An aggregation theorem for securities markets - Rubinstein, Mark (Journal of Financial Economics, 1974)
Alternative sets of sufficient conditions are developed under which equilibrium security rates of return are determined as if there exist only identical individuals whose resources, beliefs, and tastes are a composite of the actual individuals in the economy. These conditions include as special cases all those previously examined in the literature (including conditions sufficient to produce the two-parameter mean-variance model), as well as others. Whenever such a composite individual exists it is shown that (1) valuation equations take a specific form and contain only exogenous parameters of the economy; (2) market exchange arrangements are Pareto-optimal; and (3) competitive value-maximizing firms make completely specified Pareto-optimal production decisions both over dates and states. These results rely on the observation that under popular homogeneity assumptions regarding beliefs and tastes, even though the securities market may be incomplete, equilibrium rates of return are determined as if there were an otherwise similar Arrow-Debreu economy.