The peak of oil extraction and a modified maximin principle

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 criteria are considered for the construction some curves of switching to decreasing paths of the resource depletion. Consumption paths have diverse behavior patterns along these curves, including a path of unlimited growth. A new approach to the Rawlsian maximin criterion which allows for growth of consumption is offered.