UTILITY OF WEALTH I55 not always the case. For example, suppose curve which is consistent with our specifica that our hypothetical stranger, rather than tions is given in Figure 5 offering to give you SX or a chance of SY 2.2. An examination of had instead first given you the SX and then that the above hypothesis is consistent with ad offered you a fair bet which if lost would the existence of both "fair (or slightly"un cost you -SX and if won would net you fair")insurance and"fair"(or slightly"un- S(r-X). These two situations are essen- fair")lotteries. The same individual will buy ially the same, and it is plausible to expect insurance and lottery tickets. He will take the chooser to act in the same manner in large chances of a small loss for a small oth situations. But this will not always be chance for a large gain. the implication of our hypotheses if we in- The hypothesis implies that his behavior st that the second inflection point always will be essentially the same whether he is corresponds to present wealth. We can re- poor or rich--except the meaning of"large" solve this dilemma by assuming that in the and"small"will be different. In particular case of recent windfall gains or losses the there are no levels of wealth where people second inflection point may, temporarily, prefer large symmetric bets to any other wealth which corresponds to the second in- ance companies, even at an expected loss flection point will be called customar Thus we see that the hypothesis is con- wealth. Unless I specify otherwise, I shall sistent with both insurance and lotteries, as assume that there have been no recent wind- was the F-S hypothesis. We also see that the fall gains or losses, and that present wealth hypothesis avoids the contradictions with the two dife wealth"are equal. Where common observations to which the F-S hy wealth"(i.e, the second inflection point) 2.3. I shall now apply the modified hy remain at the origin of the graph. Later I pothesis to other phenomena. I shall only will present evidence to support my conten- consider situations wherein there are objec tions concerning the second inflection point tive odds. This is because we are concerned and justify the definition of"customary with a hypothesis about the utility function wealth and do not want to get involved in questions To summarize my hypothesis: the utility concerning subjective probability beliefs.It function has three inflection points. The may be hoped, however, that a utility func middle inflection point is defined to be at the tion which is successful in explaining be stomary"level of wealth. Except in havior in the face of known odds(risk) will cases of recent windfall gains and losses, cus- also prove useful in the explanation of be- tomary wealth equals present wealth. The havior under uncertainty. first inflection point is below, the third It is a common observation that in card flection games,dice games, and the like, people play The distance between the inflection p nore conservatively when losing moder a nondecreasing function of wealth ately, more liberally when winning moder ately. Anyone who wishes evidence of this is curve is monotonically increasing but referred to an experiment of mosteller and ounded;it is first concave, then convex, Nogee to Participants in the experiment were then concave, and finally convex. We may asked to write instructions as to how their also assume that U(-XI>U(X), X> money should be bet by others. The instruc- o(where X=o is customary wealth). A tions consisted of indicating what bets It may also be a function of other things, Thereto"An imental Measurement of utilit is reason to believe, for example, that the distance Journal of Political Economy, LIX (1951), 3 between inflection points is typically greater for The above evidence would be more conclusive if it bachelors than for married men represented a greater range of income levels