, CA

Keywords:

Parking garages

. anEctowruispaarag

market power on parking garages. Spatial competition between parking garages, as modeled in Arnottmpetition between downtown parking garages and downtown parking policy.

owntowto its

Regional Science and Urban Economics 39 (2009) 114

Contents lists available at ScienceDirect

Regional Science and

j ourna l homepage: www.e la downtown destination that is associated with parking. Informalestimates of one half seem too high. It seems warranted to say,however, that economists have paid less attention to downtownparking than its importance merits. There is a large literature ineconomics on urban auto congestion but only a few recent paperson the economics of downtown parking (which will be reviewedbelow).

cruising for parking contribute to trafc congestion as well. Underreasonable assumptions, Arnott and Inci demonstrated the existenceand uniqueness of steady-state equilibrium with saturated parking,and also examined curbside parking policy in the context of themodel.

Denser downtown areas have garage as well as curbside parking.Because of economies of scale in garage construction, garages arediscretely spaced. The friction of space then confers market power We would like to thank Eren Inci, Robin Lindseyparticipants at Clark University, Emory University, thRiverside, the University of Colorado at Boulder, the Univthe University of Massachusetts at Amherst, and the Univhelpful comments, and Junfu Zhang for pointing out an Corresponding author.

E-mail addresses: richard.arnott@ucr.edu (R. Arnott)

0166-0462/$ see front matter 2008 Elsevier B.V. Aldoi:10.1016/j.regsciurbeco.2008.08.001sing for parking and, there are no reliablefull price of a trip with

parkingwaiting for a parking spot to open up. The expected time spentcruising for parking adjusts to clear the market, which is achieved viaadjustment in the density of cars cruising for parking. The carswalking some distance. To our knowledgeestimates of the proportion of the averageconvenient parking garage is expecurbside parking normally entailnsive, while nding cheapers cruiParking policy

1. Introduction

Anyone who has parked in the dduring the business day will attestparking. This paper combines the ingredients of these two models, hence presenting an integrated model ofcurbside parking, garage parking, and trafc congestion, and examines curbside parking policy in this contextthrough a numerical example with parameters representative of a medium-sized US city. The central result isthat raising the curbside parking fee appears to be a very attractive policy since it generates efciency gainsthat may be several times as large as the increased revenue raised.

2008 Elsevier B.V. All rights reserved.

n area of a major cityhigh cost. Parking in a

Arnott and Inci (2006) constructed an integratedmodel of curbsideparking and trafc congestion in an isotropic downtown area withidentical drivers and price-sensitive demand. The curbside meter rateis set below its social opportunity cost. This results in excess demandfor curbside parking spaces. Parking is saturated, and cars cruise forParkingTrafc congestiongarages. Also, the stock of cars cruising for parking adjusts to equalize the full prices of curbside and garageR40[Arnott, R., 2006. Spatial coTransport Policy 13, 458469], determines the equilibrium garage parking fee and spacing between parkingDowntown parking in auto city

Richard Arnott a,, John Rowse b

a Department of Economics, University of California, Riverside, 4106, Sproul Hall, Riversideb Department of Economics, University of Calgary, Calgary, AB, Canada T2N 1N4

a b s t r a c ta r t i c l e i n f o

Article history:Received 12 December 2007Received in revised form 11 July 2008Accepted 12 August 2008Available online 20 August 2008

JEL classication:

Arnott and Inci [Arnott, Rcongestion. Journal of Urbantrafc congestion in a downcost, and the stock of cars cmarket for curbside parkingof economies of scale in g, David Malueg, and seminare University of California atersity of Florida at Gainesville,ersity of California at Irvine forerror in an earlier draft.

, rowse@ucalgary.ca (J. Rowse).

l rights reserved.92521-0427, USA

d Inci, E., 2006. An integrated model of downtown parking and trafconomics 60, 418442] developed an integrated model of curbside parking andn area. Curbside parking is exogenously priced below its social opportunity

sing for parking, which contributes to trafc congestion, adjusts to clear theces. Denser downtown areas have garage as well as curbside parking. Becausee construction, garages are discretely spaced. The friction of space confers

Urban Economics

sev ie r.com/ locate / regecon parking garages. Arnott (2006) developed a model of spatialcompetition between parking garages, which generates an equili-brium parking fee that is above marginal cost. With underpricedcurbside parking and overpriced garage parking, the stock of carscruising for parking adjusts to equalize their full prices. This papercombines the ingredients of these two models (except, to simplify, itassumes inelastic demand for downtown parking), hence presentingan integrated model of curbside parking, garage parking, and trafc

congestion, and examines curbside parking policy in this contextthrough a numerical example with parameters representative of amedium-sized, auto-oriented city such as Winnipeg, Perth, San Diego,Sacramento, or Phoenix.

Calthrop and Proost, 2006). Calthrop (2001) and Arnott (2006)considered the potential importance of garage market power,Calthrop by assuming a monopoly supplier, Arnott by modelingspatial competition between parking garages. The Los Angeles modelof Arnott, Rave, and Schb includes curbside parking, garage parking,endogenous cruising for parking, and garage market power, butprovides an unpersuasive treatment of garage market power. Arnott(2006) contained all four elements as well, but focused on the

2 R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114The addition of garage parking alters the economics of downtownparking in three interesting ways. First, the equilibrium conditiondetermining the stock of cars cruising for parking changes. With onlycurbside parking, the stock of cars cruising for parking adjusts to clearthe market for trips. In contrast, with both curbside and garageparking the stock of cars cruising for parking adjusts to equalize thefull prices of curbside and garage parking. Second, even though theoverpricing of garage parking does not create inefciency directly,since overall parking demand is assumed to be inelastic, it does soindirectly in two ways, rst, as noted already, by increasing the pricespread between curbside and garage parking and hence the stock ofcars cruising for parking, and second by causing parking garages to beinefciently small and too closely spaced. Third, the presence ofgarage parking magnies the distortion associated with the under-pricing of curbside parking, or, put alternatively, increases the socialbenet of increasing the curbside parking fee. With only curbsideparking, the equilibrium full price of a downtown trip is determinedby the intersection of the trip demand curve and the curbside parkingcapacity constraint. Raising the curbside meter rate does not alter thisfull price of trips, but simply converts travel time (which includes in-transit and cruising-for-parking time) costs dollar for dollar intometerrevenue, so that every extra dollar of revenue raised increases socialsurplus by one dollar. But with garage parking, there is a magnicationeffect. Raising the curbside meter rate does not alter the full price ofparking. Raising the curbside meter rate converts cruising-for-parkingtime costs dollar for dollar into meter revenue. But there is the addedbenet that the reduction in the stock of cars cruising for parkingreduces trafc congestion, which benets everyone. In our favorednumerical example, this magnication effect results in a $3.20increase in social surplus for every dollar increase in meter revenue.

As noted above, the literature on the economics of parking is small.We start by reviewing the broader literature, and then turn to thesmall number of papers that distinguish between curbside and/orgarage parking or analyze cruising for parking.

Early work on the economics of parking argued that parking, like anyother commodity, should be priced at its social opportunity cost (Vickrey,1954; Roth, 1965). Vickrey (1954) also developed a scheme for demand-responsive pricing of curbside parking. Over the next three decades,parkingwas largely ignored by economists, inmodal choice studies beingtreated simplyasa componentof thexedcostof a trip.Modern interest inthe economics of parking started in the early 1990s. Shoup (2005) has ledtheway ingenerating interest in theeconomicsofparking. In the1990s, hechampioned cashing out employer-provided parking, and has consideredmany aspects of the economics of parking since then. Arnott et al. (1992)and Anderson and de Palma (2004) extended the Vickrey bottleneckmodel (1969) to analyze the temporospatial equilibrium of curbsideparking when all drivers have a common destination and desired arrivaltime, such as for a special event or the morning commute. Arnott andRowse (1999) examined the steady-state equilibria of cars cruising forparking on a circle when parking is unsaturated.

Arnott et al. (2005, Ch. 2, The basic model) presented a model thatexamines the interaction between cruising for parking and trafccongestion with only curbside parking. A more thorough treatment ofthat model was provided in Arnott and Inci (2006). Several papers inthe literature have recognized that the stock of cars cruising forparking adjusts to equalize the full prices of curbside and garageparking (Calthrop, 2001; Shoup, 2005,1 2006; Arnott et al., 2005;

1 Shoup, Table 11-5, displays the results of 16 studies of cruising for parking in 11cities over an eighty- year period. The mean share of trafc cruising was 30% and theaverage search time was 8.1 min. While the study locations were not chosen randomly,

the results do indicate the potential importance of cruising for parking.treatment of garage market power rather than providing a completeanalysis of the model. This paper provides a complete analysiswith the more satisfactory treatment of garage market power, andalso provides calibrated numerical analysis of a variety of parkingpolicies.

In terms of policy insights, our principal nding which wasnoted above is that, under conditions of even moderate trafccongestion, the social benets from raising curbside parking ratesmay be several times the additional meter revenue generated, adouble dividend result. Another important nding is that, withrealistic parameter values, less space should typically be allocatedto curbside parking the larger is the wedge between curbside andgarage parking rates.

Section 2 sets the stage by presenting a simplied model in whichgarage parking is provided at constant unit cost. Section 3 presentsand analyzes the central model that takes into account the technologyof garage construction and spatial competition between parkinggarages. Section 4 presents calibrated numerical examples for thecentral model. Section 5 notes some directions for future research.And Section 6 provides some concluding comments.

2. A simple model

Understanding the central model of the paper will be facilitatedby starting with a simplied variant. A broad-brush description isfollowed by a precise statement.

2.1. Informal model description

The model describes the equilibrium of trafc ow and parkingin the downtown area of a major city.2 To simplify, it is assumedthat the downtown area is spatially homogeneous (isotropic) andin steady state, and also that drivers are homogeneous. Driversenter the downtown area at an exogenous uniform rate per unitarea-time, and have destinations that are uniformly distributedover it. Each driver travels a xed distance over the downtownstreets to his destination. Once he reaches his destination, hedecides whether to park curbside or in a parking garage.3 Bothcurbside and garage parking are provided continuously over space.If he parks curbside, he may have to cruise for parking, circling theblock until a space opens up. After he has parked, he visits hisdestination for a xed period of time, and then exits the system.Garage parking is assumed to be provided competitively by theprivate sector at constant cost, with the city parking departmentdeciding on the curbside meter rate and the proportion of curbsideto allocate to parking. The curbside parking fee (the meter rate) isless than the garage fee. Consequently, all drivers would like topark curbside but the demand inow is sufciently high that this isimpossible. Curbside parking is saturated (the occupancy rate is

2 The model differs from that in Arnott and Inci (2006) in two respects. Arnott andInci consider the situation where all parking is curbside and the demand for trips issensitive to the full price of a trip. Here, in contrast, the demand for trips is completelyinelastic, and there is both curbside and garage parking. The model specication isindependent of the form of the street network, but for concreteness one may imaginethat there is a Manhattan network of one-way streets.

3 The paper does not consider parking lots. Parking lots are difcult to treat becausemost are transitional land uses between the demolition of one building on a site and

the construction of the next.

100%) and the excess demand for curbside parking spaces isrationed through cruising for parking. In particular, the stock ofcars cruising for parking adjusts such that the full price of curbsideparking, which is the sum of the meter payment and the cost oftime cruising for parking, equals the garage parking payment. Thedowntown streets are congested by cars in transit and cruising forparking. In particular, travel time per unit distance driven increaseswith the density of trafc and the proportion of curbside allocatedto parking.

2.2. Formal model

Consider a spatially homogeneous downtown area to which thedemand for travel per unit area-time is constant, D. Each driver travelsa distance over the downtown streets to his destination, parks therefor a period of time , and then exits.4 A driver has a choice betweenparking curbside, where the meter rate is f per unit time, and parkingin a parking garage, at a rate c per unit time, equal to the resourcecost of providing a garage parking space.5 Both curbside and garageparking are continuously provided over space. By assumption (itsrationale will be given later), fbc, and the excess demand for curbside

one-way streets per unit area, then a person standing on a sidewalkwould observe a ow of (T+C)/(Mt) cars per unit time.9 Throughput isdened analogously to ow but includes only cars in transit10; thus,the throughput in terms of car-distance per unit area-time is T/t.

Steady-state equilibrium is described by two conditions. The rst,the steady-state equilibrium condition, is that the input rate into the in-transit pool, D, equals the output rate, which equals the stock of cars inthe in-transit pool divided by the length of time each car stays in thepool, T/(t(T, C, P)):

D Tt T;C; P : 1

This may be written alternatively as D=T/t(T, C, P). D is the inputin terms of car-distance per unit area-time, and T/t(T, C, P) is thethroughput. Let be the value of time.11 The second equilibriumcondition, the parking equilibrium condition, is that the stock of carscruising for parking adjusts to equilibrate the full prices of garage andcurbside parking:

3R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114parking is rationed through cruising for parking. The stock of curbsideparking is P per unit area, so that the number of garage parking spacesper unit area needed to accommodate the exogenous demand isDP. The technology of trafc congestion is described by the functiont= t(T, C, P), where t is travel time per unit distance, T the stock of carsin-transit per unit area, and C the stock of cars cruising for parking perunit area.6 The larger are C and T, the higher the density of trafc onthe city streets, so that tT and tC (subscripts denote partial derivatives)are positive, and the larger is P, the lower the proportion of streetspace available for trafc, so that tP is positive too. It is assumed as wellthat t is a convex function of T, C, and P.

D is sufciently high that, even if all curbside is allocated to parking(so that P=Pmax), there is still a need for garage parking (i.e., DNPmax).Due to the underpricing of curbside parking, the stock of cars cruisingfor parking adjusts such that the full price of curbside parking, the sumof the meter payment and the value of time lost cruising for parking,equals the full price of garage parking.7 For the moment, it is assumedthat, even when curbside parking is provided free and all curbside isallocated to parking, the street system can still accommodate theexogenous demand.8

The density of cars per unit area is T+C, their velocity, v, is 1/t, andsince ow equals density times velocity, the ow in terms of car-distance per unit area-time is (T+C)/t. If there are M distance units of

4 One could equally well assume that each driver travels a distance /2 over thedowntown streets to his destination, parks there for a period of time , then drives anequal distance over the streets to his entry point.

5 The paper neglects the subsidization of garage parking, which is practically veryimportant (Small and Verhoef, 2007, p.113). The bulk of employers, though a smallerproportion of downtown employers, heavily subsidize their employees' garageparking. Furthermore, many shoppers receive subsidized garage parking via parkingvalidation whereby a retailer pays for the garage parking of clients who havepurchased goods from his store. The subsidization of garage parking reduces the fullprice of garage parking, hence the price differential between curbside and garageparking, and hence the incentive to cruise for parking.

6 Realistically, travel time per unit distance is affected by cars entering and exitingcurbside parking spaces as well. This could be incorporated into the analysis by addingthe curbside parking turnover rate as an argument to the function t. The specicationof the technology assumes that P is divisible. This is not completely satisfactory sincehaving only one curbside parking space per block would slow down trafc almost asmuch, and perhaps even more, as having an entire curb allocated to parking. Thisobjection can be accommodated by having a certain proportion of curbside blockscompletely allocated to curbside parking with the remainder being free of curbsideparking. But this would violate the spatial symmetry assumed in the model.

7 The paper ignores possible safety differences between curbside and garageparking, as well as the search time and walking time inside the parking garage.

8 Primitive conditions for this assumption to hold are given in Section 2.6, which

examines the congestion technology in detail.c f CP

: 2

The full price of garage parking is c. The full price of curbsideparking is f plus the (expected) cost of cruising for parking. Theexpected time cruising for parking12 equals the stock of cars cruisingfor parking, C, divided by the rate at which curbside parking spotsare vacated, P/. Thus, holding xed the expected time cruising forparking, the stock of cars cruising for parking increases with thenumber of curbside parking spaces available. The cost of cruising forparking equals the expected time cruising for parking times the valueof time. Eq. (2) may be rewritten as

C cf P

; 3

indicating the equilibrium stock of cars cruising for parking as afunction of c, f, P, and .

This simple model has two equations in two unknowns, T and C.The equations are recursive. Eq. (3) determines C and then Eq. (1)determines T. Resource costs per unit area-time, RC, are simply (T+C),the stock of cars in transit and cruising for parking, times the value oftime, plus the resource cost of garage parking, c(DP).

9 Flow equals density times velocity is known as the Fundamental Identity of TrafcFlow. Applying this identity in this context requires some care. Ordinarily, density ismeasured per unit distance, so that, with velocity measured as distance per unit time,the dimension of ow is cars per unit time. Here, however, density is measured as carsper unit area, so that application of the formula gives ow in units of car-distance perunit area-time. With M miles of city street per unit area, the density in terms of carsper unit distance is (T+C)/M, and application of the Identity gives ow as cars per unittime on a street, (T+C)/(Mt).10 Since the transportation engineering literature has not analyzed situations inwhich cars circle the block, it does not make a terminological distinction between owand throughput. It seems intuitive to dene ow as the number of cars that abystander would count passing by per unit time. Throughput too seems an appropriatechoice of term.11 The large empirical literature on the value of travel time nds it to differsignicantly across travel activities and for in-transit travel to differ according to thelevel of congestion. The analysis could be extended straightforwardly to allow for theseconsiderations.12 This statement takes into account that the service discipline is random access.There are several features of the model that can be interpreted as either stochastic ordeterministic. A deterministic interpretation, with FIFO access to curbside parking oneach block, is the most straightforward. Stochastic interpretations are more realisticbut would need to be solved using queuing theory (see, for example, Breuer and Baum,

2005).

2.3. Full social optimum

The full social optimum entails no cruising for parking. The densityof in-transit trafc is then determined by Eq. (1) with C=0. Thesocial welfare optimization problem is to choose T and P to mini-mize resource costs per unit area-time, subject to the steady-state

4 R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114equilibrium condition, given by Eq. (1):

minT;P

RC T c DP s:t: Tt T;0; P D 0: 4

The shadow cost of curbside parking is the increase in in-transittravel time cost per unit area-time from having one more curbsideparking spot, which, from Eq. (1), is dT/dP=tPD/(1tTD)). If, withP=0, the shadow cost of curbside parking exceeds c, it is optimal toallocate no curbside to parking. And if, with P=Pmax, the shadow costof curbside parking falls short of c, it is optimal to allocate all curbsideto parking. Otherwise, the optimal P solves

tPD1tTD

c 0; 5

the level of curbside parking should be chosen to equalize the shadowcosts of curbside and garage parking.13

Let denote the value of a variable at the social optimum. Thesocial optimum can be decentralized by setting P=P, T=T, andf= f=c.

2.4. Constrained (second-best) social optimum

Since parking policy is local, it is poorly documented and has beenlittle studied. One empirical regularity stands out, however, at least forUS cities. In downtown areas, the curbside parking fee is considerablylower than garage parking fees. In downtown Boston, for example, themeter rate has remained at $1.00 perhour for twentyyears,while garageparking fees are as high as $10.00 for the rst hour. What accounts forthis price differential? We have posed this question to several seminaraudiences. The common answer is that downtown merchants' associa-tions lobby City Hall to set themeter rate low in order to draw shoppersaway from suburban shopping centers, where most parking is providedfree. In many downtown shopping areas, merchants pay for shoppers'garage parking by validating their garage parking stubs. Since mostcurbside parking has time limits, and since merchants cannot pay fortheir customers' curbside parking, a low meter rate subsidizes theparking of short-term shoppers. If most curbside parking is occupied byshoppers, the result is a form of price discrimination. Shoppers end uppaying less for downtown parking than non-shoppers. In this paper, wedo not attempt to model the political economy of downtown parkingpolicy, but instead simply assume that that the meter rate is set low below the marginal cost of a garage parking space by the localtransportation authority, and explore the implications of the pricewedge between curbside and garage parking.

The constrained social optimum is now considered, where theconstraint is that the curbside parking fee is set below c, with thestock of cars cruising for parking adjusting so as to satisfy the parkingequilibrium condition. The second-best optimal allocation of curb-side to parkingminimizes resource costs per unit area, subject to boththe steady-state equilibrium condition, (1), and the parking equili-brium condition, (2). Resource costs per unit area-time are given by

13 Recall that the constraint is that the inow to the in-transit pool equal the outow.In conventional trafc ow theory, there are two densities corresponding to a level ofow. The specication of the minimization problems implies the choice of the lowerdensity. This complication is addressed in Section 2.5. The convexity of the congestion

function ensures that there is a unique minimum corresponding to the lower density.(T+C)+ c(DP). Thus, the constrained social welfare optimizationproblem is to choose T, C, and P to

minT;C;P

RC T C c DP s:t:i Dt T;C; P T 0; /ii P

cf C 0; 6

where is the Lagrange multiplier on constraint i) and that onconstraint ii). The second-best optimum may entail no curbsideallocated to parking, in which case there is no cruising for parking,or all the curbside allocated to parking. An interior optimum is char-acterized by the rst-order conditions:

T : / DtT1 0 7a

C : /DtC 0 7b

P : c /DtP cf 0 7c

Substituting out the Lagrange multipliers yields

DtP1DtT

cf DtC1DtT

cf c 0: 8

A heuristic derivation is as follows: P should be chosen such thatdRC/dP=0. From the objective function, dRC/dP=dT/dP+dC/dPc;from constraint ii), dC/dP=(c f)/; and from constraint i), (dT/dP)(1DtT)=DtCdC/dP+DtP. The last term in Eq. (8) is the marginalsocial benet of P, the reduction in garage costs. The other threeterms are components of the marginal cost, all of which relate totravel costs. The rst term captures the capacity reduction effect; thisis the increase in aggregate in-transit travel costs that comes aboutthrough the reduction in the road space available, holding constantT and C. The second term captures the cruising-for-parking stockeffect; since the stock of cars cruising for parking is proportional to theamount of curbside parking, the increase in P increases the stockof cars cruising for parking, which, holding T and P xed, increasescongestion. The third term captures the cruising-for-parking conges-tion effect; via the steady-state equilibrium condition, the increase inthe stock of cars cruising for parking causes the stock of cars in transitto increase, which further augments congestion.

Let denote values at the constrained social optimum. With thecurbside meter rate set at the exogenous level, the constrained socialoptimum can be decentralized by setting T=T, C=C, and P=P.

Unless both allocations entail the same corner solution, the optimalamount of curbside to allocate to parking is greater in the full socialoptimum than in the second-best social optimum with underpricedcurbside parking, i.e. PNP. In both allocations, the marginal socialbenet of increasing P by one unit is the saving in garage resource costs,c. But the marginal social cost of increasing P is lower in the full socialoptimumthan in the second-bestoptimumsince the costs deriving fromthe cruising-for-parking stock and congestion effects are absent.

2.5. Revenue multiplier: the effects of raising the curbside parking fee

A principal theme of the paper is that the underpricing of curbsideparking is wasteful. To formalize this point, this subsection examinesthe resource savings from increasing the curbside parking fee by asmall amount when it is below c, holding P xed. From the expressionfor resource costs:

dRCdf

dTdf

dCdf

dTdC j 1 1dCdf :9

where dT/dC|(1) denotes the change in T associated with a unit

change in C when Eq. (1) is satised. Now, the revenue raised from

the parking fee, R, is Pf, so that dR/df=P. From Eq. (2), dC/df=P.Thus,

dRCdf

dTdC j 1 1dRdf : 10Hence, the resource cost saving per unit area-time from raising the

curbside parking fee equals a multiple of the increase in the parking feerevenue raised.We term this themultiplication effect. Since the full priceof parking is c, whether a driver parks curbside or in a parking garage,cruising-for-parking costs fall by exactly the amount of the increase in

shown to increase.17

2.7. Complications caused by garage construction technology

The above analysis laid out the economics of equilibrium whenthere is curbside and garage parking, when garage parking is priced at

15 Earlier, to avoid considering non-existence of a solution to the resource costminimization problems, it was assumed an equilibrium exists even when trafc is ascongested as possible, which occurs when f=0 and P=Pmax. This condition is that Db(cPmax/, Pmax). With a positive parking fee and/or less curbside allocated to parking, asolution to the resource cost minimization problems (and the correspondingequilibria) may exist when this condition is not satised.16 It is reasonable to assume that the parking equilibrium condition is always satised,so that trajectories travel along the =0 locus. T is positive above T=0 and negativebelow it. If therefore the initial level of T lies below the T =0 locus, T decreases, while if itlies above the T =0 locus, T increases. It follows that E1 is a stable equilibrium and E2 anunstable equilibrium.17 Substituting Eq. (2) into Eq. (1) gives T=t(T, (c f)P/, P)D=T^ (P). Also, from Eq. (3),C=(c f)P/. Then, dT/dC=(dT^/dP) (dC/dP)=[/(c f)]dT^/dP, and so d(dT/dC)/dP=[/(c

2 ^ 2

5R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114parking fee revenue, and there is the added benet that in-transit travelcosts fall due to the reduction in the stock of cars cruising for parking.

Dene

udRCdfdRdf

1 dTdC

j 1 11

to be the (marginal) revenue multiplier. What determines the size ofthe revenue multiplier? Or put alternatively, by howmuch does a unitreduction in the stock of cars cruising for parking reduce the totalstock of cars on the road? The answer depends on the technology ofcongestion, as well as its level. The revenue multiplier is even larger ifaccount is taken of the marginal cost of public funds exceeding 1.

2.6. The congestion technology

The steady-state equilibrium condition, (1), can be writtenimplicitly as C=C(T; P, D). Holding xed P and D, for each level of Tthe function gives the stock of cars cruising for parking consistent withsteady-state equilibrium. Under the assumption that the function t(.)is convex in T, C, and P, holding P xed the function C is concave in T.In the absence of cruising for parking, with realistic congestionfunctions there are normally two densities consistent with a givenlevel of (feasible) ow, i.e. T=t(T, 0, P)D has two solutions, onecorresponding to regular trafc ow, the other to trafc jamconditions. Fig. 1 displays the graph of the function C, termed thesteady-state locus, with these two properties. An increase in P causesthe locus to shift down; holding T xed, Eq. (1) determines anequilibrium travel time, and to offset the increase in travel time due tothe increase in P requires a decrease in C. An increase in D causes thelocus to shift down; holding P and T xed, for Eq. (1) to continue to besatised the increase in Dmust be offset by a decrease in t, and hencea decrease in C. If D increases sufciently, there is no (T, C) satisfyingEq. (1) and a steady-state equilibrium does not exist.

It is assumed furthermore that the function t(.) is weakly separable,specically that t= t(T, C, P)= t(V (T, C), P), with V dened as the effec-tive density of cars on the road14 and normalized in terms of in-transitcar-equivalents in the absence of cruising for parking, i.e. V (T, 0)=T.

Dene (C, P)=maxT T/t(V (T, C), P) to be the throughput capacity ofthe street system as a function of C and P, so that (0, P) is capacity asconventionally dened. It indicates the maximum entry rate, in terms

14 In the numerical examples presented later, it will be assumed that congestiontakes the form of a negative linear relationship between velocity and effective density:v=vf (1V/Vj), where vf is free-ow speed and Vj is effective jam density, which is aslight generalization of Greenshield's Relation. Travel time per unit distance is thereciprocal of velocity. Then letting t0 denote free-ow travel time, this relationship canbe rewritten as t= t0/(1V/Vj). It will also be assumed that a car cruising for parkingcreates 1.5 times as much congestion as a car in transit, i.e. V=T+1.5C. Eq. (1) thenbecomes T(VjT1.5C)= Dt0Vj. Thus, capacity is Vj/(4t0), the effective densitycorresponding to this capacity is Vj/2, (dC/dT)(1)= (Vj2T1.5C)/(1.5T), and the revenuemultiplier is =(Vj0.5T1.5C)/(Vj2T1.5C). We shall assume furthermore thateffective jam density is linearly decreasing in the proportion of curbside allocated toparking: Vj=(1P/Pmax), where is the effective jam density with no curbside

parking.of car-distance per unit area-time, the street system can accommodatein steady-state equilibrium for a given C and P. If D exceeds (0, P),then the entry rate exceeds throughput capacity even in the absenceof cruising for parking, and no steady-state equilibrium exists. If D isless than (0, P), then the steady-state locus lies in the positivequadrant. The parking equilibrium condition, Eq. (2), can be written asC=(c f)P/, giving the equilibrium stock of cars cruising for parking.Since the condition is independent of T, its graph in Fig. 1, the parkingequilibrium locus, is a horizontal line. If Eq. (2) lies everywhere aboveEq. (1), which occurs if DN((c f) P/, P), the entry rate exceedsthroughput capacity at the equilibrium level of cruising for parking,and no equilibrium exists.15 If Eqs. (1) and (2) intersect, they do sotwice. A straightforward stability argument16 can be applied toestablish that the left-hand intersection point is stable while theright-hand one is unstable. Thus, we take the left-hand intersectionpoint to be the equilibrium.

An initial equilibrium is indicated by E1 in Fig. 1. The revenuemultiplier equals one plus the reciprocal of the slope of the steady-state locus at the equilibrium point. If the curbside parking fee islowered, the parking equilibrium locus shifts up, causing the equi-librium to move up along the steady-state locus. Due to the convexityof the congestion technology, the slope of the steady-state locus at theequilibrium point falls, and hence the revenue multiplier increases.Now consider the effect of increasing the amount of curbside allocatedto parking. The steady-state locus shifts down and the parkingequilibrium locus shifts up. The equilibrium T and C increase; effectivedensity increases, which, along with the decrease in road capacity,causes trafc congestion to worsen; and the revenue multiplier can be

Fig. 1. Steady-state equilibrium. Notes: 1. C(T;P,D) is the steady-state locus, Eq. (1).2. C cf P is the parking equilibrium locus, Eq. (2). f)]d T/dP , which can be shown to be positive.

constant unit cost, and when curbside parking is priced below thislevel. Unfortunately, the model is unrealistically simple in assumingthat garage spaces are supplied uniformly over space at constant unitcost. The technology of garage construction and other factors result inparking garages being discretely spaced.18 To reduce his walking costs,a driver is willing to pay a premium to park in the parking garageclosest to his destination. Parking garages therefore have marketpower and may exercise it by pricing above marginal cost. Further-more, spatial competition between parking garages may result in theirbeing inefciently spaced. Taking these considerations into accountcomplicates the economics, since there will then be three distortionsthat need to be taken into account, not only the underpricing ofcurbside parking but also the overpricing and inefcient spacing ofgarage parking.

In the next section, the model of this section is extended to take

individual curbside parker to cruise for parking on his destinationblock, or the spatial homogeneity of trafc ow.21 These assumptionstogether imply that the steady-state equilibrium condition for the

6 R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114into account the exercise ofmarket power causedby thediscrete spacingof parking garages. The exact reason for the discrete spacing of parkinggarages is secondary. It is assumed that the discrete spacing arisesfrom the xed land area required for a central ramp, which generateshorizontal economies of scale. The optimal spacing minimizes overallresources costs. The equilibrium spacing is the outcome of spatialcompetition between parking garages.

3. The central model

The primitives of the model differ from those of the simple modelof the previous section in three respects. First, the garage cost functionincorporates horizontal economies of scale, reecting the xed costsassociated with the central ramp. Second, to avoid dealing with pricediscrimination based on parking duration, parking duration ratherthan visit duration is taken to be exogenous. And third, a grid streetnetwork is assumed.

In many cities, there are both public and private parking garages.To keep the analysis manageable, however, it is assumed that allparking garages are private.19 The social optimum is solved rst, thenthe spatial competition equilibrium is solved when the governmentintervenes only through its curbside parking policy.20

3.1. Social optimum

Since travel demand is perfectly inelastic, the social optimumentails minimizing resource costs per unit area-time. There are threecomponents to resource costs per unit area-time: garage costs per unitarea-time (GC), walking costs per unit area-time (WC), and in-transittravel costs per unit area-time (TT):

RC GCWC TT: 12

It is assumed that the presence of parking garages does not alterthe distance drivers travel over city streets, or the decision of the

18 Suppose, for the sake of argument, that parking garages are continuouslydistributed over space. It would be cheapest to construct garage parking on theground oor of every building, but this space is especially valuable for retail purposes.Constructing below-ground parking may be cost effective at the time the building isconstructed, but is expensive for buildings that were originally constructed withoutunderground parking. Constructing above-ground parking in multi-use buildingsraises structural issues. In most situations, the cost of constructing garage space isminimized with structures specically designed as parking garages. Even if parkingwere distributed continuously over space, parking garage entrances would not be.Because of the xed width required for a garage entrance and the xed area requiredfor a central ramp, parking garage entrances would be discretely spaced. Considerationof aesthetics and trafc circulation may play a role as well. Zoning may require thatparking garages be located away from major trafc arteries to reduce the congestionand visual nuisance they cause.19 An obvious direction for future research is to investigate the situations where allgarage parking is provided by the public sector, and where some is provided publiclyand some privately.20 Less formal derivation of the results is provided in Arnott (2006).simple model, T=t(T, 0, P)D, continues to hold. Denoting the cor-responding equilibrium in-transit density as a function of P by T(P)gives TT=T (P).

Efciency entails identical parking garages being symmetricallyarrayed over space,with diamond-shapedmarket areas. Let s be the gridor Manhattan distance between parking garages, x the capacity of eachparking garage, andK(x) theminimumcost per unit time of a garage as afunction of capacity. Each garage services an area of s2/2. With demandinow D per unit area-time and parking duration , the total numberof parking spaces in a garage's service area is Ds2/2. Since Ps2/2curbside parking spaces are provided in the service area, garage capacityis x=(DP)s2/2 and GC=K((DP)s2/2)s2/2. Since the demand forgarage parking is uniformly distributed over space, the average distancewalkedbya garage parker is 2s/3 so that averagewalking time is 2s/(3w),where w is walking speed, and WC=2s(DP/)/(3w). Combining theabove results gives

RC K DP s22

s22

2s DP

3w T P : 13

Solution of the social optimum entails minimizing Eq. (13) withrespect to P and s. The optimum may entail no curbside allocated toparking, all curbside allocated to parking, or only a fraction of curbsidebeing allocated to parking. In the last case, the rst-order conditionwith respect to P is

K 02s3w

dTdP

0: 14

Expanding curbside parking capacity by one unit per unit arearesults in garage capacity being reduced by one unit per unit area,leading to a saving per unit area-time in garage costs of K and inwalking costs of 2s/(3w), but in less curbside being allocated totrafc, resulting in an increase in in-transit travel costs of dT/dP(an expression for which is provided below Eq. (4)). With a realisticgarage construction technology, the optimal spacing between parkinggarages solves the rst-order condition of Eq. (13) with respect to s:

2 DP K 0s

4Ks3

2 DP

3w

0:

Dividing through by 2(DP/)/s and using x=(DP)s2/2 yields

K 0Kx

s3w

0: 15

The social optimum minimizes resource costs per unit area-time.Since the input rate per unit area is constant, it also minimizesresource costs per driver. And since, in the choice of s, P and hence theratio of garage parkers to drivers are xed, the optimal choice of sminimizes resource costs per garage parker. Since in-transit travelcosts are independent of the spacing between parking garages, theoptimal spacing between parking garages minimizes garage pluswalking costs per garage parker. Let aGC and mGC be the average andmarginal garage costs per garage parker, and dene aWC and mWCaccordingly. Since an average is minimized where the marginal equalsthe average, the optimal spacing between parking garages solves

aGC aWC mGCmWC; 16

21 Solving for optimal trafc ow over space, taking into account the spatial

inhomogeneity introduced by parking garages, would be formidably difcult.

equilibrium stock of cars cruising for parking, and intuitively22 on thedeadweight loss deriving from the market power that the friction ofspace confers on parking garages.

Arnott (2006) derived the BertrandNash equilibrium parkingfee. Here we simply state the result and provide the intuition forit. The BernardNash equilibrium parking fee for parking for a

7R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114which coincideswith Eq. (15) since aGC=K/x, mGC=K, aWC=2s/(3w),and mWC=s/w because the marginal garage parker walks to theboundary of the garage service area.

3.2. Equilibrium

Parking garage structures are prohibitively costly to relocate andvery costly to expand. It is also impractical to convert a parking garageto an alternative use, and adding garage capacity to buildings in otheruses requires constructing underground parking, which is very costly.Thus, to a rst approximation, a garage's location and capacity can beregarded as xed. In most downtown areas, the demand for garageparking is increasing over time. The natural way to model spatialcompetition between parking garages is therefore as a dynamic two-stage game with growing demand. In each period's second stage,garages compete in fee schedules, taking the location and capacity ofother garages as xed. In each period's rst stage, potential entrantsdecide simultaneously on entry, capacity, and location, anticipatingthe future evolution of market equilibrium.

Given the current state of game theory, such a model is intractable.We have chosen instead a particularly simple specication of theparking garage game, which we present below. It is an adaptation of afamiliar, two-stage spatial competition game that Tirole (1988)ascribes to Salop (1979), but which is discussed in Vickrey (1964)and likely has more distant origins. The friction of space resultsin parking spaces in different garages being differentiated products.In the second stage, garages play a Bertrand game with differentiatedproducts in mill prices, with mill price undercutting being excludedby assumption, and choose the height of their parking garages tominimize cost. In this stage of the game, garages take as given thelocation of their neighbors, which are by assumption arrayed sym-metrically, and ignore the effects of their actions on trafc conditions,and capacity constraints are ignored. In the rst stage of the game, thenumber of parking garages, and hence the uniform spacing betweenthem, adjusts such that garage prots are zero.

This specication of the parking garage game yields intensecompetition between parking garages for the same reason thatBertrand competition yields intense competition. In an appendix tothe paper, we discuss how treating capacity constraints would alterthe game. In particular, we review the game-theoretic literature onduopoly games with capacity constraints, rst when products arehomogeneous and then when they are differentiated. Two qualitativeconclusions emerge. The rst is that the addition of capacityconstraints makes the analysis of the game much more complicated,so much more that the problem with differentiated products has notyet been solved. The second is that capacity constraints relax com-petition. The intuition is that when my competitors are capacityconstrained, I can raise my price without losing customers to them. Awell-known result in game theory (Kreps and Scheinkman, 1983) isthat, with homogeneous products (and under a reasonable set ofassumptions concerning rationing when there is excess demand outof equilibrium in the price sub-game) Quantity Precommitment(viz., capacity constraints) and Bertrand Competition Yield CournotOutcomes. With inelastic demand up to a choke price, duopolistswould choose the choke price. The results are considerably morecomplicated under alternative rationing mechanisms, and includemixed strategy equilibria. And the game when products are dif-ferentiated as parking garages are has not been solved. Never-theless, it seems safe to say that the full equilibrium of the parkinggarage game entails a parking fee between the BertrandNashequilibrium with spatially differentiated products, which is the onewe solve for, and the corresponding CournotNash equilibrium, whichentails a parking fee equal to the choke price. Thus, our specicationof the parking garage game provides a lower bound on the markup ofthe equilibrium mean price over marginal cost, hence on the mean

price differential between curbside and garage parking, hence on theperiod is

Se K 0 sw

17

which entails garages charging a markup over marginal garagecost equal to the walking cost incurred by a driver at the boundarybetween garage service areas. The intuition is as follows. In aBertrandNash equilibrium, a garage must perceive it as unprotableto either raise or lower its parking fee, taking as given the parking feescharged by its neighbors. If it raises its fee by a small amount , it willgain net revenue from its inframarginal customers but lose custo-mers at the boundary of its market area. Since its service area is s2/2and since the customer density is D, its revenue gain from infra-marginal customers is s2D/2. Under the Bertrand assumption, itperceives its service area to be 2[s/2w(S0S)/(4)]2, where S0 is thefee it charges and S the common fee charged by its neighbors, so that=S0S. It therefore perceives that its service area will shrink by anamount ws/(2), and hence that its net revenue will fall by anamount D(SK)ws/(2) from the customers it loses. Equating thegain and the perceived loss gives Eq. (17). In the rst stage of the game,entry and exit occur, driving prots to zero:

D P

K 0 s

w

s22K 0: 18

Dividing Eq. (18) through by (DP/)s2/2 yields

aGC mGCmWC: 19

Comparing Eqs. (16) and (19) implies that, under this form ofspatial competition, parking garage market areas are inefcientlysmall.

It is assumed that, with discrete parking garages, curbsideparkers drive to their destination block and then circle that blockcruising for parking, as was the case with continuous parkinggarages, and that at each location (indexed by grid distance fromthe closest parking garage, m) the in-transit travel time is the samefor curbside parkers as for garage parkers.23 Under these assump-tions, the stock of cars cruising for parking at location m adjusts toequilibrate the full prices of garage and curbside parking there.In contrast to the simple model, the full price of garage parkingnow includes walking costs. The parking equilibrium condition atlocation m is then

Se 2mw

f C m P

; 20

where C(m) is the density of cars cruising for parking at location m,and Se is given by Eq. (17), so that

C m Se 2mw

f

P

: 21

To close the model, T(m), the equilibrium density of cars in transitat each location, must be derived. Since there is no nice way to do this,

22 The deadweight loss will depend on the equilibrium of the full game entry,capacity, and location in the rst stage, and pricing in the second and not just thepricing game.23 Properly, the equilibrium spatial pattern of trafc ow with drivers optimizingover route and cruising-for-parking strategy should be determined, but this problem is

intractable.

it is assumed that T(m) is the solution to the analog of the steady-stateequilibrium condition at location m:

T m t T m ;C m ; P D 0:

In-transit travel costs per unit area (TT) are obtained by averagingT(m) over the garage market area, and cruising-for-parking costs perunit area (CP) are obtained analogously.

to capacity constraints. But since the game-theoretic literature has notyet solved the price equilibrium in oligopoly games with spatiallydifferentiated products and capacity constraints, we chose to ignorethe capacity constraints. Intuitively, ignoring these constraints resultsin our describing competition between parking garages as ercerthan it actually is. Thus, our analysis tends to understate themarkup ofgarage price over marginal cost, and hence the distortions deriving

8 R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 1143.3. Second-best parking policy

Regulation of private garage pricing, capacity, and location is notconsidered. Government intervention is restricted to curbside parkingpolicy. Since modeling the full game between a local parking autho-rity, with strategy variables f and P, and private parking garages, withstrategy variables S and s. would be complex,24 the only policy to beinvestigated will be the local parking authority's second-best optimalchoice of P on the assumptions that the government behaves as aStackelberg leader and that the meter rate is set sufciently low thatparking garages do not have an incentive to undercut it. Relative to thesocial optimum, there are three sources of distortion. The under-pricing of curbside parking and the overpricing of garage parkinginduce cruising for parking, which generates cruising-for-parkingcosts and increases in-transit travel costs. Also, spatial competitionbetween parking garages results in parking garages being inefcientlyclosely spaced.

Let GC (P) denote garage costs per unit area-time, as a function ofP in the social optimum, etc., and GCe(P) the spatial competitionequilibrium, etc. The second-best optimal level of P, P, minimizesRCe(P)=GCe(P)+WCe(P)+TTe(P)+CPe(P). If RCe(P) has a unique local,interior minimum, then [dRCe(P)/dP]P N0 is a necessary and sufcientcondition for PbP. Letting DWL(P) denote the deadweight loss inthe spatial competition equilibrium relative to the social optimum, asa function of P, we have that

DWL P RCe P RC P GCe P WCe P GC P WC P

TTe P CPe P TT P ubDWL P bbDWL P :

22

wherebDWL P is the deadweight loss related to garages being in-efciently close in the spatial competition equilibrium, and bbDWL P is that related to cruising for parking. Since [dRC(P)/dP]P=0, [dDWL(P)/dP]P=[dRCe(P)/dP]P. Thus, if RCe(P) has a unique local, interiorminimum, a necessary and sufcient condition for PbP is thatdeadweight loss be increasing in P at P. It can be shown thatbbDWL P isincreasing25 in P, but the sign of the derivative ofbDWL P is ambiguous,depending in a complicated way on the properties of the garage costfunction. Thenext sectionprovides severalnumerical examples inwhichthe second-best level of P is less than the rst-best level but also one inwhich the second-best level exceeds the rst-best level.

The analysis of this section's model was fairly complete but twothorny game-theoretic issues were sidestepped. The rst concerns themodeling of spatial competition between parking garages. Realisti-cally, the price sub-game between parking garages takes place subject

24 Calthrop (2001) considers the prot-maximizing pricing of a garage monopolist inthe face of an exogenous curbside meter rate, ignoring the discreteness of parkinggarages. If the meter rate is set above a critical level, it is protable for the garagemonopolist to undercut the meter rate. In the context of the model of this section, thefull game between a local parking authority and private parking garages would need totake this undercutting possibility into account, and the equilibrium might involvegarages undercutting curbside parking close to the parking garage but not furtheraway.25 It can be shown that in the spatial competition equilibrium, dC/dPN0. It thenfollows from the convexity of the congestion function in T, C, and P that bbDWL P is

increasing in P.from the exercise of garage market power, especially those related tocruising for parking. The second thorny game-theoretic issue concernsthe modeling of the game between private garage operators and thelocal parking authority. The paper has considered the choice of thelocal authority qua Stackelberg leader concerning howmuch curbsideto allocate to parking but took the curbside meter rate as xed.Modeling the complete game between parking garage operators andthe local authority will be difcult. And this difculty will becompounded when the local authority's policy instruments areexpanded to include regulation of parking garage fees, locations, andcapacities, and when the political economy considerations that affectthe authority's policy choices are taken into account.

4. Numerical examples

4.1. Calibration

Arnott and Inci (2006) present numerical examples for a modelsimilar to the one employed here, except that all parking is curbside anddemand is price sensitive. This paper adopts all their values for thecommonparameters and functions, except for the jamdensity, and addsa parameterized garage cost function and the level of demand as well.

The following parameters are employed. The units of measurementare hours for time, miles for distance, and dollars for value.

2:0 2:0 f 1:0 20:0 P 3712

The in-transit travel distance is 2.0 miles; the parking duration is2.0 h; the curbside parking fee is $1.00 per hour; the value of time is$20.00 per hour; and the number of curbside parking spaces is 3712per squaremile in the base case.We do not knowof data onmean non-residential parking duration over the entire downtown area, but 2 hseems reasonable when account is taken of non-work trips and autotrips taken by downtown employees during theworking day. Since themodel ignores downtown residents, the ratio of 1 mile traveled ondowntown streets per hour parked seems reasonable too. The hourlymeter rate for curbside parking is that employed in Boston. The value oftime of $20.00 per hour might seem high, but the average downtownparker is more highly paid and busier than the typical traveler.26 Thevalue of P chosen is for the base case, forwhich parking is on one side ofthe street, and requires explanation. Assuming 8 city blocks permile onaManhattan grid, a streetwidth of 33 ft, a parking space length of 21 ft,and allowance for crosswalks, 29 cars can be parked on one side of ablock. With parking on one side of the street, there are 58 curbsideparking spaces around each block. Andwith 64 blocks per square mile,there are 3712 curbside parking spaces per square mile.

The value of D is taken to be 7424 per ml2-h. Since parkingduration is 2 h, this implies that the stock of parking spaces needed toaccommodate the exogenous demand is 14848 per square mile. Thus,in the base case, one quarter of the cars park curbside and the rest in aparking garage.

26 Small et al. (2005) nd slightly higher mean values of travel time on the CaliforniaState Route 91 Freeway in Orange County. The standard rule of thumb, based on manyempirical studies, is that the value of travel time is half the wage rate, and the meaneffective wage rate in the downtowns being considered must be around $40.00 perhour, corresponding to an annual salary (48 weeks a year and 35 h per week) of

$67,200.

The form of the congestion function employed was describedearlier, in fn. 14. It is

t t01 VVj

with Vj X 1P

Pmax

and V T C: 23

This congestion function has four parameters. Three are the sameas in Arnott and Inci (2006) but a different calibration was used todetermine jam density (see fn. 14):

t0 0:05 X 5932:38 Pmax 11;136 1:5A value of t0, free-ow travel time per mile, of 0.05 corresponds to

a free-ow travel speed of 20 mph is jam density in the absence ofcurbside parking. Vj is jam density with curbside parking, which isassumed to equal jam density in the absence of curbside parking timesthe proportion of street space available for trafc. 1P/Pmax. Pmaxis calculated on the basis that a 33-foot-wide, one-way road canaccommodate three lanes of trafc and that parking on one side of thestreet reduces this to two lanes of trafc. The value ofwas calibratedto generate a base case social optimum travel speed of 15 mph, but is

for (k0+k1h)+(F0+F1h)/x of $0.875/h. It is assumed that k1=0.125k0,F1=0.125F0, and F0=10k0. That leaves two parameters, k0 and R.The values k0=0.5 and32 R=$2.5105 are chosen. For a parkingstructure with 1000 spaces, which corresponds to the average atUCLA, the cost-minimizing height is 7.55 oors, so that the averageamortized construction cost computed according to the aboveformula is $0.982/h. The amortized cost of land per garage space is$0.488/h. The ratio of land to construction costs seems reasonable.Average garage cost (corresponding to K/x in the theory) is therefore$1.470/h, and marginal garage cost (corresponding to K in the theory)$1.449/h.33 Though the parameters chosen for the garage cost functionyield reasonable results, there is evidently considerable scope forimprovement.34

What kind of city does this parameterization correspond to?Parking in Boston (Boston Transportation Department, 2001) reportsthat in 1997/8 per square mile the number of employees in Downtown

9R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114also consistent with more basic trafc engineering reasoning.27 isthe in-transit PCEs (passenger car-equivalents) of a car cruising forparking. Since we know of no studies of its value, our estimate is aguess.28

The garage cost function is assumed to have the form

K^

29

x;h R A0 axh

k0 k1h x F0 F1h;

where K^ is the amortized (per hour) cost, x garage capacity, hgarage height (number of oors of parking), R land rent, A0 the areaused for the central ramp, a the oor area needed for each additionalcar, F0+F1h the cost of constructing the central ramp in a parkinggarage with h oors of parking, and k0+k1h the unit cost of anadditional parking space in a garage of h oors. We assume that anadditional car needs 400 square feet of oor space, 200 square feet ofparking space per se and 200 square feet of added space for trafccirculation, yielding a=1.44105 square miles, and that the parkingramp has a radius of 20 ft and therefore an area of 400 square feet,yielding A0=4.52105. In choosing cost parameter values, we drawheavily on Shoup (2005), Chapter 6. Table 6-1 gives an average cost in2002 dollars per space added for garages constructed on the UCLACampus between 1977 and 2002 of about30 $28,000. Amortizingthis cost, assuming that the garage is used for 8 h a day, 200 days ayear and that the annual user cost of capital is 0.05, which is con-sistent with a real interest rate of 4% and a 40-year life,31 yields a gure

27 With the street geometry assumed, excluding intersections there are about 15.2street-miles per square mile. =5932.38 then corresponds to one car every 13.5 ft ofstreet. Since, in the absence of curbside parking, a street has three lanes of trafc, thiscorresponds to one car every 40 ft in a lane or 132 cars per lane-mile. In the absence ofcruising for parking, with the assumed congestion function capacity throughput isachieved at one-half jam density or 66 cars per lane-mile, and the associated velocityand ow are 10 mph and 660 cars per lane-hour, respectively. These gures accordwith those given in Table 16-17 of the Transportation and Trafc Engineering Handbook(Institute of Transportation Engineers, 1982), Maximum Lane Service Volumes onUrban Arterials Based on 50% Cycle Split and Average Density and Speed Criteria.28 Shoup (2007, p.19) remarks: Most drivers who are cruising for parking try to avoidfollowing directly behind another car that appears to be cruising, so as to maximize thechance of being the rst to see a vacant spot. This suggests that the passenger carequivalent for a cruising car is appreciably greater than one.29 Chapter 14 of the Trafc Engineering Handbook (Institute of TransportationEngineers, 2004), Parking and Terminals, discusses the design of parking garagesbut does not provide engineering cost data. The form of the cost function in (27) waschosen for its ease of interpretation and analysis, and not on the basis of engineeringdata.30 In calculating this number, Shoup divided construction costs by the number ofadded parking spaces, on the assumption that the land was previously used as anon-ground parking lot.31 The real interest rate and the amortization period are those chosen by Shoup, Table

6-3, and he judged these to probably underestimate the user cost of capital.Boston was 160,000 and the number of garage, non-residential, non-hotel parking spaces was 29,000. Downtown Boston TransportationPlan (Boston Transportation Department, 1995) reports that, in 1990,36% of Downtown workers drove alone and 11% carpooled orvanpooled. On the assumption of no curbside parking, if all downtownworkers had commuted by car, the required number of garage parkingspaces would have been about 62,000 per square mile. This gureindicates that the calibrated city has a considerably lower employ-ment density than Boston. Furthermore, applying the ratio for Bostonof the garage parking spaces if all downtown workers had commutedby car to the number of employees, suggests that a garage parkingdensity of 11,136 per square mile corresponds to an employmentdensity of around 29,000 per square mile. According to Demographia(2007), such downtown employment densities are found inWinnipeg,Perth, San Diego, Sacramento, and Phoenix.

4.2. Numerical results

4.2.1. Base case outcomesAll the numerical exercises are for the central model. Table 1

presents the numerical results with the base case set of parametervalues. Each of the columns corresponds to a different exercise. Eachrow gives the value for a particular variable across the variousexercises. Column 1 describes the social optimum with the base caseallocation of curbside to parking space of P=3712, corresponding tocurbside parking on one side of the street. The social optimum isdened to have no cruising for parking. Column 2 provides thenumbers for the social optimum with the rst-best allocation ofcurbside to parking. Column 3 presents the base case equilibrium.Column 4 displays results for the same case as column 3 but with theallocation of curbside to parking optimized. Column 5 gives the resultsfor the base case equilibrium, but with the meter rate raised from$1.00 to $1.50 per hour. Finally, column 6 shows the equilibrium for

32 This is the amortized cost per ml2-h. It has been assumed that a garage space isutilized for 1600 h per year. Thus, the land rent per ml2-year is $4.0108. Since thereare 640 acres per square mile, this corresponds to a land rent of $6.25105 per acre-year. Since land does not depreciate, an interest rate of 4% should be applied. Assumethat land rent grows at the rate of 1% per year and that the property tax rate is 1% peryear. Under these assumptions, the value of land per acre is $15.625 million.33 Cost-minimizing building height increases as capacity increases. If building heightwere held xed, marginal cost would be constant. The exibility of building heightcauses marginal cost to fall. Average cost falls too, due to this effect and the xed costof the central ramp.34 Since Shoup's assumptions on the real interest rate and the amortization periodlikely underestimate the user cost of capital, and since administrative, operating, andmaintenance costs (which for the UCLA parking garages add about 35% to costs seeShoup, Table 6-3) have been ignored, it seems likely that the base case parameteriza-tion underestimates garage costs. In the numerical examples, the case in which garagecosts are 40% higher than those of the base case is treated and seems to yield more

reasonable results.

between the equilibrium and the social optimum. First, spatial com-petition results in suboptimal spacing between parking garages.Second, since curbside parking is underpriced and garage parkingoverpriced, there is cruising for parking in the equilibrium, with thestock of cars cruising for parking adjusting such that the full prices ofcurbside and garage parking are equalized, and the cars cruising forparking slow down cars in transit.

In this equilibrium, the capacity of each parking garage is abouthalf that in the social optimum, while the spacing between them isabout two-thirds that in the social optimum. Since average garage

10 R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114the same case as column 5 but with the allocation of curbside toparking optimized.

Consider rst the social optimum, described in column 1, in whichcurbside parking is permitted on one side of every street, so that onequarter of drivers park curbside. The Manhattan spacing betweenparking garages is 0.15 miles, and each garage holds 125 cars and has7.30 oors. All trafc is in transit and travel speed is 15.0 mph. GC isgarage cost per unit area-time, and D is throughput in cars per unitarea-time, so that GC/D is garage cost per driver (or, equivalently, per

Table 1Numerical results with base case parameter values

1 2 3 4 5 6

SO SO(P) E E(P) E E(P)

P=3712 f=1 f=1 f=1.5 f=1.5

P=3712 P=3712

s 0.150 0.152 0.104 0.096 0.104 0.115x 125 124 60 65 60 54h 7.30 7.30 7.03 7.06 7.03 6.97S 3.59 3.54 3.59 3.67P 4144 718 6694v 15.0 14.5 12.6 14.6 13.8 12.5CP/(TT+CP) 0 0 0.14 0.033 0.084 0.14GC/D 2.42 2.33 2.70 3.37 2.70 2.02WC/D 0.50 0.49 0.35 0.41 0.35 0.28TT/D 2.67 2.76 3.18 2.74 2.89 3.21CP/D 0 0 0.51 0.095 0.26 0.53RC/D 5.59 5.58 6.73 6.61 6.20 6.04F 7.23 6.71 6.95 7.39

1. The unit of time is an hour, of distance a mile, and of value a dollar.2. GC/D is the garage cost per driver (including those who park curbside) or averagegarage cost. Similarly, WC/D is average walking cost, CP/D average cruising-for-parkingcost, TT/D average in-transit travel cost, and RC/D average resource cost.3. A driver's in-transit travel time per mile is calculated as his in-transit travel cost (TT/D),divided by , and v, velocity, as the reciprocal of in-transit travel time. CP/(TT+CP)measures themeanproportion of trafcow that is cruising for parking. And F, the averagefull price of a trip, is calculated as average resource cost per driver plus curbside parkingrevenue per driver.4. Blank cells correspond to variables that are not relevant for the exercise.trip), including those who park curbside, or average garage cost.Similarly, WC/D is average walking cost. TT/D average in-transit travelcost. CP/D average cruising for parking cost, and RC/D average resourcecost. Average garage cost is $2.42, average walking cost $0.50, averagein-transit travel cost $2.67, average cruising-for-parking cost zerosince there is no cruising for parking in the social optimum, andaverage resource cost $5.59. The cells for S (the garage parking charge)and F (the average full price of a trip) are blank since the socialoptimum allocation does not entail prices, and P is blank since itsvalue is exogenous. The relative importance of average garage parkingcost (GC/D+WC/D) to average driving cost (TT/D+CP/D) reects theratio of travel distance to parking duration, which in the example is setat 1.0.

Column 2 describes the social optimum in which the amount ofcurbside parking is chosen to minimize resource costs. Comparingcolumns 1 and 2 indicates that the optimal amount of curbside toallocate to parking is not very different from that assumed in the basecase, 4144 parking spaces per square mile (55.8% of curbside) ratherthan 3712. Not surprisingly, therefore, optimizing the amount ofcurbside parking results in only small resource savings. Because moredrivers park curbside, average garage parking costs fall but average in-transit travel cost increases by almost the same amount, resulting inan average resource savings of only about $0.01.

Column 3 describes the equilibrium in which the meter rate(the hourly curbside parking fee) is $1.00/h, and curbside parking is onone side of the street. Comparison of columns 3 and 1 is particularlyinteresting since it indicates the effects of moving from the socialoptimum to the equilibrium, holding constant the proportion ofcurbside allocated to parking. There are two qualitative differencesparking cost is $2.92 in the social optimum and $3.05 in theequilibrium, average social cost associated with this distortion isrelatively small, $0.13. The distortion generated by cruising for parkingis considerably larger.35 The distortion has two components. The rst,average cruising-for-parking cost is, $0.51. The second, the increase inaverage in-transit travel cost due to the increased congestion causedby the cars cruising for parking, is $0.51 (that these two numbers areidentical is a coincidence). The average deadweight loss caused bycruising for parking is therefore $1.02, which is an order of magnitudelarger than that generated by the suboptimal spacing between parkinggarages. Cars cruising for parking constitute 14% of the trafc densityand slow down trafc from 15.0 to 12.6 mph. The results indicate thateven a relatively small (compared to the numbers presented in Shoup,2005. Table 11-5) proportion of cars cruising for parking can cause asubstantial increase in congestion. Since free-ow travel speed is20.0 mph, congestion causes travel speed to fall by 5.0 mph in thesocial optimum and by 7.4 mph in the equilibrium. Thus, even thoughthey constitute only 14% of cars on the road, cars cruising for parkinggenerate an almost 50% increase in the time loss due to congestion.This result is due to the convexity of the congestion function. Thecombined effect of the two distortions is to raise average resource costby $1.14, slightly more than 20% relative to the social optimum. Thefull price of travel exceeds average resource cost because of thecurbside parking fee, which is a transfer from curbside parkers to thegovernment. One quarter of drivers pay $2.00 for curbside parking,causing the full price of travel to exceed average resource cost by$0.50.

Column 4 gives the second-best equilibrium, in which the meterrate remains at $1.00 and the proportion of curbside allocated toparking is optimized conditional on the distorted meter rate.Comparing columns 3 and 4 indicates by how much the deadweightloss due to the two distortions is reduced by optimizing the amount ofcurbside allocated to parking. It is second-best efcient to substan-tially reduce the amount of curbside allocated to parking to 9.7% ofcurbside in order to reduce the stock of cars cruising for parking.Since a larger proportion of drivers then park in a garage, the averagegarage parking cost increases from $3.05 to $3.78, but this is morethan offset by the decrease in average driving costs, with averagecruising-for-parking cost decreasing from $0.51 to $0.10 and averagein-transit travel cost from $3.18 to $2.74. Average resource cost fallsfrom $6.73 to $6.61. Thus, optimizing the amount of curbside parkingreduces the deadweight loss from the two distortions by about 10%.

Column 5 shows the equilibrium when one side of the street isallocated to curbside parking, as in the base case, and the parking fee israised from $1.00/h to $1.50/h. Raising the parking fee has no effect on

35 In Section 3.3, the deadweight loss was decomposed into that associated withcruising for parking and that associated with the inefcient spacing of parking garages.This decomposition might give the misleading impression that the deadweight lossassociated with private provision of parking garages is small. Cruising for parkingderives from not only the underpricing of curbside parking but also the overpricing ofgarage parking. In the example being considered, for the two-hour visit, the curbsideparking charge is $2.00, the marginal cost of garage parking is $2.90, and the garageparking charge is $3.59. Thus, a proportion (3.592.90)/(3.592.00)=0.43 of cruising-for-parking costs are attributable to the overpricing of garage parking. In the exampleof column 5, all cruising-for-parking costs are attributable to the overpricing of garage

parking.

second-best amount of curbside parking to the meter rate is drivenby cruising for parking. As well, under even the moderate trafccongestion of the examples, the social cost of the increased congestioncaused by cruising for parking can be more than double the directcruising-for-parking costs.

4.2.2. Outcomes with higher garage construction costsThe aim of the numerical examples is to come up with reasonable

numbers in order to provide insight into the absolute and relative

11R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114average garage or walking cost, but, by reducing the differencebetween the on-street and garage parking prices, almost halves thestock of cars cruising for parking, which reduces congestion and henceaverage in-transit travel time cost. It is of particular interest toexamine the revenue multiplier the ratio of the increase in socialbenet to the increase in parking fee revenue due to the rise in themeter rate, holding xed the curbside allocated to parking. Averagemeter fee revenue rises by $0.25 (one quarter of drivers park curbsideand each of these pays $1.00more) and average social benet by $0.53.The revenue multiplier is therefore about 2.1; for every extra dollar ofrevenue raised from the increase in the meter rate, social benet risesby about $2.10. This seems almost too good to be true, but reects howdistortionary is the wedge between the curbside and garage parkingrates.

Comparing columns 5 and 6 shows how the equilibrium changeswhen the allocation of curbside to parking is optimized conditional onthe higher curbside meter rate rather than set at its base level.Comparing columns 4 and 6 shows how the equilibrium changeswhen the meter rate increases, with the allocation of curbside toparking being optimized conditional on the meter rate. The mostnotable feature of the results is the almost ten-fold increase in theoptimal allocation of curbside to parking with the increase in themeter rate. Holding P xed at 718, the increase in themeter rate wouldcause the difference between the garage parking fee and the meterprice of curbside parking, S f, to fall from $1.54 to $0.54. Since theincrease in the stock of cars cruising for parking induced by anincrease in curbside parking would then be reduced by almost two-thirds, it is efcient to allocate more curbside to parking. When thecurbside allocated to parking is optimized conditional on the parkingfee, raising the parking fee causes average resource cost to fall by$0.57.

It is also noteworthy that the second-best amount of curbsideparking with f=1.5 exceeds the rst-best level. Since there is cruisingfor parking in the second-best equilibrium but not in the socialoptimum, this must (recall the discussion of Section 3.3) derive fromthe increase in curbside parking reducing the deadweight loss fromthe inefcient spacing of parking garages.

Now consider particular rows across the six allocations. First,the differences for s, x, and h are greater between the optimal andequilibrium allocations than among the equilibrium allocations.Second, the differences for s, x, and h across the equilibrium allo-cations follow directly from the amounts of curbside parking andhence the amounts of garage space needed. Third, recalling that thegarage parking charge entails a markup over the marginal cost of agarage space equal to the cost of walking to the boundary of the garagemarket area, the small differences in the garage parking charge acrossequilibrium allocations can be explained by differences in themarginal cost and the markup. Fourth and obviously, across theequilibrium allocations, average garage parking cost is strongly relatedto the proportion of drivers who garage park. Fifth, across theequilibrium allocations, travel time (the reciprocal of v), the propor-tion of cars cruising for parking, cruising for parking costs per capita,and in-transit travel costs per capita move together and are directlyrelated to the stock of cars cruising for parking. Sixth, across theequilibrium allocations, trafc congestion is moderate. In the leastcongested equilibrium allocation, 3% of cars in trafc are cruisingfor parking and travel speed is 14.6 mph; in the most congestedequilibrium allocation, 14% of cars in trafc are cruising for parkingand travel speed is 12.5 mph.

Examining all six allocations simultaneously, what is most strikingis the dominant importance of cruising for parking, even though theproportion of cars cruising for parking is less than 15% in all theequilibrium allocations. Almost 90% of the higher resource costs inthe base case equilibrium compared to the base case social optimumare due to the cruising for parking induced by the wedge bet-

ween curbside and garage parking charges. Also, the sensitivity of themagnitudes of various policy changes. When we looked at the resultsof the base case, we judged the garage parking fees to be un-realistically low. To correct this, all the garage cost parameters, R, F0,F1, k0, and k1 were rst doubled. With a meter rate of $1.00 per hour,an equilibrium does not exist. More expensive garage construction(and land) results in a higher garage parking fee, increasing the pricedifferential between curbside and garage parking and inducing morecruising for parking. With the increased cruising for parking causedby doubling the garage cost parameters, the exogenous level ofthroughput D could not be supported by the street system.36 Thegarage construction costs parameters were then lowered to 40% abovetheir base case levels,37 for which equilibrium did exist for all cases.The results are displayed in Table 2.

How the increased garage costs alter the social optimal allocationsis straightforward. Since unit transport costs remain unchanged whileunit garage costs increase, the social optimum entails a substitutionaway from garage costs towards transport costs, which is achieved byallocating more curbside to parking. Increased garage costs have twoconicting effects on the qualitative properties of the equilibriumallocations. On one hand, there is the same substitution away fromgarage costs towards transport costs. On the other hand, the increasedgarage costs cause an increase in the marginal cost of a garage space,hence on the garage parking charge, hence on the price differentialbetween curbside and garage parking, and hence on cruising-for-parking time costs. The latter effect dominates. Holding the propor-tion of curbside allocated to parking xed, cruising for parking in-creases, and to offset this it is efcient to reduce the number ofcurbside parking spaces. This effect is so strong that with f=1 it issecond-best efcient to have no curbside parking. With one half thecurbside allocated to parking, the revenue multiplier associated withraising the parking fee from $1.00/h, to $1.50/h, is 3.2. Parking feerevenue rises by $0.25 per capita while resource costs fall by $0.80.The higher garage costs result in the base case equilibrium being morecongested. The increase in themeter rate causes the same reduction inthe stock of cars cruising for parking but, because the congestiontechnology is convex, causes a greater reduction in in-transit traveltime costs. The increase in garage costs causes the various equilibria tochange in the ways that would be expected from earlier discussion.There is, however, one noteworthy qualitative difference betweenTables 1 and 2. When f=1.5, with the base case garage costs the rst-best amount of curbside parking falls short of the second-best level,but with the higher garage costs the rst-best amount of curbsideparking exceeds the second-best level. The higher garage constructioncosts more than double the equilibrium price differential betweencurbside and garage parking, which causes cruising for parking to bemore of a problem. With cruising for parking more of a problem, it issecond-best optimal to devote less curbside to parking.

36 When walking costs are taken into account, the cost differential between garageand curbside parking (Se+2m/w f), and hence the stock of cars cruising for parking(recall Eq. (21)), is higher for destinations further away from a parking garage. In termsof Fig. 1, at least at a subset of locations close to the boundary between garage marketareas, the steady-state locus (the graph of Eq. (1) in TC space) and the parkingequilibrium locus (the graph of (21)) did not intersect.37 The garage parking fee is still lower than that observed in major downtown areas.To obtain an allocation for which equilibrium exists with a realistic garage parking fee

would require either price-sensitive demand or mass transit.

assumptions that there is an entry rate to downtown of 7424 driversper square mile-hour and that downtown operates at capacity for1600 h per year, a $0.80 social saving per trip translates into almost

Table 2Numerical results with garage construction costs 40% higher than in base case

1 2 3 4 5 6

SO SO(P) E E(P) E E(P)

P=3712 f=1 f=1 f=1.5 f=1.5

P=3712 P=3712

s 0.168 0.172 0.116 0.106 0.116 0.111x 157 153 75 83 75 78h 7.36 7.35 7.13 7.17 7.13 7.15S 4.84 4.76 4.84 4.80P 4506 0 2188v 15.0 14.0 10.4 15.0 12.2 13.5

12 R. Arnott, J. Rowse / Regional Science and Urban Economics 39 (2009) 114The numerical results for the equilibria are unrealistic in oneimportant respect travel speeds are too high. With the assumedfunctions and parameter values, travel speed corresponding toequilibriumE1 cannot fall belowabout 7mph.38 But in heavily congesteddowntown areas, average travel speeds of 6mph and even lower are notuncommon. To obtain realistic travel speeds likely requires analternative treatment of downtown trafc congestion that focuses onqueuing at intersections.

Another feature of the numerical analysis is that in none of ourexercises was the proportion of cars in trafc that are cruising forparking as high as the average 30% that the cruising-for-parkingstudies cited in Shoup (2005) found. This derives from the choice ofparameter values. It can be shown39 that, in the base case, themaximum value of C/T that can be achieved is 22%. To achieve highervalues of C/T, the parameter values would have to be adjusted.

Cruising for parking stems from the underpricing of curbsideparking and the overpricing of garage parking. The most extreme caseconsidered (Table 2, column 3) is not extreme compared to actualtrafc conditions in the downtown areas of major cities. The pricedifferential between curbside and garage parking for the two-hourstay was $2.84 (considerably less than that in downtown Boston. forexample), the proportion of cars cruising for parking was 18%, andtravel speedwas 10.4 mph. The per-trip resource cost was $2.14 higher

CP/(TT+CP) 0 0 0.18 0 0.15 0.10GC/D 3.32 3.09 3.63 4.76 3.63 4.10WC/D 0.56 0.53 0.39 0.47 0.39 0.42TT/D 2.67 2.86 3.84 2.67 3.29 2.97CP/D 0 0 0.84 0 0.59 0.34RC/D 6.55 6.48 8.69 7.90 7.89 7.82F 9.19 7.90 8.64 8.27

Notes: See previous table.in the equilibrium than in the corresponding social optimum, with$0.84 of the cost increase being cruising-for-parking time cost, $1.17higher in-transit cost due to the increased congestion caused by thecars cruising for parking, and $0.13 higher garage parking costsderiving from inefcient spacing of parking garages. Raising the meterrate from $1.00 to $1.50 per hour resulted in social savings of $0.80 perdriver. Eliminating curbside parking entirely with the $1.00 meter ratehad almost exactly the same benet. Since they are expressed in perdriver terms, these numbers might appear small. But under the

38 Travel time is increasing in effective density. Thus, on the positively-sloped portionof T=0, travel time is highest at the peak of the function. From the algebra in fn. 14, itfollows that at the peak of the function 2T+1.5C=Vj, and that everywhere along thefunction T(VjT1.5C)=Dt0Vj. Combining these two results yields T=[Dt0Vj]1/2. Also,at the peak of the function, t= t0Vj/T=[t0Vj/(D)]1/2, which is maximized when nocurbside is allocated to parking so that V j=. Substituting in the numerical values ofthe example yields t=0.141.39 With P xed, the maximized value of C/T consistent with Eq. (1) can be shown tobe Vj/(4Dt0)1/. The maximized value of C/T is therefore increasing in Vj anddecreasing in , D, t0, and . Note too that, in this maximized value, , D, and t0 enteras their product, which is aggregate free-ow travel time per unit area-time. In thesimple model, with P variable, the maximized value of C/T consistent with both Eqs.(1) and (3) can be calculated by maximizing C/T subject to Eqs. (1), (3), and Vj=(1P/Pmax), with respect to C, T, P, and f.$10 million per square mile every year.In this paper we have assumed that the government sets the

curbside parking fee low and that spatial competition between privateparking garages results in the garage parking fee being set high. Thefee differential generates cruising for parking. This characterization ofthe downtown parking situation is oversimplied andmay exaggeratethe magnitude of cruising for parking. For one thing, curbside parkingtime limits reduce the excess demand for curbside parking. Foranother, the institutional arrangement of garage parking appears torun the gamut, from all garages being operated by the municipalauthority in some European cities to all garages being operatedprivately in someUS cities, withmost cities containing amix of privateand public garages, and some cities regulating the fees charged byprivate garages. What determines the institutional arrangementchosen, and how the institutional arrangement chosen affects theprice gap between curbside and garage parking, has not, to ourknowledge, been explored.

5. Directions for future research

This paper is the fourth of an integrated series that investigatesdowntown parking policy from the perspective of steady-stateequilibrium models of downtown parking and trafc congestion thattake into account that the underpricing of curbside parking and/or theoverpricing of garage parking leads to cruising for parking. Chapter 2of Arnott et al. (2005)