Evaluating economies of scope and potential merger: an alternative approach

In data envelopment analysis literature, the estimation of economies of scope involves comparing two frontiers: one for diversified firms producing two outputs together (the diversified frontier) and the other involving additive firms (the additive frontier). A firm’s scope economies can be assessed by comparing the costs of its outputs against these two frontiers. If the cost for the additive frontier exceeds or falls short of that for the diversified frontier, one can determine the presence or absence of scope economies for the diversified firm. However, constructing the additive frontier requires the assumption that the cost of joint production by a diversified firm equals the cost of separate production by specialized firms. In the absence of such an additive cost structure in empirical studies, scope economies evaluation becomes problematic. To address this, we propose an alternative measurement scheme. Using the free disposability postulate of production theory, our scheme creates two sets of virtual specialized firms from the observed diversified firms, then updates them within their respective specialized firm sets. This approach enables an evaluation of a firm's scope economies by comparing the cost of separate production against updated specialized technologies with the joint production cost against diversified technology. Finally, the scheme also allows an examination of whether a merger between any two specialized firms would be profitable.