How could the non-sustainable Easter Island have been sustained?

The collapsing scenario of Easter Island has been analyzed by Brander and Taylor (1998) as a predator-prey model in a Malthusian world, in which the household is only concerned with its instantaneous utility. This paper develops an endogenous growth model with a renewable resource and analyzes the possibly non-sustainable growth as a steady state, in spite of the household being deeply concerned with all its future lifetime utility. Our analysis shows that the ignorance of future lifetimes in present decision-making is indeed crucial to economic non-sustainability. We then examine whether a deforestation tax set by the government could have reduced the resource exploration rate and thereby held back the economic collapse. We also demonstrate using phase-diagrams how such a tax can switch the economic dynamics from non-sustainability to sustainability.