Chipping off to compute Sraffa's Standard ratio

This note describes the construction of two versions of an algorithm to compute the Standard ratio as described by Piero Sraffa in his famous Production of commodities by means of commodities (PCMC). The procedures do not rely on linear algebra operations. Each routine has its advantages and some efficiency experiments are presented. Two of the initial results that deserve deeper investigation are worth mentioning. First, for a given "technology" (interpreted here as the average productivity of each industry), the average Standard ratio obtained over a large number of simulations tends to diminish as the number of industries increases. Second, the number of iterations to reach the solution (the Standard ratio) in each simulation, on average does not seem to depend on the number of industries; in fact the standard deviation diminishes. Finally, a productivity shock affecting the least productive industry is more effective in increasing the overall Standard ratio than an equivalent shock to the highest productive industry. The implication for economic policy would appear to be in favor of financing Research and Development (R&D) in more "traditional" sectors.