From economies of density and network scale to multioutput economies of scale and scope: a synthesis.

For more than twenty years transport industry structure in general, and that of the airline industry in particular, has been analyzed with the helpof indices like Returns to Density (RTD) and Returns to Scale with variable network size (RTS). Along this period, caveats, corrections and improvements to calculate these measures have arisen. Nevertheless, both RTD and RTS have been established as the textbook indices to study, from a cost perspective, important issues like merging, optimal network size and shape, and the scope for competition. The objective of this paper is to organize this discussion, offering a synthesis of many years of research, and to prescribe what is, in our view, the best way to go about the empirical analysis of industry structure. We conclude that recently suggested methods to calculate i)(corrected) economies of density, ii) the multiproduct degree of economies of scale and iii) the degree of economies of scope, should beused. Both RTD and RTS are defined as scale concepts and calculated as the inverse of the sum of certain product elasticities of costs. Regarding RTD, the basic idea is to analyze the effect on costs of product growth holding network size constant. Yet, in some cases, some authors introduce (many times implicitly) a second condition, namely holding the route structure constant. This introduces ambiguities about what the index is really capturing. On the other hand, RTS is aimed at analyzing costs as both output and the network grow. Both concepts are usually applied within the contextof product specified as a vector of aggregate descriptors, but no generalconsensus about what descriptors should be used has been reached. This generates a second source of ambiguity regarding the use of these indices, as different authors consider different aggregate elasticities. In our paper, we note that the aggregate descriptors are a function of the many transport flows that firms move from many origins to many destinations. We thenargue analytically that, in transport, the multiproduct degree of returnsto scale gives raise to two different indices, one of which correspond toan improved version of what is currently understood as RTD, while the second -though informative- has not been identified yet. Finally, we sustain that the calculation of economies of spatial scope should replace the calculation of RTS. For the covering abstract see ITRD E135582.