Equilibrium Forward Contracts on Nonstorable Commodities in the Presence of Market Power

Authors:
Lingxiu Dong;Hong Liu
Affiliations:
John M. Olin School of Business, Washington University in St. Louis, St. Louis, Missouri 63130;John M. Olin School of Business, Washington University in St. Louis, St. Louis, Missouri 63130
Venue:
Operations Research
Year:
2007

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Abstract

Bilateral supply contracts are widely used despite the presence of spot markets. In this paper, we provide a potential explanation for this prevalence of supply contracts even when spot markets are liquid and without delivery lag. Specifically, we consider the determination of an equilibrium forward contract on a nonstorable commodity between two firms that have mean-variance preferences over their risky profits and negotiate the forward contract through a Nash bargaining process. We derive the unique equilibrium forward contract in closed form and provide an extensive analysis. We show that it is the risk-hedging benefit from a forward that justifies its prevalence in spite of liquid spot markets. In addition, while a forward does not affect production decisions due to the presence of spot markets, it does affect inventory decisions of the storable input factor due to its hedging effect against the inventory risk. We also show that price volatilities and correlations are important determinants of the equilibrium contract. In particular, the equilibrium forward price can be nonmonotonic in the spot price volatility and can decrease as the initial spot price increases.