226 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 98
Contrasting with this view is the position, expressed among
others quite explicitly by Professor ALLAIS [1947, Ch. VI, X],
that the balancing of the interests of different generations is an
sthical or political problem, in which the competitive market
solution has no valid claim to moral superiority over other
solutions that depend for their realization on action by the
state. À more specific optimality concept is implied in the
strictures of Professor HARROD [1048, p. 40] and of FRANK
RAMSEY [1928, p. 543] against any discounting of future uti-
lites. These authors leave little doubt that they regard only
equal weights for the welfare of present and future generations
as ethically defensible.
The purpose of the present paper is to do some « logical
experiments », in which various mathematical forms of the
optimality criterion are confronted with a very simple model
of technology and of population growth, to see what their
maximization leads to. Our study is similar in purpose to
RAMSEY’s classical paper, and to TINBERGEN’s recent explo-
ration [1960] of the same problem. The underlying idea of
this exploratory approach is that the problem of optimal
growth is too complicated, or at least too unfamiliar, for one
to feel comfortable in making an entirely a priori choice of
an optimality criterion before one knows the implications of
alternative choices. One may wish to choose between prin-
ciples on the basis of the results of their application. In order
‘0 do so, one first needs to know what these results are. This
is an economic question logically prior to the ethical or political
choice of a criterion.
What is a suitable mathematical formalization of the idea
of an optimality criterion? The most basic notion is that of a
preference ordering of growth paths. Such an ordering states
for each pair of alternative growth paths whether they are
equally good, and if not, which is preferred. Indifference, pre-
ference and preference-or-indifference are usually required to
be transitive.
4] Koopmans - pag. 2
