Collective Decision Mechanisms and Efficient Stock Market Allocations: Existence of a Participation Equilibrium

Abstract

Much of the recent work in the theory of general equilibrium under uncertainty has focused on the choice of objective functions for guiding the behavior of firms when the set of markets in the economy is not complete. With the exception of the recent paper by Helpman and Razin [1978], no one has provided a decision rule that firms can use that will always lead to constrained Pareto optimal (CPO) equilibria unless the economy possesses the Ekern-Wilson spanning property., In this paper, we demonstrate the generic nonexistence of an equilibrium relative to the Helpman-Razin decision mechanism, proving that their result is essentially vacuous. However, we further show existence of an equilibrium relative to Hurwicz's [1976] Shared Cost Mechanism within the context of a stock ownership economy and that the equilibrium allocations are CPO provided each firm can choose only the scale of a given activity and is not confronted with a choice from among several possible activities. Of particular importance is that the other results showing optimality (Leland [1974], Ekern-Wilson [1974], Diamond [1967], and Helpman-Razin [1978]) all depend on firms not being able to choose among activities. To complete our characterization we show that the Shared Cost Mechanism is unbiased.