Edgeworth was an Irish economist (1845-1926), professor of Political Economy at the University of Oxford, whose most important contributions to economic science were statistical in nature, primarily in the area of index numbers, highlighting also the mathematical apparatus needed for the drawing of indifference curves and the contract curve, from the first analysis of W.S. Jevons. Although it would be Vilfredo Pareto, in 1906, who would draw an indifference map, as we know the representation of various indifference curves nowadays.

In his “Mathematical Psychics: an Essay on the Application of Mathematics to the Moral Sciences”, published in 1881, Edgeworth designed what is now known as an Edgeworth box, which basically allows us to compare two mathematical functions represented as curves using the same axis. However, it was also Pareto in 1906 who would depict this Edgeworth box as we know it, as a “box”. It was also in “Mathematical Psychics” where utility functions started to be written as F(x_n, y_n, z_n), closer to what we see in today’s textbooks. It must be said, as an anecdotical fact, that Edgeworth mentioned in a footnote this book, when interpreting an earlier book form J. J. Thomson, that “energy is the product of mass and the square of velocity”, which is generally attributed to Einstein or other physicists.

In 1894, Edgeworth published a diagram in “Theory of International Values” explaining the terms of trade from a geometrical perspective, basing this article on J. S. Mill‘s work on trade and his theory on reciprocal demand.

Alfred Marshall was an English economist (1842-1924), and the true founder of the neoclassical school of economics, which combined the study of wealth distribution of the classical school with the marginalism of the Austrian School and the Lausanne School. Professor at Cambridge, he was the author of “Principles of Economics”, 1890, which became the most widely read manual in microeconomics in his time. This book, which is his major work, established a radical change on how economics were taught. Instead of just writing long pages, Marshall draw diagrams throughout the chapters, allowing a better understanding of economic theories and models, such as J. S. Mill’s reciprocal demand, or an analysis on the differences between fixed and variable cost, and the importance of time periods when analyzing these matters. In fact, Marshall is the precursor of today’s cost analysis.

Of unquestionable educational clarity and filled with profound social principles, Marshall contributed to economic science with concepts such as elasticity and the further development of other subjects, surpluses for instance. Although he did not invent the term nor did he initiate this theory, he did made a clearer separation and definition of different kind of surpluses, such as consumer’s and producer’s surplus.

Also in his “Principles of Economics”, he stated the differences between internal and external economies of scale, as well as a diagram which depicted the fluctuations in supply and demand that took place before arriving to a steady state, a general equilibrium. This equilibrium was reached by means of changing amounts, not prices, as Léon Walras stated.

He is also considered as founder of the Cambridge School, where he taught economics until his retirement. Other renowned economists belonging to this school are Arthur C. Pigou and J. M. Keynes.

Léon Walras, a French economist (1834-1910), is considered, along with W. S. Jevons and Carl Menger, a co-founder of marginalism and theory of utility. He is regarded as the founder, along with Pareto, of the Lausanne School. On his “Elements of Pure Economics”, 1874, Walras made his major contribution to economics, general equilibrium theory, on which all demands are interrelated into a coherent set of relationships.

This general equilibrium was reached by means of a “tâtonnement”, changes in price that would gradually approximate supply and demand until a steady statewas reached. A few decades later, Alfred Marshall would present a different general equilibrium theory, on which the steady state would be reached by means of changes in quantities.

Carl Menger, was an Austrian economist (1840-1921), who is considered to be, along with W. S. Jevons and M.-E.-L. Walras, a co-founder of marginalism and of the theory of utility, and was also founder of the Austrian School, where his main followers Wieser and Böhm-Bawerk were his disciples. In his “Principles of Economics”, 1871, Menger attacked as incorrect the labor theory of value, expressing his view that the factor determining the value of a good is not the amount of work nor other goods needed to produce it, but the importance we place on the basis of the satisfaction we believe that it can offer.

Jevons was a British economist (1835-1882), who is considered, along with Carl Menger and M.-E.-L. Walras, a co-founder of marginalism and theory of utility. Jevons is the author of the book “The Theory of Political Economy”, 1871, in which he devised the concept of marginal utility, from an additive and separable utility function, although it was not measurable on cardinal terms. These studies were possible thanks to Johann H. von Thünen’s works, who was the first economist to use the word “marginal”, which meaning Jevons adopted in his works using the term “final”. He is also considered as a precursor of Econometrics for his work on business cycle, index numbers and moving averages, topics on which he used his extensive knowledge of mathematics.

Although his works on marginal utility are considered pioneer during the marginal revolution, and important for the development of neoclassical economics, Jevons considered there would be only one possible solution when considering barter exchange. However, there are infinite solutions, as was demonstrated later on by Francis Y. Edgeworth, whose indifference curves are based on Jevons’ earlier work.

Marginalism is a method of analysis used in microeconomics, which seeks to explain economic phenomena through mathematical functions (production, consumption, etc..). The term “marginal” was first used by Johann H. von Thünen in his “The Isolated State”, in 1826. The Marginal revolution, which took place a few decades later, around 1870, brought the prevailing classical view of value theory to an end. Indeed, thanks to the work of three economists: W. S. Jevons, Carl Menger and M.-E.-Léon Walras. Even though these economists worked independently, they shared a few ideas which made their work the beginning of the utility theory:

–utility was measurable in cardinal units, such as monetary units;

-the utility function is additive and separable;

-they all use the Gossen’ laws.