Variable and constant returns-to-scale production technologies with component processes

We consider nonparametric production technologies characterized by several component production processes, and allow both component-specific and shared inputs and outputs. Each process uses its specific inputs and an unknown part of the shared inputs, to produce its specific outputs and an unknown part of the shared outputs. For the described setting, we develop two new models of production technologies, under the assumptions of variable and constant returns to scale (VRS and CRS). These models are based on the worst-case assumption about the allocation of the shared inputs and outputs to component processes and, therefore, do not require exact knowledge of the actual allocation. The new models are larger than the standard VRS and CRS technologies. We provide a formal axiomatic derivation of the new technologies, explore their dual interpretation and demonstrate their usefulness in an application.