Growth, resource extraction and production in a small open economy

This paper analyzed the optimal growth of a resource exporting economy in the framework of a Ramsey-type model. Two versions of the same model are used. In the first version (where the aggregate production function uses the conventional inputs, namely labor and capital) it was shown that along the optimal paths the resource would be exhausted in finite time and that the economy approaches asymptotically the modified golden rule capital intensity, well known from one-sector growth theory. Subsequently the impact of the changes in resource prices on the rate of extraction are investigated by considering an exponentially rising price. In the second version of the model, the resource extracted is divided between domestic production (the aggregate output of the economy is produced by means of labor, capital and the resource input) and export. Under this assumption, it is demonstrated that when the relative price of the resource is constant and given exogenously, the opening of trade (i.e., resource exports) depends on the relative magnitudes of the marginal product of the resource and its price. Furthermore the paper showed that even if trade opens, resource extraction for export will come to an end in finite time. After the economy stops exporting the resource, its optimal growth will be determined simultaneously by the elasticity of substitution between capital and the resource input and the dynamic behavior of the marginal product of the resource input, as explained in detail by Dasgupta and Heal [1974]. Finally, when the resource price has an exponential trend, resource extraction will continue both for domestic production and export purposes.