15Although the second-order for the second-stage p1 choice is satisfied, the second-order condition
for the first-stage f1 choice requires f1
3 < αγ/3θ2, which is assumed to hold.
16One change, however, concerns the profit impact of a tighter noise constraint. The Lderivative
of the first-stage profit function can be shown to equal zero, so that the previous
profit impact of the noise limit vanishes (see footnote 14).
17See Girvin (2006b) for details of the derivation. The second-order conditions under simultaneous
choice require f1 > γ/2α, or 2α2/γ > θ, while the second-order condition for the
first-stage choice of f1 in the sequential case requires f1 > γ/3α, or 3α2/γ > θ.
18Airline profit is now independent of n under both simultaneous and sequential choice.
19As mentioned earlier, Nero and Black (2000) analyze the effect of airline taxes in a related
model where noise per aircraft is fixed and taxes are levied on a per-flight basis, while Hsu
and Lin (2005) analyze the effect of noise taxes in a complex simulation-based network model.
20See Girvin (2006b) for details.
21While noise taxation and cumulative noise regulation are equivalent in the model, a tax may
be superior in the case where the airlines have different characteristics (cost per seat for
example). In this case, the optimal cumulative noise limits would differ between the carriers,
while a single noise tax would presumably be desirable (see the welfare analysis below).
22To show ∂f/∂ < 0, note that (25) can be rewritten as
γ
8θL2(L/)2 + 4L2(L/)
= t.
Since L is increasing in , it follows that L/ must be decreasing in to maintain this equality
as rises, implying ∂f/∂ < 0 from (23). To show ∂p/∂ > 0, the term /n in the price
solution can be rewritten as 2Lt and the previous results for L used.
23For a cost-benefit analysis of the FAA noise regulation, see Morrison, Winston and Watson
(1999).
24Empirical estimates of noise damage are generated through hedonic housing price models.
See McMillen (2004) for a recent example and Nelson (2003) and Schipper, Nijkamp and
Rietveld (1998) for up-to-date surveys.
32
25It should be noted that the airport itself, which may earn profits from its operations, is
not considered in the welfare analysis. Such profits would arise from unmodeled charges
levied on the airlines, or from noise taxes under a tax regime. However, since airport profits
represent a transfer from the airlines to the airport, they would cancel in a welfare function
that equals the sum of airline and airport profits and consumer surplus. As a result, the
interests of the airport can be ignored in the welfare analysis. Airport behavior, however,
plays a key role in other types of models; for representative studies, see Morrison (1987),
Oum and Zhang (1990), and Zhang and Zhang (2003).
26With the second-best values of both f and L lower than the first-best values, a comparison
of the n levels (given by f/L ratio) is inconclusive.
27Since W and none of the sequential f solutions depend on α, the value of this parameter
need not be specified. Recalling that satisfaction of the airline second-order conditions in
the first stage of sequential case is not guaranteed, it can then be assumed that α takes a
value such that these conditions hold.
28The full set of numerical results is available in Girvin (2006b). In contrast to Proposition
7, numerical examples in Girvin (2006a) show that, in the monopoly case, cumulative noise
regulation is slightly superior to per-aircraft regulation everywhere in her chosen parameter
space. This finding, of course, does not establish a general result.
29These aircraft include the Boeing 777, 737-700 to -900, and 717, along with the Airbus
A320/321, A330 and A340.
33
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