A MATHEMATICAL STUDY OF THE SRAFFIAN MODEL
This paper has two primary objects. On the one hand, it presents a rigorous derivation of the Sraffa model recurring to some theorems discovered by Frobenius and Perron at the beginning of the twentieth century. This presentation is used to study the concept of productive economies or surplus economies, the solution to the price system and also to provide a clear derivation of the concept of the Standard Commodity.
The second goal of the paper is to sketch von Neumann's balanced growth model and show how Sraffa's model is related to Neumann`s model. Showing the role of the assumptions, one can establish the relationship between both models, particularly the role of irreducibility to obtain uniqueness and unify the study of both models.