HARRY MARKOWITZ falling to wa. The chance of rising to wI or "poor"; a person with wealth greater than D falling to W, is preferred to having Wa with is presumably well to do. Friedman and certainty. The first example may be thought Savage go so far as to suggest that these may of as an insurance situation. A person with represent different social classes. The wealth W, would prefer to be sure of W. amount(D-C)is the size of the optimal than to take a chance of falling to wa. The lottery prize (i.e, the size of prize which it is second example may be thought of as a lot most profitable for lottery managers to of tery situation. The person with wealth wo fer). Those poorer than C will never take a Wa) for a lottery ticket in the fair bet. Those richer than D will never take hope of winning(W'I-W1). Even if the a fair bet. Those with wealth between C and insurance and the lottery were slightly "un- D will take some fair bets. fair, "7 the insurance would have been taken We shall now look more closely at the and the lottery ticket bought pothesized behavior of persons with vari- Thus the Friedman-Savage hypothesis ous levels of wealth. We shall see that for explains both the buying of insurance and some points on the W axis the F-S hypothe- the buying of lottery tickets. sis implies behavior which not only is not observed but would generally be considered peculiar if it were. At other points on the curve the hypothesis implies less peculiar, but still questionable, behavior. At only one region of the curve does the F-S hypothesis imply behavior which is only ob his in itself analysis should be modified Consider two men with wealth equal to C+i(D-C)(i. e, two men who are mid between C and D). The which these men would prefer, in the way of a fair bet. rather than one in which the loser would fall to C and the winner would rise to FIC. 3 D. The amount bet would be(D-C)/2- half the size of the optimal lottery prize. At I.2. In this section I shall argue that the the flip of a coin the loser would become Friedman-Savage(F-S) hypothesis contra- poor; the winner, rich. Not only would such dicts common observation in important re- a fair bet be acceptable to them but spects. In the following section I shall pre- would please them more sent a hypothesis which explains what the We do not observe persons of middle in- F-S hypothesis explains, avoids the contra- come taking large symmetric bets, we dictions with common observation to which pect people to be repelled by such bets. If the F-S hypothesis is subject, and explains such a bet were made, it would certainly be still other phenomena concerning behavior considered unusual and probably irrational Inder uncertainty Consider a person with wealth slightly In Figure 3 a line l has been drawn tan- less than D. This person is"almost rich gent to the curve at two points .& A person The bet which this person would like most, with wealth less than C is presumably according to the F-S hypothesis, is one hich if we to D, W+ (aW.>Wo, ai+ would lower him to C. He would be willing (I-aoywi<W. For limits on the amount of un- to take a small chance of a large loss for a Friedman and Savage, opcil,p large chance of a small gain. He would not