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Abstract
The dynamics of a population and a resource are investigated in a
maximin model based on Brander and Taylor’s stylization of Easter Island, in order
to consider the sustainability of the society represented. There are continua of
both regular and non-regular maximin solutions, the type depending on the initial
conditions. A non-regular maximin steady state corresponds with the steady state
in Brander and Taylor’s model. All solutions are time consistent and Pareto optimal.
For the regular paths, a partial analytic characterization and a simulation are
provided. The non-regular paths involve two regular sections and one degenerate
solution in which the maximin constraint is not effective. The high degree of mathematical
subtlety of the solution to this ostensibly simple problem calls into question
the likelihood of a planner’s being able to devise and follow a program of efficient,
sustained development.