condition with Equation (3) yields an average cost relationship:
where c is the average cost of the fishery. The average costs of supplying more fish to the market are also increasing, and as shown in Figure 4-2, an increase in the wetland habitat will also lower these average costs. However, welfare gains from an increase in this ecological service are now measured by the change in consumer surplus only. Since there are no profits in an open-access fishery, there is no producer surplus gain from the improved ecological service.
A dynamic approach adapts bioeconomic fishery models to account for the role of a coastal habitat in terms of supporting the fishery, usually by assuming that the effect of changes in habitat area is on the carrying capacity of the fish stock and thus indirectly on production. Defining Xt as the stock of fish measured in biomass units, any net change in growth of this stock over time can be represented as
Thus, net expansion in the fish stock occurs as a result of biological growth in the current period F(Xt, St), net of any harvesting h(Xt, Et), which is a function of the stock as well as fishing effort Et . The influence of wetland habitat area St as a breeding ground and nursery habitat on growth of the fish stock is assumed to be positive, ∂F/∂S > 0, because an increase in mangrove area will mean more carrying capacity for the fishery and thus greater biological growth.
To simplify this analysis, it will be restricted to the open-access case. The standard assumption for an open-access fishery is that the effort in the next period will adjust in response to real profits made in the current period (Clark, 1976). Letting p(h) represent landed fish price per unit harvested, w the unit cost of effort, and Φ > 0 the adjustment coefficient, the fishing effort adjustment equation is
In the long run, the fishery is assumed to be in equilibrium, and both the fish stock and the effort are constant: that is, Xt+1 = Xt = XA and Et+1 = Et = EA. In Equation (5), this implies that any harvesting h(XA, EA) just offsets biological