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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2§
But the purpose of the simplified model is not to produce
a decision or a design, but rather to establish plausible ranges
of values for the design and operating parameters. When this
has been done the second approach can be invoked. It de-
pends on the fact that the elaborate calculations required to
obtain a single point on the performance functions can be
mechanized and thereby made quick and cheap. Thus although
it may not be possible to write out these complicated functions
explicitly, or even to manipulate them if written out, it is
feasible to ascertain a finite number of points on any of the
functions. Even these mechanical calculations may be quite
elaborate. In particular, if there is a large stochastic element it
may be necessary to simulate the operation of the investment
over a substantial period of time in order to estimate a single
point on the function. But such simulations are now feasible in
the great majority of practical instances and are rapidly be-
coming cheaper to carry out.
Since it is possible to estimate points it is possible to estimate
differences between points, i.e. first derivatives. And therefore
it is possible to apply any one of a number of steepest ascent
procedures to determine iteratively the solution to any of the
problems I discussed earlier. I shall forebear to go into details
since the procedures I have in mind are fairly well standardized
and improved ones are appearing constantly. All the proce-
dures have the property of producing the shadow prices re-
quired for testing preassigned target level along with the so-
lution for each target assignment.
I do not wish to give the impression that the approaches
[ have suggested solve all the problems of deciding on public
investment. Far from it. This is a very difficult field with
many, many open questions. To mention only two of the
pressing controversial issues, there is the problem of chosing
the social rate of discount, and the problem of incorporating
uncertainty into decision criteria. Besides, many problems.
remain to be solved with respect to the kinds of benefits that
31 Dorfman - pag. 18
