Journal Article The Measurement of Utility Get access C. Hillinger C. Hillinger Case Western Reserve University, Cleveland Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 36, Issue 1, January 1969, Pages 111–116, https://doi.org/10.2307/2296348 Published: 01 January 1969 Article history Received: 19 February 1968 Revision received: 15 July 1968 Published: 01 January 1969

This paper gives a necessary and sufficient condition for the following proposition, in which ⪯ and ⪯ i for i = 1,…, n are weak orders on a finite set X. There are real-valued functions f 1 , f 2 ,…, f n on X such that, for all x and y in X and i in {1,…,n}x⪯ i y if and only if f i (x) ≤ f i (y), and x ⪯ y if and only if f l (x) + ⋯ + f n (x) ≤ f l (y) + ⋯ + f n (y). The condition can be viewed as an extension of a simple unanimity or dominance condition.

OST models of portfolio selection have M been one-period models. I examine the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model whzere his income is generated by returns on assets and these returns or instantaneous growth rates are stochastic. P. A. Samuelson has developed a similar model in discrete-time for more general probability distributions in a companion paper [8]. I derive the optimality equations for a multiasset problem when the rate of returns are generated by a Wiener Brownian-motion process. A particular case examined in detail is the two-asset model with constant relative riskaversion or iso-elastic marginal utility. An explicit solution is also found for the case of constant absolute risk-aversion. The general technique employed can be used to examine a wide class of intertemporal economic problems under uncertainty. In addition to the Samuelson paper [8], there is the multi-period analysis of Tobin [9]. Phelps [6] has a model used to determine the optimal consumption rule for a multi-period example where income is partly generated by an asset with an uncertain return. Mirrless [5] has developed a continuous-time optimal consumption model of the neoclassical type with technical progress a random variable.

I. Introduction, 110. — II. The model, 112. — III. The model and Philippine experience, 115. — IV. Demand patterns, demographic change, and economic growth, 120. — V. Implications and conclusions, 124. — Appendix, 125.