Equilibrium Model for Commodity Prices: Competitive and Monopolistic Markets∗

In this article, we develop an equilibrium model for storable commodity prices. The model is formulated as a stochastic dynamic control problem and considers two state variables the exogenous supply and the inventory. The inventory is a fully controllable endogenous variable. We assume that the uncertainty arises from the supply, which evolves as a Ornstein-Uhlenbeck stochastic process. This model is developed under a general framework which provides two distinct forms for the alternative economic scenarios of perfect competition and monopolistic storage. Since an analytical solution to the problem is not possible, we obtain a numerical solution that provides an optimal storage policy and generates the price dynamics. We also compute and analyse the equilibrium forward curves that result from the steady state optimal storage policy. The results are consistent with the theory of storage: the presence of storage in both economies stabilizes the natural prices. We also show that this effect is greater when the storage is competitive. The resulting forward curves take two fundamental shapes. If the initial spot price is greater than the long-run natural price we observe backwardation; otherwise the market is in contango. Furthermore, the degree of contango is greater in the competitive market.