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Bounding the CRRA Utility Functions

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  • Suen, Richard M. H.

Abstract

The constant-relative-risk-aversion (CRRA) utility function is now predominantly used in quantitative macroeconomic studies. This function, however, is not bounded and thus creates problems when applying the standard tools of dynamic programming. This paper devises a method for "bounding" the CRRA utility functions. The proposed method is based on a set of conditions that can establish boundedness among a broad class of utility functions. These results are then used to construct a bounded utility function that is identical to a CRRA utility function except when consumption is very small or very large. It is shown that the constructed utility function also satisfies the Inada condition and is consistent with balanced growth.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 13260.

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Date of creation: 07 Feb 2009
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Handle: RePEc:pra:mprapa:13260

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Keywords: Utility Function; Elasticity of Marginal Utility; Boundedness;

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  12. Juan Pablo RincÛn-Zapatero & Carlos RodrÌguez-Palmero, 2003. "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case," Econometrica, Econometric Society, vol. 71(5), pages 1519-1555, 09.
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