Political economy of commuting subsidies

Journal of Urban Economics 57 (2005) 478–499
www.elsevier.com/locate/jue
Political economy of commuting subsidies
Rainald Borck a,∗, Matthias Wrede b
a DIW Berlin, 14191 Berlin, Germany
b Department of Economics and Business Administration, RWTH Aachen University, 52056 Aachen, Germany
Received 2 August 2004; revised 6 December 2004
Available online 22 January 2005
Abstract
We study the political economy of commuting subsidies in a model of a monocentric city with two
income classes. Depending on housing demand and transport costs, either the rich or the poor live
in the central city and the other group in the suburbs. Commuting subsidies increase the net income
of those with long commutes or high transport costs. They also affect land rents and therefore the
income of landowners. The paper studies how the locational pattern of the two income classes and
the incidence of landownership affects the support for commuting subsidies.
 2005 Elsevier Inc. All rights reserved.
JEL classification: R14; R48
Keywords: Commuting subsidies; Voting; Monocentric city
1. Introduction
Many countries subsidize commuting to work. Germany and France, for example, al-
low taxpayers to deduct commuting expenses from their income tax liability. It is estimated
that scrapping tax deductibility in Germany would raise about 5.5 billion Euro in revenue
(Bach [3]). Other countries such as Canada and the US do not allow for a special tax treat-
ment of commuting expenses. However, even in those countries commuters may not pay
their full costs since transport is subsidized in many other ways. Brueckner [6] cites evi-
* Corresponding author.
E-mail addresses: rborck@diw.de (R. Borck), mwr@fiwi.rwth-aachen.de (M. Wrede).
0094-1190/$ – see front matter  2005 Elsevier Inc. All rights reserved.
doi:10.1016/j.jue.2004.12.003

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479
dence that fares for public transit cover only 25 percent of capital and operating expenses
in the US and 50 percent of operating costs in Europe, while user fees, gasoline taxes and
the like cover about 60 percent of total outlays for highways in the US. Gomez-Ibañez [9]
analyzes five US and European studies which arrive at a similar conclusion. However, total
transportation costs including costs of congestion, air pollution and accidents exceed user
payments by far (two to more than ten times as high).
In this paper, we use a model of a monocentric city with two income classes to study
reasons for the existence of commuting subsidies. Individuals choose their location within
the city, and depending on parameters, either the rich or the poor live in the central city
while the other group lives in the suburbs. We then study the effect of commuting subsi-
dies (which may be negative, i.e., a tax on commuting) on the groups’ equilibrium utilities.
At the heart of the model are the redistributive effects of the subsidy. While city residents
pay for the subsidy through general tax revenue, the subsidy redistributes income between
residents with long and short commutes as well as between renters and land owners. These
redistributive effects form the basis for the political support for or against commuting sub-
sidies (or taxes).
Our main results are as follows. When land is owned by absentee landlords, all city
residents may benefit from commuting subsidies if these reduce average land rent. With full
citizen landownership, however, it must be the case that one group of residents benefits at
the expense of the other. When landownership is symmetric across income classes, we find
that the rich generally benefit from commuting subsidies at the expense of the poor if the
rich live in the suburbs and the poor in the city. The converse, however, is not necessarily
true: If the rich live in the center, they may still prefer subsidizing commuting since in
this case their marginal transport costs must be sufficiently larger than those of the poor.
Finally, if landownership is asymmetrically distributed, we find that if the rich own more
land than the poor, they will tend to oppose commuting subsidies.
The literature on commuting subsidies has largely followed two different paths. First,
there are a number of studies which analyze the welfare properties of commuting subsidies,
for instance, Brueckner [6], Richter [13], and Wrede [15–17]. Brueckner [6] uses a spatial
model like ours and finds that subsidizing transport is inefficient (see also Fujita [8]). Subsi-
dies may be efficient, however, in a second best world. In a multicentric-metropolitan-area
framework Wrede [17] shows that commuting subsidies may be second-best efficient if
labor income is taxed and if some production factors are immobile. The basic argument is
that the choice of working place would be distorted by the labor income tax if commuting
costs were not deductible from the income tax base.1 Zenou [18] shows that commuting
subsidies can be beneficial by reducing urban unemployment. Second, there are positive
papers which study the effect of subsidies on urban sprawl, which is generally found to be
positive (Brueckner [6], Arnott [1]).
As far as we know, while the redistributive effects of subsidies for commuting have
been mentioned by commentators and calculated by empirical analysts, there is no formal
1 Focusing on the consumption–leisure choice, Wrede [15] and Richter [13] analyzed tax deductions for
work related expenses within an optimal-taxation framework. Deductions for commuting expenses are possibly
second-best efficient if household production (of time) generates non-taxable pure profits. Otherwise commuting
expenses should probably be taxed.

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analysis of their effect in a spatial model. On the empirical side, Kloas and Kuhfeld [11]
use survey data from Germany and find that the tax deductibility of commuting expenses
benefits high income individuals who have long commutes. If this is correct, why would
the poor majority not scrap the subsidy? This paper aims to provide possible answers to
this question.
Methodologically, our paper builds on the model of a monocentric city model with two
income classes (see Wheaton [14], Hartwick et al. [10], and Fujita [8]). Moreover, we use
a model with (partial) public land ownership, a case which was analyzed by Pines and
Sadka [12]. A model with two income groups and disagreement over public goods levels
is presented by de Bartolome and Ross [7].
The paper proceeds as follows. We introduce our model of a linear city in the next
section. Section 3 introduces our voting framework. In Section 4, we study how the results
change if the city is circular. Section 5 analyzes the effect of financing subsidies through
income taxes. The last section offers some conclusions.
2. The model
2.1. The monocentric city
Our model of a monocentric city is the standard model with two income classes (see,
e.g., Wheaton [14], Hartwick et al. [10], and Fujita [8]). We begin with the case of a linear
city with unit width. All individuals travel to the central business district (CBD) to work.
The CBD is located at zero and has zero length. There are two groups of residents indexed
i = l, h who differ by income and transport cost. Income is denoted yi , and we assume
group l is poor and group h rich, yl < yh (more below). There is a total of n residents
and ni individuals in group i where nl > nh, so the poor form the majority in the city.
The round trip commuting cost for an individual who lives r km from the CBD is tir for
i = l, h. Since part of commuting costs consist of the opportunity cost of time, we assume
that th
tl, i.e., the rich have higher commuting costs than the poor.
Commuting costs are subsidized at rate σ ∈ [−1, 1].2 Note that we allow for nega-
tive subsidies, i.e. taxes on commuting expenditures. Examples of commuting taxes would
include road pricing, gasoline taxes etc in excess of the true costs of commuting. For sim-
plicity, we assume that the subsidy covers a certain percentage of all commuting costs (time
and monetary costs). This assumption could be questioned. For instance, one might argue
that the rich have higher time costs, but only money costs of commuting are subsidized via
tax deductions. While this is true, other forms of subsidies such as infrastructure invest-
ments do affect time costs. Also, in general, the rich choose more expensive (viz faster)
transport modes. Brueckner [6] studies transport mode choice by different income classes
in the same framework as ours. He shows that the rich opt for transport modes with higher
2 In practice, commuting might be subsidized at more than 100%. However, this would imply that individual
bid rent increases with distance from the CBD (see (4)), which would preclude the existence of an equilibrium in
the monocentric city model.

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481
money and lower time costs than the poor. Hence, it would be possible to endogenize the
differing time and money costs of commuting and reach similar conclusions as we do now.
To balance the budget, a lump-sum tax of T is levied on each city resident.3 We assume
that city residents vote on the level of the subsidy and lump sum tax prior to choosing their
place of residence and consumption of goods and housing. We solve the model backwards
and first analyze consumption and location choices and turn to the determination of the
voting equilibrium in the next section.
Individuals have identical, strictly increasing and quasiconcave utility functions,
u(x, z), defined over consumption x and housing (lot size), z. We assume consumption
and housing to be normal goods. Let the price of housing be q. Let individual labor in-
come be wi and assume that an individual of type i receives a fraction θi of average
differential land rent (ADR). Letting αi ≡ ni/(nl + nh) be group i’s population share, we
require αlθl + αhθh = θ , where θi
0, i = l, h, θ ∈ [0, 1], and 1 − θ is the degree of ab-
sentee land ownership. Total income for an individual in group i is then yi = wi + θiADR.
We assume wl < wh and θl
θh, i.e., the poor have lower labor income and lower or equal
rental income than the rich. Individuals are assumed to be perfectly mobile. In equilib-
rium, therefore, an i-type individual must attain the same utility level regardless of his or
her place of residence.
We model the city as closed, i.e., the utility level ui attained by an i-type citizen in
equilibrium is endogenous, whereas the number of i-type residents, ni , is exogenous. Con-
versely, in an open city, ui is exogenous while ni is endogenous, where changes in fiscal
parameters lead to migration responses of citizens from or to other cities.4 The open city
model would be more appropriate if the goal of the analysis is the introduction of commut-
ing subsidies by a single city. However, if we want to study the effect of a coordinated use
of subsidies in a system of cities, the closed city model is more appropriate.
2.2. The urban equilibrium
The consumer chooses x and z to maximize utility subject to the budget constraint,
x + qz = yi − T − (1 − σ )tir, or using the budget constraint in the utility function:
max u yi − T − (1 − σ )tir − qz, z .
(1)
z
The first-order condition for an interior solution is:
−qux + uz = 0,
(2)
where ux ≡ ∂u/∂x, etc. Mobility implies that in equilibrium a household with income yi
must achieve a constant utility level, ui , regardless of his or her residence:
u yi − T − (1 − σ )tir − qz, z = ui.
(3)
3 The form of financing the subsidy has obvious distributional consequences. We return to this question in
Section 5.
4 See Brueckner [5] and Fujita [8] for the distinction between the open and closed city models and the differing
comparative statics.

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The lot size (the ‘bid max’ lot size) which solves (2) and (3) is denoted zi = z(yi − T ,
(1 − σ )ti, r, ui). Condition (3) together with the optimality condition (2) also defines an in-
dividual’s bid rent function R(yi − T , (1 − σ )ti, r, ui), i.e., the maximum rent an individual
living at r would pay to achieve utility level ui . In order to ensure that individuals attain
the same equilibrium utility regardless of location, the bid rent must vary with distance
to compensate for varying transport costs. Differentiating (2) and (3), using the envelope
theorem, gives:
cRi = 1
= −(1 − σ )ti
= −(1 − σ )r
y
> 0,
Ri
< 0,
Ri
< 0,
z
r
t
i
zi
zi
(4)
Ri = − 1
u
< 0,
ziux
ziy < 0,
zir > 0,
zit > 0,
ziu > 0,
(5)
where Ri ≡
y
∂R(yi − T , (1 − σ )ti, r, ui)/∂yi , and so on. Individual bid rent decreases with
distance and transport costs and with ui and increases with income. Bid max lot size in-
creases with distance from the CBD and transport costs as well as with ui and decreases
with income.
Landlords are assumed to rent land at the agricultural land rent RA and subsequently
rent out to the highest bidder in the city. The land rent function is:
Φ(r, ·) ≡ max R yl − T , (1 − σ )tl, r, ul , R yh − T , (1 − σ )th, r, uh , RA .
(6)
Based on (4), we focus on two possible location patterns (where Ri(r, ·) ≡ R(yi − T ,
(1 − σ )ti, r, ui) for i = 1, 2):
Assumption 1 (PIC). If Rh(r, ·) = Rl(r, ·), then tl/zl > th/zh, where zi ≡ z(yi − T ,
(1 − σ )ti, r, ui). That is, at a point of intersection the bid rent function of the poor is
steeper than that of the rich.
Assumption 2 (RIC). If Rh(r, ·) = Rl(r, ·), then tl/zl < th/zh. That is, at a point of inter-
section the bid rent function of the poor is flatter than that of the rich.
Under Assumption 1, the bid rent function becomes flatter with rising income, since the
income elasticity of housing demand is assumed to exceed the income elasticity of trans-
port cost.5 This implies that the poor outbid the rich in the center and the rich outbid the
poor in the suburbs. Hence, the mnemonic PIC (poor in city). Conversely, under Assump-
tion 2, the rich have steeper bid rent functions than the poor; hence, in this case the rich
live in the center and the poor in the suburbs (for this case we use the mnemonic RIC, rich
in city).
In the following, we use the subscripts c to denote city residents and s for suburban
residents, respectively. That is, Assumption 1 implies c = l, s = h, and conversely, As-
sumption 2 implies c = h, s = l.
5 Since transport costs differ, the income elasticity of housing demand should be interpreted as the elasticity
with respect to income net of transport cost.

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483
Average differential land rent is then defined as:
r1
ADR = 1
R yc − T , (1 − σ )tc, r, uc dr
n
0
r2
+
R ys − T , (1 − σ )ts, r, us dr − r2RA ,
(7)
r1
where r2 is the city border and r1 the border between central city and suburb.
The equilibrium in our model can now be completely defined by the following condi-
tions:
R yl − T , (1 − σ )tl, r1, ul = R yh − T , (1 − σ )th, r1, uh ,
(8)
R ys − T , (1 − σ )ts, r2, us = RA,
(9)
r1
1
dr = nc,
(10)
z(yc − T , (1 − σ )tc, r, uc)
0
r2
1
dr = ns,
(11)
z(ys − T , (1 − σ )ts, r, us)
r1
T = σ ˜t,
(12)
where
r1
r2
˜
r
r
t ≡ 1 tc
dr + ts
dr
n
z(yc − T , (1 − σ )tc, r, uc)
z(ys − T , (1 − σ )ts, r, us)
0
r1
denotes average transport costs. Equation (8) is the condition that the bid rent of the poor
equals that of the rich at the boundary between the two classes, r1. Likewise, (9) defines
the city border, where the bid rent of the suburbanites (either rich or poor) equals the
agricultural land rent. Equations (10) and (11) are the market clearing conditions for the
housing market: for example, in the central city, integrating population density (1/z(·))
over all locations from 0 to r1 must equal total central city population nc. Finally, Eq. (12)
is the government budget constraint.
Using (9) and (4) in (10) and (11) and integrating gives:
r1
(1 − σ )tcnc = −
Rr yc − T , (1 − σ )tc, r, uc dr
0
= R yc − T , (1 − σ )tc, 0, uc − R yc − T , (1 − σ )tc, r1, uc ,
(13)
r2
(1 − σ )tsns = −
Rr ys − T , (1 − σ )ts, r, us dr
r1
= R ys − T , (1 − σ )ts, r1, us − RA.
(14)

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Further, integrating (12) by parts, using (9), (8) and (4) gives:
r1
(1 − σ )˜t = 1
R yc − T , (1 − σ )tc, r, uc dr
n
0
r2
+
R ys − T , (1 − σ )ts, r, us dr − r2RA ,
(15)
r1
that is, in a linear city with linear transport costs, average transport cost net of subsidies
equals average differential land rent (Arnott and Stiglitz [2]). With (15) and (12) (and
noting yi = wi + θiADR), the utility function (see Eq. (3)) can be rewritten as:
u wi + θi − (1 + θi)σ ˜t − (1 − σ )tir − qz, z .
(16)
Differentiating (16) gives the effect of the subsidy and average transport costs on individual
bid rent:
Ri = tir − (1 + θi)˜t
= θi − (1 + θi)σ
σ
,
Ri
,
i = l, h.
(17)
z
˜t
i
zi
The subsidy lowers net commuting costs by tir, but also increases the lump sum tax by ˜t
and reduces average differential land rent by ˜t. The net effect is therefore positive if tir −
(1 + θi)˜t > 0. For instance, if θi = 0 and tl = th, the subsidy has a positive income effect
(and hence, increases the bid rent) for all individuals who live farther from the CBD than
average. The subsidy will also affect bid rent through its effect on average transport costs ˜t.
If ˜t increases by a unit, this increases the lump sum subsidy by σ and changes average
differential land rent by (1 − σ ), which is positive.
3. Voting
We now turn to the description of the voting game. Each individual votes for her
preferred subsidy and lump-sum tax. Brueckner [6] shows that an efficient allocation is
characterized by zero commuting subsidies: taking account of landowner welfare, the equi-
librium without subsidies is efficient. Hence, in the case where all land is owned by city
residents, the subsidy redistributes between the income classes. However, when the degree
of absentee landownership is high, it is possible that both groups benefit from commuting
subsidies since part of the cost may be borne by absentee landowners.
Equations (8), (9), (13)–(15) implicitly define the endogenous variables r1, r2, ul, uh
and ˜t as a function of the parameters, σ, tl, th, wl, wh, nl, nh, θl, θh and θ . We will use the
notation Rij ≡ R(yj − T , (1 − σ )tj , ri, uj ) and likewise for other variables, where r1 and
r2 are as defined before and r0 = 0. For example, R1l would be the bid rent of the poor
at r1.
The voter’s problem is to choose the subsidy rate which maximizes her utility subject
to the government budget constraint.

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485
Before explicitly deriving expressions for the reaction of equilibrium utility levels to the
subsidy, we will try to give a preview of the pertinent effects. Consider the indirect utility
function
v(Φ, Mi) ≡ v Φ, wi + θiADR − (1 − σ )tir − σ ˜t ,
(18)
where Φ is defined in (6). Totally differentiating (18) with respect to σ , using Roy’s iden-
tity, we have
dv(Φ, Mi) =
dΦ
∂ADR
vM −z
+ tir + θi
− ˜t − σ ˜tσ
(19)
dσ
dσ
∂σ
=
dΦ
vM −z
+ tir − (1 + θi)˜t + θi − (1 + θi)σ ˜tσ ,
(20)
dσ
where the second line follows from (15). We can discern the following effects on utility.
First, the subsidy will influence the price of land through income effects and the relocation
of residents: A resident may benefit if the subsidy causes the price of land to fall. Second,
there is an income effect which is positive if tir > (1 + θi)˜t. If θi = 0 and tl = th, this
will be the case if the individual lives farther from the CBD than average. Otherwise, this
income effect is positively influenced by ti and negatively by θi (for given ˜t). Note the
asymmetry of this income effect: Assumption 1 implies that the income effect will be
positive (on average) for the rich since they have larger marginal transport costs and live
farther from the CBD than the poor. Assumption 2, however, implies the poor live farther
from the CBD than the rich but, since their marginal transport cost is lower, it is not clear
that the income effect is positive for them. Third, income is also affected via the reaction of
average distance: if average distance increases, the lump sum subsidy increases. Moreover,
if the subsidy reduces average differential land rent, net income falls as long as θi > 0 and
this effect will be more severe the larger θi . Since ∂(ADR)/∂σ = −˜t + (1 − σ ) ∂ ˜t/∂σ , we
would expect average differential rent to fall if average distance increases only moderately.
In order to view the difference in the changes between cases PIC and RIC, consider
Fig. 1, which depicts the ‘first round effects’ of a commuting subsidy.6 Panel (a) depicts
case PIC and panel (b) case RIC. For the sake of argument, assume θi = 0, i = l, h, and that
r1 equals the average distance, ˜r, in both cases. With absentee landownership, subsidies
imply a positive income effect and, therefore, an increase in the bid rent if tir > ˜t for
group i, or in words, if a resident has lower transport costs than average. Define ˆrj = ˜t/tj
for j = c, s to be the distance where transport costs for a type i resident just equal average
transport costs, and hence, the subsidy increases bid rent for group i at distances r > ˆrj (see
Eq. (17)). PIC implies ˆrs < ˜r < ˆrc: since the poor live in the center and tl < th, transport
costs for a poor individual would equal average transport cost at a distance greater than
r1 whereas the transport cost of a rich individual would equal average transport cost at a
distance less than r1. Conversely, RIC implies ˆrc < ˜r < ˆrs . This is shown in the figures,
where bid rent functions rotate around points A (for central city residents) and B (for
suburbanites). It is also obvious that the effect of this would be to decrease r1 in case
6 The bid rent functions are shown as lines in Fig. 1, but they are really convex to the origin unless housing
consumption does not vary with r .

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R. Borck, M. Wrede / Journal of Urban Economics 57 (2005) 478–499
(a)
(b)
Fig. 1. Effect of commuting subsidies.
PIC and increase r1 in case RIC. An increase in r1 increases utility of city residents. This
discussion shows that in case PIC group l—the poor central city residents—is likely to
oppose the subsidy. In case RIC, however, rich central city residents do not necessarily
oppose the subsidy, since the income effect for them may be positive and the boundary
between the two groups may shift out.
Of course, these first round effects lead to further adjustments which then determine the
reaction of equilibrium utilities, along with the effect on r1 and r2. Consider for instance
case PIC. If r1 were to decrease and r2 to increase as suggested by the figure, the rich
would have more space than necessary to house them.7 To restore equilibrium, rich utility
would have to increase so that the bid rent of the rich shifts down and housing consumption
increases. Similar arguments apply to the poor: If r1 were to decrease, and at the same time
population density would fall in the central city,8 the poor territory would be ‘too small’
to house all poor residents. To restore equilibrium, poor utility would have to fall which
would then decrease housing consumption and increase density. However, it may be that in
equilibrium r1 increases and poor utility increases too, since the poor benefit from the fact
that the rich move further out. In fact, this is what we find in some of our examples below.
Before proceeding, we provide a useful intermediate result.
Lemma 1. Increasing σ decreases equilibrium land rent at the CBD (r = 0) and at the
border between rich and poor (r1).
Proof. Differentiating (14) shows dΦ(r1)/dσ = −tsns . Using this in (8) and substituting
in (13) gives dΦ(0)/dσ = −tsns − tcnc. 2
7 This follows since zy < 0: for a given utility, increasing income leads to higher bid rent and hence to lower
housing consumption. But this implies that for given ¯uh population density would increase for all r1 < r < r2,
while the rich ‘territory’ has increased.
8 Again, zy < 0 would imply desired housing consumption increases for the poor for a given utility.

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Commuting subsidies reduce the willingness to pay for a residence close to the CBD.
The lemma shows that with commuting subsidies the land-rent function becomes some-
what flatter, as might be expected.
The degree of landownership is a crucial determinant of preferences for commuting sub-
sidies in our model. We first analyze commuting subsidies when only citizens are landlords,
i.e. when θ = 1. We then consider the other extreme of complete absentee landownership,
i.e. θ = 0.
For citizen-landownership we get the following fundamental result.
Proposition 1. If θ = 1, starting from σ = 0, there will not be unanimous support for a
(small ) commuting subsidy. In particular, one group of voters will benefit and the other
lose from the introduction of a subsidy (except in the knife-edge case where both groups
vote for a subsidy rate of zero).
Proof. See Appendix A.
2
If there are no absentee landlords, there is an exact distributional antagonism between
rich and poor (except in the knife-edge case mentioned in the proposition). Hence, if one
group loses the other one benefits from a small subsidy. To understand the result, consider a
homogeneous city with all land owned by residents. In this case, we know that subsidies, as
well as taxes, on commuting are inefficient (Fujita [8], Brueckner [6]). The optimal subsidy
rate from the residents’ viewpoint is zero. Any positive or negative rate would decrease
residents’ welfare. Now introduce some heterogeneity among the residents. With complete
citizen landownership, subsidies and taxes are still Pareto inefficient. Thus moving from
a subsidy rate of zero in any direction benefits one group of voters at the expense of the
other.9
However, we cannot say in general which group will benefit from the subsidy. To end
up with less ambiguity, we consider uniform citizen landownership in the next proposition.
Proposition 2. If θl = θh = 1, starting from σ = 0, (i) in case of PIC the poor majority
votes against a small subsidy while the rich vote for it, provided that th − tl is not too
large.
(ii) The same holds in case of RIC if z0h
z1l .
Proof. See Appendix A.
2
To understand the result, note from Lemma 1 that equilibrium land rent at the CBD,
Φ(0), falls by tcnc + tsns . This fall can be decomposed into the partial effects of σ, uc
and ˜t. Since R0c = −
σ
2˜t/z0c < 0 and Ru < 0, the fall in land rent must be due to an increase
in central city residents’ utility if R0c ˜
˜ t
t
σ is larger than 2 ˜
t/z0c − (tcnc + tsns). Writing out
the corresponding expressions leads to Eq. (A.3).
9 With absentee landownership, commuting subsidies may be Pareto efficient from the viewpoint of city resi-
dents. They are still inefficient if the welfare of absentee landowners is taken into account.

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