A “long-run equilibrium” price system is a set of prices that, once the wage rate has been fixed, assures a uniform rate of profit on capital invested in the various industries. Such prices are called “natural prices”, or “normal prices”, or “pro - duction prices”. A rigorous formulation of this notion, whose roots can be found in Classical economists (in particular Ricardo and Marx) can be found in Sraffa (1960). For a single production economy in which the wage rate is con stituted by a given bundle of physical commodities, production prices are the solution for p of the following equation system:2


We will suppose, for simplicity, that only one technology is available and that matrix A is irreducible. It can be shown that system (1) has an economic

meaningful solution for p and r that is unique once a numeraire has been fixed. Let us indicate by p* and r* this solution; r* = 1/M(A) – 1, where M(A) is the dominant eigenvalue of A and p* is its correspondent eigenvector.3 Moreover we will suppose, for simplicity, that constant returns to scale prevail.