SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE ETC. 
38 
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 hypo- 
thesis, 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 result- 
ing 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. Cer- 
tainly 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 apo- 
logize 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