240 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
that, starting from the golden rule path #, £ of the preceding 
section as a base line, we welcome equally a unit increase in 
consumption per worker in any one future decade, say. Mere 
numbers do not give one generation an edge over another in 
this scheme of values. 
The next difficulty we face is a technical one. A previous 
investigation by KooPmANs [1960], continued by Koopmans, 
DIAMOND and WILLIAMSON [1962], has shown that there does 
not exist a utility function of all consumption paths, which at 
the same time exhibits timing neutrality and satisfies other 
reasonable postulates which all utility functions used so far 
have agreed with. A way out of this dilemma was shown by 
RAMSEY [1928]. One can define an eligible set of consump- 
tion paths on which a neutral utility function can be defined. 
Moreover, the eligible set is a subset of the feasible set such 
that the remaining, ineligible, paths are clearly inferior to the 
eligible ones, in a sense still to be defined. In RAMSEY’S case, 
in which population was assumed stationary, the criterion of 
eligibility was a sufficiently rapid approach over time to what 
he called a state of bliss. This state was defined as either a 
saturation of consumers with consumption goods, or a satu- 
ration of the productive system with capital to the point where 
its marginal productivity has vanished — whichever state would 
be encountered first. We shall find that in the present case of 
a steady population growth the golden rule path can take the 
place of RAMSEY’s state of bliss in defining eligibility. Thus 
RAMSEY’s device can be applied to our case with what seems 
a lesser strain on the imagination in regard to situations outside 
the range of experience. 
We have one more technical choice to make. For reasons 
of mathematical simplicity, and at some cost in « realism », 
we shall model our utility function after the finite-horizon 
example of 
/T 
u(x,, dt 
4] Koopmans - pag. 16