Charasoff and Dmitriev: An analytical characterisation of origins of linear economics

Abstract

Georg von Charasoff was one of the first economic theorists to recognise that the price of production is an eigenvector of the input matrix, and to determine the rate of profit using its eigenvalue. He anticipated, at this analytical level, most of the arguments that were proposed later in the course of the 'transformation problem'. This paper aims to reformulate his significant arguments in a formal manner and to reveal their logical relationship by reproducing the mathematical reasoning, so that the logical characteristic of his system can be identified in comparison with Dmitriev's and Bortkiewicz's linear economic system.

Why didn't Charasoff and Remak use Perron–Frobenius mathematics?

“…105À28) showed that the rate of profit is determined by the rate of growth of Urkapital. Therefore, some authors, for example, Kurz and Salvadori (1995, p. 390) and Mori (2011), give him credit for discovering a simple duality between the price system and the quantity system. In mathematical terms, the equality qA D 0.8q illustrates that the Urkapital vector q is a row eigenvector of the matrix A, corresponding to the dominant eigenvalue 0.8.…”

“…8 In the 1980s the scientific reputation of Charasoff suddenly started to grow, thanks to the amazing discoveries of Egidi and Gilibert (1984). In the following years, many other authors studied Charasoff, for example, Duffner and Huth (1987), Kurz and Salvadori (1993, 1995, 2000, Stamatis (1999), and Mori (2007Mori ( , 2011, all awarding Charasoff the status of a remarkable pioneer. It is now well known that Charasoff independently discovered some Sraffa-like tools.…”

“…Charasoff used his Urkapital and his production sequences for many purposes: determination of prices and the rate of profit (and the law of the rising, not falling rate of profit); distinction between Grundprodukte and other products, where only the production conditions of Grundprodukte (see corn and bread above) determine the rate of profit; balanced growth with profit rate equal to growth rate; convergence of the transformation of labour values or any other value vector into prices; construction of a sort of Sraffian subsystem and dated labour to determine labour values etc. (Egidi and Gilibert 1984, Duffner and Huth 1987, Mori 2011.…”