Overlapping generations models with or without production or a portfolio demand for money display a fundamental indeterminacy. Expectations matter; and they are not, in the short run, constrained by the hypotheses of agent optimization, rational expectations, and market clearing. No short run policy analysis is possible without some explicit understanding of how agents expect the economy to respond to the policy. In this framework of perfect foresight and market clearing prices, it is possible to make Keynesian assumptions about the rigidity of money wages and the exogeneity of “animal spirits” of investors, to use the standard IS-LM apparatus, and to derive Keynesian conclusions about the short run effectiveness of policy. Alternatively, starting from different but no less rational expectations, one can derive the “new classical” neutrality propositions.

[We solve the problem of the restrictions imposed on the Jacobian A at prices p̄ of the aggregate excess demand function x(p) of m agents in an exchange economy with l commodities, under the assumption of individual rationality. Given an arbitrary differentiable function x(p) satisfying homogeneity and Walras' law, we attribute rational individual excess demand functions x^1 (p), ..., x^m (p) to the m agents such that at any arbitrarily specified vector p̄ aggregate excess demand is equal to x(p̄) and the following condition is satisfied: There exists a subspace M of dimension m such that the Jacobian at p̄ of x(p) and the Jacobian at p̄ of the aggregate excess demand function define the same linear function on M. If x(p̄) ≠ 0, M can be taken to have dimension (m+1). As an immediate consequence of our proof for m=1 we show that even if p̄, x(p̄), and Dx(p̄) are known for the excess demand function of a single agent, the substitution effect and the income effect cannot be unambiguously determined without knowledge of the utility function. We extend the results proved at a point to large open neighborhoods. We show that if x(p) is an arbitrary function which bounded from below and satisfies homogeneity and Walras' law, and if x(p̄) ≠ 0, then we can find an open neighborhood G of p̄ and (l-1) individually rational excess demand functions x^1(p), ..., x^l-l (p), such that Σ_k=1^l-1 x^k (p) = x(p) everywhere on G.]