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Pezzey-Anderies Model

Model Type
SES Library XPP model

This model describes the Pezzey-Anderies extension to the Brander-Taylor Easter Island model. In addition to the parameters in the Brandor-Taylor model, Pezzey and Anderies have introduced $tax$ and $h_m$. Pezzey and Anderies (2003) gives the following overview: \"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\".

Default Dynamics
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$$\frac{dL}{dt} = L\left(\phi h - \sigma\right)$$
$$h=\frac{\beta(\alpha S-h_{u})}{1+t-\beta t}+h_{u} \ \ \ \ (\mbox {If} \ \ \alpha S > h_{u})\\ h=\alpha S \ \ \ \ (\mbox {otherwise})$$
$$\frac{dS}{dt} = rS\left(1-\frac{S}{K}\right)-Lh$$
pezzey-anderies_model.ode
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