A Model of Regulated Open Access Resource Use

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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 .
REGULATED OPEN ACCESS RESOURCE USE 7 FIG. 3. Regulator season length choice and joint regulated equilibrium. relevant instrument is the season length T, although it would be straightforward to generalize. 7 Suppose that the biomass measured at the beginning of the fishing season is X . 0 Then if the quota target is applied to the initial biomass, we have an allowable harvest quota of Q c dX 0, which, if realized, will leave a final end of season biomass of X X Ž c dX .. In the second stage, we thus assume that T 0 0 regulators select the season length instrument level which ensures that the target will be achieved. This is found by substituting the quota into Eq. Ž. 3 , so that we have Q X 1 e qET . 6 0Ž . Ž . This equation can be solved for the season length T as a function of capacity, beginning biomass, the harvest quota, and the catchability coefficient. In particular, the regulators are assumed to behave by choosing T so that 1 X 0 T ln . Ž 7. qE X Q Note that, once X0 is given, this describes a rectangular hyperbola in T, E space as shown in Fig. 3. When fishing capacity is large as at point A, regulators will only allow fishing over a short season but when capacity is low as at point B, a longer season can be permitted. A jointly determined regulated open access equilibrium occurs at a capacity level and season length as depicted at the intersection of the two curves. The industry 7 For example, since aggregate fishing capacity is E in our model, we could disaggregate to incorporate input controls by defining the capacity function to be effective capacity Ž on the grounds. which is a function of various regulatable inputs. If effective capacity is assumed to be a function of a vector of inputs, regulators could further be assumed to be able to choose the attributes of those inputs or to regulate their levels directly. For example, fishing capacity is certainly a function of gear dimensions and other specifications and these are almost always directly regulated. The complication introduced by multiple inputs is that one must also develop a theory about instrument choice which answers questions like: if both season length and mesh size restrictions can be used to curtail aggregate effective fishing pressure, how would the mix of the two be chosen by regulators? 0
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A Model of Regulated Open Access Resource Use

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