Price Uncertainty and Derivative Securities in a General Equilibrium Model

Consider an exchange economy with multiple competitive equilibria. Agents know the set of equilibria, but not which will be selected. To insure against unfavorable equilibrium outcomes, they trade on markets for commodities contingent on the equilibrium price vector. Such price-contingent contracts allow agents to insure fully against the risk stemming from uncertainty about the equilibrium to be chosen. However they introduce further uncertainty because there may be several possible equilibrium prices for price-index-contingent commodities. The introduction of higher-order of derivative products removes this uncertainty, but in turn introduces uncertainty about the prices of these products. We prove that in regular economies this process converges in a finite number of steps to a unique fully-insured Pareto efficient allocation. The introduction of price-contingent commodities or securities and further derivative securities removes all endogenous uncertainty associated with lack of knowledge of equilibrium prices. We thus provide a mechanism for resolving non-uniqueness in economies with multiple equilibria and also give an important resource-allocation role to derivative securities based on price indices.