Monday, June 21, 2010

Formalism in Economics

I think many mainstream economics equate formalism with use of equations. But analytical categories that are not easily set out as the value of a variable in a numerical equation can provide a kind of formalism. And, if you want mathematics, one could, I suppose, set out an ontology, using model theory, for such categories. (I'm not sure what would be the point of that.) To illustrate my claim, I point to two sets of triples that some economists have developed.

Structure, Organization, and Agency need to be analyzed if one wants to understand the provisioning process in capitalist economies. The interindustry dependencies shown in Input-Output tables, macroeconomic income flows, and money flows show some structures important for understanding capitalist economies. Business enterprises, government and quasi-government bureaus, and families are important organizations in such economies. Agency occurs, that is, decisions are made by individuals, in a context provided by such structures and organizations (Lee 2009).

Oligopoly involves a small number of firms maintaining special privileges in a market environment where other firms might enter (Rothschild 1993). Ever since the work of Joe Bain and Paolo Sylos Labini (Modigliani 1958), economists have analyzed oligopoly on the basis of Structure, Conduct, and Performance. The structure of a market is more or less stable in time, observable, and influences the conduct of market participants. Conduct includes the choice of which commodities to buy, the prices to post, decisions about advertisement, etc. Performance is a matter of comparing market results with some sort of ideally efficient results (Schmalensee 1987).

  • Frederic Lee (2009) A History of Heterodox Economics: Challenging the Mainstream in the Twentieth Century, Routledge
  • Franco Modigliani (1958) "New Developments on the Oligopoly Front", Journal of Political Economy, V. 66, N. 3 (June): pp. 215-232.
  • Kurt W. Rothschild (1993) "Oligopoly: Walking the Sylos-Path", in Markets and Institutions in Economic Development: Essays in Honour of Paolo Sylos Labini (Edited by S. Biasco, A. Roncaglia, and M. Salvati), St. Martin's Press
  • Richard Schmalensee (1987) "Industrial Organization", in The New Palgrave: A Dictionary of Economics (Edited by J. Eatwell, M. Milgate, and P. Newman), MAcmillan


Alex said...

Yes, somehow economists think of mathematics when asked about formalism or rigour. In fact, most economists are not aware that rigour has no single definition in mathematics. Velupillai had some interesting comments to make on the kind of rigour employed by Sraffa in a paper which would be 2-3 years old.

Robert Vienneau said...

Yes, the constructivist views Velupillai reads in Sraffa are simpatico with Wittgenstein's views on the foundations of mathematics. I find this philosophy challenging and intriguing. One place to read Velupillai is his paper "Sraffa's Economics in Non-Classical Mathematical Modes", in Sraffa or An Alternative Economics (ed. by G. Chiodi and L. Ditta), Palgrave Macmillan (2008).

A good book on changing views on mathematics and their influence on economics is E. Roy Weintraub's How Economics Became a Mathematical Science, Duke University Press (2002).

The point of my post was the narrow one that analytical categories can be useful and can be considered as providing a kind of formalism.

John Ryskamp said...

The problem, as I have already suggested, is to locate precisely the constructivist intervention Sraffa made in his argument. That is what all constructivists are obliged to do. They feel logic inherently leads to paradox (they are mightily impressed by the ridiculous "paradoxes"), so they must make an arbitrary insertion in their arguments so those arguments don't end in paradox.

I have already located the one in Einstein's formulation of the relativity of simultaneity. Where is it in Production of Commodities?

Of course, the biggie is: where is it in the Pythagorean theorem?

Ryskamp, John Henry, Paradox, Natural Mathematics, Relativity and Twentieth-Century Ideas (June 17, 2008). Available at SSRN: