SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE ETC. 383 
With regard to one remark made by Professor ALLAIS, I should 
make clear I did not prove, in the paper presented here, that the 
interest rate had to be larger than the growth rate. The inequality 
between the two rates was introduced as a sufficient condition for 
a general result concerning optimal programs. However, in most 
particular cases I considered here, the rate of interest is larger than 
the rate of growth all the time. 
ALLAIS 
The point is, if this proposition cannot be proved in a genera. 
way, there cannot be an optimal path with the condition : smaller 
than g. I therefore cannot see the meaning of the preceding pro- 
position. 
AAT INVATIT 
In this paper, I introduced the condition only because I was 
unable to find a result without it. But I may remark incidentally 
that a finite horizon was present in the cases where optimal pro- 
grams were found with an interest rate smaller than their 
orowth rate 
KOOPMANS 
Supplementing Professor MALINVAUD’s remarks I do not think 
that the response to the difficulties I have pointed out should be to 
drop the infinite horizon. I think it you make a very large horizon, 
the same difficulty that shows itself starkly with an infinite horizon 
will also show itself somewhat less starkly but in an equally disturb- 
ing manner with a verv large finite horizon. Thus the infinite 
Malinvaud - pag. 83