restrictions, is imposed by Amsterdam’s Schiphol Airport (AMS), London’s Heathrow Airport
(LHR), and Long Beach Airport (LGB) in California.4 Even though cumulative noise limits
are not widespread currently, Figure 1 suggests that they are likely to become more common
as time passes, making an understanding of their effects important.
Under noise taxation, explicit constraints are removed, but the airline instead pays a tax of
t per unit of noise, so that its total tax liability is tnf. Although noise taxes are not used much
in the U.S., they are more common elsewhere, being levied through landing-fee adjustments
that depend on an aircraft’s noise level. For institutional background, see Nero and Black
(2000) and Morell and Lu (2000).
In the analysis, the effect of each of the three regulatory regimes is considered in isolation,
ignoring the fact that different regimes often coexist in reality. This potentially unrealistic
approach is meant to gain insight into the economics of the regimes, and its practical lessons
are considered in the conclusion. Another unrealistic element is the linear fashion in which
noise is added across flights under the cumulative limit. Under the actual regulations, noise
is added in a semi-logarithmic fashion, which makes total noise more sensitive to noise per
flight than to the number of flights.5 While incorporating this feature would complicate the
analysis, the main qualitative conclusions are likely to be unaffected.
The analysis solves the airline’s profit-maximization problem under cumulative and peraircraft
noise regulation and under the noise-tax regime. Comparative-static analysis shows
the effects of parameter changes on the airline’s choice variables, results that are immediate
given that the model generates closed form solutions for all the variables. In addition, a key
equivance result between noise taxation and cumulative noise regulation is established.
While the cumulative or per-aircraft noise limits are treated as parameters in the
comparative-static analysis, the next step is to consider the social planner’s problem, where L or
n is chosen optimally, taking into account the environmental damage from noise. Even though
the choice of a regulatory regime (cumulative vs. per-aircraft noise regulation) is immaterial
in characterizing the first-best social optimum, the two regimes generate different outcomes in
the second-best case, where the planner must accept the (inefficient) profit-maximizing choices
of the airline. An interesting question is then which regime yields a higher welfare level. This
3
question cannot be addressed analytically, but it is investigated via numerical analysis. The
analysis also characterizes the noise tax rates that support the first-best and second-best social
optima.
The entire analytical agenda described above can be carried out either under a monopoly
market structure, with a single airline, or in an oligopoly setting. Since the monopoly case
has already been analyzed by Girvin (2006a), the present paper analyzes an oligopoly model,
with the specific case of a duopoly considered. As seen below, the duopoly setup is actually a
special case of the monopoly model, and the results for this latter model are briefly summarized.
The duopoly model is drawn from the analysis of Brueckner and Flores-Fillol (2006), and its
key element is idiosyncratic airline brand loyalty on the part of consumers, which governs
competition between the two duopoly carriers.
The plan of the paper is as follows. Section 2 develops the basic model. Section 3 introduces
the cumulative and per-aircraft noise constraints and solves the airline profit-maximization
problem under these two different regimes. Section 4 analyzes noise taxation, section 5 carries
out the welfare analysis, and section 6 offers conclusions.