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 can destabilize the steady state; 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.