The Effect of Prices on Risk Aversion

Affiliation(s)

University of Canterbury, Christchurch, New Zealand.

Universidad Autónoma de Madrid, Madrid, Spain.

University of Canterbury, Christchurch, New Zealand.

Universidad Autónoma de Madrid, Madrid, Spain.

ABSTRACT

Traditionally, risk aversion (both absolute and relative) has been expressed as a function of wealth alone. The charac- teristics of risk aversion as wealth changes have been extensively studied. However, prices, as well as wealth, enter the indirect utility function, from which the typical risk aversion measures are calculated. Given that, changes in prices will affect risk aversion, although exactly how has not been considered in the literature. This paper provides such an analysis. In particular, we firstly remind the reader that both absolute and relative risk aversion are homogeneous functions, and as such independently of their particular slopes in wealth, there is a natural effect that holds relative risk aversion constant and decreases absolute risk aversion when prices and wealth are increased by a common factor. We also show that the size of relative risk aversion as compared to the number 1, which is of much importance to the comparative statics of the economics of risk and uncertainty, depends on how changes in prices affect marginal utility. Under plausible (and standard) theoretical assumptions we find that relative risk aversion is likely to be increasing, and that increases in prices will have a tempering effect on risk aversion.

Traditionally, risk aversion (both absolute and relative) has been expressed as a function of wealth alone. The charac- teristics of risk aversion as wealth changes have been extensively studied. However, prices, as well as wealth, enter the indirect utility function, from which the typical risk aversion measures are calculated. Given that, changes in prices will affect risk aversion, although exactly how has not been considered in the literature. This paper provides such an analysis. In particular, we firstly remind the reader that both absolute and relative risk aversion are homogeneous functions, and as such independently of their particular slopes in wealth, there is a natural effect that holds relative risk aversion constant and decreases absolute risk aversion when prices and wealth are increased by a common factor. We also show that the size of relative risk aversion as compared to the number 1, which is of much importance to the comparative statics of the economics of risk and uncertainty, depends on how changes in prices affect marginal utility. Under plausible (and standard) theoretical assumptions we find that relative risk aversion is likely to be increasing, and that increases in prices will have a tempering effect on risk aversion.

Cite this paper

R. Watt and F. Vázquez, "The Effect of Prices on Risk Aversion,"*Theoretical Economics Letters*, Vol. 2 No. 1, 2012, pp. 40-44. doi: 10.4236/tel.2012.21007.

R. Watt and F. Vázquez, "The Effect of Prices on Risk Aversion,"

References

[1] K. Arrow, “Essays in the Theory of Risk Bearing,” Amsterdam, North Holland, 1971.

[2] L. Eeckhoudt, J. Meyer and M. Ormiston, “The Interaction between the Demands for Insurance and Insurable Assets,” Journal of Risk and Uncertainty, Vol. 14, No. 1, 1997, pp. 25-39. doi:10.1023/A:1007717719423

[3] D. Meyer and J. Meyer, “A More Reasonable Model of Insurance Demand,” In: C. D. Aliprantis, K. J. Arrow, P. Hammond, F. Kubler, H. M. Wu, and N. C. Yannelis, Eds., Assets, Beliefs, and Equilibria in Economic Dynamics. Essays in Honor of Mordecai Kurz, Studies in Economic Theory, Vol. 18, Springer-Verlag, 2004, pp. 733-742.

[4] J. Meyer and M. Ormiston, “Demand for Insurance in a Portfolio Setting,” The Geneva Papers on Risk and Insurance Theory, Vol. 20, No. 2, 1995, pp. 203-211. doi:10.1007/BF01258397

[1] K. Arrow, “Essays in the Theory of Risk Bearing,” Amsterdam, North Holland, 1971.

[2] L. Eeckhoudt, J. Meyer and M. Ormiston, “The Interaction between the Demands for Insurance and Insurable Assets,” Journal of Risk and Uncertainty, Vol. 14, No. 1, 1997, pp. 25-39. doi:10.1023/A:1007717719423

[3] D. Meyer and J. Meyer, “A More Reasonable Model of Insurance Demand,” In: C. D. Aliprantis, K. J. Arrow, P. Hammond, F. Kubler, H. M. Wu, and N. C. Yannelis, Eds., Assets, Beliefs, and Equilibria in Economic Dynamics. Essays in Honor of Mordecai Kurz, Studies in Economic Theory, Vol. 18, Springer-Verlag, 2004, pp. 733-742.

[4] J. Meyer and M. Ormiston, “Demand for Insurance in a Portfolio Setting,” The Geneva Papers on Risk and Insurance Theory, Vol. 20, No. 2, 1995, pp. 203-211. doi:10.1007/BF01258397