Model Description
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
(Please describe default dynamics for this model.)
$\frac{dL}{dt} = L\left(\phi h - \sigma\right)$ |
| Rate of change in population. |
$h=\frac{\beta(\alpha S-h_{u})}{1+t-\beta t}+h_{u} \ \ \ \ (\mbox {If} \ \ \alpha S > h_{u})\\
h=\alpha S \ \ \ \ (\mbox {otherwise})$ |
| Individual consumptions of the resource good (per capita harvest or nutrition) |
$\frac{dS}{dt} = rS\left(1-\frac{S}{K}\right)-Lh$ |
| Rate of change in resource stock. |
#parameters #from original: sig=d-b par alpha=1e-5, beta=0.4, r=0.04, sigma=0.1, phi=4, K=12000 par tax=0, hm=0 #Initial conditions init s=12000, L=40 # harvest per person hpp=if( alpha*s>hm )then( hm+beta*(alpha*S-hm)/(1+tax*(1-beta)) )else( alpha*s ) S'=r*S*(1-S/K)-L*hpp L'=L*( phi*hpp - sigma ) @ dt=0.1, total=500, xplot=S,yplot=L,axes=2d @ xmin=0,xmax=15000,ymin=0,ymax=15000 @ xlo=0,ylo=0,xhi=15000,yhi=15000 @ maxstor=200000 @ bounds=100000 done
Anderies JM, Arizona State University.
Bozicevic M, Arizona State University.
. 2003. The effect of subsistence on collapse and institutional adaptation in population-resource societies. Journal of Development Economics. 72:299-320.
