On network two stages variable returns to scale Dea models

Multiplicative decomposition of stages indices is shown to be consistent with Vrs network technologies. It is also shown why the primal dual correspondence breaks for serial network Vrs models. Different Vrs models can be associated with alternative transfer pricing systems, within the network. Multiplicative decomposition implies marginal cost pricing across stages. While other pricing systems (full cost) correspond to some of the known non-multiplicatively decomposable Vrs models, proposed in the literature. Stages indices, therefore, respond not only to efficiency, but also to the network’s distributive criteria across stages. The distributive contents of stage indices provide the key element for a solution to the problem of measuring scale efficiency in network systems. Multiplicative decomposable Vrs models can be extended to more general network systems, containing both parallel and in series structures. The cost of this generalisation is that efficiency indices are referred to modified stages, that is to stages that include dummy processes. In perspective, these results contribute to show how organisational aspects, such as transfer pricing systems, could be modelled once network technologies are approached from the multiplier (ratio) side.