Let us now examine the possible implications of the discussed results in terms of market or-
ganization. First of all, it has to be noted that the observed data are such that the subadditivity
test for the cost function proposed by Evans and Heckman (1984) could not be applied in a strict
sense. Actually, the levels of both passenger and freight carryings produced by FS increased less
than twofold from 1980 to 1995, so that the first constraint defining the admissible region for the
subadditivity test is not satisfied. As a consequence, we generated the fictitious observation
ðY ¼ 17985; Q ¼ 8120Þ, where passenger and freight carryings are obtained by dividing their
sample mean values by the average load factor of FS trains within the study period (taking the
value of 0.65). Thus, such output levels correspond to the maximum levels of production com-
patible with the productive capacity that on average was available to FS for providing rail services
in the study period. Note that these output levels satisfy the additional two constraints which are
required to determine the admissible region for the subadditivity test. In fact, the ratio of freight
to passenger carryings is equal to 0.45, that is included in the admissible range defined by sample
data (varying between 0.30 and 0.55). Finally, marginal costs are positive. Therefore, we evaluated
the corresponding amount of variable cost by using the coefficients of the estimated short-run
translog function.
Let us begin our analysis by setting l ¼ m ¼ 0:5, namely, let us consider a duopoly where each
firm stemming from the breakdown of the rail services monopoly divides equally the whole output
vector originally produced by FS. In this case, it is easy to obtain that SUB S ð0:5; 0:5Þ ¼ 0:31 > 0. This value highlights the possibility that the existence of two firms providing rail services in Italy
could enhance the efficiency of the industry with respect to monopoly.
Now, consider the effects of specialized production, as measured by SPECðl; mÞ. When a duop-
olistic firm specializes in passengers carryings (setting the proportion of freight carryings at
the level of the symmetric configuration, that is, m ¼ 0:5), the overall industry efficiency decreases
(see Fig. 1). On the other hand, as far as freight carryings are concerned, we obtain that a firm
specialization in this production does not determine any significant change in efficiency. This can
be explained by the fact that freight carryings hold a limited share of the total traffic units (that is,
passengers-kilometers plus ton-kilometers) produced in the period under study.
A more interesting result derives from an asymmetric industry configuration. Let us assume
l ¼ m ¼ 0:6. This industry configuration could be related to a situation in which the incumbent
(i.e. FS) maintains the production of a volume of both outputs that is greater than the one of an
entrant firm providing rail services in Italy.
In this asymmetric case, it is easy to obtain that SUB S ð0:6; 0:6Þ ¼ 0:22 > 0. As with the sym-
metric configuration, such a value indicates that a duopolistic industry structure is candidate to
increase efficiency. Since SUB S ð0:6; 0:6Þ ¼ 0:22 < SUB S ð0:5; 0:5Þ ¼ 0:31, we can derive that scale
economies are present in the operation of rail services in Italy. In the depicted asymmetric sce-
nario, the effects of a specialized production by any duopolistic firm in freight transport on
industry efficiency are still almost insignificant. As regards passenger carryings, the effect is
twofold. If it is the largest firm which specializes its production, the overall industry efficiency
reduces. On the other hand, if it is the smallest firm which specializes its production, the overall
industry efficiency increases. Thus, efficiency in passenger service increases as the share of total
output detected by any duopolistic firm tends to the one of the symmetric configuration (see
Fig. 2).
On the whole, the obtained results indicate that joint production of passenger and freight
carryings may be more or less efficient than specialized production in either output for a hypo-
thetical duopoly in rail services in Italy, depending on circumstances. In particular, a large firm
(such as the incumbent FS) may find it profitable to exploit its ability to produce passenger and
freight services by pooling certain inputs, competencies and skills, so as to use these factors more
efficiently than they would be used if production were performed separately (see Baumol et al.,