The Optimal Depletion Of An Exhautible Resource In A Dynamic General Equilibrium Model

The validity of the Hotelling's rule, the fundamental theorem of nonrenewable resource economics, is limited by its partial equilibrium nature. One symptom of this limitation may be the disagreement between the empirical evidence, showing stable or declining resource prices, and the rule, predicting exponentially increasing prices. In this paper, we study the optimal depletion of a nonrenewable resource in a dynamic general equilibrium framework. We show that in, the long run, the price of a nonrenewable (i) is constant when the nonrenewable is essential in production, and (ii) it increases only if the rate of return of capital is larger than the capital depreciation rate and if the non-renewable is an inessential input in production. We believe that our model offers a theoretical explanation to non-growing nonrenewable prices and hence at least partially solves the paradox between the Hotelling's rule and the empirical regularities. We also show that two factors play a crucial role in determining the long run behavior of non-renewable prices, namely the elasticity of substitution between input factors, and the long run behavior of the real interest rate. Another major achievement of this study is the full analytical solution of the model under a Cobb-Douglas technology.