The bioeconomic fishery model discussed in Chapter 1 is a static model. The yield curve of Fig. 1.1 depicts sustainable annual yield as a function of effort E. Switching from one effort level to another does not instantly switch from one point on this curve to another. For example, a reduction of effort in a fishery currently at bionomic equilibrium will usually result in an immediate decrease in yield, rather than an increase as suggested by the static model. The increased yield only shows up after the fish stock has had a chance to recover from past depletions. Similarly, any increase in effort will normally result in an immediate increase in yield, but this may later be tranformed into a decreased yield, as the stock becomes further depleted. These dynamic changes are extremely important economically, and a viable bioeconomic theory must include them. The dynamic theory is a bit more complicated, but vastly more meaningful and useful, than the static (i.e., equilibrium) theory.

Natural resource stocks can be considered a form of “natural capital” (Jansson et al. 1994). The question of optimal resource use is therefore a problem of optimal investment in, and consumption of natural capital (Clark and Munro 1975). Our dynamic bioeconomic fishery model will make this connection clear. But first we examine the underlying biological model. (A different biological model will be discussed in Sec. 2.7.)

A Dynamic Model

The crux of dynamic modeling is the use of a state variable to represent the current state of the system in question.