Main trends of research in the social and human ... - unesdoc - Unesco

Economics 3 2 I
games, the theory of decisions, cybernetics, and so on. It is difficult to overesti-
mate the importance of this change, and of the new habit of making an explicit
statement of the variables and parameters which go to make up a model;74 eco-
nomic thought is thereby rendered more precise and purposeful, even when the
application of mathematics does not yield a direct result in the form of algo-
rithms which can be used in the solution of practical problems. Such results can-
not be expected too quickly. It must be remembered that the difficulties of
measuring and aggregating economic magnitudes have not yet been overcome,
and that mathematicians have so far devoted little attention to the development
of mathematical theories specially designed for the needs of economics. As G.
Morgenstern has pointed out, our economic knowledge is less precise than the
information that was available about physical phenomena in the seventeenth
century, when physics was first mathematized. As a result of the example af-
forded by the natural sciences, however, the mathematization of economics is
being attempted even in areas where this is by no means necessary. This could
lead to a faulty formulation of problems, to the clothing of vague thoughts in
mathematical language, and to the abuse of sophisticated mathematical tools.
Unfortunately, no calculus is available to economics and the other social sciences
which they could use as effectively as differential calculus is used in mechanics.
We are not, of course, starting from scratch. Considerable progress has been
made in recent years in the practical application of optimization procedures.
Linear and dynamic programming is being widely used (usually in connexion
with partial problems) whenever the goal function can be unequivocally deter-
mined.
There has been no shortage of attempts to construct comprehensive models
which would ensure the optimization of a national economy over a period of
several years and hence, to devise the optimum plan. In the earlier discussion
above on growth theory, doubts were expressed about the feasibility of using
comprehensive models for optimization purposes, on the grounds that, under
present circumstances, greater scope seems to be offered, from the point of view
of praxis, by breaking down the general optimum into partial optimums by a
correct choice of techniques, of foreign trade patterns and of the pattern of con-
sump ti or^.^^ The problem of the uniform goal function still represents the main
obstacle to building a comprehensive optimization model. Theoretically, a
discount rate can be used to reduce future consumption to its value in the initial
period; this however begs the question, since no objective criteria are available
to determine what this discount rate should be.
But to suggest that there are no applications for comprehensive models would
be doubly wrong.
First, it is impossible to say what possibilities may be revealed - especially in
countries which go in for comprehensive planning - by a method which has been
elaborated only recently and which is now subject to widescale research.
Secondly, these models are to some extent already in actual use in planning,
supplementing traditional planning methods. With due regard to the need of
guarding against over-optimism, the following possible applications of com-
prehensive models would seem to exist.76