Pezzey-Anderies Model

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. 

You can adjust total time of simulation below.
This model has two state variables. You can set their initial values below.
This model has eight parameters. You can set their values below.
Enter the axes to be plotted for this model.