470 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

|*; = *,_,| in Section 3. Therefore, we shall approximate the
expression (2.8) by -b(x,-x,_,), where b is regarded as a
fixed coefficient (about equal to 1%).
Equation (2.7) is now written as

(2.9) À [log (C,/N,)] = - bx, + (b+1/e)x,_, - v,,

which is the form with which we shall work in the remainder
of this paper.

3. THE PREFERENCE FUNCTION

Our decision maker is supposed to formulate a quadratic
preference function which he wishes to maximize. We shall
consider a very simple quadratic function, which amounts to
a sum of squares as far as the successive log-changes in per
capita consumption is concerned. This should not be regarded
in the sense that we really believe that the decision maker’s
desires are quadratic; it means only that we try to approximate
 the decision maker’s preferences by a quadratic
function in the relevant range (in the same way as the constraints
 of the economy are approximated linearly in the relevant
 range).
Specifically, let d, be the « desired rate » of increase of the
logarithm of per capita consumption in year £. For example,
d,=0.1 (10%); then, given the quadratic character of the
preference function, an actual rate of increase of 5% will have
a disutility of (5 — 10)”=25, a 4% increase will have a disutility
 of (4 - 10)?=36, and so on. Let us write y, for the discrepancy
 between the actual and the desired rate of increase in
year t:

(3.1)

y,=ATlog (C,/N,)1 - d, 3

271 Theil - pag. 6