Research Article

Economic Theory

, Volume 30, Issue 2, pp 337-362

First online:

A contribution to duality theory, applied to the measurement of risk aversion

  • Juan E. Martínez-LegazAffiliated withDepartment d’Economia i d’Història Econòmica, Universitat Autònoma de Barcelona
  • , John K. -H. QuahAffiliated withDepartment of Economics, Oxford University Email author 

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This paper determines the precise connection between the curvature properties of an objective function and the ray-curvature properties of its dual. When the objective function is interpreted as a Bernoulli or cardinal utility function, our results characterize the relationship between an agent’s attitude towards income risks and her attitude towards risks in the underlying consumption space. We obtain these results by developing and applying a number of representation theorems for concave functions.


Risk aversion Concavity Duality Homotheticity Cost curves

JEL Classification Numbers

C61 D11 D81