Stabilization property of speculative long-time storage in the model of standardized commodity market

We investigate a model of standardized commodity market and activity of three economic agents on this market: producer, consumer and speculator. Producer and consumer are characterized by linear functions of supply and demand. We consider the ratio between the slopes of demand and supply functions is as such that market equilibrium without speculator is unstable. We investigate two speculative strategies which stabilize an equilibrium. The first strategy of speculator restricts price oscillation by some vicinity of an equilibrium price. This strategy is based on long-time storage and fixed speculative amount of commodity. The second strategy provides a convergence of price-formation process to an equilibrium value. The second strategy is also based on long-time storage, but in this case the speculator maximizes the amount of commodity to be bought, i.e. speculative amount is variable