The Sequential Indeterminacy Problem

General equilibrium models generically are determinate and have a finite number of equilibria. But, with linear activities and some inelastically supplied factors of production, the economies that arise endogenously as perfect-foresight equilibria proceed through time can robustly be indeterminate. During the initial period of an intertemporal model, the perfect-foresight equilibria typically are well-behaved, but they can generate later-period endowments for agents such that the equilibria that validate perfect-foresight expectations lie amid a continuum of other equilibria. Since later-period equilibria are not continuous functions of endowments and other parameters, agents (even if small relative to the market) have an incentive to manipulate market prices; the assumption that agents are price takers therefore breaks down. Sequential indeterminacy is related to Sraffa’s indeterminacy results in that (1) smooth “neoclassical” technologies eliminate indeterminacy, and (2) the dimension of sequential indeterminacy matches the dimension of indeterminacy in Sraffa’s model. Despite the link to Sraffa, long-run equilibria, where relative prices are constant through time, are generically determinate.