Economic Theory

, Volume 30, Issue 2, pp 337–362 | Cite as

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

Research Article

Abstract

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.

Keywords

Risk aversion Concavity Duality Homotheticity Cost curves 

JEL Classification Numbers

C61 D11 D81 

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References

  1. Berge C. (1997). Topological spaces. Dover, Mineola, NYGoogle Scholar
  2. Duncan G.T. (1977). A matrix measure of multivariate risk aversion. Econometrica 45:895–904CrossRefGoogle Scholar
  3. Hanoch G. (1977). Risk aversion and consumer preferences. Econometrica 45:413–426CrossRefGoogle Scholar
  4. Karni E. (1979). On multivariate risk aversion. Econometrica 47:1391–1402CrossRefGoogle Scholar
  5. Khilstrom R.E., Mirman L.J. (1974). Risk aversion with many commodities. J Econ Theory 8:361–388CrossRefGoogle Scholar
  6. Khilstrom R.E., Mirman L.J. (1981). Constant, increasing, and decreasing risk aversion with many commodities. Rev Econ Stud 48:271–280CrossRefGoogle Scholar
  7. Mas-Colell A. (1985). The theory of general economic equilibrium: A differentiable approach. Cambridge University Press, CambridgeGoogle Scholar
  8. Mas-Colell A., Whinston M.D., Green J.R. (1995). Microeconomic Theory. Oxford University Press, OxfordGoogle Scholar
  9. Levy H., Levy A. (1991). Arrow-Pratt measures of risk aversion: the multivariate case. Int Econ Rev 32:891–898CrossRefGoogle Scholar
  10. Pratt J.W. (1964). Risk aversion in the small and in the large. Econometrica 32:122–136CrossRefGoogle Scholar
  11. Quah J.K.-H. (2000). The monotonicity of individual and market demand. Econometrica 68:911–930CrossRefGoogle Scholar
  12. Quah, J.K.-H. (2003). The law of demand and risk aversion. Econometrica 71:713–721CrossRefMathSciNetGoogle Scholar
  13. Stiglitz J.E. (1969). Behavior towards risk with many commodities. Econometrica 37:660–667CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department d’Economia i d’Història EconòmicaUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Department of EconomicsOxford UniversityOxfordUK

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