Specific subsidy for resident passengers
A specific subsidy for residents consists of granting fixed amount S to all passengers living in remote region A, independently on the ticket price. Obviously, this fixed amount should be lower than the maximum ticket price, and hence, we assume that 0 < S < a. How does this specific subsidy for resident passengers affect the ticket price, the demanded quantity by residents and nonresidents and the carrier’s profits? To answer this question, let us proceed in a similar way that we did with an ad valorem subsidy.
Strategy 1: the carrier charges the same ticket price as before the subsidy
The analysis for this case completely coincides with the one described earlier (ad valorem subsidy for resident passengers). With strategy 1, the carrier charges the same ticket price that it would charge in absence of the subsidy for residents. With this strategy, on the one hand, residents end up paying a lower ticket price, and thus, their demand increases. On the other hand, nonresidents’ demand remains unaltered. Optimal results per passenger are given by
where and represent the quantity demanded by residents and nonresidents, respectively, when a specific subsidy is introduced and the ticket price
* — R — NR
is the same as before the subsidy - that is, P . Notice that QS),> QSperif,c ~ that is, the demanded quantity by residents - is higher.
When a specific subsidy is granted only for residents and the carrier uses strategy 1, the carrier’s total profits are given by
Strategy 2: the carrier raises the ticket price to capture residents’ subsidy
Let us denote by PR the ticket price finally paid by residents and by P the ticket price charged by the carrier. Since resident passengers are entitled to receive the subsidy, the ticket price finally paid by those passengers is equal to the ticket price charged by the carrier minus the specific subsidy - that is, PrfR = P — S. If the carrier aims to capture residents’ subsidy, it will solve the following maximisation programme:
Optimal results are given by
Contrary to what happens with an ad valorem subsidy, with a specific subsidy, the carrier is not able to appropriate the whole subsidy. The ticket price still rises.
With strategy 2, the carrier raises the ticket price higher than that of the case in which no specific subsidy for residents is granted. This allows the carrier to appropriate half of the subsidy. On the one hand, residents’ demand increases. On the other hand, nonresidents’ demand decreases:
When a specific subsidy only for residents is applied and the carrier uses strategy 2, the carrier’s total profits are given by
To obtain the preferred strategy for the carrier, we need to compare total profits given by expression (9) and expression (13).
Proposition 2: For every specific subsidy for residents, S, the carrier prefers strategy 1 (strategy 2) if the proportion of resident passengers in route AB is lower (higher) than or equal to 0.5.
T-ri
Proof: Let us define the function II’ .. — IISef.,t = ----------- , which
is strictly increasing in a, where 0 < a < 1. If this function is positive, the carrier chooses strategy 2, and if it is negative, the carrier chooses strategy 1. Il|Wf - =0 when a = 0.5. Thus, if a < (>) 0.5,
the carrier prefers strategy 1 (strategy 2). This completes the proof.
Figure 8.2 depicts the result in proposition 2.
Figure 8.2 Preferred strategy for the carrier with a specific subsidy for residents
