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Interpretations

Let us come back to the nondimensionalized system in order to interpret these results. The unstable equilibria are never reached and are of little interest. Let us focus on the stable equilibrium and on the evolution towards equilibrium.

The equilibrium resource size increases with the renewal rate of the resource r, the capital depreciation rate , and decreases with the rate of production , the efficiency of the harvesting and the amount of people involved in the harvest, L (equation 5). The fact that the equilibrium capital is inversely proportional to L simply reflects the replacement of capital by labour in the Cobb-Douglas expression 1. also increases with r and decreases with .

is small, giving rise to oscillations, whenever resource renewal is fast with respect to capital depreciation, which is probably the case for most fisheries. The resource renewal rate for most species of fish is of the order of a few years, while boats last for a couple of decades at least (major pieces of fishing gear typically last for seven years). The situation for forest exploitation might be the opposite, with and no oscillations and a fast decay towards equilibrium.

An important result is that is independent of the production coefficients and : can be increased by technological or marketing improvements that decrease the quantity of a natural resource used in a given product. This would not change the oscillatory nature of the solutions. In the case of forest exploitation such an improvement might be using less wood for a given piece of furniture or making use of a larger proportion of each tree; for fisheries it might be practices enabling the industry to use a larger fraction of the catch by marketing surimi or flour for cattle breeding. On the other hand, such practices can improve the situation by increasing the equilibrium resource size, which is a good defense against natural or artificial hazards which could suddenly deplete the resource below the threshold level necessary for reproduction.



next up previous
Next: Carrying capacity Up: The simplest model: Previous: More general production



weisbuch
Fri Feb 7 13:18:37 GMT+0100 1997