Economics Keynes The Scope and Method of Political Economy

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with a less expenditure of effort than is required in the country from
which it obtains them. The citation of examples is not, however, a method
whereby general conclusions can be obtained; and the use of arithmeti-
cal illustrations may involve the danger of our forgetting that after all
they are nothing more than illustrations. It is difficult or even impos-
sible to guarantee the typical or representative character of the particu-
lar numerical data that have been selected, or to be certain that if they
were varied the same general conclusion would always result. The con-
sequence may be a failure to discriminate between that which is essen-
tial and that which is merely accidental.149
�3. Exact numerical premisses not essential to the employment of
mathematical methods. If the use of mathematical symbols and dia-
116/John Neville Keynes
grams is rightly to be called a method, it must do more than yield merely
isolated examples, and must be free from imperfections such as those
just pointed out. The economist must by the aid of his symbols and
diagrams be enabled to deduce conclusions having general validity un-
der conditions that can be precisely determined. It is, however, neces-
sary here to guard against a misapprehension that has led some econo-
mists to reject mathematical methods far too summarily. Professor
Cairnes, for instance, seems to imply that the employment of such meth-
ods is necessarily barren unless we can obtain premisses capable of
being stated with numerical accuracy.150 He is here indeed only follow-
ing in the footsteps of Mill, who remarks that mathematical principles
are manifestly inapplicable, where the causes on which any class of
phenomena depend are so imperfectly accessible to our observation,
that we cannot ascertain, by a proper induction, their numerical laws. 151
Professor Cliffe Leslie argues similarly against the application of math-
ematics to political economy on the ground that economic premisses are
not capable of exact quantitative determination.152 And Dr Ingram says
bluntly, The great objection to the use of mathematics in economic
reasoning is that it is necessarily sterile. If we examine the attempts
which have been made to employ it, we shall find that the fundamental
conceptions on which the deductions are made to rest are vague, indeed
metaphysical, in their character. Quantitative conclusions imply quanti-
tative premisses, and these are wanting. There is then no future for this
kind of study, and it is only waste of intellectual power to pursue it. 153
The impossibility of obtaining exact numerical premisses in politi-
cal economy is fully recognised by Cournot and other mathematical
economists. But at the same time they shew clearly that such premisses
are not always essential to the employment of mathematical methods.
Cournot, for instance, remarks that while the law of demand for any
commodity might conceivably be expressed by an empirical formula or
curve, we cannot as a matter of fact hope to obtain observations suffi-
ciently numerous or exact for this purpose. But he adds that it by no
means follows that the unknown law of demand cannot by means of
symbols be usefully introduced into analytic combinations. For one of
the most important functions of mathematical analysis is to discover
determinate relations between quantities whose numerical values are
unassignable. Functions, while remaining numerically unknown, may
possess known properties; and on the assumption that certain general
relations between quantities hold good, it may be possible mathemati-
The Scope and Method of Political Economy/117
cally to deduce further relations that could otherwise hardly have been
determined.154
Cournot himself exemplifies the process which he thus describes.
He starts with simple formulae to express relations between demand
and price, cost of production and price, and the like, and assuming that
these relations will conform to certain specified conditions, deduces by
mathematical manipulation some of the consequences resulting there-
from. He deduces, for example, with the greatest clearness and preci-
sion the general laws determining, what price will yield to a monopolist
a maximum profit; and he then proceeds to deal with the difficult prob-
lem of the incidence, under different suppositions, of taxes on monopo-
lies. Other problems are treated in a similar manner with more or less
success; and at no point in the reasoning is it essential that numerical
values should be assigned to the symbols.
What is true of algebraical formulae is true of diagrams also. Rep-
resenting, for example, by a curve the manner in which the demand for
a commodity varies with its price, general laws to which this curve will
conform may be determined, and results deduced.
But this does not necessitate that curves of demand for different
commodities should be capable of being drawn with numerical accu-
racy.
�4. Advantages resulting the use of symbolical and diagrammatic
methods in political economy. The employment of symbolical and
graphic methods independently of specific numerical data is of course
confined mainly, if not wholly, to the pure or abstract theory. Those,
therefore, who deny the utility of abstract political economy in any form,
and maintain that the only fruitful method of economic enquiry is induc-
tive and empirical, will naturally reject mathematics as an instrument.
This general question has, however, been sufficiently discussed already;
and, therefore, in briefly enquiring what kind of advantages may result
from the employment of mathematical methods, it will be taken for
granted that the economist ought sometimes to have recourse to abstract
and deductive reasoning. The advantages are partly direct, and partly
indirect; and a brief reference may in the first place be made to the
latter.
When mathematical processes are employed in the solution of a
problem, attention can hardly fail to be called to the conditions assumed
as the basis of the argument, and due importance is likely to be attached
to the exact enunciation of these conditions; a more thoroughgoing quan-
118/John Neville Keynes
titative analysis of fundamental conceptions is also necessary; it be-
comes less easy to slur over steps in the reasoning; and difficulties are [ Pobierz całość w formacie PDF ]

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