The Kurz–Salvadori Eigenequation for the Profit–Price–Money Wage Rate Relationships, Piero Sraffa and Alfred Brauer: A Mathematical Note

The Kurz–Salvadori eigenequation concerns Sraffian closed, single‐product–circulating capital economies and determines the unique economically relevant profit rate and price vector that correspond to an exogenously given money wage rate. This paper approaches the Kurz–Salvadori eigenequation as a (semi‐)positive rank‐one matrix perturbation of the zero‐wage price system and shows the connection between Piero Sraffa's linear profit–money wage rate relationships and Alfred Brauer's theorem for the eigenpairs of special rank‐one perturbations of a matrix. Thus, it also points out that Sraffa implicitly provided a proof (though not a general or complete one) of Brauer's theorem.