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.