SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIOUE ETC. 
‘ 
pra 
An important class of preference orderings is that represent 
able (!) by a continuous preference function (utility function, 
indicator, etc.). A particular function which has been fre- 
quently used has the form 
1° 
for consumption paths (x,, x,, ...) of infinite duration with 
discrete time #=1, 2, … . This form can be interpreted as 
a discounted sum of future one-period utilities u(x,) with a 
discount factor of x per period. This form has been derived 
by the present author (?) from postulates expressing, among 
other requirements. 
(a) noncomplementarity of consumption in an three sub- 
p y p y 
periods into which the future mav be partitioned: 
(D) stationarity in the sense that the ordering of any two paths 
is not altered if both consumption sequences are postponed 
by one time unit and identical consumptions are inserted in 
the gaps so created in each path. 
The utility function so obtained is « cardinal » only in the 
limited sense that the simple form of a discounted sum is con- 
served only by linear transformations of the utility scale. If 
below we occasionally use the expressions « utility difference », 
« marginal utility », these must be interpreted as elliptic 
() Conditions of continuity under which a given preference ordering per 
mits such a representation have been studied bv Worp [19431 and bv Dr 
BREU [1954]. 
2) KooPMANC 
"1060 
especiallv Section 
4] Koopmans - pag. 3