The cost functions obtained for the two nodes system and for various cases in the three
nodes system have similar structures. They are separable into two terms: a pure flow term
related with expenses on terminal operations, and a flow-distance term directly related with
en-route expenses. This latter was shown to represent the optimal transport supply
(capacity) offered by the firm (e.g. seat-kilometers), a very reasonable result as en-route
expenses depend on the fleet size, frequency and distance traveled, variables that are
optimized in order to minimize cost in the production of a given vector Y. Thus, transport
supply indices representing product proxies, sometimes used in the empirical work, have
received here theoretical support provided the firm is operating in a technically optimal
way. The pure flow term was shown to be relevant in the selection of a route structure
because some structures imply additional loading and unloading. Thus, given the key role
of the route structure in the generation of scope economies, pure flow terms are particularly
important for industry structure analysis using aggregated output. When only distance
related variables are used to describe output (as is the case in many applied studies)
loading/unloading costs may not be adequately captured.