Communities, Competition, Spillovers and Open

Space1

Aaron Strong2 and Randall Walsh 3

October 12, 2004

1The invaluable assistance of Thomas Rutherford is greatfully acknowledged.2Department of Economics, University of Colorado at Boulder3Department of Economics, University of Colorado at Boulder.

Abstract

We explore the impact of both the number and spatial distribution of local jurisdictions on

the decision to commit developable acreage to the provision of open space. Our analysis

differs from the existing literature on the provision of public goods in a number of ways.

First, we demonstrate that the mixed public good nature of open space (in relation to pri-

vate lot consumption) can yield outcomes where a single land rent-maximizing community

over-supplies open space relative to the utility maximizing open space level. Second, by

explicitly incorporating the spatial distribution of open space spillovers, our stylized model

shows how competition can lead not only to inefficient levels of open space provision, but

also to inefficiencies in the spatial distribution of open space. Finally, the efficacy of a

market-based approach to restore open space levels is considered.

Key Words: Open Space, Competition, Land Use.

JEL: H41, R14, Q15

1 Introduction

Open space protection is a focus of local governments across the United States. Communities

are motivated to protect open space both for its amenity and recreation value and as a tool

to manage urban growth. In the 2003 election alone, there were at least 134 ballot initiatives

regarding open space preservation in the United States. Of those, 100, or 75%, were passed

by voters generating over $1.8 billion for land conservation(Land Trust Alliance). With this

ongoing policy focus on land protection, it is important to understand how competition

between jurisdictions affects the provision of open space. To this end, we evaluate the

impacts of competition between jurisdictions on the provision of protected open space in a

spatially differentiated general equilibrium framework.

Open space is an interesting public good for two reasons that we explore in this paper.

First, the input to open space is land. Land is also an input to the private good in question,

namely residential lots. That is, through the provision of open space, we are automatically

increasing the scarcity of land for residential development. We know from hedonic studies

that proximity to undeveloped land can have a marked impact on housing prices.1 Hence,

open space protection impacts housing prices through two channels – the amenity value of

open space increases the value of proximate houses and additional land protection leads to

reductions in the supply of residential land. The second key characteristic of open space

as a public good is that the spatial distribution of open space is equally as important as

the level of provision. This spatial link implies that even when a large quantity of land

is allocated to open space, it is possible that only a few residents will benefit due to sub-

optimal distribution(al) patterns. For instance, from the perspective of households located

near the urban core, the amenity benefits of large quantities of open space at the urban

fringe may be much lower than those provided by small parks in the immediate vicinity.

1Examples of this include: Riddel (2001), Bolitzer and Netusil (2000) and Schultz and King (2001)

1

To explore these issues, a general equilibrium model incorporating homogeneous resi-

dents and land rent maximizing spatially delineated jurisdictions is constructed. Our analy-

sis within the framework of the model starts by considering the implications of different

spatially delineated competition regimes on open space allocation, jurisdiction land values

and welfare. We then consider the efficacy of market based and command and control policy

approaches for addressing inefficiencies in open space provision.

Our basic problem is to model how jurisdictions in close proximity compete in scalable

public goods with spillover benefits to the residents of neighboring jurisdictions. Our ap-

proach draws on several strands of the literature. Key concepts include: the link between

urban spatial structure and amenities; the capitalization effect of public goods when there

are spillovers; and the role of a jurisdiction/social planner’s decision in the allocation of

public goods.

First, consider the relationship between urban spatial structure and open space ameni-

ties. Begin with an area of land that is slated for residential development. The question

that this paper asks is “are more or fewer jurisdictions adventageous to the optimal provi-

sion of open space?” Our approach builds on earlier work by Brueckner (1983) in which he

explicitly models the trade off between land in the residential building footprint and land

in yard space within the context of the monocentric city model. We extend this work by

incorporating the spillovers of communal undeveloped land from one jurisdiction to another

and consider the impact of differing competition structures. Wu and Plantinga (2003) also

consider the impact of environmental amenities on urban spatial structure. Their work

focuses on how municipalities may develop given an exogenous environmental amenity such

as a hill or stream. Our work differs from this by considering an endogenous environmental

amenity.

We focus on how much open space is provided under different competition regimes.

Each competition regime implies different patterns of spatial capitalization. We model

2

these spillovers as a continuous analog to the work of Cremer, Marchand, and Pestieau

(1997). In their work, they consider how two neighboring municipalities decide to allocate

a single non-scalable public good such as a recreation center or stadium. They consider a

Nash equilibrium in public good provision and find that although the efficient level of the

public good is not typically provided in the non-cooperative equilibrium, there does exist

a cooperative system such that both municipalities share the cost and construct a single

public good – the efficient outcome of their model. Our model constructs reaction functions

for each jurisdiction in open space and suggests a result similar to that of Cremer et al.

(1997). Specifically, that when the spillovers of open space provision cannot be captured,

in general, competition will lead to under provision.

In order to highlight capitalization effects in our model, we fix the boundaries of the

development region. As suggested by Brasington (2002), if the jurisdictional boundary may

fluctuate, capitalization may not occur since more land can be allocated if the boundary is

not fixed, driving down the price to marginal cost. Thus, communities located at the center

of a metropolitan area may have greater capitalization effects than edge cities. Further,

if the boundaries are allowed to fluctuate, any jurisdiction may capture all of the amenity

rents that a potential buyer may have for the amenity.

The role of the jurisdiction in our model is that of a land rent maximizer. There is a large

body of work on the role of property value maximization in the provision of efficient public

good levels. Early examples of this literature include: Sonstelie and Portney (1978), Son-

stelie and Portney (1984), Bruekner (1983), and Epple and Zelenitz (1984). These papers

outline assumptions that equate property value maximization with the efficient provision

of public goods. In contrast, we find that under a variety of competition assumptions, in-

cluding a single jurisdiction, property value maximization does not equate to the efficient

provision of public goods. This is the result of the dual nature of open space and the fact

that an individual jurisdiction may not be able to capture all of the amenity benefits of pro-

vision. Thus, by explicitly incorporating the input to public goods production, the results

3

of the previous work is overturned.

2 The Model

The model is comprised of a set of N identical households, J spatially delineated developable

regions of area Aj and a set of K jurisdictions each controlling a development district com-

prised of one or more development regions. Households choose consumption of a numeraire

good (which includes housing but not the residential lot) whose price is normalized to 1, a

location in one of the development regions and conditional on location choice, a quantity

of land (residential lot size). We abstract from the notion of housing in order to reduce the

jurisdictions decision on vertical development and concentrate only on the horizontal aspect

of development. The relationship between lots, regions, and districts is shown in Figure 1.

Households choose development region j to maximize their indirect utility function:

Vj = V (Pj , Qj , Y ), (2.1)

where Y is the shared income level, Pj is the price of land in region j and Qj measures the

open space amenity in region j. This choice of price-environmental quality pair is similar to

the choice faced in jurisdictional competition models where households face a price-public

good pair. The open space amenity level is the spatially weighted sum of the amount of

open space Oj in the given region and its neighboring regions. The level of the open space

amenity in region j is given by:

Qj =∑j′∈J

φj′,j ∗ (Oj′); (2.2)

where φj′,j is a weighting matrix that defines how the contribution of open space to envi-

ronmental quality decays as a function of distance from region j. Because all individuals

are identical, in equilibrium, prices adjust such that Vj is identical across all regions. Con-

4

ditional on region choice, demand for lot size is given by Roy’s identity.

Dj = D(Pj , Qj , Y ) (2.3)

Jurisdictions control a set of development regions, which are aggregated into a district,

and choose the quantity of open space to provide in each region subject to the constraint

that developable land in a given region Lj is given by Lj = Aj − Oj . A jurisdiction’s rent

from a given region,Πj is then given by Pj ∗ Lj . Where Pj is determined by the market

clearing conditions:

V (Pj , Oj , Y ) = V (Pk, Ok, Y ); ∀j, k, (2.4)

D(Pj , Oj , Y ) ∗ nj = Aj −Oj ; ∀j, (2.5)

and,

∑J

nj = N. (2.6)

We consider a closed model for simplicity of analysis.2 The equilibrium outcome that arises

from competition between rival jurisdictions in quantity of open space is characterized as a

Nash Equilibrium in which each jurisdiction plays the rent maximizing strategy contingent

on the actions of their competitors.

For the second set of analyses, we incorporate a market-based policy mechanism. It is

assumed that an income tax τ is assessed on each household. The income tax is used to

finance a per acre subsidy on open space provision. A further discussion of the income tax is

provided below. Finally, to close the model and simplify the welfare analysis, jurisdictional

2Qualitatively the results of an open city model as well as an intermediate migration scenario providesimilar results.

5

land rents are recycled equally to all households. This allows us to focus exclusively on the

welfare of the households. These assumptions yield the following two budget constraints:

PjLj + Xj = (Y + (∑j

πj)/N)(1− τ) (2.7)

τ(Y +∑j

πj/N)N =∑j

subsidyOj (2.8)

The complexity of the model’s spatial Nash equilibrium precludes analytical solutions.3

We therefore adopt a numerical strategy for analyzing the implications of the model. Toward

this end, it is assumed that household utility takes a nested constant elasticity of substitution

(NCES) form. Environmental quality and lot size are placed in one nest and numeraire

consumption in the other. Thus, residents maximize utility with choice of development

region:

U(Xj , Lj , Qj) = (αXρj + (1− α)(βLγ

j + (1− β)Qγj )ρ/γ)1/ρ (2.9)

subject to the budget constraint:

Xj + PjLj = (Y +∑j

πj/N)(1− τ). (2.10)

The environmental quality function is assumed to take the form:

Qj =∑j′∈J

φ0/√

distj′,j (2.11)

We calibrate the numerical model to a benchmark. In this benchmark, individuals spend

70% of their income on consumption of the numeraire good, leaving 30% for housing lot

consumption. Further in the benchmark, individuals live on approximately 14 acre lots and

approximately 16 of the land in any development region is allocated to open space. We

3Cremer et al. (1997) are able to derive analytical results in a two location model with a non-scalablepublic good and no explicit consideration of space.

6

assume an elasticity of substitution on the upper level of the nesting structure of 1.2 and

an elasticity of substitution between land and open space of 0.8. Under this specification,

the lot-open space bundle has a stronger substitutes relationship with the numeraire than

do open space and lot size in the lower nest.

The development area is defined as follows. We assume that there are 100 one acre

regions of developable land arranged in a square 10 X 10 grid and parameterize to a popu-

lation of 342.4 Note also that household income is normalized to one. This corresponds to

a baseline utility level of 1 using the calibrated share form of the NCES utility. That is, if

the resident purchases the baseline lot-numeraire bundle with the environmental quality as

specified under the baseline assumptions the individual will achieve a utility of 1.

3 Numerical Method

We solve for the Nash Equilibrium in the model using a diagonalization method. In our

model, once the choice of open space for each development region is made by the juris-

dictions, all other variables are uniquely determined by the market clearing equilibrium

conditions. Here, individual jurisdictions compete in both quantity of residential land and

environmental quality. From a given choice of open space, we derive the open space amenity

associated with all development regions using the weighting matrix defined in equation 2.2

with the weights declining with the sqareroot of distance.

The solution algorithm is as follows. For each jurisdiction, we initialize the amount of

open space that they provide to an initial level. Next, consider first one of the jurisdictions.

Taking all other jurisdictions open space allocations as given, the jurisdiction maximizes

rents by choosing a level of open space in each of the regions that it controls. Next, we

iterate over each of the jurisdictions in the economy identifying their optimal reponse and

4This population corresponds with the benchmark condition on land consumption.

7

updating the open space levels in their region.5 We continue to iterate over the set of

jurisdictions until the system converges. For the social planner’s problem (shared utility

maximization), we simply iterate over choices of open space in each parcel until the system

converges to a maximal shared utility level.

4 Baseline Results and Welfare Calculations

We first consider the case of a social planner maximizing the shared utility level of the

residents. Results are presented in Figure 4a and Table 4. Given our calibration, under the

socially optimal outcome, in the aggregate there is a 14.5% allocation of open space in the

development area.6 Because fewer regions benefit from spillovers when land is protected

near the boundary, this open space is not evenly distributed over the development area.

Thus, we see in Figure 4a, there is a greater concentration of open space in the center of

the development area. Under the social planner, the allocation maximizes the value of any

parcel of open space accounting for the spillovers. As we perturb the spillover coefficient, φ0,

not only is the amount of open space perturbed but also the distribution. As we decrease

spillovers, the total amount of open space increases and the slope, as we move from the

center, decreases. That is, the distribution becomes flatter and more uniformly distributed.

Analysis of welfare changes in the model is complicated by the general equilibrium

nature of the simulations. To assess these issues, we adopt a specification of compensating

variation that is consistent with the model. As a baseline utility for the welfare calculations

we use the socially optimal shared utility level. Because households at different locations

consume different bundles of numeraire, land and environmental quality implying different

5Each iteration requires identifying the equilibrium outcome under each possible set of open space levelsand identifying those levels which maximize jurisdiction’s profit.

6Note this outcome is not identical to the calibration used for the utility paramaters becuase in ourcalibration, we have not taken into account the spatial nature of open space provision. Thus, the calibrationis not supportable as an equilibrium even given the pricing structure derived to calibrate the parameters.

8

welfare implications for the uses of land resources, we do not allow households to relocate in

the welfare calculation. Further, because location is fixed and open space level within the

region is fixed, we also do not allow lot size adjustments in the welfare calculation. Thus,

the only portion of households allocations that will be allowed to adjust in the welfare

calculation is that of the numeraire good. Thus, to identify the compensating variation

for a given location under a given regime, we compute the amount of income that would

have to be given to an individual in order to restore their utility level to that of the socially

optimal utility level conditional on that money being spent on the numeraire good. Further,

since incomes may vary across regimes due to the recycling of jurisdictional land rents, we

normalize by the income level, 1 +∑

j∈J Πj , of the regime outcome in question. Thus,

compensating variation (CV) is given by:

U(xj + CV, Lj , Qj) = U(xSOj , LSO

j , QSOj ) = U

SO (4.12)

where the superscript represents the socially optimal allocation and barred variables are

fixed according to the regime and location under consideration. Our welfare measure there-

fore monetizes the welfare loss to the household under a given regime relative to the socially

optimal utility level.

5 Competition without Spillovers

In order to analyze the role of competition in a systematic manner, we begin by isolating the

market power effect of open space provision and abstract from the role of benefit spillovers

across jurisdictions and within jurisdictions. In our model, this amounts to setting φj =

0,∀j ∈ J . First, we consider a duopoly case and evaluate different configurations of land

within the development area. Second, we consider symmetric configurations with increasing

numbers of jurisdictions.

To consider the role of market power in the duopoly case, we assume that a small

9

developer is located along one edge of the development region. Results for this analysis are

contained in Table 1 and Figure 2. The first observation to make is that moving from a

monopoly case to a case with a small competing jursidiction (90%-10% split), has a large

effect on the provision of open space. This small decrease in market power leads to a large

decrease in welfare loss relative to the socially optimal, on the order of 66%, as competition

alleviates the under provision of residential land that occurs in the single jurisdiction case.

As we further decrease this market power in steps of 10%, we see roughly a halving of the

welfare loss at each step. Thus, market power plays a key role in the provision of open

space. With even a small amount of competition, we see a reduction in excess open space

provision by the dominant jurisdiction. This relaxes the monopoly derived housing supply

restriction by 41%.7

As a second approach to the analysis of the impact of market power in the absence

of spillovers, we consider the impact of moving from a single jurisdiction to a model with

multiple symmetric jurisdictions. We progress from a monopoly jurisdiction through the

case of two and 4 jurisdicitons to a case of 100 separate jurisdicitons that we call the

“competitive model.” Results from this analysis appear in Table 2. As with the case of

an increasingly larger competing jurisdiction without spillovers, decreased market power

moves each jurisdicition toward the socially optimal allocation. The largest increase in

welfare from competition comes at the first step, that of moving from the monopoly to the

duopoly. Under this change, we see a weakening of the over provision of open space on the

order of 86%.

7The reduction in the over provision of open space is given by: 29.726−23.3529.726−14.500

.

10

6 Competition with Spillovers

We now consider how competition affects the allocation of open space when spillovers are

present. As discussed in the model section, in this experiment we assume that there exist

spillovers between each development region and not just between jurisdicitons. As in the

no spillovers case, we begin by considering the duopoly case and consider the role of market

power with different initial allocations of land. Results are presented in Table 3 and Figure

3. First, with a very small jurisdiction, we see free riding by the small jurisdiction on

the over provision by the large jurisdiction. In fact, the small jurisdiction would like to

expand its boundaries in order to provide even more area for residential lots. Our second

observation is that as market power decreases and jurisdictions become more symmetric,

welfare increases. Although in the limit, we have an underprovision of open space, the

welfare loss is not that great. Finally, decreasing the market power beyond a 70-30 split has

virtually no effect on welfare. Although jurisdicitons are better able to capture spillovers

and there is less market power, these effects move in opposite directions and almost perfectly

offset each other.

The next step in the analysis is to consider the role of symmetric competition in the

presence of spillovers. As above, the analysis begins with a single jursidiction and progresses

through a system of symmetric jurisdictions ending with each parcel of land owned by one

of 100 different jurisdictions.

The analysis assumes that the jurisdictions have perfect information regarding the pref-

erences of potential residents. Thus, in the monopolist case with a fixed population size, we

have a perfectly price discriminating jurisdiction. Under this framework, initial intuition

might suggest that the monopolist will provide the optimal level of open space because the

value of open space is capitalized in the price of the lot and all spillovers are captured by

the monopolist. As we have already seen in the case without spillovers, this is not the case.

Given the dual nature of open space as an input to both the private as well as public good

11

and the fact that there is a fixed a set of individuals in the development area, the closed

city assumption, the monopolist chooses to over-provide the public good in order to restrict

the amount of the private good available on the market. Thus, we may say that, in general,

property value maximization does not necessarily lead to utility maximization. However,

the general shape of the distribution is similar to that of the socially optimal distibution,

that of larger amounts of open space at the center of the development area with decreasing

open space toward the edge of the development area. Results for this analysis appear in

Table 4 and Figure 4.

Next, consider the case of a duopoly. Assume that the two jurisdictions have equal areas

and are symmetric within the development area. Under this specification, not only is the

total amount of open space provided below the efficient level, but the spatial distribution

is also much more inefficient than under the monopolist. Because the jurisdictions are

acting to maximize their land rents, in the Nash equilibrium they will allocate most of

the open space away from where the other jurisdiction is located in order to maximize the

internalization of the spillovers. This implies that most of the open space occurs not at

the center of the development area, but at the center of the district controlled by each of

the two competing jurisdictions. Under this competition regime, each jurisdiction provides

approximately 12.1% of their area to open space. Thus, we see a shift from an over provision

by the monopolist to a slight under provision with the imposition of competition. As

we move to greater competition, these results are further exacerbated in both levels and

distribution. In the competition without spillovers case, we saw a move toward the socially

optimal with increased competition. By introducing spillovers, competition reduces the

ability of the jurisdiction to capture rents from open space provision. There is an inherant

trade off with increased competition between reducing the supply restriction and the ability

of the jurisdiction to capture rents. Thus, as competition increases, open space necessarily

decreases and the inablity to capture benefits dominates, causing an underprovision.

12

7 Market Based Instrument vs. Command and Control

Finally, we consider the effectiveness of a uniform market-based instrument in the presence

of inter-jurisdictional competition and cross-jurisdiction spillovers – identifying the utility

maximizing income tax-open space subsidy pair under each competition regime. Under

this market-based instrument, a per unit open space subsidy is first identified and then in

equilibrium an income tax rate is set which raises exactly the level of revenue needed to

fund the resulting subsidies. The subsidy level is then chosen to maximize the shared utility

level. We compare the outcome under this optimal uniform market-based instrument to a

command and control regulation that mandates a uniform quantity of open space per acre.

Table 5 and Figure 5 present the results from this analysis. First note that in the single-

jurisdiction model, because the unregulated equilibrium leads to an overprovision of open

space, the optimal tax and subsidy are both negative. As the first column in Table 5 shows,

in the case of a single jurisdiction, a subsidy of -0.3442 units of income per acrereturns the

system to the socially optimal levels of open space, land rents, income and shared utility

level. This result is fairly intuitive. Because all households receive the same income, the

income tax is identical to a non-distortionary head tax. In equilibrium, each subsidy level

is associated with a specific aggregate open space level. And, because the single jurisdiction

internalizes all spillovers, the jurisdiction chooses the optimal distribution of open space

across locations for each unique aggregate open space level. For comparison, the final column

of table 5 reports the optimal level of open space under a uniform command and control

regulation. Because the command and control regulation does not allow for adjustments to

reflect the variation in spillovers across location, the command and control policy slightly

under-performs the market instrument under a single jurisdiction.8

Once we move from the single jurisdiction case, because of the spatial inefficiencies

8Since we are uniformly fixing the open space percentage for each region in this command and controlregulation, the command and control level is independent of competition regime.

13

that are introduced by spatially discrete competing jurisdictions, it is no longer possible

to return the system to the social optimal via the tax-subsidy instrument. As is shown in

Table 5, once competition is introduced the open space “tax” is replaced by a subsidy. The

required subsidy increases with competition from 0.1775 under the duopoly case to 0.9860

in the competitive model. Further, in contrast to the single jurisdiction case, once spatial

inefficiencies in open space associated with the competing jurisdictions are introduced the

uniform command and control regulation clearly dominates the optimal uniform tax-subsidy

pair.

8 Conclusion

This paper highlights two important types of market failure that link the spatial structure

of jurisdictional competition to the provision of open space. First, because open space is an

essential input to the development of residential lots, when rent-maximizing jurisdictions

are able to exert market power they may provide open space purely as a by-product of their

attempts to drive up prices through supply restrictions. Second, when open space amenities

spillover across jurisdictional boundaries, changes in the spatial distribution of of competing

jurisdictions lead to changes in the ability of these jurisdictions to internalize the benefits

of open space provision.

Our analysis considers the tradeoffs inherent between these two types of market failure.

Specifically, we demonstrate that the incentives for a monopoly jurisdiction to restrict supply

(potentially leading to the provision of open space beyond the efficient levels) provides

an incentive to encourage greater levels of jurisdictional competition while the inability

of multiple spatially fragmented jurisdictions to internalize the spillover benefits of open

space encourages reductions in jurisdictional competition. The results from our numerical

simulations suggest that externalities related to market power are largely ameliorated at

low levels of competition. Given the problem of internalizing amenity spillovers as the

14

number of competing jurisdictions grows, the analysis therefore finds that social welfare is

maximized when jurisdictional competition exists, but at low levels. Although these results

are for a single parameterization of the model, the qualitative results will hold for most

parameterizations of the model.

The final thrust of our analysis considers the efficacy of uniform market-based instru-

ments relative to a uniform command and control regulatory approach in the face of these

competing market failures. In the case of a single jurisdiction, we find that the market

based-instrument is capable of restoring the socially optimal open space allocation and

therefore clearly dominates the command and control regime. However, once jurisdictional

competition is introduced, inefficiencies in the spatial distribution of open space that are

introduced through this competition cause the market-based approach to under-perform

relative to the command and control strategy.

15

Figure 1: Definition of the Development Area

Development Area

Region

District

Lot

16

Figure 2: Open Space Percentage Under Duopoly Competition with Different Levels ofMarket Power and No Spillovers

0.16

0.17

0.18

0.19

0.2

0.21

0.22

(a) 90-10 Split

0.155

0.16

0.165

0.17

0.175

0.18

0.185

0.19

0.195

0.2

(b) 80-20 Split

0.16

0.165

0.17

0.175

0.18

(c) 70-30 Split

0.162

0.164

0.166

0.168

0.17

0.172

0.174

(d) 60-40 Split

17

Figure 3: Open Space Percentage Under Duopoly Competition with Different Levels ofMarket Power with Spillovers

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

(a) 90-10 Split

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

(b) 80-20 Split

0.06

0.08

0.1

0.12

0.14

0.16

0.18

(c) 70-30 Split

0.05

0.1

0.15

(d) 60-40 Split

18

Figure 4: Open Space Percentage Under Competition with Increased Number of Jurisdic-tions with Spillovers

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

(a) Socially Optimal

0.285

0.29

0.295

0.3

0.305

(b) Monopoly

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

(c) Duopoly

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

(d) Quadopoly

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

(e) Perfectly Competitive

19

Figure 5: Open Space Percentage Under Optimal Tax Instrument and Spillovers

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

(a) Socially Optimal

0.11

0.12

0.13

0.14

0.15

0.16

(b) Monopoly

0.06

0.08

0.1

0.12

0.14

0.16

0.18

(c) Duopoly

0.06

0.08

0.1

0.12

0.14

0.16

0.18

(d) Quadopoly

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.21

(e) Competitive

20

Table 1: Impact of Size of Jurisdiction in Duopoly Case with No SpilloversSocial Optimal Monopoly 10% and

90%20% &80%

30% &70%

40% &60%

Percent Open Space 14.500 29.726 14.67 &23.35

15.06 &20.40

15.49 &18.65

16.00 &17.50

CV as % of income 0.0 2.28% 0.79% 0.34% 0.16% 0.08%Rents 118.086 120.162 12.35 &

107.3524.16 &95.09

35.89 &83.06

47.61 &71.17

Ave Lot Size 0.2500 0.2055 0.239 &0.225

0.241 &0.234

0.245 &0.239

0.2447 &0.2419

Welfare Rank 1 6 5 4 3 2

Table 2: Impact of Competition on Open Space Provision with No SpilloversSocial Optimal Monopoly Duopoly Quadopoly Competitive

Percent Open Space 14.500 29.726 16.636 15.285 14.525CV as % of income 0.0 2.28% 0.06% 0.009% 0.000009%Rents 118.086 120.162 118.731 118.344 118.095Ave Lot Size 0.2500 0.2055 0.2438 0.2477 0.2499Welfare Rank 1 5 4 3 2

21

Table 3: Impact of Size of Jurisdiction in Duopoly Case with SpilloversSocial Optimal Monopoly 10% and

90%20% &80%

30% &70%

40% &60%

Percent Open Space 14.469 29.714 0.00 &20.00

5.39 &17.13

8.69 &14.48

10.67 &13.46

CV as % of income 0.0 2.29% 0.36% 0.21% 0.18% 0.18%Rents 118.061 120.134 12.91 &

105.8624.13 &93.62

35.47 &81.83

46.93 &70.13

Ave LotSize 0.2500 0.2055 0.265 &0.237

0.266 &0.246

0.263 &0.251

0.260 &0.254

Welfare Rank 1 6 5 4 2 3

Table 4: Impact of Competition on Open Space Provision with SpilloversSocial Optimal Monopoly Duopoly Quadopoly Competitive

Percent Open Space 14.469 29.714 12.136 9.722 5.781CV as % of income 0.0 2.28% 0.18% 0.55% 2.16%Rents 118.061 120.134 116.984 115.591 111.887Ave Lot Size 0.2500 0.2055 0.2569 0.2640 .02755Welfare Rank 1 5 2 3 4

22

Table 5: Comparison of levels of optimal tax with different levels of competition and Com-mand and Control

Monopoly Duopoly Quadopoly Competitive Command & ControlPercent Open Space 14.469 14.597 14.613 14.578 14.980Shared Utility 1.2863 1.2855 1.2854 1.2855 1.2861CV as % of income 0.000% 0.053% 0.061% 0.043% 0.009%Rents 118.061 112.421 117.962 118.022 118.213Ave Lot Size 0.2500 0.2497 0.2496 0.2497 0.2486Optimal Income Tax -1.09% 0.56 1.48% 3.03% NAOpen Space Subsidy/Tax -0.3442 0.1775 0.4728 0.9860 NAWelfare Rank 1 4 5 3 2

23

References

Bolitzer, B. and Netusil, N. (2000). The Impact of Open Spaces on Property Values in Portland, Oregon.Journal of Environmental Management, 59, 185–193.

Brasington, D. M. (2002). Edge versus Center: Finding Common Ground in the Capitalizatino Debate.Journal of Urban Economics, 52, 524–541.

Brueckner, J. (1983). The Economics of Urban Yard Space: An ”Implicit-Market” Model for HousingAttributes. Journal of Urban Economics, 46, 216–234.

Bruekner, J. (1983). Property Value Maximization and Public Sector Efficiency. Journal of Urban Economics,14, 1–15.

Cremer, H., Marchand, M., and Pestieau, P. (1997). Investment in Local Public Servies: Nash Equilibriumand Social Optimum. Journal of Public Economics, 65 (1), 23–35.

Epple, D. and Zelenitz, A. (1984). Profit Maximizing Communities and the Theory of Local Public Expen-diture: Comment. Journal of Urban Economics, 16, 149–157.

Riddel, M. (2001). A Dynamic Approach to Estimating Hedonic Prices for Environmental Goods: AnApplication to Open Space Purchases. Land Economics, 77, 494–512.

Schultz, S. and King, D. (2001). The Use of Census Data for Hedonic Price Estimates of Open-SpaceAmenities and Land Use. Journal of Real Estate Finance and Economics, 22, 239–252.

Sonstelie, J. and Portney, P. (1978). Profit Maximizing Communities and the Theory of Local PublicExpenditure. Journal of Urban Economics, 5, 263–277.

Sonstelie, J. and Portney, P. (1984). Profit Maximizing Communities and the Theory of Local PublicExpenditure: Reply. Journal of Urban Economics, 20, 250–255.

Wu, J. and Plantinga, A. J. (2003). The Influence of Public Open Space on Urban Spatial Structure. Journalof Environmental Economics and Management, 46 (2), 288–309.

24