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

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.

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References

  1. Berge C. (1997). Topological spaces. Dover, Mineola, NY

    Google Scholar 

  2. Duncan G.T. (1977). A matrix measure of multivariate risk aversion. Econometrica 45:895–904

    Article  Google Scholar 

  3. Hanoch G. (1977). Risk aversion and consumer preferences. Econometrica 45:413–426

    Article  Google Scholar 

  4. Karni E. (1979). On multivariate risk aversion. Econometrica 47:1391–1402

    Article  Google Scholar 

  5. Khilstrom R.E., Mirman L.J. (1974). Risk aversion with many commodities. J Econ Theory 8:361–388

    Article  Google Scholar 

  6. Khilstrom R.E., Mirman L.J. (1981). Constant, increasing, and decreasing risk aversion with many commodities. Rev Econ Stud 48:271–280

    Article  Google Scholar 

  7. Mas-Colell A. (1985). The theory of general economic equilibrium: A differentiable approach. Cambridge University Press, Cambridge

    Google Scholar 

  8. Mas-Colell A., Whinston M.D., Green J.R. (1995). Microeconomic Theory. Oxford University Press, Oxford

    Google Scholar 

  9. Levy H., Levy A. (1991). Arrow-Pratt measures of risk aversion: the multivariate case. Int Econ Rev 32:891–898

    Article  Google Scholar 

  10. Pratt J.W. (1964). Risk aversion in the small and in the large. Econometrica 32:122–136

    Article  Google Scholar 

  11. Quah J.K.-H. (2000). The monotonicity of individual and market demand. Econometrica 68:911–930

    Article  Google Scholar 

  12. Quah, J.K.-H. (2003). The law of demand and risk aversion. Econometrica 71:713–721

    Article  MathSciNet  Google Scholar 

  13. Stiglitz J.E. (1969). Behavior towards risk with many commodities. Econometrica 37:660–667

    Article  Google Scholar 

Download references

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Correspondence to John K. -H. Quah.

Additional information

The work of Juan E. Martínez-Legaz has been supported by the Spanish Ministry of Science and Technology and the FEDER, project BEC2002-00642, and by the Departament d’Universitats, Recerca i Societat de la Informació, Direcció General de Recerca de la Generalitat de Catalunya, project 2001SGR-00162. He also thanks the Barcelona Economics Program of CREA for its support. John Quah would like to acknowledge with gratitude the financial support of the ESRC (grant number R000271171). He would also like to thank the Department of Economics at UC Berkeley, whose hospitality he enjoyed while completing this project. Both authors would like to thank Simon Cowan for pointing the way to some important references. They are also very grateful to the referee whose insightful suggestions led to a much improved paper

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Martínez-Legaz, J.E., Quah, J.K.H. A contribution to duality theory, applied to the measurement of risk aversion. Economic Theory 30, 337–362 (2007). https://doi.org/10.1007/s00199-005-0053-7

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Keywords

  • Risk aversion
  • Concavity
  • Duality
  • Homotheticity
  • Cost curves

JEL Classification Numbers

  • C61
  • D11
  • D81