THE UTILITY ANALYSIS OF CHOICES INVOLVING RISK much more a man will spend when he is sumption is contradicted by experience rich than when he is poor to avoid any can easily be shown by hundreds of ex given amount of pain or discomfort o amples [including] the participation of Some of the comments that have been individuals in lotteries in which their the utility analysis of von Neumann and ity)is negative, Tation of gain(util- published by competent economists on mathematical expe Morgenstern are even more remarkable testimony to the hold that diminishing 2. OBSERVABLE BEHA TO BE RATIONALIZED rey remarks: "There is abundant evi- The economic phenomena to which the dence that individual decisions in situ- hypothesis revived by von Neumann and ations involving risk are not always made Morgenstern is relevant can be divided in ways that are compatible with the nto, first, the phenomena ordinarily sumption that the decisions are made ra- garded as gambling tionally with a view to maximizing the ond, other economic phenomena involv mathematical expectation of a utility ing risk. The latter are clearly the more function. The purchase of tickets in lot- important, and the ultimate significance teries, sweepstakes, and'numbers'pools of the hypothesis will depend primarily would imply, on such a basis, that the on the contribution it makes to an under marginal utility of money is an increasing standing of them. At the same time, the rather than a decreasing function of in- influence of risk is revealed most mark come. Such a conclusion is obviously edly in gambling and insurance, so that unacceptable as a guide to social pol- these phenomena have a significance for icy. Kaysen remarks, " Unfortunately, testing and elaborating the hypothesis these postulates [underlying the von out of proportion to their importance in Neumann and Morgenstern discussion of actual economic behavior utility measurement] involve an assump- At the outset it should be confessed tion about economic behavior which is that we have conducted no extensive em- contrary to experience.. That this as- pirical investigation of either class of This elemental argument seems so clearly to phenomena. For the present, we are con justify diminishing marginal desirable even now to sta how this phe- the literature, or obvious from casual ob assumption of increasing marginal utility of money. servation, to provide a first test of the It is only necessary to suppose that the avoidance of hypothesis and to impose significant sub Lin and the other goods that can be bought wi money are related goods and that, while the margin- stantive restrictions on it. al utility of money increases as the amount The major economic isions of an money increases, the marginal utility of avoiding dividual in which risk plays an important pain increases even faster. role concern the employment of the re William Vickrey, ""Measuring M XIII (1945), sources he controls: what occupation to by Reactions to Risk, "econometr The quotation is from pp 327 and 328."The follow, what entrepreneurial activity to f tickets in lotteries, sweepstakes oIs"does not imply that marginal engage in, how to invest (nonhuman) ncreases with income everywhere capital. Alternative possible uses of re- sources can be classified into three broad the quantity that individuals are as maximizing with a quantity C. Kaysen, " A Revolutic en s