Sofia F. Franco* Nova School of Business and Economics Universidade Nova de Lisboa & UECE. May 25th, Abstract

Transcription

1 Downtown Parking Supply, Work-Trip Mode hoie and Urban Spatial Struture Sofia F. Frano* ova Shool of Business and Eonomis Universidade ova de Lisboa & UEE May 25th, 2015 Abstrat This paper examines the effets of hanges in downtown parking supply on urban welfare, modal hoie deisions and urban spatial struture using a spatial general equilibrium model of a losed monoentri ity with two transport modes, endogenous residential parking and a form of bottlenek ongestion at the BD. Our analysis shows that parking reforms at the BD that inrease delay ongestion osts in the short-run suh as parking supply limits an be welfare improving if other ommuting externalities suh as air pollution an be redued. In addition, beause parking limits an also hange loation deisions suh as where to live and invest they may omplement anti-sprawl poliies efforts by leading to a more ompat urban spatial struture in the long run. We also show that hanges in downtown parking supply an have different spatial impats on the market supply of residential parking by affeting urban residents loation deisions. Finally, we disuss the role of parking priing as a omplementary tool of ongestion priing to ombat ongestion in entral areas and investigate whether the self-finaning theorem of transportation eonomis holds within the ontext of our spatial urban model. Key words: Downtown Parking, Bottlenek ongestion, Urban Form, Modal hoie * Mailing Address: ova Shool of Business and Eonomis (ovasbe), ampus de ampolide P , Lisboa, Portugal. sfrano@novasbe.pt. Phone umber: + (351) UEE (Researh Unit on omplexity and Eonomis) is finanially supported by FT (Fundação para a iênia e a Tenologia), Portugal. I thank Ken Small, Rihard Arnott and Antonio Bento for their omments and, espeially Jan Bruekner for his very helpful omments and suggestions whih improved the presentation. I also thank the finanial support of a grant from the Multiampus Researh Program and Initiative (MPRI) of the University of alifornia (award number ). The views expressed in this paper are nevertheless solely mine. In addition, any errors or shortomings, of ourse, are also mine. 1

2 1. Introdution Traffi ongestion is often seen as a sign of a ity s eonomi and soial health and vitality. However, eonomists have long reognized that ongestion tends to exeed eonomially effiient levels beause auto ommuters do not bear the full ost of their use of the roads and parking failities. In heavily traffiked areas suh as downtown areas, eah additional vehile auses additional traffi delay on all the other auto users. Yet no auto user is harged for this negative externality. The result is that traffi delay slows eonomi ativity and an redue some of the agglomeration benefits that haraterize entral business distrits. 1 In reent years planners have given inreasing attention to the possibility of reduing downtown use of ars by ontrolling parking- either by restriting the number of spaes available, or by harging users to park. 2 After all, empirial evidene has shown that parking pries and parking availability are two of the key fators in auto users deision on whether to drive to work or use publi transportation (Shoup 2005). Among the possible benefits of these auto-restraint shemes are redutions in traffi delay osts, air pollution and energy onsumption (STH Report 2009; Kodransky and Hermann, 2011; Weinberger et al., 2010). 1 Shoup (2011a) found that, in a single year, drivers wasted 100,000 hours while ruising for underpried urb parking in a 15-blok business distrit in Los Angeles, A, USA. 2 While some European ities suh as London and Stokholm have managed to implement ongestion priing to redue auto use, more are turning to parking. For example, Hamburg, Zurih and Budapest have instituted aps on the total parking supply in the ity enter, reforming the building odes to freeze the existing inventory and ban any further inreases. London and Paris have also abolished parking minimums and several other ities suh as Zurih, Amsterdam and Strasbourg have established zone-based maximums. Antwerp and Zurih have also redued parking maximums and minimums in loations proximate to transit failities. Kodransky and Hermann (2011) examine ten different European ities on a variety of parking measures ranging from priing mehanisms to regulatory measures (suh as supply aps and parking minimums and maximums) to redue vehile kilometers travelled and shift travel from ar trips to other mode transports. The ase studies examined on the report highlight that expanding the supply of free, heap, or exessive parking-one viewed as neessary to eonomi vitality and to inrease mobility- has been reassessed aross Europe. On the other hand, Weinberger et al. (2010) provide an overview of the best praties in parking management in the United States. The report emphasizes that many US ities still take a passive approah to managing parking and just a few ities (hiago, ew York ity and San Franiso) are taking steps to align parking poliy with the broader ity goals of aessibility, eonomi development and better quality of life. Even though experiments in alternative parking approahes are still quite new in the US, the overall onlusion of the Weinberger et al. (2010) report is that dysfuntion will ontinue as long as parking poliy is viewed independent of transportation poliy and as long urbside and off-street parking are treated independently. 2

3 Even though parking reform has been a hot topi in the poliy arena in several parts of the world, there is remarkably little analytial work on how parking reform affets the urban form. Yet, parking priing and supply poliies may have a onsiderable impat on the transport and land use system within an entire urban region. The reason is beause parking is a key link between transportation systems and land use. It is therefore quite surprising that this issue has been overlooked, given the urrent advoay to move away from parking minimums to parking maximums and to erase employer transportation subsidies as ways to redue solo driving and to ahieve less dispersed urban spatial struture (Shoup 2005; Shoup 2011; STH Report 2009; Kodransky and Hermann, 2011; Weinberger et al., 2010). Most of the theoretial studies on parking poliies fous on (i) the effiieny of seond-best priing of parking spots in the absene of ongestion tolls (Arnott et al. 1991; Glazer and iskanen 1992; Verhoef et al. 1995; Arnott and Rowse 1999; Anderson and de Palma 2004) and a ordon system (althrop et al. 2000), (ii) on the effets of parking and transit subsidies on the BD size (Voith 1998), (iii) on the effets of urbside parking fees on ruising for parking in downtown areas (Arnott and Ini, 2006), (iv) on the optimal on-street parking poliy in the presene of an off-street parking market (althrop and Proost, 2006), or (v) on the effets of road-tolls shemes and parking fees on the traffi patterns of morning and evening ommutes (Zhang et al. 2008). Other analytial studies have foused either on the role of employer-paid parking for the desirability of ongestion tax reform and for the relative effiieny of reyling instruments (De Borger and Wuyts 2009) or on the optimal urbside parking apaity in downtown areas in first and seond best settings (Arnott et al. 2013). 3 3 For a very nie brief review on the eonomis of parking see Arnott et al. (2013). 3

4 All this previous researh has definitely offered valuable insights not just on how parking poliy affets ommuters short run deisions suh as trip frequeny, mode, parking loation or sheduling but it has also improved our understanding of the potential effiieny gains of supplementing road priing with parking regulation to ombat road and BD traffi ongestion. Still, beause these studies do not develop a spatial general equilibrium model (with an expliit representation of spae) that allows onsideration of interations between residential hoies, modal hoies, residential parking and floor-spae supplies and ongestion, their frameworks are not suitable to apture long run adjustments of loation and building stok hanges and thus, examine how hanges in downtown auto restraints influene land use and urban form. One exeption is the work by Anderson and De Palma (2007). The authors integrate parking land and parking ongestion (ruising) into a simple monoentri ity framework in whih households and parking operators ompete for land. The study shows that losest to the BD are parking lots while residential use loates further out. It is also shown that the soial optimum onfiguration is idential to the market equilibrium provided that parking lots are monopolistially pried. As the number of parking operator goes to infinity, eah parking operator lot sets a peruser prie equal to the ongestion externality-ost. The goal of this paper is twofold. First, we develop a spatial losed ity model that allows one to examine how hanges in downtown parking supply when parking is underpried affet the urban spatial struture, welfare, modal hoie and residential parking supply outside the BD. Then, we disuss the optimal value of a budget-balaning parking fee when parking apaity is hosen to maximize the equilibrium utility of urban residents and explore the impliations of our results for the self-finaning theorem. 4

5 In this sense, our approah is omplementary to the model of Anderson and De Palma (2012) in that we look at a spatial urban equilibrium with parking provision in the presene of auto externalities and at the interations between optimal priing and optimal parking apaity at the BD, whereas they fous solely on the relation between market performane and the optimum. In addition, our model is based on residential loation and inludes two ompetitive transport modes. Housing is portrayed as a ommodity with floor spae and parking spaes, whih are both hoie variables of the housing developer. Residential parking is assumed to onsume a fixed amount of land per parking spae. All urban residents are ar owners and ommute to job sites in a ongested downtown distrit. Auto ommuting generates air pollution, whih affets both auto and transit users equally. Downtown parking supply is exogenous. Expansions of the ongested downtown parking apaity are fully paid with parking fees that only over infrastruture osts. Within this framework we then examine how hanges in BD parking supply affet residential land rents, residential parking supply, modal hoie, urban welfare, share of auto-ommuters, population densities and ity size. All the impats are expressed in terms of behavioral elastiities. This allows for an easy interpretation, while elastiities an be linked to empirial estimates obtained from observed behavior. Furthermore, we examine how the optimal hoie of BD parking supply affets the value of a budget-balaning parking fee. Our analysis shows that when the auto-travel elastiity with respet to parking apaity is inelasti and finaning relies on budget-balaning parking fees, an expansion in downtown parking supply in the presene of underpried parking tends to derease overall parking ongestion at the BD. However, inreased parking supply also inreases automobile ommuting and redues transit rides and, as a result ontributes to an inrease in air pollution. Provided that the primary effets dominate the effets from indued demand, an inrease in BD parking supply is welfare 5

6 improving. In addition, the overall derease in ongestion delay osts at the BD makes automobile-dependent loations in the long run more attrative to urban residents, potentially leading to an expansion in the ity size. Another interesting finding of our analysis is that when downtown parking apaity is hosen to maximize the equilibrium level of urban utility, a balaned-budget parking fee oinides with the optimal ongestion toll despite the presene of environmental spillovers. Moreover, the selffinaning equality (where revenues from ongestion tolls over apaity osts) remains valid even if an environmental tax is levied to internalize the air pollution externality from auto ommuting. The remainder of the paper is organized as follows. In the next setion, we develop our theoretial model and disuss the optimality onditions. Setion 3 analyses the spatial behavior of hoie variables, and setion 4 disusses the urban equilibrium onditions. Setion 5 presents the market equilibrium omparative statis of a hange in downtown parking supply and setion 6 fouses on the interations between priing and parking apaity hoies, and between parking revenues and apaity osts. Finally, setion 7 disusses some poliy impliations while our last setion offers onlusions. 2. Model Suppose a linear ity exists extending from a entral Business Distrit (BD), loated at zero, to the urban fringe x. The ity onsists of urban residents who are assumed to be renters, ar owners and to have idential tastes and inome. For simpliity, urban residents own the same type of vehile. Urban residents reside outside the BD and ommute to work either by ar or publi transit. All ar ommuters park at work. 6

7 The use of automobiles generates two types of external effets in the urban area. The first is that eah additional parker adds to parking ongestion osts at the workplae, inreasing ommuting time for all drivers. The other external effet is that driving automobiles auses air pollution. The level of pollution for any urban resident at a partiular loation is assumed to be a funtion of the number of residents ommuting by ar, and hene, of the transport and residential loation hoies. Let x denote distane from the plae of residene to the BD, driving to work and the total number of residents b the number of residents using publi transit. To the extent that all residents either take the publi transit or drive to work in the BD, the urban population satisfies the ondition b. (1) Land is owned by absentee landowners and r a is the exogenous rural land rent. Transportation osts The ost of auto ommuting to work is represented by travel time osts and monetary osts [ t y] x [ y f ] (2) where t x denotes a part of ost varying proportionally with distane suh as fuel osts, x is the time spent in regular ar travel, is parking supply at the BD (whih we assume to be exogenous) and f represents a parking fee at the BD. The auto ommuter faes a delay time 7

8 ost at the BD beause of loal traffi ongestion, whih is represented by time and delay time osts are valued at the individual wage rate, y. y. 4 ar travel On the other hand, ommuting to work by publi transit osts fb b yx (3) where fb denotes the fixed osts suh as fares and yx b represents the time ost to an urban resident using publi transit. We assume that b and f fb. ommuting by ar is faster but entails a higher fixed ost. In addition we assume the variable ost of using the ar is lower than that of using publi transit: t y b y. Under the ost funtions (2) and (3), an urban resident hooses between the two transport modes aording to his loation and takes the number of ar ommuters and parking supply at the BD as given. That is, an urban resident loated x miles from the BD hooses ommuting to work by publi transit if 4 Workers who drive to work in a entral business distrit have a wide range of alternative parking options suh as multi-story or underground parkades where stalls are rented to the publi, un-metered on-street loations and in some ases parking options arranged by their employers. Parking loation hoie at the BD an be influened not only by money ost and proximity to final destination as well as by whether or not it is likely to spend some time searhing/or waiting for a stall. Sine our goal is to understand how hanges in downtown parking supply affet mode hoie behavior and the urban form, for simpliity we have assumed that auto-ommuters just fae delay time osts due to ongestion in downtown. Even though delay osts may result from ruising and road traffi at the BD, for simpliity we have assumed that our ongestion funtion in downtown depends on the overall parking apaity and number of drivers to the BD. For a more detailed representation of the downtown parking problem see Arnott and Rowse (1999) and Arnott and Ini (2006). It is also worth mentioning that our bottlenek ongestion funtion is different from the traditional bottlenek ongestion setup in the literature (see for example Arnott et al. 1993). Trips to work are the most essential trips for most people. Shoup (1993) has reported that ommuters who worked in downtown Los Angeles responded to parking prie rises only by hoosing a different mode for their trips, not by hanging the number of trips they made or the time at whih they travelled. But for other trip purposes, travelers would respond to a ongestion toll not only by hanging the transport mode but also shifting their travel time and destination. Sine in our model we are just modeling work trips, for simpliity we have disregarded the possibility of workers hoosing alternative times to ommute by ar to the BD. Arnott et al. (1993) present a bottlenek model of downtown but without an endogenous urban form. 8

9 [ t y] x f y fb b yx. (4) Therefore, there is a utoff distane, denoted the modal boundary ( xˆ ), where urban residents are indifferent between using the ar and publi transit and whih satisfies the following onditions y f fb x ˆ b y y t (5) and 0 xˆ x. (6) onditions (5) and (6) imply that both modes are used in the ity and that lose to the BD urban residents will always ommute by publi transit. In addition, ondition (5) also helps to explain the demand for BD parking sine the demand for parking depends on how many people want to drive to downtown. The deision of driving downtown, in turn, hinges, as seen in (4) and (5), on the fration of people who hoose to drive rather than use mass transit to the BD, parking apaity, and quality of alternative means of transportation to the BD as well as the osts assoiated with driving downtown, inluding parking. If transit servies to downtown are widely available (low b y ), of high quality (low b ), and reasonable pried (low f b ), urban residents will use transit as a viable alternative to ars to go to the BD and, hene, will lower the demand for parking. If a parking fee must be paid in downtown (whih ould be aptured by f ) or if ongestion is too severe at the BD, urban residents may hoose to use publi transportation. In this ase, demand for BD parking is lower beause driving osts to work are high. Residential Bid Rent Funtions 9

10 Residents tastes are represented by U( q,, m, E) ( q) ( ) m E where m is onsumption of a numeraire non-housing ommodity, is the number of parking spaes per dwelling and q is onsumption of housing, measured in square feet of floor spae. We assume that q 0, qq 0 and 0, 0. In addition, urban residents also reeive utility from environmental quality, E. Environmental quality deteriorates with air pollution, whih is diretly related to the number of urban residents driving to work, E ( ) with E 0. While the prie of the omposite good is assumed to be the same everywhere in the ity (taken to be unity for simpliity), the rental prie per square foot of housing floor spae, denoted R, varies with loation. Sine urban residents are idential, the urban equilibrium must yield idential utility levels for all individuals. Spatial variation in R allows equal utilities throughout the ity. In partiular, the prie per square foot of housing varies over spae so that the highest utility level attainable at eah loation equals a onstant level of utility U. Given residents hoie of transport modes implied by (5) and (6), the maximum amount an urban resident living at distane x from the BD would be willing to pay for a dwelling of size q with parking spaes at a given utility level, inome and downtown ongestion levels satisfies ( q) ( ) U E y f ˆ b b yx for 0 x x R( q,, x; ) (7) ( q) ( ) U E y f [ t y] x y for xˆ x. where U, E, y,, ) when 0 x xˆ and ( U, E, y, f,, t,, ) when xˆ x. ( f b b The bid funtion is inreasing and onave in the housing attributes, and dereasing in the given level of utility. ote, from (4), that urban residents do not onsider the environmental and ongestion onsequenes of their mode hoies and as a result, driving to work is underpried. 10

11 The osts of Residential Parking For simpliity, we assume the only type of residential parking provided in the ity is surfae parking. The ost per residential parking spae an be represented as ik rl (8) where r and i are the pries of land and apital, K is the fixed amount of apital per surfae parking spae and l is the fixed amount of land per surfae parking spae. While the prie of apital is assumed to be exogenous and uniform aross spae, the prie of land is endogenously determined and varies over spae. Housing Developers The amount of floor spae in a developer s omplex is given by H ( K, L), where K is the apital input and L is the amount of building land. We assume that H is stritly onave and homogenous of degree one. The intensive form of this prodution funtion is written as h (S), where S is apital per unit of overed land or strutural density and h satisfies h s 0 and h ss 0. h (S) represents residential total floor spae per unit of building land. Sine q is floor spae per dwelling, it follows that the number of dwellings in a omplex is given by H ( K, L), whih an q be written as Lh ( S). q Given the preeding disussion, the developer s profit equals h( S) L R( q,, x, ) [ rl ik ] is r (9) q 11

12 12 where the expression in brakets in (9), denoted, is profit per are of building land and ),,, ( x q R is defined by (7). For fixed L, developers hoose q, and S to maximize (9) and ompetition bids up land rent r until maximized profit per are equals zero. Sine total profit is zero regardless of the value of L, the sale of the developer s building is indeterminate. Assuming an interior solution, the first-order onditions for hoie of strutural density, dwelling size and parking spaes per dwelling that must be met are respetively 5 0 ]] [ ),,,, ( [ ) ( i ik rl E U x q R q S h S s (10) 0 ] ] [ ),,,, ( [ ) ( q ik rl E U x q R R q S h q q (11) 0 ] [ ) ( ik rl R q S h (12) and the zero profit ondition is 0 ] [ ),,,, ( ) ( r is ik rl E U x q R q S h. (13) Equation (10) says that strutural density is expanded until the marginal inrease in revenue per are of building land equals the marginal inrease in ost from the extra apital plus the marginal inrease in parking land ost required to hold parking spaes per dwelling fixed. 5 While the utility level U and are ultimately endogenous, they are viewed as parametri at this stage in the analysis. If we onsider the ase where surfae parking spaes per dwelling equals zero (a orner solution), then ondition (12) would be replaed by the following three Kuhn Tuker onditions: 0, 0 ] [ ) ( k i rl R q S h and 0 ] [ ) ( k i rl R q S h.

13 Equation (11) says that dwelling size is expanded until the marginal derease in revenue per are of building land equals the marginal derease in parking land ost from holding the number of parking spaes per dwelling fixed. Finally, equation (12) says that the number of parking spaes per dwelling should be inreased until the net inrease in revenue per are of building land equals zero. The Hessian matrix of evaluated at the solution to (10)-(12) may be written D h q ss [ R [ rl 0 0 ik ]] h q 0 0 R qq 0 0 h R q (14) The negative definiteness of D required by the seond-order ondition is guaranteed by h ss 0 and the strit onavity of R, where R qq 0 and R 0. Thus, D 1 0, D 2 0 and D 2 hssrqqr h [ R [ rl 3 q ik ]] 0. We now proeed to examine how the main endogenous variables vary over spae. 3. Spatial Behavior of the Main Endogenous Variables Spatial Behavior of S, q, and l q / h We now fous on the spatial behavior of strutural density ( S ), dwelling size ( q ), parking spaes per dwelling ( ) and land per dwelling ( l q / h ). Differentiating (13) with respet to x while taking into aount (7) and (10)-(12) yields, after some manipulations, 13

14 rx b y 0 q l h( S) [ t y] 0 q l h( S) for for x xˆ x xˆ (15) Aording to (15) residential land rent dereases with distane from the BD but exhibits a kink at the boundary between the two transport modes. At the modal boundary xˆ, strutural density, dwelling size and the number of parking spaes per dwelling are the same regardless of whih mode the urban resident selets sine transportation osts are the same at xˆ. 6 Equation (15) shows that the residential land rent assoiated with the automobile is less steep at x xˆ. Totally differentiating (10) - (12) taking aount of the dependene of r on x and solving for S x, q x and x using ramer s rule gives, after simplifying, the following results: Sx h srxq 0 hssh[ R [ rl ik ]] (16) r q x x 0 (17) hrqq lr x x 0. (18) R Let l q / h. Taking advantage of the results thus far, it is possible to derive the spatial behavior of the amount of land per dwelling in the following way: q h h q l x x x x 0. (19) 2 q 6 ote that r (x) is not differentiable at x xˆ beause R (x) is not differentiable at x xˆ and right differentiable at that point. 14, but left

15 Moreover, the amount of land at loation x is given by ( x) ( x) where (x) is the number of dwellings. Thus, ( x) 1 represents population density at loation x whih, exhibits a ( x) ( x) ( x) spatial behavior desribed by 1 x x 0 2. (20) Aording to (16)-(18), buildings have fewer storeys farther from the BD and dwellings are bigger loser to the edge of the ity. Moreover, the number of residential parking spaes per dwelling inreases with distane from the BD, implying that bigger houses are bundled with more parking spaes. This pattern is atually onsistent with the fat that per apita vehile ownership and travel tend to be higher in automobile-dependent suburban areas while publi transit travel tend to be higher in urban areas (Litman 2013). Equations (19) and (20) also reveal that urban residents onsume more land as we move away from downtown (where land is typially more expensive) and population density dereases with distane from the BD. 4. Urban Equilibrium onditions ext, we turn to the analysis of the urban equilibrium under the assumption of a losed ity, where population ( ) is viewed as fixed, while the urban utility level is determined within the system. The first spatial equilibrium ondition requires that urban land rent at the edge of the ity, x, must equal the agriultural land rent: r( x, U,,, E, f ) r a. (21) 15

16 The seond equilibrium ondition is that population must fit inside the ity. The population ondition must also reflet mode hoie: 7 xˆ 0 x 1 1 dx dx ( x) ( x) b xˆ (22) or 8 r( xˆ, U, E)[ b y y t] r(0, U, E)[ t y] b y [ t y] ra. (23) Sine 1/ ( x) represents population density and the ity is linear with unit width, the integrals in (22) aggregate total residents out to the urban boundary and equate it to. Finally, the number of workers ommuting by ar is determined as x 1 r( xˆ, U, E) r dx ( x) t y xˆ a. (24) Another ondition that must be met is a balane-budget parking ondition stating that parking infrastruture osts are overed through the use of a parking fee f i (25) where i represents the exogenous unitary ost of providing one unit of parking apaity and represents the (exogenous) supply of parking in the BD. 9 7 We define i with i b, as the total amount of land per dwelling under mode i. 8 Reall that land size at loation x is fixed and equal to 1. From (15) we get 16 r 1 / x bx b ( ) b y and r 1/ x ( x) t y whih, we insert bak into (22). Then, integrating while taking into aount (21) and that rb ( xˆ) r ( xˆ) yields, after some manipulations, (23). 9 The supply of parking in a BD depends on several fators suh as prodution osts namely land pries as well as on maintenane and operation osts and regulations. Sine our goal is to understand how hanges in parking supply in a BD affet urban welfare and the urban spatial struture, for simpliity we have not expliitly modeled the problem of parking suppliers in downtown or distinguished between urbside and off-street parking. ote also that in our model, the number of auto ommuters using the parking apaity equals the share of urban residents hoosing to drive to work. Therefore the number of auto ommuters represents the demand for BD parking.

17 The left-hand side of (25) represents total revenues generated with parking fee f while the right-hand-side represents the ost of providing downtown parking apaity. Sine this ost is linear, parking apaity is produed under onstant returns to sale. In addition, note that apaity ongestion, y, is homogenous of degree zero in traffi volume and apaity, onditions that lead to the self-finaning theorem of transportation eonomis. Under these onditions, ongestion tolls should exatly over the ost of an optimal-size ongested transportation faility. Suboptimal Parking Fee Before proeeding further, it is onvenient at this point to draw attention to an assumption that provides useful interpretations when examining the impats of a hange in the supply of downtown parking on mode hoie for the work trip and on the urban spatial struture. The parking prie that should be harged when a faility is ongested should be equal to the marginal infrastruture osts plus an additional fee whih is equal to the marginal external ost of ongestion. This guarantees that individual users of the parking faility pay for the speifi marginal osts they ause. The private ost of travel by automobile is given by (2). ote from (2) that travel by ar is subsidized when downtown parking is underpried that is, f y. Sine the individual parking-ongestion ost is given by y, the effet of an extra parker on this ost is the derivative y, while the effet on all parkers (the external ost) is y, whih is the optimal ongestion harge. On the other hand, from (25) the balaned-budget parking fee is given by i. Therefore, the auto travel subsidy is measured by y i. 17

18 The relationship between the balaned-budget parking fee and the optimal ongestion harge depends nevertheless on whether is set optimally. For what follows, we assume that apaity is initially fixed at some level suh that the balaned-budget parking fee (user fee) falls short of y i the optimal ongestion harge, implying that 0 holds, whih in turn yields a nonzero 2 auto ommuting subsidy. ext we explore the effets of hanging the BD parking apaity when parking is underpried on the optimal values of U, x, xˆ and. Later, in setion 6, we show that when is hosen to maximize the equilibrium urban utility, the budget-balaning parking fee and the optimal ongestion harge oinide. Thus, the self-finaning theorem holds in the ontext of our model. In other words, when parking apaity is hosen optimally, the ongestion toll and the balaned-budget parking fee oinide (even in the presene of environmental spillovers), so that aggregate total parking revenue just overs apaity osts. 5. The effets of a hange in the supply of BD parking Together (5), (21), (23), (24) and (25) onstitute a system of equations that an be solved for the unknowns U, x, xˆ, and f.10 We now use the framework just developed to examine the effets of a marginal inrease in when parking is underpried on the long run optimal values of 10 From (21) and (23) we get the solutions for U and x onditional on into (24) and (25), whih then determine 18 and f. These solutions are then substituted and f as funtions of the underlying parameters a, f b, i and, with the latter parameter being the one of interest. Finally, the resulting solutions for r,, y, b,, t and f are substituted bak into (21) and (23), whih then determine U and x as funtions of the mentioned parameters. In order to make the exposition lear, all the parameters not relevant for this paper analysis will be suppressed in the equilibrium solutions.

19 strutural density, dwelling size, residential parking supply, ommuting mode hoie, ity size and urban welfare. Impats on the Modal Boundary Differentiating equation (5) with respet to yields I II i d i y y dxˆ 0 ( y y t ) b (26) sine it an be shown that d y i [ (0) ][ ( ˆ) (0)]][ ] 2 2 b y t y x b y y t ( ) b y y i [ (0) ][ ( ˆ) (0)]][ ] 2 2 b y t y x b y y t ( ) 1 (27) y i d with 0, ( x ˆ) (0) and 2 2 b y y t implying that 0 1. ( ) The sign of (26) aptures the net effet of a hange in the supply of BD parking on modal substitution. The sign of (27) represents the net impat on the equilibrium urban residents driving to work. 11 To understand the signs of (26) and (27), note that, initially, an inrease in generates a gain from dereased ongestion delay osts in downtown ( 2 y ) and also an inrease in the balaned- 11 Totally differentiating (24) with respet to and using (26) and (28), yields after simplifying (27). The fat that the parking elastiity (27) is inelasti is onsistent with empirial studies that have shown that the elastiity measure of auto use for work trip with respet to parking osts is around (Gillen 1997). The reason for suh low parking ost elastiity is that urban residents faed with inreased parking osts (suh as for example parking fees or redution in parking supply whih inrease their parking time osts) are able to substitute between money and time osts by swithing modes. 19

20 budget parking fee to over the ost from the additions to parking supply ( i ). We denote the differene between the gain from redued ongestion and the inrease in the parking fee as the primary (or partial equilibrium) effet on the prie of driving of a marginal inrease in. The primary effet is aptured by term I in (26). Sine the primary effet is positive, there is a derease in the prie of driving to work. 12 The magnitude of the primary effet depends nevertheless on the level of the parking subsidy. However, by relieving the bottlenek ongestion and thus reduing the generalized ost of driving to work, the inrease in also indues more urban residents to drive downtown whih in turn rebounds on BD ongestion delay osts, pushing the prie of driving to work up. 13 We denote this negative effet on driving osts from indued driving as the rebound effet of a marginal inrease in. The rebound effet, aptured by term II in (26), is the produt of the primary effet and the indued driving demand measured by the driving demand elastiity of parking apaity expansion. It is worth mentioning that the magnitude of the rebound effet depends on the value of this elastiity, whih represents how sensitive auto travel ativity is to a hange in the prie of driving. 14 Whenever there is a hange in, there is also a hange in time osts and thus in the ost (prie) of driving to work. 12 In equilibrium the marginal soial benefit from the apaity expansion ( y ) should be equal to the marginal 2 soial ost ( i y ). Beause parking is underpried, there is a gap between y and i whih orresponds 2 to y. Sine y 0, the primary effet is positive. 13 ote that it is not the apaity expansion itself that generates travel but the redution in ongestion delays. 14 Stated differently, this elastiity is the prie elastiity of demand of the number of ars that ommuters drive to (and park) at work. 20

21 To the extent that this elastiity is inelasti, that is, has a value lower than unity, the rebound effet is small. Sine the rebound effet pushes the modal boundary outwards while the primary effet works in the opposite diretion, the rebound effet partially offsets the primary effet of a hange in on the modal boundary. Yet, beause the driving demand elastiity of parking apaity expansion is less than unity, the rebound effet is atually outweighed by the primary dxˆ effet and the modal boundary shortens ( 0 ), meaning that the enlarging of the existing BD parking apaity has atually dereased ongestion delay osts in downtown. Together with (27) we may onlude that downtown will be arrying more vehiles, that is, more urban residents will d be driving to work after the parking apaity expansion ( 0 ). This theoretial outome is also evidened by Mildner et al. (1997) who show that inreased parking supply tends to inrease automobile ommuting and redue transit and ridesharing. Impat on Utility level Totally differentiating (23) with respet to while substituting (26) and (27), yields the impat of an inrease in downtown parking apaity on residents welfare as du d 0) b y1 (0) y ( 2 b i y t y ( xˆ) (0) E E d E 0. (28) where E E represents the elastiity of environmental quality (air pollution) with respet to auto travel to the BD. The deomposition of the welfare soures in (28) shows that the indued 21

22 driving demand from an inrease in, given by quality by affeting traffi air pollution. d, also impats the ity environmental d Sine 0 1 it is likely that the indiret rebound effets aused by the parking apaity expansion would be small. In this ase, it may be possible that the diret benefits of the apaity expansion that would our with no hange in travel behavior (that is, holding the number of drivers,, unhanged) dominate and an inrease in utility ours. To the extent that these same diseonomies pull utility down as auto ommuting inreases and depend on the elastiity of environmental quality, the net effet of an inrease in downtown parking supply on welfare annot be asertained a priori. Impats on Residential Land Rent The impats of an inrease in on residential landowners welfare an be desribed by the hange on the residential land rent profile. dr(0) 1 du E (0) d b y1 (0) y b d i 2 y t y ( xˆ) (0) 0 (29) and 22

23 dr( xˆ) 1 du dxˆ E b y ( xˆ) d d i b y[ y t ] 1 2 y [ y y t ][ (0)[ y y t ] ( xˆ)[ t b b 0. y]] (30) The above omparative stati analysis reveals that the impat of an inrease in downtown parking on residential land rent is not the same everywhere in the ity. Urban residents make tradeoffs between transportation osts (time and money) and loations deisions. It is therefore likely that hanges in vehile ommuting osts will affet the desirability of automobile-dependent loations and therefore the amount of urban fringe development that ours. Beause the primary effet outweighs the rebound effet, residential land rent near the BD dereases while residential land rent at loations farther from the business distrit inreases. An inrease in downtown parking supply dereases driving osts to work in the long run beause the net effet is to derease ongestion delay osts in downtown. Sine auto travel to work is less expensive, some of the urban residents who originally were ommuting by mass transit will swith to the ar mode. Sine they will use the ar, they are motivated to move farther away from their jobs. On the other hand, for those urban residents who keep using mass transit, the inome net of transport ost inreases. These two effets together bid up housing bid rents in the area of the ity where the ar is the transportation mode to ommute to work, while depressing housing bid rents near the BD. Two notes are now in order. First, the rise in auto-ommuting inreases air pollution throughout the ity, affeting all urban residents the same way. The reason is that air pollution is assumed to be a global externality and environmental damages to be the same in every loation. onsequently, residential bid rents experiene the same derease everywhere in the ity due to inreased vehile air emissions. This 23

24 derease in housing rents in turn inreases residents urban welfare. In equilibrium, these two effets anel out. However, beause the net effet of the apaity expansion is to derease ongestion osts in downtown and inrease the number of residents ommuting by ar, there is an overall inrease in aggregate air pollution whih pushes down the equilibrium urban utility. This effet is aptured by the seond omponent of (28). Seond, sine attributes of mass transit did not hange, workers already ommuting by transit must enjoy a higher utility. This is atually onsistent with the lower housing rents everywhere in their residential area. The reason for lower rents in entral areas where transit is the work mode of transportation is the inrease in the desirability of farther loations beause parking ongestion osts at the workplae dereased after the apaity expansion. This, in turn, results in lower residential land rents in entral areas and higher residential land rents farther away from the downtown distrit (where there is an exess demand for residential land) as some urban residents reloate from entral to suburban residential areas. Impat on the urban boundary Totally differentiating (21) with respet to while substituting (27) and (28) yields, dx d i ( xˆ) (0) 1 y 2 b y (0) [ y t ][ ( xˆ) (0)] sine ( x ˆ) (0). 0 (31) The key observation regarding (31) is that an inrease in BD parking supply an atually ause the urban spatial struture to beome less ompat. Sine the rebound effet on delay ongestion osts is dominated by the primary effet, the ity size inreases. Further intuition an be gained by examining the impats on population densities. 24

25 Impat on strutural density, dwelling size and residential parking spaes per dwelling Totally differentiating (12) with respet to while taking into aount the dependene of the land rent on, yields d(0) l R dr(0) 0 d( xˆ) l dr( xˆ) and 0 R (32) given (29) and (30) and that R 0. Aording to (32), the number of residential parking spaes per dwelling inreases in entral loations and dereases at farther loations from the BD following an expansion in. This suggests that hanges in BD parking supply also influene residential parking supply throughout the ity beause of its heterogeneous impat on land rents throughout the urban area. This in turn means that limited parking in downtown areas influenes developers investment deisions in other parts of the urban area. The impats on strutural density at the BD and at the modal boundary an also be examined by first omputing S u and S E and then using (28) and (26) to evaluate, yields The partial effet of u S was determined by totally differentiating the system of equations (10)-(12) evaluated at the initial equilibrium with respet to the exogenous parameter of interest while taking into aount the dependene of r on U and then using ramer s rule to find the result. 25

26 ds(0) and S h h h u ss ss ss h (0) du S h q (0) de (0) h[ R(0) rl ik ] hsq du de (0) [ (0) ] h R rl ik d hsqb y1 h[ R(0) rl ik ] (0) y ss s E hsq dr(0) 0 h[ R(0) rl ik ] du b h hsq de (0) h[ R(0) rl ik ] ss 2 i y t y ( xˆ) (0) (33) ds( xˆ) S x h h dxˆ ( xˆ) S ss ss u ( xˆ) du S h[ R( xˆ) rl ik ] hsq dr( xˆ) 0. h[ R( xˆ) rl ik ] h q y t s b E de ( xˆ) d y1 (0) y t y ( xˆ) (0) y y t b 2 i y b (34) By a similar method, we an find the effets on dwelling size at the ity enter and at the modal boundary by determining the sign of The partial effet of u q was determined by totally differentiating the system of equations (10)-(12) evaluated at the initial equilibrium with respet to the exogenous parameter of interest while taking into aount the dependene of r on U and then using ramer s rule to find the result. 26

27 dq(0) and du de qu qe 1 du h(0) (0) R qq ds b y h(0) Rqq 1 h(0) Rqq d 1 (0) b y dr(0) 0 de 2 i y t y ( xˆ) (0) (35) dq( xˆ) dxˆ qx q b y ( xˆ) hr 1 ( xˆ) h( xˆ) R 1 h( xˆ) R qq u qq du de qe dxˆ 1 h ( xˆ) R qq dr( xˆ) 0. ds qq du du dxˆ de b y 1 h ( xˆ) R qq de (36) The effets on strutural density and dwelling size of an inrease in downtown parking supply are onsistent with the impats already disussed on residential land rents. Residential land rents near downtown fall while suburban residential land rents inrease. This indues smaller dwellings and taller buildings in the suburbs whih inreases suburban population. The opposite ours in loations near the BD. Sine there is a fixed number of urban residents that must be housed in the ity, this an also explain the expansion of the ity size after an inrease in. Impat on the parking subsidy 27

28 Let s y i. Reall that we assumed downtown parking to be underpried. The impat of a hange in the BD parking apaity on the automobile travel subsidy from underpried parking is aptured by ds 1 y i d 1 0. (37) d Sine 0 1 holds, the sign of (37) is negative. An inrease in parking apaity on the one hand inreases the budget-balaning parking fee but on the other hand it dereases the marginal external ost of ongestion. The net result of these two ountervailing effets is to derease the level of the parking subsidy. Unless the expansion in is suh that the new apaity leads the budget-balaning parking fee to oinide with the external ongestion osts of the parking apaity usage, there is still a positive (yet lower) auto subsidy. Table 1 summarizes our omparative statis results. TABLE 1: omparative Stati Results of a hange in under Underpried Parking xˆ x S (0) S (xˆ ) q (0) q (xˆ ) (0) (xˆ ) r (0) r (xˆ ) U /- The omparative stati results from table 1 yield two interesting onlusions. Proposition 1: When parking at the BD is underpried and its finaning relies on budgetbalaning parking fees, an expansion in downtown parking supply tends to derease overall parking ongestion at the BD. However, inreased parking supply also tends to inrease automobile ommuting and redue transit rides and as a result, ontributes to an inrease in air pollution. Provided that the primary effet dominates the rebound effet and the inrease in air pollution, an inrease in BD parking supply is welfare improving. In addition, the overall derease in ongestion delay osts at the BD makes automobile-dependent loations in the long run more attrative to urban residents, potentially leading to an expansion in the ity size. 28

29 Proposition 1 implies that parking supply poliies that inrease the amount of downtown parking supply in the presene of suboptimal parking fees may atually work at ross purposes with anti-sprawl poliies. In ontrast, aps on the amount of downtown parking, while reduing total auto travel as well as ity size, an be welfare dereasing beause they exaerbate (rather than alleviate) the overall parking ongestion in entralized workplaes. With this mind we may further onlude that Proposition 2: When parking is underpried, inreases in parking apaity tend to satisfy unpried demand and to redue the severity of ongestion osts from parking underpriing. However, over the long run, suh supply deisions ontribute to a self-reinforement yle of automobile dependeny and sprawl. 6. Optimal Parking apaity and Self-Finaning In this setion we relax the assumption that is exogenously set and disuss how optimal parking apaity provision affets the omparative stati results of setion 5 as well as its impliation for the self-finaning of a ongested faility. Optimizing apaity Substituting (27) into (28) yields after some manipulations du y i (38) 2 where with (0) b y (0) b y t y ( xˆ) (0) and 29

30 E 1 y i 1 (0) b y 1 y i b y [ (0) b y [ t [ (0) [ ][ ( ˆ) (0)]][ ] ( ˆ) (0) b y t y x b y y t t y x y][ ( xˆ) (0)]][ y y t b ]. (39) ow suppose that downtown parking apaity is hosen to maximize residents equilibrium utility. It an be shown that when parking apaity is hosen suh that 2 2 y i (40) du is satisfied then 0, whih is a ondition that must be satisfied for the optimal apaity hoie. Under apaity rule (40), parking apaity is hosen until the total time-ost savings from an inrease in downtown parking apaity (given by the left-hand-side of (40)) equals the marginal ost of adding apaity. Self-finaning of apital ost However, if the investment rule (40) is satisfied, then the following marginal-ost priing rule also emerges given (25) y i y f. (41) The parking fee derived in (41) may be viewed as a harge for the use of the parking apaity in the downtown area. This parking fee also ats as a ongestion fee sine it aptures the parkingongestion damage from an extra auto ommuter to the BD. 17 Sine this parking fee satisfies the 17 In this paper we abstrat from the ase of seond-best apaity. For a study that has examined optimal apaity in the presene of unpried ongestion see Wilson (1983). The author shows that whether the optimal apaity of a road is affeted by a toll fixed below its optimal value depends on the value of the prie elastiity of travel demand at the seond-best optimum. If this prie elastiity is suffiiently high, the priing onstraint lowers the optimal apaity. However, if the prie elastiity is less than the ratio of the private prie of travel to the private ongestion ost at the 30

31 balaned budget onstraint (25), it further follows that parking apaity osts equal the ongestion toll-revenue (the self-finaning result). Summarizing yields Proposition 3: When downtown parking apaity is hosen to maximize the equilibrium level of urban utility, a balaned-budget parking fee oinides with the optimal ongestion toll albeit the presene of environmental spillovers (air pollution). The reason why the result in proposition 3 ours is beause air pollution from auto ommuting is a global externality. Therefore, when apaity in downtown is hosen to internalize BD ongestion, it also maximizes utility in our setting. This optimal utility is never the less a seond best result beause too muh ar ommuting still ours sine air pollution from auto usage is not being fully internalized. It is also interesting to note that the equality from the self-finaning result still applies even if other harges (say a pollution tax) are levied to over other auto ommuter externalities (for example air pollution). The intuition is as follows. Remember that ommuting to work by ar generates two externalities. On the one hand it reates parking ongestion (in the form of time delay osts) in the downtown area and on the other hand, it generates air pollution whih in turn affets equally all households in the urban area. For the sake of illustration, let the environmental effet of an extra auto ommuter be onstant and equal to e. Then the external effet on all urban households is given by e, whih orresponds to the optimal environmental harge. If it is the ase that this environmental tax is harged to every auto ommuter, the ost of auto ommuting defined by (2) hanges to seond-best optimum, then a suboptimal toll raises the optimal apaity. Within the ontext of our model, we an nevertheless observe from (28) that the optimal apaity when parking is underpried implies further inreases in apaity as long as the environmental impats are small. This in turn suggests that there is a need to ompensate for lak of priing by building or providing more parking. Moreover, finanial balane is not a guarantee of effiieny sine there are several ombinations of apaity and parking fee that satisfy (25). 31