256 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
Now if T is increased, the benefitted generation becomes 
a more and more distant one. If T=o0, there is no benefitted 
generation, and the limiting position of the curve in Figure 10, 
while mathematically well-defined, merely describes a path of 
indefinite and fruitless sacrifice. 
The problem appears in even sharper light if technological 
progress is also recognized. A study by INAGAKI [1963] uses 
a CoBB-DOUGLAS production function 
F(Z, L, t) = const. ef Z*1.1-¢ 
subject to exogenous technological progress at the constant pro- 
portional rate 3, an instantaneous utility function 
(53) 
wr) ~ logs -- log x 
as 
exhibiting suitable behavior for large values of x, and a labor 
force growing exponentially at the rate A. Among other re- 
sults, INAGAKI finds that, for the integral V(p) as defined in (19) 
to converge on the counterpart of our path (x,, z,) =(£(p), #(e)), 
it is necessary that 
-— Œ- 
“4] Koopmans - pag. 32