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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
in terms of a one-period utility function #(x) and an aggregator 
function V(x, U). This formulation allows the (scale-invariant) 
discount factor 
(Fe 7) 
OU u=u(x), U=U(x, x .. 
associated with a constant path to increase or decrease with 
the level x at which the path proceeds. The second alternative 
"KoorPMmANS, 1962] is an attempt to express formally the idea 
of a present preference for flexibility in future preferences be- 
tween different commodity bundles of the same timing, or 
between physically the same bundles spread out differently 
over time, or between bundles differing in both respects. 
Further analysis will be needed to determine whether the first 
idea is sufficiently flexible to enable us to avoid the difficulties 
we have encountered, or, if not, whether the second idea can 
be made workable. 
8. TECHNICAL PROGRESS AND POPULATION GROWTH AS Pos- 
SIBLE Poricy VARIABLES 
So far we have treated both technical progress and popula- 
tion growth as exogenously given. It should now be recognized 
that both variables can be, and are in many countries, influ- 
enced by public and private policies and attitudes. Technical 
change is furthered by government conduct or support of re- 
search and of education, by the tax treatment of depreciation 
and obsolescence, and by business policies with regard to 
research and development. Population growth is influenced 
4] Koobmans - pag. 34