American Economic Association

Dialektische oder Rationale Methoden in der Nationalökonomie? Eine Erwiderung an J. M.Keynes by Hans BolzaReview by: John V. SpielmansThe American Economic Review, Vol. 27, No. 3 (Sep., 1937), pp. 534-536Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1802055 .

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534 Reviews and New Books [September

The author's recognition of the limitations on the applicability of his methods and conclusions enhances the value of his work, especially as an introduction of economic principles to over-credulous beginners in theory; and the ingeniously devised diagrams afford visual assistance in under- standing difficult points of the discussion.

IRSTON R. BARNES Yale University

Dialektische oder Rationale Methoden in der National8konomie? Eine Erwiderung an J. M. Keynes. By HANS BOLZA. (Munich: Duncker und Humblot. 1936. Pp. 83. RM.2.80.)

By "dialectic" the author means the method of expressing one's thoughts in ordinary discourse, by "positive-rational" the method of casting them into mathematical form (especially graphs, it seems). His thesis is that only the positive-rational method is capable of giving insight into economic processes clear enough to enable man to exercise intelligent control over economic forces, in particular to stabilize the business cycle.

The author refers-very conspicuously in the subtitle, and again in the introduction, though nowhere else--to Mr. J. M. Keynes's latest book, The General Theory of Employment, Interest, and Money, as an example of "the hopelessness to which the dialectic method is doomed in attempting to penetrate into economic interrelationships which in the work of so prominent an economist as Mr. Keynes . . . must be regarded as especially tragic" (p. 4). This statement may well astonish students of Mr. Keynes who in this latest work as well as in earlier ones has used mathematical formulations whenever he found them applicable.

Mr. Bolza grants that not all so-called economics can be treated mathe- matically. Its human aspects he relegates into the field of sociology, reserving for economics only the concern with strictly measurable economic magni- tudes ultimately reducible to terms of money. His mathematical methods now consist in this: Having rid his subject of all actual complexities and interdependencies of economic factors (by relegating them into sociology), he reduces economics to the study of reciprocal deliveries of goods between two parties paying each other in goods and money and keeping track at every moment of who owes whom how much. (In due course the two initially non-distinguished parties, A and B, become identified with "in- dustry" on the one side, and "the state" on the other.) This simple eco- nomic scheme is next represented in various forms of graphs showing the growing aggregates of goods delivered and received by the two parties as functions of the time. At first Cartesian co6rdinates are used; afterwards cylindrical co6rdinates, the radius of the cylinder being made proportional to the volume of the media of exchange. Under this second scheme the

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1937] General Works, Theory and Its History 535

curves appear as helix lines winding around the cylinder, very attractive and important to look at.

Now prior to, and of course totally independent of, any graphs he chose to make, Mr. Bolza entertained the opinion that all-round prosperity can persist only if the total quantity of the media of exchange is made to grow continually according to an exponential (compound interest) law. After his economic scheme has been cast into the form of graphs this opinion can, of course, be stated in geometrical form: The divergence of the two aggre- gate curves of goods delivered and received means prosperity, since industry is earning money. Their convergence means bad times, since industry is losing money; for the "cylinder" to expand like a trumpet widening in the direction of growing t (time) means good times, and a trumpet pointing with its thinner end into the future spells depression.

These "results" now Dr. Bolza-most strangely-seems to regard as being revealed by, deduced from his graphs-as though it were a compelling argument in itself, that for a trumpet to widen out was a good and prosper- ous thing to do. Truly, of course, these "results" are nothing but the author's originally held views first read into and afterwards again out of the graphs. The whole procedure is as though Newton had demonstrated the truth of his law of gravitation and the superior power of the mathematical method

ml * m2

by drawing a graph of his formula (F k . ) showing the force r2

F as a function of the distance r, and had next derived out of this graph the conclusion that his law has been proved true by a mathematical method, because his curve F (r) showed approach to the r-axis inversely as the square of the distance. What truly did demonstrate the power of the mathematical method and the correctness of the law of gravitation was that Newton was able to deduce mathematically from this law (and the three general laws of motion) practically all the known and several then unknown motions of bodies in the heavens and on earth.

Few economists with any knowledge of mathematics, least of all, Mr. Keynes, deny that at times there are advantages in using mathematical forms of expression and they freely do use them. Symbols may be shorter, more concise, more easily manipulated than corresponding verbal proposi- tions; graphs may produce more vivid and more integrated impressions of functional relationships than verbal descriptions or tables. But, first of all, such mere substitution of mathematical for verbal expressions can hardly be called a mathematical method of investigation unless out of such expressions new results can be mathematically deduced which, though im- plied by the original assumptions, might have been too remotely related to them to be inferred by the "dialectic" method. Secondly, where not handled

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536 Reviews and New Books [September

judiciously, the "positive-rational" method instead of being a source of enlightenment, turns easily into "dust in the eyes," particularly by giving ponderously-important aspects to propositions whose commonplaceness would be at once revealed if they were translated into the "dialectic" form.

If the author had introduced his subject for what it is-a graphical representation of his particular economic views-there need be no quarrel with it, though many might question his economic views. But when he comes forth with the claim of having demonstrated the sole validity of the rational method and thereby having refuted theories presented in the dialectic method, one cannot but reject his assertion as quite groundless, or at any rate as a gross exaggeration.

JOHN V. SPIELMANS

Washington, D.C.

Etudes d'Economie Politique Applique6e (Theorie de la Production de la Richesse Sociale). By LE'ON WALRAS. 2nd ed. by GASTON LEDUC. (Paris: Pichon et Durand-Auzias. 1936. Pp. 495.)

Etudes d'Economie Sociale (The'orie de la Re'partition de la Richesse So- ciale). By LEON WALRAS. 2nd ed. by GASTON LEDUC. (Paris: Pichon et Durand-Auzias. 1936. Pp. viii, 488.)

The celebration in 1934 of the centenary of Leon Walras' birth gave a fillip to the interest in his writings. Fortunately for those interested, his three major books are now in print in definitive editions. The fourth and definitive edition (1900) of the EleMments d'Economnie Politique Pure was reprinted in 1926. The Etudes d'Economie Sociale and the Etudes d'Econo- mie Politique Applique'e, which had not been republished since they first appeared in 1896 and in 1898, now have been revised in final form by Gaston Leduc from the manuscripts left by Walras.

The keenest recent interest has lain in the division of Walras' studies which he worked out in the Ele'ments and called pure economics. But it ought not to be forgotten that, although Walras made his most memorable contributions in pure economics, he thought intently and wrote voluminous- ly in two complementary segments of economics which he labored to sepa- rate from each other and to distinguish plainly from pure economics. The Etudes treat of pure economics but incidentally and are occupied mainly with the two less noticed parts of his economic studies which he developed separately. In the Economie Sociale Walras explores the connection of justice to the problem of personal distribution, and in the Economie Poli- tique Applique'e he applies pure economics to the problem of production. Thus, only in the limited sense that the Etudes deal sparingly with the pure economics for which Walras is best known today do they contain his lesser writings.

These less known and less discussed writings assembled in the Etudes

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