Vilfredo Pareto, referring to the equations that determine equilibrium, wrote:

These equations do not seem new to me, they are old friends. They are the equations of rational mechanics.

This quotation appears in the paper On the Economic Phenomenon: A Reply to Benedetto Croce he doesn't make clear what specific equations he's referring to. As someone with a physics background I am curious if anyone knows/could guess what he is referring to.

  • $\begingroup$ He might be alluding to equations of rational expectations which is economic theory that was developed in the early 60's and 70's. ( see Muth, 1960, 1961 ). Of course, I could be totally wrong here. $\endgroup$
    – mark leeds
    Jan 14, 2020 at 18:59
  • 2
    $\begingroup$ @markleeds given that this paper pre-dates that theory by at least 30 years, yes. You're totally wrong. :) $\endgroup$
    – heh
    Jan 14, 2020 at 20:39
  • $\begingroup$ The mistake maybe depends on the fact that in italian classical mechanics is also called 'rational' mechanics. $\endgroup$ Jul 29, 2022 at 0:00

2 Answers 2


Pareto believed economics could be studied with the same mathematical rigor as physics, so it's quite possible he was speaking to the similarities between mathematical economics and classical mechanics (the latter of which was just coming into its own in the early 1900s). I'm a physicist by training too, and those similarities helped me rapidly cover a great deal of ground my colleagues in economics had to learn fresh, so your intuition makes sense to me.

  • $\begingroup$ My guess is that he is associating the utility function with a potential so that equality of specific marginal utilities means balancing forces. $\endgroup$ Jan 16, 2020 at 16:24
  • $\begingroup$ @UtilityMaximiser Could be. The mathematical analogs are pretty clear, but I don't want to speculate on how much physics-of-the-day Pareto actually knew. :P $\endgroup$
    – heh
    Jan 16, 2020 at 19:27

I read the paper you linked and, actually, Pareto doesn't specify what equations is referring to. But I think he speaks of equilibrium between demand and supply in a market. So, I suppose he is referring to equilibrium in classical mechanics, and to equations as Lagrange or Newton equations in mechanics.

Pareto, I think, is comparing the equilibrium of mechanical objects with the equilibrium in a market when demand equals supply. The ‘forces’ that make prices change, that is excess demand or supply, are represented by the dynamic equations that rule the movement of prices. Such equations may be viewed as an analogous of equations of mechanics.

I say that because Pareto explicitly speaks of demand and supply equilibrium and of an analogy with the equations of classical mechanics in his Principles of pure political economy. For instance, he speaks of certain equations he had written before, relative to demand/supply and prices and says that

In the study of economic equiibrium [such equations] have an analogue function as the equations of Lagrange in the study of equilibrium of mechanics. (Corso di economia politica, p. 152, italian edition, UTET, 1987, my translation from italian).

Moreover, Pareto speaks of mathematics in economics, comparing it with classical mechanics, in his Applied political Economy: here we can see that he knows well classical mechanics.

As far as I know, Applied political Economy hasn't been tranlated in english. But I speak Italian, so I can read Pareto’s operas in italian. I read some passages of his 'Applied Political Economy’, and I can translate some here.

In this work Pareto devotes some pages to a comparison between economic system and mechanical systems and defends the application of mathematics to economics, particularly mathematical tools analogous to the classical mechanics equations.

In paragraph n. 592 of Applied Political Economy, Pareto makes an explicit comparison between economics concepts and mechanical concepts. He devotes a whole page to a scheme, where he puts on the left of the page mechanical concepts and on the right economics concepts.

He writes (ibid., p. 646):

The equilibrium of an economic system presents surprising analogies with the equilibrium of a mechanical system. When one knows well this latter equilibrium, has also clear ideas about the former.

Then he proceedes with the scheme, comparing 'mechanical phenomena' with 'economics phenomena'. For example:

Mechanical phenomenon Given a certain number of material bodies, the relations of equilibrium and motion are studied[...], abstracting from other properties.

Social phenomenon Given a society, the relations are studied which production and exchange arouse among people, abstracting from other circunstances.

And he continues the scheme with other similar analogies.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.