In this section it is supposed that there exists a non-renewable resource in fixed and finite supply which can be extracted at zero cost. The existing literature on the rate at which such an exhaustible resource should be depleted generally focuses attention on the possible mitigation effects of capital accumulation and/or technological change in the growth process. Population is assumed exogenous to these models and so plays only a limited role [10, 18]. This assumption is now relaxed; our interest being the interdependence between alternative resource depletion policies and population policies. However, in order both to simplify the analysis and illuminate better the role of population policy, total consumption is identified with the quantity of the resource extracted in each period and capital accumulation is ignored; a full synthesis incorporating population, capital and exhaustible resource will not be attempted here. Furthermore, only “first bet” solutions will be considered.
KeywordsOptimal Policy Population Growth Rate Capital Accumulation Social Welfare Function Optimal Programme
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