Switching to a sustainable efficient extraction path

The economy depends on the essential nonrenewable resource and the path of extraction is nondecreasing and inefficient. At some point the government gradually switches to a sustainable (in sense of nondecreasing consumption over time) pattern of the resource use. Technical restrictions do not allow to switch to the efficient extraction instantly. Transition curves calibrated to the current pattern of world oil production are used as the extraction paths in the "intermediate" period. However, there is no solution in finite time for the "smooth" switching from the optimal "transition" to the optimal efficient path, constructed with respect to the same welfare criterion. We analyze numerically two approaches for the approximate solution: "epsilon-smooth" switching and "epsilon-optimal" transition curve with smooth switching. Both cases give the unexpected result: the consumption path along the "inefficient" transition curve is always superior to the constant which we obtain after switching to the "efficient" Hartwick's curve. The result implies that for the correct switching to the efficient curve in finite time the saving rule must be adjusted. We estimate the importance of following the efficient path by comparing the consumption along the plausible transition path and the efficient pattern of the resource use. For simplicity we use in our examples the constant per capita consumption as a welfare criterion and the Hartwick rule as the benchmark of investment rule.