MILTON FRIEDMAN AND L. J. SAVAGE any consistency among the choices of ginal utility. If the marginal utility of this kind that individuals make? Do money diminishes, an individual seeking they neglect the element of risk? Or does to maximize utility will never participate it play a central role? If so, what is that in a" fair"game of chance, for example, a role? game in which he has an equal chance of These problems have, of course, been winning or losing a dollar. The gain in considered by economic theorists, par- utility from winning a dollar will be less ticularly in their discussions of earnings than the loss in utility from losing a dol- in different occupations and of profits lar, so that the expected utility from par in different lines of business. Their treat- ticipation in the game is negative. D ment of these problems has, however, minishing marginal utility plus maxim never been integrated with their ex- zation of expected utility would thus im- planation of choices among riskless alter- ply that individuals would always have atives. Choices among riskless alterna- to be paid to induce them to bear risk. 4 tives are explained in terms of maximiza- But this implication is clearly contra- tion of utility individuals are supposed dicted by actual behavior. People not to choose as they would if they at- only engage in fair games of chance,they tributed some common quantitative engage freely and often eagerly in such haracteristic designated utility-to unfair games as lotteries. Not only do various goods and then selected the risky occupations and risky investments combination of goods that yielded the not always yield a higher average return largest total amount of this common than relatively safe occupations or in characteristic. Choices among alterna- vestments, they frequently yield a much tives involving different degrees of risk, lower average return r example, among different occupa- Marshall resolved this contradiction tions, are explained in utterly different by rejecting utility maximization as an by ignorance of the odds or by explanation of choices involving risk. He ct that young men of an ad- need not have done so, since he did not venturous disposition are more attracted need diminishing marginal utility or by the prospects of a great success than indeed, any quantitative concept of util- hey are deterred by the fear of failure, ity--for the analysis of riskless choices by "the overweening conceit which the greater part of men have of their 4 See Marshall, op. cit, p. I35 n; Mathematical abilities, by"their absurd presump Appendix, n. ix(p. 843)."Gambling involves an their own good fortune, or by fair and even terms. .. a theoretically fair insu s The rejection of utility maximization 135). The argument that fair gambling is an eco- similar deus ex machina. 3 an explanation of choices among dif- than that, firstly the pla es no further assumpti ferent degrees of risk was a direct conse- values of 1, where g(a)is the pleasure derived from quence of the belief in diminishing mar- wealth equal to x.. It is true that this loss of a E. g, see Adam Smith, The Wealth of pleasure derived from the excitement of gambling ed. ) pp. 106-11; Alfred Marshall, Prin that pleasures of gambling are in Bentham's phrase s (8th ed i London: Macmillan 'impure '; since experience shows that they are likely Ltd,rg20),pp.398-4o,554-55,613 3 Marshall, op. cil,, p. 554(first quotation); for steady work as well as for the higher and more Smith, op. cit p. Io7(last two quotation solid pleasures of life"(p. 843)