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AbstractThis paper is concerned with a method for the assessment of utility functions of multi‐numeraire consequences. It is proven that given von Neumann and Morgenstern's axioms of "rational behavior" and two additional assumptions, the utility function for (x, y) consequences can be written as U(x, y) = Ux(x) + Uy(y) + KUx(x) Uy(y).K is a constant that must be evaluated empirically. This form shall be designated as a quasi‐separable utility function. It is more general than the separable utility function and is shown to be nearly as easy to use.Implications and ramifications of such a utility function and its requisite assumptions are discussed. A technique for practical application of this work is presented.

Benchmark two‐good utility functions involving a good with zero income elasticity and unit income elasticity are familiar. In this paper we derive utility functions for the additional benchmark cases where one good has zero cross‐price elasticity, unit own‐price elasticity and zero own‐price elasticity. It is shown how each of these utility functions arises from a simple graphical construction based on a single given indifference curve. Also, it is shown that possessors of such utility functions may be seen as thinking in a particular sense of their utility, and may be seen as using simple rules of thumb to determine their demand.

The construction of a representative multiattribute utility function is important in decision analysis. Existing methods focus mainly on constructions of utility functions on the whole domain of attributes. In some cases, decision makers may provide partial information on their local utility assessments. Therefore, it is a challenging and interesting task to construct utility functions that are compatible with local assessments provided by decision makers. This paper proposes the patchwork construction to accomplish this task. We first define a special local preference structure, the local utility independence and then discuss the patchwork construction that unifies local utility independence on different local domains. The utility function elicited by the patchwork approach under the local utility independence condition is named as the local-utility-independent utility function. Three types of local-utility-independent utility functions on three typical partitions are proposed. These local-utility-independent utility functions have concise and tractable functional forms and indicate intuitive preference structures while matching prior known local utility assessments. Furthermore, the preference structures implied by these three types of local-utility-independent utility functions have a close relationship with the n-switch independence. Sufficient and necessary conditions guaranteeing these local-utility-independent utility functions to indicate n-switch independence are provided, respectively. All three types of local-utility-independent utility functions also have an important application in the approximations of arbitrary utility functions when only some local assessments are provided. As approximations, they are robust and have high accuracy.

ABSTRACTThirty empirically assessed utility functions on changes in wealth or return on investment were examined for general features and susceptability to fits by linear, power, and exponential functions. Separate fits were made to below‐target data and above‐target data. The usual "target" was the no‐change point.The majority of below‐target functions were risk seeking; the majority of above‐target functions were risk averse; and the most common composite shape was convex‐concave, or risk seeking in losses and risk averse in gains. The least common composite was concave‐concave. Below‐target utility was generally steeper than above‐target utility with a median below‐to‐above slope ratio of about 4.8. The power and exponential fits were substantially better than the linear fits. Power functions gave the best fits in the majority of convex below‐target and concave above‐target cases, and exponential functions gave the best fits in the majority of concave below‐target and convex above‐target cases. Several implications of these results for decision making under risk are mentioned.