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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
= 
in which there is just one good that can be used either for con- 
sumption or as capital in production. Notwithstanding differen- 
ces in notation, my model is very similar to his. I am, how- 
ever, 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 pro- 
vided 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 in- 
finite sums that might not converge. 
Section 3 is devoted to the determination of sufficient con- 
ditions 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