Competitive Storage and Commodity Price in Continuous Time

Abstract

This paper offers a time-continuous competitive storage model and provides an analysis of the model solution. The model is relevant to the mineral commodity markets with traders managing inventories and getting speculative profits. The model includes serially correlated shocks of net supply and an upper boundary on the storage capacity. The no-arbitrage conditions on commodity trade imply the existence of the equilibrium price function under the standard boundary conditions on speculative trade. The equilibrium price is determined by the state variable defined as the long-term availability of commodity, which is the sum of storage and the expected cumulative disturbances of net supply. An approximate solution for a low-elastic net demand on commodity is derived in the explicit form. Numerical simulations of the equilibrium price function are conducted to examine the effects of the model parameters on this function.