ABSTRACT
Those readers of the Journal des Economistesi who are interested in trying to apply mathematics to economics (believe me, I do not have any illusions about their number) will perhaps remember a memoir titled: Principe d’une théorie mathématique de l’échangeii that I read in August 1873 to the Académie des sciences morales et politiques, and that was published by this review in April 1874. In that memoir, I presented the mathematical theory of barter with two goods in the following way. First, starting from one of those goods’ effective demand by each of the holders of the other one, expressed by curves falling as a function of the price, I observed that the effective supply of a good in exchange for another one is equal to the effective demand of the latter multiplied by its price in terms of the former. Consequently, I deduced the effective supply curves from the partial and total effective demand curves, and by the intersection of the former curves with the latter, I found the current price; that is, the price for which total effective demand and supply are equal. Finally, from the utility of each of the goods for any of the exchangers expressed as decreasing functions of the quantity consumed, I demonstrated that, for a person who exchanges at a certain price, a certain amount of a good in his possession for a certain amount of another good not in his possession, the condition of maximum satisfaction of wants is that the ratio of the raretés, that is the intensities of the last wants satisfied, be equal to the price.iii Hence, from the utility curves, combined with the quantities possessed, I deduced the effective demand curves; this [352] demand being the one that procures the greatest possible satisfaction of the wants at any given price. Thus having showed successively (1) how current or equilibrium prices result from demand curves, and (2) how the demand curves in turn result from the utility and quantity of the goods, I have made clear the relation that links the utility and the quantity of goods to their market prices.2,iv,v
As can be seen, there are here two quite distinct issues, [353] both equally essential to the solution of the problem of barter with two goods. The first one leads to the current price, the second deals with the elements of this price. The latter is therefore the basis of the former and the theorem relating to it, which I called the theorem of maximum satisfaction, is the cornerstone of the application of mathematics to economics. It would be wrong to judge its importance by the degree to which it is immediately useful in practical matters: that would show a very poor scientific way of thinking. Statics teaches us: When a body rests on a horizontal plane, touching it at several points, and is in equilibrium, then the vertical line passing through its centre of gravity must intersect that plane in the interior of the polygon formed by the points of contact. Now, this theorem, that is so fruitful in its consequences for pure and applied theory, is not of any use for keeping us standing upright. Thus, when Philamente and Bélise said to Lépine when he fell down:
Look there, the crazy guy! Must people fall After having learned about the equilibrium of things? Don’t you see the causes of your fall, you dummy? That comes from having put aside the fixed point That we call the centre of gravity,
he replied ironically: ‘Yes, I noticed that, Madam, being flat on the ground.’vi
However, if this mischievous young man went further along that line of thought, meaning to insinuate that knowledge of the properties of the centre of gravity and of the mathematical conditions of the equilibrium of a body would be useless, he would be the one to be laughed at, because it is the proper role of science to search for and to find the how and why of things that ordinary persons accomplish or are subjected to every day without realizing it. So, we hope it will be understood that knowledge of the mathematical conditions of market equilibrium can be [354] fundamental knowledge in theoretical economics, and also that each of us, when exchanging one good for another, achieves maximum satisfaction of his wants without bothering to determine whether the ratio of the intensities of his last wants satisfied is equal to the price, and even without suspecting that this must be the case. That being so, it is not astonishing that after having read my memoir, Mr. W. Stanley Jevons, then professor of economics at Owens College, Manchester, immediately claimed priority regarding this theory, because he had already presented, in 1871, in his Theory of Political Economy, the expression of utility in mathematical form and the condition for maximum satisfaction. In the June 1874 issue of the Journal des Economistes, the correspondencevii can be read in which he asked me for that priority, and I restored it to him. For the same reason, it is quite natural that Mr. Jevons and I, alerted by this remarkable coincidence, have carefully inquired into the varied endeavours preceding ours, and were thereby led to the joint compilation of the ‘Bibliography’ of works relating to the application of mathematics to economics that appeared in the December 1878 issue of the Journal des Economistes.viii The present article, aimed at doing justice to Gossen analogously as I had already done to Jevons, is in a sense the last act of the incident of which I have just recalled the successive phases. I hope that the managing editor of this Review will extend to me once more his hospitality, and my few readers their attention. I believe that they will acknowledge, after having read my account, that there is, among the quite numerous examples of scientific coincidence, hardly anything as remarkable as the concordance of Gossen, Mr. Jevons, and myself on the starting point of mathematical economics. Personally, I will go further and say that, among the equally numerous examples of scientific injustice, there is none so blatant as the ingratitude received by Gossen. This man was completely overlooked during his whole life, but, in my opinion, he was one of the most [355] remarkable economists who ever lived. I do not pretend to say everything that could be said about his work and his career, but only to make known what I know of the subject in such a way as to put on the right path those who, later on, will want to render to this great, neglected man the homage of which he is worthy. On 15 September 1878, when I had just sent to Mr. Joseph Garnier the corrected galley-proofs of the bibliography mentioned above, Mr. Jevons wrote to me.ix
The matter has been rather complicated, too, by the discovery of a work, published at Brunswick in 1854, which contains many of the chief points of our theory clearly reasoned out. It is by Hermann Heinrich Gossen and is
entitled somewhat as follows: Entwickelung der Gesetze des Menschlichen Verkehrs.x The book seems to be totally unknown even in Germany, and as I do not read German I was absolutely ignorant of its existence. My successor Professor Adamson of Owens College found it mentioned in some history of political economy, not that of Roscher,xi who seemed ignorant of it I am told. Adamson is going to prepare me an abstract of the book from a copy which he accidentally procured.
