The peak of oil extraction and consistency of the government's short- and long-run policies

The term "oil peak" usually is connected with the positive analysis problem, namely, with the problem of defining the year when the increase in the rate of oil extraction will be physically impossible. However, a normative approach to the problem of optimal extraction of a nonrenewable resource seems more important. We consider the economy which depends on the essential nonrenewable resource and the rate of the resource extraction increases over time. At some instant the government gradually switches to a sustainable (in sense of nondecreasing consumption over time) pattern of the resource extraction. Different approaches are offered for the construction of the paths of switching to decreasing resource use. Some seemingly attractive short-run policies of switching to decreasing extraction can run counter to long-run criteria. Reformulation of the short-run criterion can imply the optimal transition path consistent with the long-run government goals. It is shown analytically and numerically that there are values of parameters for the transition paths of extraction that consumption along these paths is asymptotically constant or infinitely growing. Numerical examples show for different reserve estimates that the "sustainable" peak of oil extraction must be earlier than the expected "physical" peak. A new approach to the Rawlsian maximin criterion which allows for growth of consumption is offered.