Time-inconsistent preferences in a general equilibrium model

This paper introduces time-inconsistent preferences in a multicommodity general equilibrium framework with incomplete markets. The standard concept of competitive equilibrium is extended in order to allow for changes in intertemporal preferences. Depending on whether or not agents recognize that their intertemporal preferences change, agents are called sophisticated or naive. This paper presents competitive equilibrium notions for economies with naive agents and economies with sophisticated agents and provides assumptions under which both types of equilibria exist. Surprisingly, the set of naive equilibria in societies populated by time-consistent households is not allocationally equivalent to the set of competitive equilibria. For sophisticated equilibria, the equivalence holds. Time-inconsistency also raises conceptual issues about the appropriate concept of efficiency. Choices have to be made concerning the incorporation of future preferences and the appropriate instruments to create Pareto improvements. For both naive and sophisticated societies, we present four possible efficiency concepts. Suitable conditions are specified for which both naive and sophisticated equilibria satisfy appropriate efficiency concepts.