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 P

_{max}, 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 P

_{max}, 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.