SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE ETC.

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Koopmans paper the preference function is a function of one varia
ble x, only; in the MALINVAUD paper it is a function of two varia
bles n, and c, work and consumption. The way in which the utility
functions are discounted is also open to discussion. From the point
of view of the theory of optimum allocation of resources I do not
see any economic reason for such discounting. It is a pure hypothesis,
 and in the general theory of optimum allocation of resources
no justification of this procedure is to be found.
In my second point I join Prof. FriscH’s position, but only
from a theoretical point of view. I think that from the standpoint
of theory, it is very interesting to separate the problem of optimal
economic growth into two problems. The first is the study of what
happens if we limit ourselves to the production function; the second
is the introduction of preference functions. I think that in economic
programming, this procedure is not valid, but from the point of
view of theory, it is very useful indeed, since the difficulties resulting
 from the consideration of the utility function can be avoided.
Namely, is it possible to consider only one utility function? and if
so what utility function must we consider? etc. In fact, we can
obtain very general results even if some strong hypothesis such as
convexity in the ordinary sense is not taken into account.
Third point: for this reason, I think my point is bound up
with the second one. Professor Koopmans has said that there is no
optimal path with a negative value of the rate ¢ of his paper. Certainly
 this conclusion is absolutely true for the model considered by
Professor Koopmans. All these models are logically consistent. But
in my opinion it is very interesting to study independently the path
which can be considered as optimum if no attempt is made to take
the psychological point of view into account. And in this case very
precise conclusions can be derived even if the rate o has a negative
value.
Fourth point: so far as MALINVAUD’s paper is concerned, I apologize
 for repeating what I said in Cambridge last July. Under the
hypothesis considered by MALINVAUD, the rate of interest must be
greater than the rate of growth of primary income. This result is

5] Malinvaud - pag. 81