UTILITY OF WEALTH I53 contrary he would be anxious to underwrite mally of many people and have typically re insurance. He would even be willing to ex- ceived the answers indicated. But these tend insurance at an expected loss to him-"surveys"have been too unsystematic to serve as evidence; I present these questions gain such behavior is not observed On and typical answers only as a heuristic in- the contrary we find that the insurance busi- troduction. After this hypothesis is intro ness is done by companies of such great duced, I shall compare its ability and that of wealth that they can diversify to the point the F-S hypothesis to explain well-estab of almost eliminating risk. In general, it lished phenomena. The hypothesis as a seems to me that circumstances in which a whole is presented on page I55 moderately wealthy person is willing to risk Suppose a stranger offered to give you a large fraction of his wealth at actuarially either io cents or else one chance in ten of unfair odds will arise very rarely. Yet such a getting SI(and nine chances in ten of get willingness is implied by a utility function ting nothing). If the situation were quite ke that of Figure 3 for a rather large range impersonal and you knew the odds were as stated, which would you prefer? Another implication of the utility func tion of Figure 3 is worth noting briefly. A (r) Io cents with certainty or one chance in person with wealth less than C or more than ten of getting Sr? D will never take any fair bet(and, a for- Similarly which would you prefer(why not tiori, never an unfair bet). This seems pe- circle your choice? culiar, since even poor people, apparently as (2)SI with certainty or one chance in ten of much as others, buy sweepstakes tickets, getting SI play the horses, and participate in other (3)Sio with certainty or one chance in ten of forms of gambling. Rich people play roulette getting SIoo? and the stock market. We might rationalize (4)Soo with certainty or one chance in ter this behavior by ascribing it to the "fun of participation,or to inside information. but (s)SI, ooo with certainty or one chance in ten people gamble even when there can be no of getting SIo, inside information; and, as to the joy of(6)S1,ooo, ooo with certainty or one chance in participation, if people like participation but en of getting $Io,ooo,ooo do not like taking chances, why do they not Suppose that you owed the stranger always play with stage money It is desir- cents, would you prefer to pay the able(at least according to Occam's razor )to (7)Io cents or take one chance in ten of have an alternative utility analysis which owing Sr? can help to explain chance- taking among the rich and the poor as well as to avoid the less Similarly would you prefer to owe defensible implications of the F-S hypothe-( 8)SI or take one chance in ten of owing SIo? (o)Sio or take one chance in ten of owing Another level of wealth of interest corre- SIoo? F-S curve. We shall find that the implica- St,0otoo or take one chance in ten of owing ons of the F-s hypothesis are quite plau (Ir)SI, ooo, ooo or take one chance in ten of sible for this level of wealth. I shall not dis cuss these implicatons at this point, for the The typical answers (of my middle-in alysis is essentially the hat of the come acquaintances)to these questions are modified hypothesis to be presented below. as follows: most prefer to take a chance on 2. I. I shall introduce this modified hy- I rather than get Io cents for sure; take a pothesis by means of a set of questions and chance on Sio rather than get SI for sure answers. I have asked these questions infor- Preferences begin to differ on the choice be-