Resource stocks can fluctuate considerably over time, and some so severely that the fishery is entirely closed down on occasion, while alternative stocks may not be available, or available to only a limited extent (Hannesson, 1993b). Resource stocks can also be distributed unevenly, what Wilson (1982) refers to as patchiness. In all of these instances, when stocks are not stable and evenly distributed over time and place, catches can, on occasion, be large but infrequent. Wilson (1982) draws the analogy to the peak load problem encountered by utilities. Gulland (1974; page 152) observed that a given capacity (defined as available fishing effort and measured as a given number of ships of a certain type) restricted to a single stock would exert a different mortality, in effect take a different catch, from year to year in accordance with changes in the distribution and migrations of the stocks, and changes in the overall abundance of the resource stock. Gulland (1974; page 152) further observed that changes in resource stock abundance will affect the catch, but is also likely to change the mortality; the more fish there are, the less time is spent actually fishing or searching for fish.
Hannesson (1993b) considers the choice of optimum fishing capacity (available fishing effort) for fish stocks that vary at random given some permitted catch. The optimum capacity depends on the price of fish, the cost of capacity, and the harvest rule linking the permitted catch to the size of the fish stock. The paper observes that these harvest rules should be based on an economic optimization taking into account the biology of the stock, but that in practice, the permitted harvest is based on some simple biological rule of thumb, such as target escapement or fixed fishing mortality.
Hannesson (1993b) observes that the rate of utilization of the fixed factors can be varied by varying the variable inputs. The paper defines full capacity utilization as the combination of the ex-post vector of fixed factors (boats and equipment) and maximum economical variable inputs, corresponding to an intuitive notion such as so many fully utilized vessels. Due to the interaction with the random fish stock, this does not necessarily correspond to a unique value of catch rate. Utilization of the fishing fleet may vary according to the status of the fish stock at a given time. Due to the minimum cost combination of the various elements in the vector of fixed factors, there exists an aggregate expression of this vector, which measures capacity as defined. Capacity used is referred to as fishing effort, which is less than or equal to capacity. Since the average degree of utilization of the fleet will probably be lower the larger it is, the optimum fishing capacity for any given probability distribution of the permitted catch is likely to depend on the cost of fishing capacity. Finally, the normal capacity of each production unit could be defined as the minimum of the long-run average total cost curve.
Huppert (1981) and Charles and Munro (1985) discuss the trade-off between the cost of idle capacity (available fishing effort) and the ability to take large but infrequent catches. Wilson (1982; pages 424-425) uses the concept of available fishing effort or effort capacity to discuss the potential for idle capacity that can occur when stocks fluctuate considerably over time or place. Wilson notes the need to adjust capacity to the irregular peak load-type problems caused by patchiness and that even sole-ownership regimes will not be able to eliminate excess capacity. Wilson (1982), referring to Greenwood (1981), further observes that because of the patchiness-induced need for each individual fisher to invest in excess capacity and the uncertainty associated with the combined problems of patchiness and variability, the amount of fishing effort in place in a complex system with free entry is likely to be much less than would be the case in a stable system.
Flam (1990) reviewed the essential features of the problem to choose the right catch capacity, conceived as an output measure, under stochastic variations in annual quotas. Flam argued that uncertainty in quotas only causes a relatively small fine-tuning of the capacity selected under deterministic conditions. Flam considered the use of multistage stochastic programming and the notion of irreversible investment.