The Sraffian Combinatorial Explosion

Mirowski On Markomata

In the title of this post, I introduce a new technical term. Consider a Leontief input-output matrix characterizing the technique in use, in physical terms. Suppose n industries are producing n commodities. If an alternative process is available in one industry, then a problem of the choice between two techniques arises. If two processes are available in each industry, the choice is among 2ⁿ techniques. If three processes are available in each industry, 3ⁿ techniques exist.

Some researchers are quite aware of the challenges posed by combinatorics. Christian Bidard has what he calls a market algorithm. I have written a bit about a similar algorithm in my 2017 Review of Political Economy article. I think Yoshinori Shiozawa, Masashi Morioka, and Kazuhisa Taniguchi's 2019 book Microfoundations of Evolutionary Economics also has something about this sort of algorithm. By the way, D'Agata's example of the non-existence of a cost-minimizing technique is an example of an infinite loop in this market algorithm.

When analyzing the analysis of the choice of technique, Bidard champions Lemke's algorithm so that the observing economist can avoid looking at all combinations and permutations. Stefano Zambelli, Bertam Schefold, and each of their collaborators had to address combinatorial challenges in obtaining their empirical results.

Kumaraswamy Vela Velupillai, for example, in his Computable Foundations for Economics is another post-Sraffian addressing these issues. If you want to fully understand this stuff, which I do not, you might want to study algorithmic game theory, Norbert Wiener on cybernetics, Claude Shannon on information theory, the Chomsky heirarchy, and so on. I think those building on Sraffa have a contribution to make here.

I have not read a lot of the above. One might think of 'the' market as a distributed system. Markets with different rules for settling transactions can be thought of as types of automata. Somehow, many of these interacting automata comprise a capitalist economy.