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A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System

Oded Galor

Abstract

This paper develops a two-sector overlapping-generations model. It characterizes the dynamical system globally and establishes sufficient conditions for the existence of a globally unique perfect-foresight equilibrium. The paper provides therefore a useful framework for global dynamic analysis of phenomena whose modeling requires a multi-dimensional commodity space. The analysis demonstrates that gross substitutability in consumption is not sufficient to ensure the determinacy of equilibrium in this production economy. However, if in addition the investment good is capital intensive and second period consumption of two-period-lived individuals is a normal good, then the perfect-foresight equilibrium is globally unique. If the consumption good is capital intensive, global uniqueness does not hold despite the existence of gross substitutability and normality in consumption. The paper establishes in this case sufficient conditions for local determinacy, local indeterminacy, and global indeterminacy.