SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE LETC. 237 
It 2 represents the rate of growth of the labor force, Z repre- 
sents a capital stock per worker so large that the investment 
required to keep it at the same level absorbs all output, leaving 
nothing for consumption. If z,>2z, it will therefore be neces- 
sary to allow gz, to decrease at least to some level below Z. To 
avoid the uninteresting complication arising if z,>Z we shall 
from here on simply define « feasibility » so as to imply 
O< 2,52. 
Although we have not vet defined a maximand, it may be 
observed that the attainable set is now defined in a space 
where the « point » is a pair of positive functions x,, z, of time, 
defined for o=¢<oco. This is an infinite-dimensional space for 
the double reason that we use a continuous time concept and 
an infinite horizon. It remains infinite-dimensional if we limit 
ourselves (!) to twice differentiable functions z, and once dif- 
ferentiable functions x. 
5. THE PATH OF THE GOLDEN RULE OF ACCUMULATION 
To answer an important preliminary question, we first con- 
sider a KANTOROVICH type restriction of the problem to a one- 
dimensional one. The latter problem has been formulated and 
solved in the last few years, independently and in one form 
or another, by (*) ArLaIs [1962], DESROUSSEAUX [1961], 
PHELPS [1961], JoAN ROBINSON [1062], SwAN [1060], VON 
WEIZSACKER [1962]. 
Remove from the definition of the attainable set the restric. 
(") Due to twice differentiability of the data functions f(z) above and 
u(x) below we will not be excluding any optimal paths by that requirement. 
However, a slightly weaker requirement will be found useful in the Appendix. 
(°) Dates are bibliographical only and refer to the list of references below. 
Some of these authors used somewhat more general models involving ar 
exponential technological improvement factor in the production funcHon 
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