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Linear fractional relative risk aversion

Author

Listed:
  • Kristian Behrens
  • Yasusada Murata

Abstract

We characterize the family of utility functions satisfying linear fractional relative risk aversion (LFRRA) in terms of the Gauss hypergeometric functions. We apply this family, which nests various utility functions used in different strands of literature, to monopolistic competition and obtain the profit-maximizing price by generalizing the Lambert W function. We let firm-level data decide whether the RRA in each sector or in the aggregate economy is increasing, decreasing, or constant, which in turn determines whether markups are decreasing, increasing, or constant with respect to marginal costs.

Suggested Citation

  • Kristian Behrens & Yasusada Murata, 2025. "Linear fractional relative risk aversion," Papers 2509.09865, arXiv.org, revised Oct 2025.
    • Handle: RePEc:arx:papers:2509.09865
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    References listed on IDEAS

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    1. Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(4), pages 401-414.
    2. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
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