All-engaging Systems

A multiple product system is represented by a couple of matrices that describe the inputs and outputs of every process. Under specific assumptions on the matrices, the economy behaves like a single-product system, at least locally. It is called ‘all-engaging’ if the economy is indecomposable and ‘all-productive’ otherwise. An exhaustive study of the mathematical and economic properties is proposed. This approach is useful to formalize the notion of sector.