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This economic concept applies to renewable resources. It is based upon the idea that a resource stock grows very quickly when the population is low and less and less quickly as the population approaches the carrying capacity. Basically, the population function (with respect to time) always has a positive derivative, a negative second derivative, and a limit equal to the environmental carrying capacity as time approaches infinity.

If you look at the graph of the first derivative, you can see that it is a bell curve. This indicates, for example, that if you start with just two rabbits in a field the rate of growth will be extremely high. The food supply will be sufficient for the rabbits to reproduce at the highest rate that is biologically possible (extremely high in rabbits). Quickly, then, the population will rise. It will rise faster and faster as more mating pairs of rabbits exist to add to the birth rate. Eventually, food and space start to constrain the population and the rate of growth slows. Finally, the entire number of rabbits that the field can sustain will be alive. Any additional rabbits will starve to death and the carrying capacity will be maintained.

For any level of population, therefore, there is a specific rate of growth. That rate is dictated by available resources, conditions, and the number of mating pairs. At a certain population size, designated Pmax, the population is growing as fast as it is capable of growing. At any population size, it is possible to harvest the resource. The amount of resource harvested is called the yield. If a resource gatherer chooses to harvest an amount equal to the rate of growth at that particular population size, the actual size of the population will remain unchanged. Harvesting at this level is called taking the sustainable yield. The sustainable yield is very small when the population is very high or low, because there are either two few breeding pairs or too much crowding and a lack of resources. A resource can therefore be most efficiently harvested at Pmax, the point where the rate of growth is highest. This is also the point where the marginal revenue is equal to the marginal cost (because the amount of effort required to collect a resource varies inversely with the size of the resource stock P): the profit maximizing point. If there is only one agent harvesting the resource, this is the point where resource exploitation will cease. If there are numerous agents, however, each will try to grab as much as they can, anticipating that if they do not the others will. This means that, instead of harvesting at the level of sustainable yield they will harvest up until the point where their total costs are equal to their total revenue: the output maximizing point. In almost all cases, this will lead to resource depletion.

This market failure is generally addressed through government regulation and licensing, designed to make the actual yield similar to the sustainable yield and thus keep the resource stock constant.

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