Preface

The science of Political Economy has so much interested thinkers for a century.

• It is today more diffused than ever before.

It shares with politics proper the attention of the great journals, which are today the most important means of spreading information.

But the public is so tired of theories and systems. Now, the demand is for “positive” matter in political economy. Examples are:

• custom-house abstracts,
• statistical documents,
• government reports

These will throw the light of experience on the important questions which are being agitated before the country, and which so greatly interest all classes of society.

• This is good.

But theory should not be confounded with systems, although in the infancy of all sciences the instinct of system necessarily attempts to outline theories.

Theory should always have some part, small though it may be, in the development of a science; and that, to a man of my profession in particular, more than to any other, it should be permissible to consider from an exclusively theoretical standpoint, a subject of general interest which has so many different sides.

I intend to apply to Political Economy the forms and symbols of mathematical analysis.

Reputable theorists will condemn me for this.

• With one accord they have set themselves against the use of mathematical forms.

It will be difficult to overcome today a prejudice which thinkers, like Adam Smith and other more modern writers, have contributed to strengthen.

This prejudice is caused by:

• the false point of view from which theory has been regarded by few of those who have thought of applying mathematics to it
• the false notion which has been formed of this analysis by men otherwise judicious and well versed in the subject of Political Economy, but to whom the mathematical sciences are unfamiliar.

There have been few attempts in this direction.

• I only know Les Principes de l'Économie Politique by Canard, a small work published in 1801 and crowned by the Institut.

These pretended principles are so radically wrong. The application of them is so erroneous, that the approval of a distinguished body of men was unable to preserve the work from oblivion.

It is easy to see why essays of this nature should not incline such economists as Jean-Baptiste Say and David Ricardo to algebra.

Most authors who have devoted themselves to political economy seem also to have had a wrong idea of the nature of the applications of mathematical analysis to the theory of wealth.

They imagined that the use of symbols and formulas could only lead to numerical calculations, and as it was clearly perceived that the subject was not suited to such a numerical determination of values by means of theory alone, the conclusion was drawn that the mathematical apparatus, if not liable to lead to erroneous results, was at least idle and pedantic.

But those skilled in mathematical analysis know that its object is not simply to calculate numbers. It is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression.

Thus, the theory of probabilities furnishes a demonstration of very important propositions, although, without the help of experience, it is impossible to give numerical values for contingent events, except in questions of mere curiosity, such as arise from certain games of chance.

Thus, also, theoretical Mechanics furnishes to practical Mechanics general theorems of most useful application, although in almost all cases recourse to experience is necessary for the numerical results which practice requires.

The employment of mathematical symbols is perfectly natural when the relations between magnitudes are under discussion; and even if they are not rigorously necessary, it would hardly be reasonable to reject them, because they are not equally familiar to all readers and because they have sometimes been wrongly used, if they are able to facilitate the exposition of problems, to render it more concise, to open the way to more extended developments, and to avoid the digressions of vague argumentation.

There are authors, like Smith and Say, who, in writing on Political Economy, have preserved all the beauties of a purely literary style.

But there are others who have not been able to avoid algebra.

• They have only disguised it as long and tiresome arithmetical calculations.
• An examples is Ricardo

Anyone who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labour and pains.

Differential and Integral Calculus

The theory of wealth raises questions which can be solved essentially not on elementary algebra, but on differential and integral calculus.

• This is because such calculus comprise arbitrary functions, which are merely restricted to satisfy certain conditions.
• These only consider very simple conditions

I fear that calculus may be too abstruse to most people who like the topic of wealth.

• But these will not deserve the attention of professional mathematicians, except as they may discover in it the germ of questions more worthy of their powers.

A famous French school gives thorough mathematical training. Its graduates have directed their attention to applications of those sciences which particularly interest society.

• Theories of the wealth of the community must attract their attention.

In considering them they are sure to feel, as

The previous authors have thought fit to write about wealth, something generally indeterminate and often obscure, in ordinary language.

• But I have felt the need to write analyses using familiar mathematical symbols to render them determinate.

I wrote this book to help them and lessen their labour.

The first notions of competition and the mutual relations of producers, the writers might notice certain relations which are very curious from a purely abstract standpoint, without reference to proposed applications.

I am not making a complete and dogmatic treatise on Political Economy.

• I did not include questions to which mathematical analysis cannot apply, and those which seem to me entirely cleared up already.

I am not supporting any system or any party. I believe that:

• there is an immense step in passing from theory to governmental applications
• theory loses none of its value in remaining preserved from contact with impassioned polemics
• my essay will make clear how far we are from being able to solve, with full knowledge of the case, many questions which are boldly decided every day.