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.