It is useful to consider the history of Easter Island after the 18th century. The story is a very sad one— much worse than the endogenous boom-and-bust cycle that had already occurred on Easter Island. From the time of James Cook in the late 18th century through the mid-19th century, conditions on Easter Island gradually improved and the population increased gradually. Population was reliably esti­mated at something exceeding 3000 in 1862. In 1862 and 1863, slave traders from the Spanish community in Peru invaded the island and took about one-third of the islanders as slaves. Most of these slaves died of smallpox and other infectious diseases within a few years. A few returned to Easter Island, inadvertently causing a smallpox epidemic that killed most of the remaining Islanders.

By 187...

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A presumption underlying the analysis here is that property rights were incomplete, perhaps not to the point of full open access, but at least to the point where it was hard to prevent increased harvesting as the population increased. Specifically, in Eq. (1) harvesting is assumed to be increasing with popula­tion size for any given stock. This need not be the case if property rights are complete, because an efficient owner or manager of the resource would restrict access beyond some optimal point.

It is unlikely that Easter Island was characterized by complete open access, but it is very likely that property rights were incomplete in the sense that different competing harvesters probably had access to some common part of the forest...

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Geothermal power stations have their own unique developmental, operational, technical, and environ­mental problems. Many geothermal resources occur in or near national parks or remote uninhabitable locations because they are normally associated with volcanoes and have beautiful surface manifestations and so become public reserves and tourism hot spots. Most of these geothermal resources do not get developed for power generation. Examples include Yellowstone Park in the United States and Orakei Korako Geyserland in New Zealand. However, geothermal resources that exhibit little surface manifestation in national parks do get developed. Examples include Hatchobaru and Otake in Japan.

Volcanoes, and hence geothermal resources, are also associated with mythical power and beliefs...

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Simulation of Easter Island

Perhaps the most revealing method of analysis of this dynamic system is through simulation. It is possible to estimate plausible values for the parameters in Eqs. (1) and (2) and simulate the evolution of Easter Island. The necessary parameters are a, b, n, r, and environmental carrying capacity K. It is also neces­sary to specify the size P(0) of the initial founding population.

Simulation of Easter Island

FIGURE 2 A flow diagram of stocks and flows.

The environmental carrying capacity and the initial forest stock are taken to be the same. Of course, the size of this stock can be normalized to any value...

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Population Growth

To describe population growth, we adopt the linear form used by Lotka and Volterra in their original predator-prey formulations. The first component is a base net fertility rate, n, that would apply in the absence of a resource stock (and would presumably be negative in our environment). In addition, there is a second term that, from our point of view, captures the Malthusian idea that net fertility rises when per capita consumption rises. This implies that propor­tional net fertility should rise when, other things equal, the resource stock is larger. The effect follows because a higher stock (for a given population) would normally give rise to higher per capita consumption. This reasoning leads to the following population growth function:

dP/dt = nP + bPS, (2)

where b is a parameter that...

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The total installed geothermal power generating capacity in the world is approximately 9000 MWe from 21 countries, with the United States leading at nearly 3000 MWe and The Philippines with nearly 2000 MWe (Table II). Other major countries are Italy, Mexico, Indonesia, Japan, and New Zealand, with between 400 and 800 MWe each.

Geothermal power stations have very high avail­ability, load, and capacity factors (>90%). They are most suitable as base load power stations. Liquid – dominated reservoirs are not suitable for peak load generation because two-phase flow and the separa­tion process make their operations and control at changing flows difficult.

A geothermal power station that uses steam turbines to generate electricity is similar to a conventional fossil fuel-fired power station...

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Open Access, Property Rights, and Harvesting Behavior

The natural growth of the forest stock provides part of the story in characterizing the evolution of the forest stock. The other part of the story depends on the harvesting behavior of the Easter Islanders. The key economic point is that under conditions of incomplete property rights, it is natural to expect that, for any given stock, the amount harvested at any given time period, H(t), is increasing with population size. In other words, for any given set of external conditions and any given forest stock, we expect more harvesting to occur if there is a larger population seeking to use the forest stock. Similarly, for a given population, harvesting is easier if the stock is larger, and therefore more harvesting would be likely to occur...

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Other Growth Functions

The logistic growth function is no doubt far from being a perfect approximation to the growth of the Jubaea chilensis forest on Easter Island. Various extensions to the logistic growth function are possible. For example, it is quite possible that at very low values of the stock, the proportional growth rate actually tends to decline. This is referred to as ‘‘depensation’’ or the ‘‘Allee effect.’’ The logistic growth function can be augmented to allow for depensation, but that will not be pursued here. The basic logistic growth function does allow for the critical elements of biological renewable resource growth that are needed to capture at least the qualitative experience of Easter Island.

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