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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2°
investment. The result of the analysis will be, not a single
benefit-cost ratio with some marginal comments, but model of
the investment whose performance can be ascertained in respect
to any targets that higher policy may dictate.
Is such an ambitious mode of analysis really practicable?
[ believe it is, and should like to submit some technical sug-
gestions for its implementation.
The critical sticking point is the various performance func-
tions which are very complicated, unknown, and hard to
ascertain. In most cases there is a great deal of pertinent
technical knowledge, but it is not in the proper form. Consider,
for example, one of the more favorable cases: the relationship
between the height of a dam and the amount of irrigation
water it can provide. In the first instance the height of the
dam controls the amount of water that can be impounded in
the reservoir behind it. Given any height, a hydrologist can,
by studying the contours of the land to be flooded, estimate the
the volume of water that can be retained. By making such
studies for a number of dam heights he can generate a functional
relationship between height and contents. Because of irregul-
arities in contours this is likely to be a very complicated fun-
ction but, generally, reasonable smooth and simple approxima-
tions to it can be found.
But this is only a half-way step because the relationship
between reservoir capacity and usable irrigation water supply
— «yield » for short — is even more intricate. There are at
least two complicating features. One is that the reservoir may
not fill annually. As a general rule, the larger the reservoir,
the lower the probability that it will fill in any year. Therefore,
although usable water supply is an increasing function of ca-
pacity up to a point, it increases at a diminshing rate. The
other complicating feature has to do with timing. If the annual
inflow to the reservoir is concentrated in a rainy season that
does not coincide with the time of year at which irrigation
water is demanded then, clearly, the contents of the reservoir
"31 Dorfman - pag. 16
