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The Fundamental Nature of HARA Utility

Gadi Perets () and Eran Yashiv ()
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Gadi Perets: Université de Lyon, Lyon (University of Lyon)

No 1522, Discussion Papers from Centre for Macroeconomics (CFM)

Abstract: Many models in Economics assume a utility function belonging to the HARA family. This paper shows that HARA utility is more fundamental to economic analysis. The HARA functional form is the unique form which satisfies basic economic principles in an optimization context. Using HARA is therefore not just a matter of convenience or tractability but rather emerges from economic reasoning, i.e., it is inherent in the economic optimization problem. The paper applies Lie symmetries to the optimality equation of Merton’s (1969, 1971) widely used intertemporal model of the consumer-investor in order to show the inherent nature of the HARA utility function. Lie symmetries derive the conditions whereby the optimal solution remains invariant under scale transformations of wealth. The latter arise as the result of growth over time or due to the effects of policy. The symmetries place restrictions on the model, with the key one being the use of HARA utility. We show that this scale invariance of agents’ wealth implies linear optimal solutions to consumption and portfolio allocation and linear risk tolerance (and vice versa). The results have broad implications, as the model studied is a fundamental one in Macroeconomics and Finance. The paper demonstrates the use of Lie symmetries as a powerful tool to deal with economic optimization problems.

Keywords: HARA Utility; Invariance; Economic Optomization; Consumption and Portfolio Choice; Macroeconomics; Finance; Lie Symmetries (search for similar items in EconPapers)
JEL-codes: D01 D11 D91 E21 G11 C60 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-mac and nep-upt
Date: 2015-09
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