Fig. 7. a Bifurcation diagram for Easter Island model with subsistence. b Phase plane showing limit cycle and representative trajectory for h
min
= 0.02.
Further, this abrupt cessation of manufacturing suggests, as previously mentioned, a different in-
terpretation for why institutional adaptation did not occur. From around 1000 up until 1430, the
population shifts labor into the bioresource sec- tor. By doing so, per capita intake of bioresources
can be maintained above h
min
. The population peaks near 1450 and subsequently crashes to half
this peak in 150 years. Such change might have been far too rapid for institutional responses to
occur. The ability of the population to increase its work effort and maintain its material well-being
hides the feedback from the resource base. When change finally does occur, the resource base is so
degraded that the change is rapid and dramatic, precluding any hope of institutional response. A
present day parallel is overcapitalization in fisheries. Thus, a relatively small change in model
assumptions
produces a
quite different
interpretation.
6. Discussion
The motivation for this paper was to illustrate how the analysis of stylized models of traditional
societies might help us better understand key ele- ments of individual behavior and social institu-
tions that determine whether degradation of a common property resource can be avoided. From
the comparison of the models, some general ideas emerge. Concerning individual behavior, there are
two general conclusions:
The more complex neo-classical models of hu- man behavior do not necessarily produce a
richer characterization of behavior in a dy- namic context than do simple common sense
considerations. The Cobb – Douglas production function produces a constant labor proportion
in agriculture, just as assumed in the Tsembaga model. The Stone – Geary production function
causes labor allocation to shift as the popula- tion attempts to meet minimum nutritional re-
quirements in a qualitatively similar fashion as does Eq. 5 in the Tsembaga model. The ma-
jor difference between the two approaches is that in the former case, the labor allocation
adjusts instantaneously, while in the latter, it adjusts at a finite rate, l. Further, when times
are good, the Stone – Geary representation al- lows for more labor to allocated to producing
agricultural goods than is required to meet their minimum nutritional target, while Eq. 5
will tend to force the labor allocation towards the minimum requirement. In this sense, Eq.
5 produces a labor allocation similar to the Stone – Geary with a very low value of b — i.e.
a very weak preference for agricultural goods once nutritional needs are met.
Regardless of the model for the underlying behavior, the relaxation of the constant labor
proportion assumption
is fundamentally
destabilizing in both models. When agents are allowed to adjust their labor allocation based
on nutritional status, both models exhibit more dramatic overshoot and collapse behavior.
Concerning the
evolution of
institutions, conclusions are much more difficult to draw. As
in the case of the Tsembaga, given the social institution we could study how it may have
worked but can say nothing about how it might have come about. In the Easter Island case where
very little is known, we can do little more than speculate. The best we can do is suggest
conditions that might promote or inhibit the evolution
of effective
resource governance
institutions. Two important points emerge from the models:
When individual agents can increase the rate of exploitation of their resource base in an effort
to meet a minimum demand, the time scale upon which institutional adaptation can occur is dras-
tically shortened. Increasing exploitation rates enables the population to maintain a given
trajectory longer, before individuals in the pop- ulation receive real feedback in the form of
malnutrition that their resource base is degrad- ing, and their population level is not sustainable.
Even if all the necessary ‘institutional ingredi- ents’ are in place, successful institutional adapta-
tion still may not occur. This is very clear from the Tsembaga model. As discussed above, the
ritual cycle has all the necessary ingredients for successful common property governance. How-
ever, its success depends critically on the nature of physical system of the Tsembaga. Namely,
success depends on the fact that several enemy tribes are contained in a fixed area so that the
number of ways pig invasions can occur rises faster than linearly as the human population
increases. Without this, the ritual cycle is ineffec- tive. Thus, there is an underlying ‘geometry’ of
the human-resource system that may determine the success or failure of resource governance
institutions, rather than the nature of the insti- tutions themselves.
Given the above points, it seems improbable that successful, timely institutional adaption based on a
recognized need to manage a resource has occurred very often. Rather, certain institutional structures
intricately woven into the fabric of society perform such resource management tasks quite by accident.
What lessons can we learn from these models about the design of modern institutions for re-
source governance? Probably the most important point is that successful institutional designs may be
highly site-specific. Although there might be
Fig. 8. Graph a: curve 1 is the population trajectory for the original Brander and Taylor model, 2 is the same for the modified model with b = 0.1 and h
min
= 0.03, 3 shows manufacturing output for the modified model. Graph b shows the labor allocations
for the modified model with the above parameters.
general design principles, a careful understanding of the ‘geometry’ of the problem may make the
difference between success and failure. Secondly, policy makers must be aware of the relationship
between the time scale on which resource gover- nance systems must be developed and the ten-
dency or ability to intensify exploitation, or more generally, on structural change in the economic
system.
7. Conclusions
