Tropical Mathematics and Classical Economics

I have just returned from a conference of the Japan Association for Evolutionary Economics at the University of Tokyo.  There I met Yoshinori Shiozawa of Osaka University who has applied a form of math I did not know of previously, tropical mathematics, to Ricardian trade theory, providing a version that depends on input-output analysis that he claims is consistent with Ricardian-Sraffian classical theory with the labor theory of value intact.  His first paper on this appeared in the journal of SIAM, the Society for Industrial and Applied Mathematics, and one last year appeared in the Japanese journal, Evolutionary and Institutional Economics Review, in a special issue edited by mathematician, Donald Saari.  His papers on this and related topics can be accessed at Research Gate.

Tropical math comes out of algebraic geometry and involves semi-rings with two operations, one a minimizing one and the other an additive one.  This generates a linear piecewise linear skeletonized hypersurface, which in the context of trade theory looks to me to bound facets of a PPT that define zones of comparative advantage for different products.   Shiozawa uses a version that depends on a variant called "sub-tropical algebra" (and geometry).  This form of math was invented by Brazilian-based (for which the name "tropical" was given) but Hungarian-born Imre Simon, who died in 2009.

The other application in economics that I am aware of has been by Paul Klemperer in designing product-mix auctions, first used by the Bank of England in 2007 for carrying out in a single auction  of multiple differentiated product what used to involve a multiple series of auctions.  Klemperer has a few papers on this, with probably the most prominent being "The product-mix auction: a new design for differentiated goods," Journal of the European Economic Association, 2010.

Barkley Rosser