Non-renewable resources in the long run

We model a competitive economy in which production is dependent on labor and a non-renewable resource, the stock of which is inhomogeneous. We solve the model analytically and show how—in infinite time—the economy moves away from an initial balanced growth path (b.g.p.) and towards a mature b.g.p. The characteristics of the initial b.g.p. match historical observations of slowly declining resource price and consumption growth tracking global product. The mature b.g.p. depends on the nature of the stock; the more steeply cross-sectional area declines with depth, the faster the rate of price increase. We show how the theoretical model may be adapted and parameterized to explain and predict the evolution of markets for specific resources, applying the model in two cases, copper and petroleum.