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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
phrases referring to a preference indicator of that particularly 
simple form. There is no intent to claim that, even in the 
absence of risk or uncertainty, there is some physical or 
psychological significance to the comparison of utility diffe- 
rences in such a scale. 
There still remains a logical gap between the derivation 
of the above utility function from the postulates referred to 
and its use in the present study: For present purposes a con- 
tinuous time concept is more appropriate. 
2. PLAN OF THE PRESENT PAPER 
We shall freely borrow from PHELPS [1961] and others 
mentioned below the assumptions of the main model considered 
in Section 4, from RAMSEY [1928] a device for maximizing 
utility over an infinite horizon without discounting, together 
with methods for applying the device, frorh SRINIVASAN [1962] 
and from Uzawa [1963] information about the results of 
maximizing a discounted sum of future consumption, and from 
INAGAKI [1063] results about the generalization of the present 
problem to the case of predictable technological progress (1). If 
this particular brew has not been served before, it is not put 
together here for any novelty of the combination. Rather, our 
eclectic model appears to have in it the minimum collection of 
elements needed to serve the two main aims of the present 
paper. 
The first aim is to illustrate the usefulness of the tools and 
concepts of mathematical programming in relation to the 
problem of optimal economic growth. 
The second aim is to argue against the complete separation 
(') Note added in proof: A study by PucacHEv [1963], which has 
several similarities with the present study, has been brought to mv attention 
by ].M. MONTIAS 
"41 Koopmans - pag. 4