#### Summary

Neoclassical economics is really the birth of mathematics as an inescapable tool for constructing theories that are internally coherent (that is, explained in and of themselves without requiring casuistic examples), escaping the slightly lackadaisical approach of many classical economists like the great Ricardo. This allowed Economics to develop at a much faster pace, and provided the basis for how Economics is studied and investigated today.#### Marginalism:

#### Neoclassical economists:

- Alfred Marshall
**Francis Y. Edgeworth**- Arthur C. Pigou
- Vilfredo Pareto
- Irving Fisher

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*.