Decomposing Efficiency and Returns to Scale in Two-Stage Network Systems

Most of real-life production technologies are multi-stage in nature. Characterization of such technologies via concept like network returns to scale is considered important to firm managers for the stage-specific analysis of their business decisions concerning expansion or contraction so as to improve their firms’ overall performance. Similarly, depicting such multi-stage technologies via network efficiency is important in identifying the sources of network inefficiency. It is, therefore, imperative to estimate both efficiency and returns to scale of a firm not only for the network technology but also for the sub-technologies so as to locate the sources of efficiency and scale economies. The primary purpose of constructing a network technology is to address allocative efficiency that is associated with the choice of how much of intermediate products to produce and consume, in addition to the economic use of primary inputs and the maximal production of final outputs. Therefore, it is necessary that not only the intermediate products are explicitly modeled, but also their optimal values are considered in the construction of sub-technologies’ frontiers so that the issue of allocative efficiency, if exists, can be addressed. Based on the premise concerning whether a network technology considers allocative inefficiency, two approaches are suggested for the estimation of network technology. The first approach makes use of a single network technology for two interdependent sub-technologies. The second approach, however, assumes complete allocative efficiency by considering two independent sub-technology frontiers, one for each sub-technology. These two approaches are, however, necessary, in modeling the output loss of a network firm suffering from allocative inefficiency, which arises due to any possible sub-optimal decision as to how much of intermediate products to produce and consume in the world of changing prices.