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Ruling out multiplicity and indeterminacy: The role of heterogeneity.

By Berthold Herrendorf, Alos Valentiny and Robert Waldman

Abstract

It is well known that economies of scale that are external to the individual decision makers can lead to self-fulfilling prophecies and the multiplicity or even indeterminacy of equilibrium. We argue that the importance of this source of multiplicity and indeterminacy is overstated in representative agent models, as they ignore the potential stabilizing effect of heterogeneity. We illustrate this point in a version of Matsuyama' s (1991) two-sector model with increasing returns to scale. Two main results are shown. First, sufficient homogeneity with respect to individual productivity leads to the instability and non-uniqueness of a given stationary state and the indeterminacy of equilibrium at that stationary state. Second, sufficient heterogeneity leads to the global saddle-path stability and the uniqueness of a given stationary state and the global uniqueness of equilibrium.Heterogeneity; increasing returns to scale; indeterminacy; stability; uniqueness;

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