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Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-sided Altruism Dynamics

Takaaki Aoki

MPRA Paper from University Library of Munich, Germany

Abstract: This article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. We analyzed the special case where the weights of two-sided altruism are dynamically inconsistent. The Bellman equation for two-sided altruism proves to be reduced to one-sided dynamic problem, but the effective discount factor is different only in the current generation. We show that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of self-consistent policy functions with distinct steady states (indeterminacy of self-consistent policy functions).

Keywords: Bellman equation; Two-sided altruism; Dynamic inconsistency; Self-consistent policy functions; Indeterminacy; Overlapping generations model. (search for similar items in EconPapers)
JEL-codes: C61 D91 O41 (search for similar items in EconPapers)
Date: 2013-03-10
New Economics Papers: this item is included in nep-dge and nep-upt
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