The Effect of Subsistence on Collapse and Institutional Adaptation in Population-resource Societies

We extend the Brander-Taylor model of population and resource development in an isolated society by adding a resource subsistence requirement to people's preferences. This improves plausibility; amplifies population overshoot and collapse, and makes the steady state less stable; and allows for complete cessation of non-harvesting activities, in line with archaeological evidence for many societies. We then use bifurcation techniques to give a global analysis of four types of institutional adaptation: an ad valorem resource tax, and quotas on total resource harvest, total harvest effort and per capita effort. In all cases we find that a higher subsistence requirement makes it harder, or often impossible, for adaptation to avoid overshoot and collapse.