With exhaustible resources, can a developing country escape from the poverty trap?

This paper studies the optimal growth of a developing non-renewable natural resource producer, which extracts the resource from its soil and produces a single consumption good with man-made capital. Moreover, it can sell the extracted resource abroad and use the revenues to buy an imported good, which is a perfect substitute of the domestic consumption good. The domestic technology is convex-concave, so that the economy may be locked into a poverty trap. We study the optimal extraction and depletion of the exhaustible resource and the optimal paths of accumulation of capital and of domestic consumption. We show that the extent to which the country will optimally escape from the poverty trap and the exhaustible resource will be a blessing depends on the characteristics of its technology and of the revenues from the resource function, on its impatience, on the level of its initial stock of capital and on the abundance of the natural resource. If the marginal productivity of capital at the origin is greater than the sum of the social discount rate and the depreciation rate, the country will accumulate capital along the entire growth path and will escape from the poverty trap, whatever its initial stocks of capital and resource, and provided that the marginal revenue obtained from the exportation of the resource is finite at the origin. On the contrary, if the marginal productivity of capital is lower than the depreciation rate whatever the level of capital and if moreover the initial stock of capital is small, then the country will never accumulate ; it will consume the revenues obtained from selling abroad the extracted resource, until there is no resource left and the economy collapses. We also show that any optimal path may be decentralized in a competitive equilibrium by using a tax/subsidy scheme for firms.