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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -

=

in which there is just one good that can be used either for consumption
 or as capital in production. Notwithstanding differences
 in notation, my model is very similar to his. I am, however,
 considering a discrete time represented by the index
t=o0, 1, 2 ... ad infinitum.
C, is aggregate consumption during period ¢, i.e. from time
t to time £+1. Similarly N, measures the labor services provided
 in period {. Equation (1), page 11, defines per capita
consumption ¢, and per capita input of labor #,. Capital at
time ¢ is denoted as K,, and the stock of good available at
time ¢ before consumption as S,=K,+C,. One constraint of
‘he model specifies that the initial stock is equal to a given
number S, Another constraint results from the production :
function, namely equation (6).
Among all programs which are feasible, I am using the
same kind of utility function as Professor Koopmans does,
except that, in some parts but not everywhere in my paper,
[ am taking the per capita labor input as an argument of the
utility function, thus allowing the amount of labor services
provided to be determined simultaneously with consumption
by the choice of the optimal program.
In order to make possible a choice among infinite programs
[ am not using the technique presented by Professor KooPMANS,
out relying on the criterion given by my definition 1, page 17,
namelv :

A feasible program @! is optimal if there is no value of T
and no other feasible program Æ such that the inequalities (14)
and (15) be simultaneously fulfiled.
Taking this as a definition, I am avoiding considering infinite
 sums that might not converge.
Section 3 is devoted to the determination of sufficient conditions
 for a program to be optimal. At this stage the model
remains general except for some assumptions on the production
and utility functions, notably that they be concave and possess:
partial derivatives.

5] Malinvaud - pag. 2