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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 between
 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 population
 growth as exogenously given. It should now be recognized
that both variables can be, and are in many countries, influenced
 by public and private policies and attitudes. Technical
change is furthered by government conduct or support of research
 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