SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIOUE ETC. 
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of the ethical or political choice of an objective function from 
the investigation of the set of technologically feasible paths. 
Our main conclusion will be that such a separation is not work- 
able. Ignoring realities in adopting « principles » may lead 
one to search for a nonexistent optimum, or to adopt an 
« optimum » that is open to unanticipated objections. 
In connection with the first aim, Section 3 recalls a few 
results of the theory of linear and convex programming in a 
Anite number of variables, that bear on the problem of opti- 
mum growth. The reading of this section is believed to be 
helpful rather than essential for what follows. Indeed, in most 
of its formulations, the problem of optimal growth is a special 
problem in mathematical programming. The main new ele- 
ment arises from the open-endedness of the future. If one 
adopts a finite time horizon, the choice of the terminal capital 
stock is as much a part of the problem to be solved as the 
choice of the path. Terminal capital, after all, represents the 
collection of paths beyond the horizon that it makes possible. 
An infinite horizon is therefore perhaps a more natural speci- 
fication m many formulations of the problem of optimal growth. 
The mathematical complications so created are the price for 
the greater explicitness of long run considerations thus made 
possible. 
Sections 4-6 analyze a model with a single producible good 
serving both as capital in the form of a stock, and as a con- 
sumption good in the form of a flow. It is produced under a 
constant technologv bv a labor force growing exogenously at 
a given exponential rate. Proofs for many of the propositions 
labeled (A), (B), ... in Section 4 are given under the same 
label in an Appendix (1). 
In Section 7 the findings of the logical experiments of Sec- 
tions 5. 6 are examined. The main conclusion is that some 
(") Approximate equivalents of propositions (E), (F), (H), (I), (J) were 
obtained independently by Davip Cass [1963]. The connection between the 
limiting case of a zero discount rate and the « golden rule of acenmnlation » 
{see Section 5) is also observed and discussed in Cass’s paper 
Konbmans - pag.