University of Virginia Library

Cours d'économie politique; Lusanne, F. Rouge, 1896, 2 vols.

I am not at all satisfied with this way of presenting my idea; but to give it more precision, without entering into a lengthy explanation, would be quite impossible without making use of mathematical symbols. The desire to keep mathematical symbols out of the text explains why in my Cours the theory of rent appears to the notes. It was impossible to give it the desired rigorousness and precisements without the employment of mathematical symbols.

Annuals of the American Academy, May 1897.

The same critic says: "A curious slip for a mathematical economist is made in the discussion of population, a slip that parallels the error of Malthus." To substantiate this he isolates a phrase which he finds in the text -- where there are no mathematics -- and gives it to the reader under the impression that to prove that the progress of wealth in England has not followed the law laid down by Malthus I furnish but this single ground of inference, viz., that between two given epochs the growth of wealth has been more rapid than that of population. He then argues at length to show that one can always make out an arithmetical progression in such form that its terms, within given limits, will be greater than those of a given geometrical progression. Without giving in detail "the complex development" of my critic's argument, it may be characterized as equivalent to the proposition that it is always possible to show that within given limits the ordinates of a straight line will be larger than those of a given curve. The reader who may not be satisfied with Mr Moore's assertion on this point, and who may be willing to take the trouble to verify the case by reference to my Cours, will find (Vol. I, page 341) the following expression for the gross income in England:

R = 346.30 X l00.01104t

The following words, which explain the phrase isolated by Mr Moore, should also be read: "On voit que la raison de la progression est beaucoup plus rapide que celle qui a été trouvée (2111) pour l'augmentation de la population. C'est ce qui explique comment la richesse par tête d'habitant a augmenté considerablement." Accordingly, in the text I have observed that in England wealth has grown more rapidly than population, and in the notes I have furnished the precise expression for the geometrical progression which has been followed by the growth of wealth. Is it not "a curious slip" for a critic not to have seen this? The reason why the explanation has to be sought for in the notes is simply this,--it could not be given without the use of mathematics and I desired to keep mathematics out of the text. In conclusion it may be said that it should not be deemed unnecessary to read the book one attempts to criticise.

This law is as follows: N = A/(x+b)a. In which N represents the number of individuals having an income greater than x or A; b is a constant which For aggregate incomes is in general zero, or very near it; a is another constant whose value lies between 1 and 2. The law applies only to incomes a little above the minimum. The form of the curve in the immediate neighborhood of this minimum income is still undetermined, for statistics do not furnish us sufficient information for its determination. Since the publication of my Cours I have examined many new statistical data, and they all verify the law which I had there formulated. The results of my later investigations have been published in the Giornale degli Economisti (Rome).

Mr. Carlos C. Closson has made an important contribution to this line of study in this JOURNAL for Septmeber 1896.