A Depletion Protocol for Non-Renewable Natural Resources: Australia as an Example

摘要

This paper examines the implications of statements by Australia’s Minister of… Resources that Australia’s exports of coal are growing rapidly and that Australia’s coal will last “110 years at current rates of production.” If one assumes that coal production P(t), follows a Gaussian curve (similar to a Hubbert curve) one can construct a family of Gaussian curves showing possible future paths of P(t) which are consistent with the cited “110 years.” Each curve reaches a maximum after which P(t) declines toward zero. Knowledge of the present value of dP/dt allows one member of the family to be identified as the most probable future path of P(t). Families of curves and tabular data are presented for resource quantities that would last 50, 100 and 200 years “at current rates of production.” If, instead, Australia’s P(t) follows a declining exponential curve (exp(−kt)) with k = (1/110) per year, the stated quantity of coal will allow production to continue forever, with P(t) declining with a half life of 76 y. This and more rapidly declining exponential paths are the only paths that can be said to be sustainable. The envelope of the family of Gaussian curves divides the (P, t) plane into “allowed” and “forbidden” areas. The declining exponential curve divides the “allowed” area into an upper area that is “terminal” and a lower area that is “sustainable.” These facts, coupled with Australia’s expectations of rapid growth of its population, suggest that Australia’s present resource policies are “anti-sustainable” and that the people of Australia need to rethink their present policy of rapidly exporting their fossil fuels.