STOCHASTIC

314 DRfezE AND MODIGLIANI
(— U^U^ii is a local measure of risk aversion at all levels of c2 in the
same sense as —Vyv /K„ provides such a measure at all levels of yt for
timeless uncertain prospects. One must, however, be careful to realize
that the value of (—t/22/l/2)c- is in general not independent of l: It
measures risk aversion along a particular cut of the utility function
orthogonal to the ct axis, but the measure may not be the same, at a given
level of c2, for different choices of Cj (different cuts of the utility function
by parallel planes).
2.3. It follows from Appendix formula (A.15) that, at any point in
(A , c2) space,
where VVVIVV and dcjdy2 are computed along the Engel curve going
through that point, and where the inequality follows from assumptions III
and IV.
The risk premium for a delayed risk must be equal to the sum of (i)
the expected value of perfect information, and (ii) the risk premium for the
same risk when timeless. 11 Thus the second term on the right hand side
of (2.9) measures "twice the expected value of perfect information per
unit of variance yt for infinitesimal risks." That second term is invariant
under monotonic transformations of the utility function; 12 it is the product
of two factors, of which the second one is most easily interpreted.
d*cjdci 2 \v is a (local) measure of curvature of the indifference loci. As
shown in the appendix formulas (A.5, A.6), it also measures the reciprocal
of the substitution effect on ct, of a rise in r. 13 That curvature of the
indifference loci should be relevant to assess the superiority of timeless
10 A necessary and sufficient condition for — C/2a/t/2 to be everywhere independent of
c, is that V = /(