Use

6
HOMANS AND WILEN
FIG. 2.
Regulator quota rule.
allowable quota or exploitation rate is a linear function of the biomass over some
range. 5 The quota would be set, then, according to the rule
Q c dX 0. Ž 5.
In Fig. 2, for example, we show a quadratic yield function with a linear harvest
quota rule superimposed. Whenever the biomass is below the desired long run
‘‘safe’’ stock level, the quota is set below yield so that the biomass grows and
conversely if the biomass is above X safe. This quota rule allows a gradual adjust-
ment toward the equilibrium stock level whenever biomass is above or below it.
Note that if c 0, this rule would also call for a moratorium when the biomass
falls to a level like X , hence a rule like Q maxŽ 0, c dX .
min
better describes
this situation. Note also that this simple rule encompasses the possibility that the
safe stock is the maximum sustainable yield stock as well as others such as the F 0.1
strategy. 6 Obviously other variants of these types of rules are possible.
In the second stage of the regulatory process, we assume that regulatory
instruments are selected to achieve the quota target determined from the quota
rule. This distinction between targets and instruments is important and often
ignored in descriptive analysis. In real fisheries, it is not enough to simply select an
aggregate harvest level since there is nothing to ensure that the industry won’t
exceed the target. Typical regulatory instruments are the levels of various constraints
on fishing technology and practices allowed by regulators, including mesh
size restrictions, area and season length closures, engine size, and gear dimensions.
By far the most commonly used instrument to ensure harvest quota adherence is
the season length restriction. For the model discussed here, we assume that the
5
Cf. the discussion in Hilborn and Walters 12 , p. 2243.
6 The F0.1
strategy prescribes a constant exploitation rate which leaves exploitation slightly less than
the one which maximizes yield per recruit, cf. Hilborn and Walters 12 .