I. Introduction, 138. — II. Outline of Arrow's model and results, 138. — III. Public goods, 139. — IV. Expenditures as produced commodities, 140. — V. Examples, 142. — VI. Conclusion, 144.

This paper formulates the notion of stochastic equilibria as invariant probability distributions consistent with the behavior patterns of individuals and the disequilibrium adjustment mechanism of the economy. Conditions for existence, uniqueness, and stability of such equilibria are examined. WE CONSIDER A CLASS of problems in this paper in which the economic environment is stochastic. We will be concerned primarily with developing an equilibrium concept for general equilibrium models of this type. However the essential ideas can be carried over directly to partial equilibrium applications. The choice of the specific general equilibrium model used results primarily from a desire to facilitate comparisons with earlier work on alternative equilibrium concepts for this model (see Hildenbrand [9] and Majumdar and Bhattacharya [2 and 3]). Randomness can arise from several sources. We will be considering, for concreteness, a simple exchange economy in which the basic data are the preferences and endowments of the economic agents. Either of these can be random. Typically, randomness of endowments can be allowed for by creating contingent markets in which case the Arrow-Debreu deterministic equilibrium suffices. It is conceptually much more difficult to create markets contingent on tastes due to the difficulties of discovering the true taste pattern of an individual, difficulties which do not arise in the case of endowment vectors which can be observed directly. We will be considering an economy without markets for every future contingency and thus there will remain some randomness. This residual uncertainty in the economy necessitates equilibrium concepts other than the Arrow-Debreu system of market clearing prices. 2. NOTATION