SEMAINE D ETUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC. 
473 
where À is the T x T matrix of the second-difference transfor: 
mation and e, the first unit vector of order T (i.e., the first 
column of the T x T unit matrix). Note that x; is a constant 
(it is given from the past), so that it can be omitted from the 
preference function. This preference function, which the de- 
cision maker wishes to maximize, is then assumed to be of the 
following form: 
3-7) 
wo 
, 
T 
4 
+ YY) 
Thus the decision maker is supposed to minimize a weight 
ed sum of squares of two sets of differences. One set deals 
with the successive differences of the savings ratio, the other 
with the differences between actual and desired log-changes 
in per capita consumption. Of course, g should be a positive 
number; it measures the seriousness of a given change in the 
savings ratio relative to that of a discrepancy between the 
actual and the desired log-change in consumption of the same 
numerical size 
. EXPECTED UTILITY AND CERTAINTY EQUIVALENCE 
Our problem in mathematical terms can in the first instance 
be described as that of maximizing the quadratic preference 
function (3.7) subject to the linear constraint (3.4). But it is 
readily seen that the real problem is more complicated. For 
carrying out this conditional maximization requires that the 
determining factors, such as the rates of increase of the po- 
pulation, are known before. This is evidently not the case, 
so that we must conclude that the decisions have to be made 
{71 Theil - pag. 9