Exhaustible Resources With Adjustment Costs: Spot and Futures Prices

Abstract

We propose an equilibrium model of exhaustible resources in a comprehensive setting, including exploration, stochastic demand, and stochastic reserve, by extending the models in Pindyck (1980) and Anderson, Kellogg, and Salant (2018). The production adjustments can be quite general, e.g., sudden or gradual changes of the instantaneous production level. The model has three advantages: (1) It can generate low elasticity of production but high elasticity of exploration with respect to prices for general exhaustible resources (e.g., coal, natural gas, etc.). (2) In terms of spot prices, the combination of exploration and adjustment costs can significantly prolong the period of time that a spot price stays at the bottom, which explains why spot prices of many commodities can be quite low for a long time. (3) In terms of futures prices, the model can explain some stylized facts observed in futures markets, such as backwardation, contango, Samuelson effect, and higher volatility conditional on backwardation.