General Properties of Isoelastic Utility Economies

33 Pages Posted: 17 Jan 2015

See all articles by Joel M. Vanden

Joel M. Vanden

Pennsylvania State University - Smeal College of Business

Date Written: January 2015


This paper studies the class of single‐good Arrow–Debreu economies in which all agents have isoelastic utility functions and homogeneous beliefs, but have possibly different cautiousness parameters and endowments. For each economy in this class, the equilibrium stochastic discount factor is an exponential function of the inverse mapping of a completely monotone function, evaluated at the aggregate consumption. This fact allows for general properties of the class to be studied analytically in terms of known properties of completely monotone functions. For example, conditions are presented under which the agents’ cautiousness parameters and a distribution of initial wealth can be recovered from an equilibrium stochastic discount factor, even if nothing is known about the agents’ endowments. This is a multiagent inverse problem since information about economic primitives is extracted from equilibrium prices. Several example economies are used to illustrate the results.

Keywords: isoelastic utility, inverse problem, preference recoverability, risk sharing, asset pricing bounds

Suggested Citation

Vanden, Joel M., General Properties of Isoelastic Utility Economies (January 2015). Mathematical Finance, Vol. 25, Issue 1, pp. 187-219, 2015. Available at SSRN: or

Joel M. Vanden (Contact Author)

Pennsylvania State University - Smeal College of Business ( email )

University Park, PA 16802
United States

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