Price, scarcity rent, and a modified r per cent rule for non-renewable resources

Since Hotelling's seminal paper on the optimal depletion of exhaustible resources, much has been published; yet confusion remains about whether scarcity rent and price increase or decrease as a resource is depleted when costs tend to rise with depletion. We show that Hotelling's fundamental results of rising scarcity rent and price paths are sustained and that the path of scarcity rent converges on the per cent rule, provided the objective function is concave. Predictions of non-monotonic or declining scarcity rent paths are due to implicit assumptions that lead to a non-concave objective function. We identify the sources of these non-concavities.