HARRY MARKOWITZ tween SIo for sure or one chance in ten of ting the Sio rather than take SI for sure SIoo. Those who prefer the SIo for sure in take a chance on Soo rather than take SIo situation(3) also prefer SIoo for sure in situ- for sure; perhaps take a chance on Sr,ooo ation(4); while some who would take a rather than take SIoo for sure But the point chance in situation(3)prefer the SIoo for would come when he too would become cau sure in situation (4). By situation(6)every- tious. For example, he would prefer Sr,ooo one erer for sure rather ooo rather than one chance in ten of All this may be explained by assuming essentially the same, in situations(1)- act than one chance in ten of SIo, ooo, ooo SIo, ooo, oo. In other words, he would that the utility function for levels of wealth someone with more moderate wealth, except bove present wealth is first concave and that his third inflection point would be then convex(Fig. 4) farther from the origin. Similarly we hy pothesize that in situations (7)-(II)he would act as if his first inflection point also were farther from the origin Conversely, if the chooser were rather poor, I should expect him to act as if his first and third inflection points were closer 0· present wealth Let us continue our heuristic introduc ion. People have generally indicated a pref than one chance in ten of owing SI; owing SI for sure rather than taking one chance in ten of owing SIo; SIo for sure rather than one in ten of SIoo. There comes a point, however where the individual is willing to take a chance. In situation(II), for example, the FIG. 5 individual generally will prefer one chance in ten of owing SIo, oo, ooo rather than Generally people avoid symmetric bets. owing SI, ooo, ooo for sure. All this may be his suggests that the curve falls faster to plained by assuming that the utility func- the left of the origin than it rises to the right tion going from present wealth downward is of the origin. (I.e, U(X)>U(-X)I a curve as in Figure 5, with three inflection To avoid the famous St. Petersburg Pa resent wealth. The functi mediately above present wealth; convex, from above. For analogous reasons I assume mmediately below it to be bounded from below How would choices in situations(1)-(Il) So far I have assumed that the second in differ if the chooser were rather rich? My flection corresponds to present wealth guess is that he would take a chance on get- There are reasons for believing that this