We incorporate a non-renewable resource in a standard framework of endogenous growth through expanding varieties. Moreover, we allow for a backstop technology that is able to produce a perfect substitute for the resource. Our model is used to analyze resource extraction and technological progress over time. Three consecutive regimes of energy use can emerge in the economy: only resource extraction, simultaneous use, and complete reliance on the backstop technology. The introduction of the backstop technology crucially affects the time paths of fossil fuel extraction and technological progress. We provide conditions under which either peak-oil emerges, or the extraction path is monotonically increasing or decreasing until exhaustion of the resource stock. The rate of technological progress is non-monotonic over time: it declines initially, starts increasing when the economy approaches the regime change and jumps down once the resource stock is exhausted
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