THE UTILITY OF WEALTH', II. Friedman and Savage 3 have ex- in Figure I, We may assume it to be a con- plained the existence of insurance and lot- tinuous curve with at least first and second teries by the following joint hypothesis derivatives. 5 Let U be utility and W be (I)Each individual (or consumer unit) wealth. Below some point 4, (a U)/(awa)< ts as if he(a)ascribed (real) numbers o; between A and B,(am/(awa)>o; called utility)to every level of wealth and above B, (a'U)/(aw )<o To tell geometrically whether or not an individual would prefer Wo with certainty or a"fair chance of rising to w or falling to (b)acts in the face of known odds so as to aximize expected utility 2)The uti This paper will be reprinted as Cowles Com- W,,, draw a line from the point(Wi, U(W1)) ission Paper, New Series, No. 5 to the point(Wa, U(W2). If this line pass C Hildreth, E Malinvaud, L. ]. Sava above the point Wo, U(o), then the ex- the article of Friedman and Savage, quoted in n3, U(Wo); the bet is preferred to having W I take it as axiomatic that the Friedman-Savage with certainty. The opposite is true if the article has been one of the major contributions to the line(W, U(W),(Wa, U(Wa))passes below nt paper leads only to a small modification of the the point(Wo, U(Wo)). In Figure to Wior W。is Friedman-Savage analysis. This modification, how- preferred to a fair chance of rising ever, materially increases the extent to which com nly observed behavior is implied by the analy The existence of derivatives is not essential to the hypothesis. what ntial is that the M. Friedman and L nalysis of Choices In y be convex below A an Risk, Journal of A and B. The discussi 说 Political Economy, LVI (August, 1948), 279-304 affected if these more general assumptions were I wish to avoid delicate of whether made the relevant utility function is the " utility 6 A fair bet is defined as one with expected gain or the utility of income. I shall assume that in- or loss o Ith equal to zero. In particular if a 15 come is discounted by some interest rate, and I shall the probability of Wr and(I-a)is that of w speak of the"utility of wealth hen aWrt(I-aw,= we