108 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
calls the naive approach. I am curious to know how that 10 per 
cent is made up. In particular, I would like to know how the ap- 
proach does in terms of the rate of growth of consumption taken 
separately on the one hand and in terms of the changes in the sa- 
vings ratio necessitated also taken separately, on the other hand. Tt 
would seem to me to be of some interest to know whether the gain 
comes principally from the variable which one is ultimately interested 
in or whether it comes from being able to cut down on the number 
of changes of policy needed to get the variable of ultimate interest 
up as high as possible. 
THEIL 
Professor LEONTIEF’s question is clearly the most fundamental 
one that has been raised in the discussion. I think it is worthwhile 
to make a distinction between strategies in general and the specific 
case of quadratic preference functions and linear constraints. As to 
strategies in general, it can be proved fairly easily by means of an 
example that if you take a decision step by step and if you do not 
combine your present decisions with those of later decisions (as is 
the case when a decision rule or strategy is used), you may lose in 
terms of expected utility. In fact, it makes also difference as to 
the first period decision. However, in the special situation of qua- 
dratic preference functions and linear constraints, this is different. 
The first-period certain equivalence theorem enables us to compute 
this maximizing first-period decision in a very simple way by just 
neglecting this difficult procedure of comparing all these possible 
strategies, 
Professor FriscH dislikes the idea of taking the rate of savings 
as an instrument. This is the result of the simplicity of the model. 
Making it more realistic would have forced me to go into a much 
more elaborate model and I am afraid that in that case I would have 
lost the main point, which is, as Professor LEONTIEF put it so aptly, 
not about the particular model or the particular preference function, 
71 Theil - pag. 34