SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC. 255 
sis associated with the proofs of (H), (I), (J) in the appendix 
now indicates that, if the level 2 is prescribed only for t=c 
and £=T, the optimal path bulges out toward the level of Z(p), 
as indicated in Figure 10. The interpretation is roughly a-: 
FIG. TQ 
follows. The negative discount rate gives the greatest weight 
to the per capita utility of the last generation living within the 
planning period [o, T]. In response to this weighting system, 
the optimal path provides for a reduction in capital per worker 
(a « disinvestment » in a per capita sense) during a terminal 
segment of the planning period, in order to allow for high 
consumption at that time. To make this possible, all preceding 
generations make a sacrifice. For the first generation, this 
takes the form of heavy investment needed to increase the 
capital stock more than in proportion to population growth. 
For the intermediate generations, it consists in approximately 
maintaining the capital stock — by continued proportional 
growth — at a per capita level in excess of that which would 
maximize per capita consumption. 
141 Koopmans - pag. 31