Research concentrated on equilibria under uncertainty under the assumption that the asset market is incomplete. The following are some of the topics addressed:
The existence of competitive equilibria with incomplete participation;
The approach involves circumventing the portfolio choices of individuals and the associated unbounded domain of portfolios and working instead with attainability restrictions on state contingent expenditures which is no more tenable, since the participation constraints are expressed in term of the access of individuals to the asset markets. Nevertheless, it is indeed possible to express the participation constraints in a manner which allows for an argument for the generic existence of competitive equilibria.
The indeterminacy of equilibria in the absence of nominal assets:
When the asset market is complete, the passage from commodity prices to generalized commodity prices has no impact on the set of competitive equilibrium allocations, since only the discounted price at an initial date event matters and is unambiguously defined. When the asset market is incomplete, generalized prices cannot be reduced to a single price, and indeterminacy arises.
Production decisions under uncertainty:
Profit maximization is not well defined when the asset market is incomplete. Production plans not in the span of the payoff marketed assets cannot be priced based on information derived from asset prices. The existence and determinacy of equilibria was characterized under the assumption that firms evaluate alternative production plans by projecting thus on the span of the payoff of marketed assets. Equilibria are generically determinate. More interestingly, the investment criterion is an approximative application of the Capital Asset Pricing Model.
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