STOCHASTIC

CONSUMPTION UNDER UNCERTAINTY 311
prospects, when the market rate of interest for safe loans is r° and v2 is
known, then such a function would coincide with V(y, r°) up to an increasing
linear transformation.
In the language of demand theory, V(y, r") measures utility cardinally
for movements along the Engel curve corresponding to r°, by assigning
utility levels to the successive indifference curves crossed by that Engel
curve. Provided dcjdy is continuous (as implied by assumption II) and
satisfies assumption III, the Engel curve will have a point in common with
every indifference curve and the assignment of utility levels to these curves
will be exhaustive. One may then construct the cardinal utility function
(/(cj, c2) by relying simultaneously on two independent and familiar tools,
namely,
1. Indifference curves, as revealed by choices among sure vectors of
present and future consumption;
2. A cardinal utility function for wealth, as revealed by choices
among timeless uncertain prospects.
2. TEMPORAL PROSPECTS, THE VALUE OF INFORMATION
AND RISK PREFERENCE
2.1. If a consumer owns a temporal uncertain prospect {y2, r) that
he cannot or does not wish to exchange for some other prospect, his
expected utility is given by
max I" U{Cl, (v, - c,)(l +r)+ y2} d