The siting of public facilities such as prisons or waste disposal facilities typically faces rejection by local populations (the "NIMBY" syndrome, for Not In My BackYard). These public goods exhibit a private bad aspect creating an asymmetry: all involved communities benefit from their existence, but only the host bears the local negative externality. We show that the well-known Lindahl pricing scheme constitutes the only cost-sharing method satisfying a set of properties specifically designed to handle the siting problem.Public Goods; Externalities; NIMBY; Location; Cost sharing.

Jeremy Laurent-lucchetti

Justin Leroux

English

Research Papers in Economics

     
 
 
  
  
Volume 30, Issue 3 
  
Lindahl prices solve the NIMBY problem 
  
 
 
Jeremy Laurent-lucchetti  
Department of Economics and Oeschger Center for 
Climate Change, University of Bern 
Justin Leroux  
HEC Montréal
Abstract 
The siting of public facilities such as prisons or waste disposal facilities typically faces rejection by local populations 
(the "NIMBY" syndrome, for Not In My BackYard). These public goods exhibit a private bad aspect creating an 
asymmetry: all involved communities benefit from their existence, but only the host bears the local negative 
externality. We show that the well-known Lindahl pricing scheme constitutes the only cost-sharing method satisfying a 
set of properties specifically designed to handle the siting problem.
We wish to thank Stefan Ambec, Olivier Bochet, Vincent Boucher, Bettina Klaus, Sidartha Gordon, Dipjyoti Majumdar, Hervé Moulin, Yves 
Sprumont, Nicolas Sahuguet, Bernard Sinclair-Desgagné and William Thomson, as well as participants of the Montréal Natural Ressources 
and Environmental Economics Workshop and FQRSC for financial support. 
Citation: Jeremy Laurent-lucchetti and Justin Leroux, (2010) ''Lindahl prices solve the NIMBY problem'', Economics Bulletin, Vol. 30 no.3 
pp. 2457-2463. 
Submitted: Jul 29 2010.   Published: September 21, 2010. 
 
     1. Introduction
The siting of public facilities such as prisons, airports or nuclear waste disposals
typically faces rejection by local populations. These goods are socially desirable but
come with local externalities. Di⁄erent factors can be the cause of such rejection:
losses in property value, the perceived loss in quality of life or the fear of negative
health e⁄ects. In economic terms, these public goods have a private bad aspect to
them creating a siting problem because only the host bears the local nuisance. This
asymmetry typically leads to costly negotiations or ine¢ cient siting1. Worse, di¢ cult
cases can even result in stalemates (e.g., the case of U.S. nuclear waste disposal; see
EPA 2002).
The governing institutions typically want to elicit the hosting cost of communities,
in order to select one site and elaborate a compensation scheme. However, in prac-
tice, the planner has access to much less information than the involved parties, which
causes a revelation problem. The mechanism design literature tackles the problem by
designing procedures procedure which are decision-e¢ cient: the chosen host should
be one which incurs the lowest hosting cost (consisting of the cost of construction and
a disutility component) among all communities. Kunreuther and Kleindorfer (1986)
propose a sealed-bid auction procedure to create an incentive for each community to
truthfully reveal their costs: each community pays its own bid. O￿ Sullivan (1993),
Minehart and Neeman (2002), Perez-Castrillo and Wettstein (2002) also propose auc-
tion mechanisms in the same vein, aiming for e¢ ciency and truthful revelation. The
traditional trade-o⁄ between e¢ ciency, incentive compatibility and budget balance
is central in these papers and they address the siting problem exclusively from a
strategic viewpoint. Ye and Yezer (1997) tackle the issue by introducing a spatial
dimension (the spatial distribution of bene￿ts and costs of alternative waste disposal
site location patterns).
However, another aspect of the siting problem relates to the sharing of the cost
borne by the host community. Taking into account such redistribution issues helps
ease the siting process itself and reinforces the stability of the agreement. Indeed,
if not carefully considered, the structure of the compensation itself could result in
the rejection of the project (Easterling, 1992; Frey et al., 1996). For example, re-
viewing several cases of waste disposal facilities in the Canadian context, Khun and
Ballard (1998) conclude that inequity perception and political dimensions (beyond
the economic implications) were the main causes of the NIMBY e⁄ect. The tradi-
tional economic approach focusing on the strategic properties of siting procedures is
silent with regards to redistribution issues.
By contrast, in a companion paper (Laurent-Lucchetti and Leroux 2009) we design
1See Minehart and Neeman (2002).
3a simple mechanism which selects an e¢ cient site, preserves incentives and implements
any individually rational cost shares. Knowing such a mechanism exists begs careful
examination of the NIMBY problem from a redistributive viewpoint. Moreover, we
can ignore strategic issues here and assume the relevant parameters are known.
We model the problem using two parameters: the bene￿t a community obtains
from the existence of the public good, bi, and the hosting cost of each community,
ci. Until now, studies have focused on the cost parameter to dictate redistribution.
Adding a bene￿t component enhances the model in at least two ways: it explicits
whether the public good should be constructed (if joint bene￿ts exceed the lowest
cost) and, most importantly, it places a bound on cost shares. Thus, ignoring the
bene￿t component amounts to ignoring the voluntary participation of communities,
which can be very problematic for the stability of any agreement. In fact, bene￿ts
are traditionally central in allocating the costs of public goods.
Other works have suggested pricing in proportion to usage (see Minehart and
Neeman, 2002; Sakai, 2008, in the context of waste treatment). Yet, despite its
desirable properties this pricing scheme may fail voluntary participation. Moreover,
bene￿ts may be unrelated to usage: a community may obtain large bene￿ts from the
existence of a prison without sending any of its inhabitants to it.
In practice, migrations are often observed after the host is announced (Baumol
and Oates, 1998). For instance, agents with a low disutility may move to the host
community because of lower housing prices or other advantages brought about by the
compensation scheme (e.g., improved public infrastructures), while agents with high
disutility may choose to move out of the host community.
We introduce axioms which speci￿cally handle the physical asymmetry of the
NIMBY problem, and the possibility of migrations once the host is announced. We
show these axioms characterize Lindahl prices. Traditionally, numerous public ￿nance
issues are settled using Lindahl prices. However, despite their well-known properties
in the standard public good case, the relevance of Lindahl prices in the NIMBY
context had yet to be ascertained. While our characterization is technically related
to those in Moulin (1987) and Ju et al. (2007) in di⁄erent contexts, we provide new
interpretations to axioms explicitly designed for the problem at hand.
2. The model and axioms
Let N = f1;:::;ng be the set of communities. Each community obtains a bene￿t,
bi 2 R, from the existence of the public good and incurs a cost, ci 2 R+, if it must
host of the public good.2 The cost parameter combines the physical construction cost
2For clarity, we use a bene￿t interpretation for the bi￿ s, but these parameters can be negative for
some communities, if they are against the project altogether.
4and the disutility from hosting the public good. Let (b;c) = (bi;ci)i￿N be a bene￿t-cost
pro￿le.3
Without loss of generality, we rank communities from lowest to highest cost: c1 ￿
c2 ￿ :::: ￿ cn. E¢ cient siting requires that the host be a lowest-cost community. We
assume
P
N bi ￿ c1 so that it is e¢ cient to build the facility. An e¢ cient cost-sharing
method assigns a vector of cost-shares x(b;c) 2 RN such that
P
N xi(b;c) = c1.
A basic incentives property is Voluntary Participation: communities should not
pay more than the bene￿ts they obtain.
Voluntary Participation (VP): For all (b;c) 2 RN￿R
N
+ and i 2 N, xi(b;c) ￿ bi.
Next, we de￿ne two properties to overcome the natural asymmetry of the problem.
The ￿rst axiom is inspired by cost monotonicity, a standard requirement in traditional
cost-sharing problems, which states that no community should pay less if the total cost
were to increase. Because we wish the solution to not treat the host asymmetrically,
Extended Cost Monotonicity holds all communities responsible for the total cost:
Extended Cost Monotonicity (ECM): For all b;b0 2 RN, c;c0 2 RN
+ and
i,j 2 N,
ci ￿ c
0
i ) xj(b;(c
0
i;c￿i)) ￿ xj(b;c)
ECM can be justi￿ed as follows: because ex ante the decision to build a facility
is a collective one, the host is not more responsible for the total cost just because its
own cost happens to be the lowest in the realized pro￿le. The sharing rule should
re￿ ect this fact.4
The next property reinforces our view that no community is responsible for the dis-
tribution of characteristics; should migrations occur between communities, the latter
would collectively pay the same amount while outside communities are una⁄ected:
Migration Independence (MI): For all b;b0 2 RN, c;c0 2 RN
+ and S ￿ N :
P
j￿S c0
j =
P
j￿S cj
and
P
j￿S b0
j =
P
j￿S bj
and mini2S(ci) = mini2S(c0
i)
9
=
;
=)
￿
xi((b0
S;b￿S);(c0
S;c￿S)) = xi(b;c);8i￿NnS
and
P
j￿S xj((b0
S;b￿S);(c0
S;c￿S)) =
P
j￿S xj(b;c) :
MI insures that the cost shares of communities not involved are una⁄ected by
those maigrations. MI is related to the well-known axiom of No Advantageous Real-
location (NAR) in claims problems. NAR addresses the problem of strategic manipu-
lation of claims and is used to characterize the egalitarian rule, the proportional rule,
and many other surplus-sharing methods (see Moulin, 1987). Therefore, eventhough
3For any community i 2 N, we denote by (b0
i;b￿i) the vector b where bi has been replaced by b0
i,
and for any subset S ( N, bS denotes the projection of b onto RS
+. Also, bN =
P
i2N bi.
4In addition, as argued in Laurent-Lucchetti and Leroux (2009), ECM also has an appealing
strategic implication: it guarantees that the outcome of the mechanism proposed there is immune
to coalitional deviations.
5our normative interpretation of MI is anything but strategic, MI also prevents prof-
itable manipulation by communities (e.g., the manipulation of electoral boundaries).
3. The Result
In our context, Lindahl prices are de￿ned by sharing the cost proportionally to ben-
e￿ts. For any i 2 N:
x
Lindahl
i (b;c) =
bi P
N bj
c1 (1)
Theorem 1. Given n ￿ 3, Lindahl prices are the unique e¢ cient cost-sharing method
meeting VP, ECM, and MI.
Proof. Clearly, Lindahl prices meet VP, ECM, and MI. Conversely, let x be an e¢ cient
cost-sharing method meeting VP, ECM and MI.
Step 1: Consider a bene￿t-cost pro￿le (b;c) 2 RN ￿ RN
+. Let c0 = (c1;c1;:::c1) 2
RN
+ . By ECM, xi(b;c) ￿ xi(b;c0) for all i 2 N. Therefore, by budget balance
x(b;c) = x(b;c0):Hence, the cost shares of communities are solely determined by b
and c1: we write x(b;c1) instead of x(b;c).
Step 2: Let i 2 N and b;b0 2 RN such that b0
i = bi and
P
Nni b0
j =
P
Nni bj. By
MI, xi(b0;c1) = xi(b;c1). So, xi(b;c1) depends only on bi;
P
j6=i bj and c1 for all i 2 N.
Alternatively, xi depends only upon bi;bN and c1 for all i 2 N. We write xi(bi;bN;c1).
Step 3: Let c1 2 R+, i;j 2 N and b;b0 2 RN be such that b0
i = bi +bj, b0
j = 0 and
b0
k = bk 8 k 6= i;j. By MI, xi(b0
i;b0
N;c1)+xj(b0
j;b0
N;c1) = xi(bi;bN;c1)+xj(bj;bN;c1).
By VP, xj(b0
j;b0
N;c1) = 0. Thus, recalling that b0
N = bN, we get
xi(bi + bj;bN;c1) = xi(bi;bN;c1) + xj(bj;bN;c1): (2)
Given c1 and bN, the cost share of community i is only determined by bi. Again,
we slightly abuse notations and rewrite (2) as follows:
xi(bi + bj) = xi(bi) + xj(bj);
which holds for all bi;bj such that bi;bj ￿ 0 and bi +bj ￿ bN. Similarly, xj(bi +bj) =
xi(bi) + xj(bj) on the same domain.
Thus, xj and xi coincide on (0;bN) for all i;j: It follows that:
xi(bi + bj) = xi(bi) + xi(bj) (3)
for all bi;bj ￿ 0 such that bi + bj ￿ bN, which is a Cauchy functional equation.
Step 4: Following a well-known result of functional equations theory (see AczŁl,
1966), the general solution of (3) is a linear function. Thus, for all bi ￿ bN,
6x(bi) = ￿bi
By budget balance, ￿ =
c1
bN, as was to be proved.
Other intuitive ways of splitting the hosting cost exist. For instance, the con-
strained egalitarian method, splitting the total cost equally up to the voluntary par-
ticipation constraint, fails to satisfy MI: migrations from an unconstrained community
"transferring" higher bene￿ts to a constrained community lead to an increase in their
aggregate share while others bene￿t. Also, sharing the hosting cost in proportion to
ci￿ s fails ECM: an increase in the hosting cost for a non-host community means it
will pay more, bene￿tting other communities.
References
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8

Lindahl prices solve the NIMBY problem

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