Non-Renewable Resources in a Ramsey Economy with Subsistence Consumption, Human and Physical Capital Accumulation: A full Characterization

Abstract

We investigate the question on how to use a non-renewable resources efficiently in the presence of a minimum subsistence level of consumption. In our model, households are characterized by Stone-Geary preferences and output is Cobb-Douglas using physical and human capital as well as resources as input factors. This setup gives rise to a six dimensional dynamic system with three control and three state variables. Despite this complexity, it is shown that a closed form solution exists in terms of the Gaussian hypergeometric function. The closed form solution allows us to calibrate the model to the situation of 108 countries using data from the World Bank on countries' endowments with physical capital and natural resources. We are able to quantify the implications of observed capital stocks for the growth perspective of each country. In particular, we analyze whether a level of subsistence consumption equivalent to the World Bank's poverty lines can be accomplished. Our calibration results also shed some light on what has been termed the "resource curse".