STOCHASTIC

312 DREZE AND MODIGLIANI
Had the same uncertain prospect been timeless, so that the value of y2
and r were known to our consumer before his choice of cx, then his
expected utility would have been
I max Ufa , (}>! - cO(l +r)+ y,} d max,, J, g(d, x)f(x) dx."
7 In order to get a measure that does not depend upon the choice of units for the
utility function, one should divide both sides of (2.5) by some appropriate index of
marginal utility — like U^ — V,, or U2 — so as to measure the EVPI in the same units
as consumption, either current or future.
8 The mass or density functions must, of course, be kept identical, not only "theoretically"
but also "practically," if spurious contradictions are to be avoided; thus, a
consumer with strong risk aversion may prefer a temporal prospect that is marketable
to a similar timeless one that is not; the appropriate density for the temporal prospect
is then given by the certainty of its market value and our proposition is not applicable.
1. TWO-PERIOD CONSUMPTION MODELS AND PORTFOLIO REVISION 463