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July 14th, 2020

Some observers like to see Easter Island as a metaphor for the modern world. However, it is important to be aware of the differences. The first point, as has been emphasized already, is that societies of the Easter Island type do not necessarily have a dramatic decline. In the case of Easter Island, the civilization was ‘‘unlucky’’ to be on an island where the main resource was very slow growing. If the resource had been faster growing, then the boom – and-bust cycle probably would have been avoided, as it was in most of Polynesia. Therefore, even if Earth as a whole could be viewed as Easter Island writ large, there would no presumption about any inevitability of the imminent decline and fall of modern civilization.

On the other hand, Easter Island should not be viewed as an isola...

Read MoreIt 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...

Read MoreA 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...

Read MorePerhaps 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.

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...

Read MoreTo 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...

Read MoreThe 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...

Read MoreThe 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.

Read MoreThe starting point for describing the evolution of a renewable resource stock is the logistic growth function. Using t to denote time, a simple logistic growth function has the form G(t) = rS(1—S/K). The variable r is the intrinsic growth rate and K is the environmental carrying capacity, or maximum possible size of the resource stock. G(t) is the growth rate defined in biomass units and G/S is the proportional growth rate (i. e., a number such as 0.1 or 10%). If the forest stock S reaches a level equal to carrying capacity K, then G = 0 and no further growth occurs. Similarly, if there is no forest stock, then S = 0 and no growth occurs. If the forest stock is small relative to carrying capacity (but positive), then S/K is negligible and G = rS...

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