1. Transpn. Res.-A. Vol. 29A, No. 2, pp. 141-156,1995
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THE ECONOMICS OF REGULATORY PARKING
POLICIES: THE (1M)POSSIBILITIES OF PARKING
POLICIES IN TRAFFIC REGULATION
ERIK VERHOEF,* PETER NIJKAMP and PIET RIETVELD
Department of Spatial Economics, Free University, De Boelelaan 1105, 1081 HV Amsterdam,
The Netherlands
(Received 1 March 1993; in revised form 20 February 1994)
Abstract-This article contains an economic analysis of regulatory parking policies as a substitute
to road pricing. The scope for such policies is discussed, after which a simple diagrammatic
analysis is presented, focusing on the differences between the use of parking fees and physical
restrictions on parking space supply. The former is found to be superior for three reasons: an
information argument, a temporal efficiency argument and an intertemporal efficiency argument.
Finally, a spatial parking model is developed, showing that it may be possible to overcome the
difficulty of regulatory parking policies not differentiating according to distance driven by specify-
ing the appropriate spatial pattern of parking fees, making individuals respond to (spatial) parking
fee differentials.
1. INTRODUCTION
One of the most serious and apparent challenges facing urbanized areas nowadays is the
handling of the urban transportation problem. The term nowadu_y~ is perhaps slightly
superfluous, as transport has traditionally generated various social costs-which have
always led to more stress in urban areas for reasons of density. For instance, with the
introduction of the automobile in the beginning of this century, it was hoped that finally
a solution was found for the growing annoyance and hindrance caused by horse manure.
However, after the dramatic growth in car ownership and road traffic over the past
decades, it is increasingly recognized that, although mobility as such is an important side
to a society’s social and economic development (leaving the question of causality aside),
road transport gives rise to new, greater pressures on city life. In particular, one may
distinguish problems associated with increasing environmental disruption (including noise
annoyance), growing congestion, severe safety problems and expanding use of urban land
for transportation purposes.
The realization of socially acceptable (or, ideally, optimal) levels of (road) transport
requires a careful evaluation of the associated social costs and benefits. Due to the
existence of external costs of road transport, this process cannot simply be left to the
market. ’ External costs can loosely be interpreted as the unpriced use of others’- often
public-goods.’ For the external costs of road transport, such goods include a clean
environment, silence, time, safety and free access to public space. External costs are an
important category of market failures. Because they are not reflected in (efficient) prices,
they will not be taken into account in individual decision-making processes but are shifted
to society instead. Consequently, efficient resource allocation (Pareto efficiency) cannot
be expected. Himanen et al. (1992) therefore speak of signal failures in this respect.
It is striking that one of the aforementioned external costs of road transport (namely,
*Erik Verhoef is affiliated with the Tinbergen Institute and participates in the VSB-fonds-sponsored re-
search project Transport and Environment.
‘Road transport activities do not give rise to any external benefits that might, to some extent, compensate
for its external costs. Road transport’s benefits are usually either internal benefits or pecuniary benefits (see
Verhoef, in press).
*The reverse does not hold: Not every free good (or bad) is an external benefit (or cost). See Verhoef (in
press) for a more thorough discussion on the definition of external effects.
141

2. 142 E. VERHOEF, NIJKAMP P. RIETVELD
P. and
congestion) was already subject to debate in the economic literature of the early 1920s.
Pigou (1920) and Knight (1924) are often mentioned as the spiritual fathers of road
pricing. The former also gave his name to the term Pigouvian taxation, which is, espe-
cially among economists, a popular instrument for correcting market failures due to
external effects. Currently popular concepts such as optimal road prices and optimal
eco-taxes are in fact Pigouvian taxes. The key characteristic of such a fee is that the
activity is taxed for the marginal external costs in the social optimum. Thus, it corrects
for the signal failure, restores the efficient workings of the market mechanism and conse-
quently secures efficient resource allocation, at least in theory.
For reasons to be outlined in Section 2, transport economists generally still regard
road pricing as the first-best instrument for traffic regulation. However, although the
Hong Kong Electronic Road Pricing (ERP) experiment has demonstrated that it is techni-
cally possible to operate successfully such a scheme nowadays,’ social and political im-
pediments appear to prevent ERP from being widely introduced and accepted, certainly
in the short run. The main objections usually raised against ERP include (a) privacy
considerations; (b) equity considerations; (c) costs of introduction and operation, possi-
bly exceeding the expected welfare benefits; (d) the possibility of car drivers following
escape routes (avoiding toll points and adding to road transport’s external effects in other
areas); (e) difficulties associated with the determination of the optimal road price and (f)
perverse incentives faced by regulatory bodies (see Button, 1992 and Andrew Evans,
1992). Of course, these objections are all to a lesser or larger extent debatable. At any
rate, in many countries plans for introducing ERP seem to be hushed up for the time
being and attention is focused on alternative instruments for traffic regulation. In The
Netherlands, for instance, such alternatives include the introduction of the spitmignet
(peak hour permits) for the Rimcity and a policy change from demand-oriented parking
policies toward regulatory parking policies. According to the Dutch government, regula-
tory parking policies are an “indispensable part of an integral transport policy aimed at
reducing the growth of road traffic” (Tweede Kamer der Staten-Generaal, 1991-1992). In
transport economics, expectations are modest as far as the actual implementation of ERP
is concerned. This shows in recent publications on alternatives to road pricing (see But-
ton, 1992, for an overview; and see Verhoef et al., 1993, for a discussion of the welfare
economic characteristics of such alternatives). Two examples are fuel taxes (see Mohring,
1989) and parking policies (see Glazer & Niskanen, 1992).
This article fits in this trend of increasing interest in alternatives to road pricing and
contains an economic analysis of the ins and outs of regulatory parking policies. In
Section 2, the scope for parking policies in traffic regulation is discussed. Section 3
contains a diagrammatic model, in which the specific form that regulatory parking poli-
cies would preferably take in discussed. Section 4 provides a spatial analysis of regulatory
parking policies along the lines of the types of models usually applied in urban economics.
Finally, Section 5 contains the main conclusions.
2. THE SCOPEFORREGULATORY
PARKINGPOLICIES
In the following sections, we will evaluate how regulatory parking policies may be
used to relieve some of the social pressures caused by excessive road traffic. Because
virtually every car has to be parked at the end of a trip, parking policies may indeed offer
a potentially strong instrument for influencing traffic flows. As stated in the Introduc-
tion, (electronic) road pricing is generally seen as the first-best economic instrument for
the regulation of traffic flows. The reason for its superiority is that the regulatory tax can
be differentiated according to various relevant trip-specific characteristics, such as trip
length, time of driving, route followed and vehicle used. Because these dimensions to a
large extent determine the (marginal) external costs of a trip, they accordingly determine
optimal Pigouvian taxes (that is, the optimal road prices) (see Verhoef et al., 1993, for
the welfare economic effects of second-best undifferentiated regulatory fees).
‘According Dawsonand Catling(1986), “Results
to wereextremely encouraging. . . the Hong Kong system
is accurate, reliable and robust enough to be extended to a full system” (p. 134).

3. Regulatory parking policies 143
A first important matter in the evaluation of regulatory parking policies is the ques-
tion of to what extent regulatory parking policies may serve as a satisfactory substitute
for this first-best instrument. In general, regulatory parking policies are only apt for
influencing numbers of trips and cannot differentiate according to trip lengths and routes
followed, simply because the policy is implemented at the end of each trip (see, however,
Section 4 for a notable exception to this rule). Therefore, using regulatory parking poli-
cies for affecting external costs which are to a large extent dependent on trip length or
route followed is not optimal and may in some (derived) respects-in particular, in terms
of associated incentives to change behaviour-even be counterproductive (see Verhoef et
al., 1993). In the terminology of Himanen et al. (1992), the risk of government (or
response) failures is indeed present.
For instance, suppose that the emission of a certain pollutant (say, C02) per trip is in
a fixed relation to the length of the trip. Using parking levies instead of road pricing for
charging road users for this external cost necessarily means that each individual road user
will be charged some weighted average of the individual marginal external costs generated
rather than his or her actual individual value (see Verhoef et al., 1993). The reason is that,
at the parking place, the regulator is simply not able to differentiate regulatory fees
according to individual trip lengths. Hence, following such a policy implies a relative
implicit cross-subsidization in favour of longer trips at the expense of shorter trips.
Although there will be a reduction in the numbers of both shorter and longer trips,
this substitution effect is clearly counterproductive. Here, a policy which allows for
differentiation according to trip lengths (fuel taxes, for instance) offers a superior alterna-
tive by providing the right incentives for shortening trip lengths. Likewise, because park-
ing levies cannot be differentiated according to specific routes followed, they can never
be a perfect substitute for road pricing when external costs differ between possible routes.
In general, regulatory policies lose more of their signal function the more they are
used for affecting external costs depending on dimensions according to which they cannot
differentiate. To determine the scope for regulatory parking policies, it is necessary to
map out the dimensions determining the external costs per trip and the dimensions along
which effective differentiation can take place using such policies. In Table 1, the main
external cost categories of automobile trips are roughly classified according to some
relevant dimensions, where the dimension of route followed is hierarchically split into
roads followed and area of driving (that is, an X in “Roads Followed” necessarily implies
an X in “Area of Driving,” whereas the opposite does not hold). Of course, the table is
not unambiguous and only serves to provide a first impression (for instance, external
costs of some forms of air pollution actually do depend on the area and/or the time of
driving, such as NO, emissions contributing to the formation of photochemical smog).
As stated earlier, parking policies can generally not be used for differentiation ac-
cording to trip length (again, with the exception of situations as considered in Section 4).
Because the first column in Table 1 is further filled with X’s, indicating that in fact all
Table 1. Dependence of various marginal external costs of automobile trips on various trip characteristics,
and the capability of regulatory parking policies for effective differentiation
Route Followed
Total
Length of Time of Roads Area of Vehicle
Trip Driving Followed Driving Used
External costs (X = strong dependence;
. = less strong dependence)
Emissions (air pollution) X X
Noise annoyance X X X X X
Safety X X X X
Congestion (on highways) X X X X
Congestion (on urban road networks) X X X
Differentiation possible using regulatory
parking policies (X = easily possible;
. = hardly possible) X X

4. 144 E. VERHOEF, NIJKAMP
P. andP. RIETVELD
external costs of an automobile trip depend on its length, this may underline the second-
best character of regulatory parking policies. Therefore, we have to use the other four
columns for determining the scope of regulatory parking policies given the inherent
limitations concerning trip lengths.
First, if well performed, parking policies can differentiate according to the time of
driving; that is, provided that time-variable parking fees are used. Furthermore, parking
policies will only to a limited extent discriminate according to the route followed. That is,
parking policies will by definition to a certain extent discriminate according to the area of
driving (namely, the area around the parking place). On the other hand, parking policies
cannot discriminate according to the actual roads followed. Finally, parking policies seem
hardly suitable for adaption according to the type of vehicle parked (except perhaps for a
rough distinction into private cars, vans, buses and trucks).
As a consequence of these limited potentials of regulatory parking policies, they do
not provide a panacea for containing road transport’s external costs of air pollution,
noise annoyance and unsafeness in its most efficient way. If anything, it seems to us that
the scope for useful regulatory parking policies is limited to the containment of conges-
tion on urban road networks, insofar as it indeed satisfies the criteria mentioned in Table
1. 4 Simply, the less these criteria are met, the more regulatory parking policies lose their
applicability. For the sake of argument, however, in the following section we will simply
assume that these criteria are indeed met. In addition, we will assume that each individual
car driver uses an equal amount of urban road kilometres for his or her trip.
Furthermore, a reasonable requirement for parking policies is that the actual activity
of parking should be properly priced. Parking markets (let alone efficient parking mar-
kets) usually do not exist. Often, parked vehicles cause annoyance and use public space
without any (efficient) price being charged. Clearly, efficiency requires the parkers to be
confronted with such external costs of parking. This may be the second goal of regulatory
parking policies. ’
The scope for regulatory parking policies is limited, considering the wide range of
external costs resulting from road transport. In accordance with the foregoing, we will
assume that the regulatory parking policy to be analyzed in the remainder of this article
serves the following two goals: (a) optimizing the level of congestion on an urban road
network, and (b) optimizing the activity of parking itself. In a more comprehensive
setting, regulatory parking policies would preferably be supported by supplementary
instruments such as fuel taxes.
3. A BASIC DIAGRAMMATIC ANALYSIS OF REGULATORY PARKING POLICIES:
REGULATORY PARKING FEES VERSUS PHYSICAL RESTRICTIONS
ON PARKING SPACE SUPPLY
This section contains a comparison of two basic forms that regulatory parking poli-
cies might take: regulatory parking fees versus physical restrictions on parking space
supply. Our basic model of regulatory parking policies is set in a simplified world. We
have already mentioned the following two assumptions: (a) Each individual car driver
uses an equal amount of urban road kilometres for his or her trip, and (b) congestion is
equally spread over the urban road network. Furthermore, we assume (c) that the govern-
ment has full control over all parking space available. Under these assumptions, which
are particularly favourable for the potential effectiveness of regulatory parking policies,
4Furthermore, certain other external costs of road transport are positively correlated with congestion (e.g.
air pollution). To the extent that this is the case, they may-analytically speaking-be interpreted as additional
external congestion costs. Under the same assumptions and restrictions, regulatory parking policies may again
be used for coping with such effects.
‘For instance, it has been calculated that the total value of land used for parking in The Netherlands
amounts to 47 billion Dutch guilders, while only a small proportion of this sum is actually paid for by the
parkers. For every Dutch car, on average three parking spots are available, which means 190 million square
meter for the Dutch vehicle stock. Often, the parking spot is more expensive than the car occupying it (Tweede
Kamer der Staten-Generaal, 1991-92). Assuming that only one third of all parking takes place for free on public
land, and assuming a 5% interest rate, a yearly external cost of 785 million Dutch guilders (approximately 0.2%
of gross domestic product) can be inferred.

5. Regulatory parking policies 145
we can concentrate on the fundamental relations that exist between parking and mobility
and, in particular, on the performance of both types of parking policies just mentioned
without having to worry about parking policies’ other second-best aspects as discussed in
Verhoef et al. (1993). Figure 1 serves as the basis for our discussion.
In Fig. la, we consider commuters arriving on the urban road network during the
morning peak. Every potential commuter will have a certain willingness to pay for making
the trip by car, which will depend on the benefits associated with the trip and on the
availability and costs of alternative modes. Ranking the potential commuters according
to descending willingness to pay yields the aggregate marginal private benefit (MPB)
curve- the demand curve (D)- for using the urban road network. The marginal private
cost of using the network is given by the MPC curve. The horizontal part of the curve
indicates the private cost of a trip under free driving conditions. With a growing inflow,
the MPC will rise progressively due to congestion. Without government intervention and
with free supply of parking space, NO trips will be made. The marginal private benefits-
associated with the last trip-are just equal to the marginal private costs. In the literature,
the MPC curve is usually set equal to the average social cost (AX) curve. The reason is
that an individual car driver will experience the average social costs (including congestion
costs) as his or her marginal private cost. It is then straightforward to derive the marginal
social cost (MSC) curve. The vertical difference between MPC and MSC gives the exter-
nal congestion costs; ZV1 gives the optimal inflow after correcting for congestion. 6
Finally, the total marginal social cost (TMSC) curve includes the (social) cost of
occupying a parking space during a working day. In this graphical approach, it has to be
assumed that all commuters have equal parking duration. The TMSC curve can then be
found by shifting the MSC curve upward by the social cost of parking. Hence, the socially
optimal number of trips in the morning peak is N*, where the marginal social costs are
equal to the marginal benefits, and the net social surplus (the area between the MPB and
Fig. 1. A basic model of regulatory parking policies.
% should be noted that on the horizontal axis of Fig. la, traffic inflow per fixed unit of time is measured
rather than the traditional variable of traffic flow. By doing so, theoretical problems (backward bending cost
curves and inconsistent aggregate demand curves) can be avoided. See, among many others, Else (1981, 1982);
Nash (1982); Hau (1991); Alan Evans (1992) for recent contributions to the ongoing discussion on the diagram-
matic and mathematical analysis of congestion.

6. 146 E. VERHOEF,P. NIJKAMPand P. RIETVELD
the TMSC curves) is at its maximum.’ The regulator’s job is therefore to reduce the free
market outcome with free parking space, No to the socially optimal number of trips, N*.
This optimum can be accomplished by means of road pricing. R* is the optimal
road price, charging the individual car driver for the optimal marginal external costs of
congestion and the social costs of occupying a parking space and therefore securing the
optimal inflow N* to emerge. Furthermore, one may try to accomplish N* by posing
some sort of a quantitative restriction on the inflow. A practical application of such a
policy can be found in cities like Athens, where cars with even (odd) number plates are
allowed to drive on even (odd) days only. However, a somewhat closer inspection of the
demand curve reveals that, if such a policy indeed leads to a number of trips equal to the
optimal number in terms of volume, this does not imply that the socially optimal outcome
(where the social surplus is maximized) is realized. There is simply no guarantee that the
most efficient trips, representing the highest utility (i.e., representing the highest willing-
ness to pay) to be found on the demand curve between 0 and N*, will remain. In the
worst case, the trips (roughly) between (No - N+) and N, are left over, yielding much
smaller benefits. It is therefore conceivable that such a policy involves social costs which
largely exceed the potential benefits and consequently leads to an outcome inferior to the
nonintervention outcome. Clearly, the formal equivalence which exists between economic
and noneconomic instruments for optimizing external costs in standard textbook, single-
producer analyses of externalities breaks down when the number of actors, rather than
the level of the activity (per actor), becomes the optimization variable. As mentioned in
the foregoing section, this is the case for regulatory parking policies, where not the trip
length per actor but merely the number of trips can be affected. Hence, a reduction in the
number of trips to a level equal to N+ by means of quantitative measures involves merely
a quasi-optimum. ’
The lower half of Fig. 1 demonstrates the workings of regulatory parking policies.
The vertical axis depicts parking space occupation. The relationship between the number
of trips and the number of parking spaces occupied is 1:l by assumption, as every car is
assumed to get parked on publicly managed parking space. This is reflected by the
physical parking function (P) in Fig. lb, which has a 4S” angle with the horizontal axis.
The government may now wish to conduct regulatory parking policies consisting of a
reduction parking space supply to P*, consistent with the optimal inflow N*. Two funda-
mental flaws of such a scheme are immediately apparent in this simple model (which is in
fact particularly favourable for the efficiency of parking policies because of the assump-
tions made).
First, there is an information problem. Before making the decision to make the trip
by car, the potential car drivers have to know whether there will be a parking space
available to them. Otherwise, we run the risk of not realizing the intended reduction in
trips. Moreover, an acute shortage of parking spaces may then occur. This may give rise
to more instead of less congestion, caused by car drivers driving around in search of a
parking space. Such situations indeed occur in cities in which physically restrictive park-
ing policies are conducted (see Vleugel et al., 1990). Second, the efficiency problem
mentioned in the discussion of purely quantitative measures on car use applies here. There
is no guarantee that the most efficient trips will remain. Therefore, even if the informa-
tion problem would be overcome, a quasi-optimum may result.
Figure lc shows the workings of regulatory parking fees. The B curve depicts the
(derived) demand for parking spaces. Because it may be expected that no direct utility is
derived from parking as such, this curve is in fact a bid function; it describes the marginal
‘In this stylized setting, the costs and benefits associated with the outflow during the evening peak are equal
to those associated with the inflow during the morning peak. Car drivers can be assumed to be aware of the
costs of outflow. Therefore, the MPE and MSC curves in fact describe the benefits and costs associated with
round trips. This has no serious implications for the analysis; shifting all curves simultaneously downward by a
factor 2 to divide all costs and benefits over both trips does not affect the outcomes.
‘Under such a scheme, a market in driving rights might develop, which will eventually secure that the most
efficient trips indeed remain. In that case, the associated transaction costs are the additional social costs of the
system. Other possible forms of induced inefficiencies of the odd-even policy include the purchase of extra cars,
the choice of different (longer) routes (such as ring roads) to get as close as possible to the point of destination
while avoiding the zone where the policy is conducted.

7. Regulatory parking policies 147
maximum bid for parking spaces. This bid consists of the willingness to pay for making
the trip by car minus the private costs of doing so. Hence, the B curve is derived by
projecting the vertical distance between the MPB curve and the MPC curve in Fig. la, via
the geometrical mirror of panel (b), into Fig. lc. The parking fee’ F, depicted along the
horizontal axis, determines the number of parkers according to the B curve and hence the
amount of trips via the P curve. With free parking place supply (F = 0), PO parking
spaces will be occupied and an inflow of No cars takes place. Any positive value of F will
result in lower values of P and N because the marginal bid of a certain number of car
drivers will be exceeded. The optimal inflow N* can thus be realized by setting the
parking fee equal to F*.
In this stylized setting, the optimal parking fee is equivalent to the optimal road
price. First, the optimal fees are equal: F* = MPB* - MPC* = TMSK* - MPC* =
R *. Furthermore, the revenues will be the same, simply because every car is assumed to
get parked and to be subject to the parking policy: F* * P* = R* * N*. A comparable
result could be obtained for the optimal toll. In this setting, these instruments only differ
in the time of levying: before, during or after the trip.
The use of parking fees overcomes the two fundamental flaws associated with mere
restrictions on parking space supply. First, the use of parking fees involves far less
stringent information requirements. The existence and level of the fee is static informa-
tion, requiring a “once-and-for-all” information flow to potential car drivers to secure the
optimal inflow (assuming stable traffic demand). On the other hand, a physical restriction
on parking space supply requires dynamic information flows on the actual occupation of
the parking space. Second, a parking fee will discriminate according to willingness to pay,
which overcomes the efficiency problem.
The aforementioned information and efficiency arguments get a different meaning if
we allow commuters, subject to a scheme of a physical restriction on parking space
supply, to make their trips earlier to increase their chances of getting a parking space.
Such a rescheduling implies a loss in the car drivers’ utilities and in that way serves as a
substitute for the price mechanism. In the first place, the process of departure time
adaptation may to a certain extent take care of an efficient allocation. The car drivers
with the highest utility may, ceteris paribus, be expected to be prepared to make the
largest adaptations in departure times. Furthermore, the information argument may to a
certain extent be overcome if car drivers know an expected chance of getting a parking
space given the time of departure. However, it is crucial to note that this mechanism of
departure time adaptation involves important welfare losses. Whereas the revenues of
parking levies can be used for whatever purpose (perhaps even lump-sum compensations
of car drivers), the implicit price paid by leaving before the preferred time of departure is
forever bygone.
A closer consideration of dynamic aspects reveals a third fundamental flaw of physi-
cal restrictions on parking space supply as opposed to regulatory parking fees. In Fig. 2,
a second successive cohort of road users is added to the model. These may be shoppers,
using the urban road network and parking facilities in period S, just after the commuters
as considered in Fig. 1 have done so in period C. The new bold demand curve Ds gives
the demand for this second kind of trips. The MPC and MSC curves do not change (their
positions depend on the technical characteristics of the network and the vehicles used).
Assuming equal parking durations for all shoppers, which are assumed to be shorter than
the commuters’ parking duration, TMSC, can be postulated. Ng is the optimal inflow for
shoppers.
If the inflow of commuters has indeed been restricted to NE by levying the optimal
parking fee F$, the second (bold) horizontal axis describes the initial situation for the
shoppers: Pz parking spaces are already occupied by the commuters’ vehicles. Analogous
to the analysis in Fig. 1, the bold Ps and Bs curves can now be derived, as well as the
optimal parking fee F:. This levy guarantees the optimal inflow N3 and results in an
additional occupation of the parking space of (P$ - Pz).
‘The parking fee Fis not defined as an hourly tariff but as a total fee for the total parking time.

8. 148 E. VERHOEF, P. NIJKAMP andP. RIETVELD
Fig. 2. Regulatory parking policies for two successive groups of car drivers.
The sketched result that F$ is smaller than FE can be explained by the general
observation that the optimal parking levey for a certain cohort will be higher if the
parking duration time is longer and if the optimal level of congestion costs during the
time of driving are higher. Consequently, for the sake of efficiency, regulatory parking
policies require fees which are allowed to vary during the day, in particular in accordance
with variations in congestion costs during times of inflow and outflow.
The third fundamental flaw of a physical restriction on parking space supply that
becomes apparent now is that, if the commuters’ inflow is restricted to NE by means of a
physical restriction on parking space supply P $, there will be no parking space left for
the shoppers. This problem might be overcome by distinguishing between parking space
for commuters and parking space for shoppers. However, because the group of shoppers
also consists of successive cohorts, this does not really solve the problem. Because of the
cumulative nature of parking, physical restrictions on parking space supply, aiming at
reducing congestion at certain times of day, will in general lead to inefficiently strict
restrictions on parking space supply to successive cohorts.
A comparable problem emerges when the total capacity of the parking space is not
sufficient to provide the necessary parking space to the (otherwise optimal) traffic flows.
For instance, in Fig. 2, the capacity might be somewhere between PE and P$ . It is then
not optimal to allow PE to get parked. Rather, an intertemporal optimum requires an
extra mark-up on both fees to divide the capacity constraint efficiently among both
cohorts. Both parking fees need to be raised in such a way that the difference between the
marginal private benefits and the total marginal social costs is equal for both cohorts
while the capacity constraint is removed.
Thus, the cumulative nature of parking gives rise to a particular form of intertempo-
ral external costs, again due to a usual incompleteness of parking markets. When early
parkers are not confronted with the implicit search costs they pose on successive cohorts,
the first-come-first-served rationing principle will lead to inefficient patterns of parking
space occupation over the day. This is, in turn, accompanied by a nonoptimal distribution
of traffic flows over the day.
Consequently, apart from the aforementioned information argument and the tempo-
ral efficiency argument, we may distinguish the intertemporal efficiency argument as a
third underpinning of our conclusion that regulatory parking policies have the largest
potential efficiency if time-variable parking fees rather than physical restrictions are used.

9. Regulatory parking policies 149
Of course, parking fees and physical restrictions are not mutual exclusive instruments but
rather complementary measures. The use of parking fees will make restrictions on parking
space supply possible and even desirable with regard to efficiency in urban land use. On
the other hand, physical restrictions on parking space supply will most likely lead to
chaotic situations unless accompanied with an appropriate pricing policy. Undoubtedly,
the use of diagrams in the foregoing analyses poses some serious limitations on the model.
However, the aim of this section was merely to demonstrate that, in a setting in which
regulatory parking fees are equivalent to the first-best policy of road pricing, mere physi-
cal restrictions on parking space supply certainly are not.
4. A SPATIAL MODEL OF REGULATORY PARKING POLICIES
The foregoing analysis was essentially nonspatial. However, one of the potentially
strong features of parking policies is that the fees may be differentiated spatially. In this
section, we will elaborate on this option. In particular, we will see that, under certain
circumstances, it may be possible to overcome the difficulty of regulatory parking policies
not being capable of differentiation according to distance driven.
Congestion is often a spatially differentiated phenomenon. Especially near and in
CBDs (central business districts), roads tend to become increasingly congested due to
relatively high densities (for instance, in terms of capital-land and labour-land ratios).
The relationship between spatial patterns of (urban) land use and traffic congestion has
accordingly received ample attention in models of urban economics (see, for instance,
Fujita, 1989, and Kanemoto, 1980). Usually, the trade-off between land use in terms of
residential use versus use for transportation is considered in such models, as well as
optimal versus market-based locations and lot sizes of households. All of these issues,
however, are in fact of a long-run nature, and the optimal (tax and investment) policies
derived from these general equilibrium models are in practice bound to be severely ham-
pered by various rigidities. In particular, changes in patterns of land use, such as achiev-
ing optimal lot sizes and the optimal distribution of land use for various purposes, may
take at least decades to materialize. In this section, we develop a short-run counterpart to
these models, in which parking locations are studied. Instead of focusing on location
taxes, we will investigate the optimal spatial distribution of parking fees, taking residen-
tial and business locations as well as existing infrastructures as given, taking account of
space capacity effects in terms of interactions between parking and road use and allowing
for an alternative mode.
Following Fujita (1989) and Kanemoto (1980), we consider commuters in a monocen-
tric city, with the CBD in the centre and the residential area around it. By taking the
distance to the edge of the CBD as the only relevant spatial characteristic of each location,
we can treat this urban space as if it were one dimensional. Let N(r) denote the number
of households located beyond a distance r from the edge of the CBD, where r = 0 (we
ignore intra-CBD traffic by taking the CBD as a spaceless point). Assuming one com-
muter per household and assuming all employment to be concentrated in the CBD, N(r)
equals the number of commuters passing through the tangent at distance r during the
morning peak. Commuters are assumed to have two modes of transport at their disposal:
car use (denoted by C) and a general alternative mode (A). Having started their trip by
car, they can switch to the alternative mode wherever they like, but of course not after
having parked their car. lo Although road usage suffers from congestion, the alternative
mode is assumed not to be congested and therefore operates at constant marginal trans-
port cost per unit of distance. The tariff charged for using the alternative mode is equal
among all individuals (and is fixed in terms of price per unit of distance). All commuters
are assumed to be identical, except for their location and the psychological cost they
attach to using the alternative mode. Finally, we assume that regulation of transport does
not affect the overall demand for transportation (i.e., no commuter quits his or her job
‘@Thereverse (i.e., starting the trip by the alternative mode and subsequently switching to car use) is
assumed not to be possible (or relevant).

10. 150 E. VERHOEF,P. NIJKAMPand P. RIETVELD
as a result of these policies). Hence, such policies only affect the modal split and thus the
point at which the individual car driver switches to the alternative mode. ”
Because the overall demand for transport is assumed to be given, we can characterize
the individual commuter’s optimization problem as the minimization of his or her trans-
port cost, given his or her location:
MIN T:(d) = r: . (tA + c;) +
4
subject to r: 2 0
ri - r: 2 0 (1)
witha’ = lifr’ - rf > O;and6’ = Oifr’ - ri = 0
Tj gives the individual transport cost from the residential location ri to the CBD; ri
gives the point at which the individual takes the alternative mode; tA gives the (per unit of
distance, pud) tariff charged for using the alternative mode; ci gives the (pud) individual
cost associated with using the alternative mode in excess of the tariff and therefore reflects
individual tastes and cc gives the (pud) private cost of road transport, which depends on
the number of road users at that distance NC(r) and (possibly) on the number of cars
parked at r, which equals the number of commuters taking the alternative mode at r:
dN,(r)/dr (note that this term includes both commuters who switch mode at r and
commuters who reside at r and start their trip by the alternative mode). This latter effect
reflects the extent to which parked cars alongside roads may hinder ongoing traffic.
Furthermore, fp(r) denotes the (daily) parking fee at distance r; and the final term c,
indicates search cost for finding a parking space, which also depends on the number of
parkers at r and on a road-use dummy 6’: If the commuter travels all the way by the
alternative mode (6’ = 0), he or she can leave the car where it is and therefore faces no
search costs. The restrictions indicate that the optimal point of modal change is naturally
bounded by r: = 0 (the commuter travels all the way up to the CBD by car) and ri = ri
(the commuter merely uses the alternative mode).
Equation 1 may be extended easily to include evening peak transport costs by assum-
ing that travel patterns during the two peaks are (reversed) replicas. The (pud) terms tA ,
CA and cc then simply have to be doubled, whereas the other terms remain the same.
Search costs for a parking space when returning home at night may then simply be
incorporated by adding a term like the one already included. However, because the
analytics remain essentially the same for both models, we will refrain from an explicit
discussion of two peaks rather than one.
Road usage may be expected to be increasingly congested toward the CBD. This is
due both to an increasing (potential) number of commuters using the road and to decreas-
ing overall space and hence presumably decreasing road space toward the CBD. (For
instance, road space decreases quadratically toward the CBD in a circular city with a
fixed share of infrastructure in total land use). Figure 3 illustrates the resulting trade-off
that a commuter located at ri will make as opposed to the socially optimal choice.
Ignoring parking costs for a moment, the commuter will change mode at r:. Because he
or she causes an external congestion cost, however, the social cost of driving an additional
unit of distance by car (denoted see) are larger than the private cost cc, and rz gives the
socially optimal point of modal change (assuming optimal pricing for the alternative
mode).
We can be more precise about the individual optimization problem by solving the
Lagrangian implied by eqn 1:
“Given our interest in parking policies, N(r) merely includes commuters who possess a car that might be
used for commuting. Other commuters by definition travel by the uncongested alternative mode and are
therefore not of any relevance to this model.

11. Regulatory parking policies 151
Fig. 3. The privately and socially optimal point of modal change.
.gi = y-;tr;) _ xi . tri _ r;) (2)
The Kuhn-Tucker conditions to this Lagrangian are
+ A’ 1 0; r: 2 0 and r: * $- = 0 (3)
A
aci a.49
ah'= ri- ri 2 0; Xi 1 0 and Xi - ah' = 0 (4)
with 6’ = 1 if A’ = 0; and 6’ = 0 otherwise (5)
Figure 4 illustrates the possible outcomes implied by these conditions (we assume that the
second-order conditions are fulfilled). There are three regimes in which the commuter can
find himself or herself. First, if Xi = 0 (and hence 6’ = 1) and r; > 0, the relevant TL
curve is the one labelled “Multi-modal trip”: The commuter makes a multi-modal trip and
finds the optimal point of modal change by putting the first inequality in eqn 3 equal to
zero. The result will be an optimal point of modal change shown by rL”. Second, if A’ =
0 and r; = 0, the relevant TLcurve is the one labelled “Road trip”: The commuter makes
the trip entirely by car and consequently has ric as the optimal point of modal change.
CBD r=,,
r 0.c
‘F r
r’
i.A
A A
Fig. 4. Total individual transport costs as a function of the point of modal change for three types of commuters.

12. 152 E. VERHOEF,P. NIJKAMPand P. RIETVELD
Finally, if hi > 0, the Ti curve is decreasing in r:, as indicated by the one labelled
“Alternative mode trip”: ry is the optimal point of modal change and the commuter
makes the trip entirely by the alternative mode.
To find the optimal spatial distribution of parking fees, the features of individual
optimization as implied by eqns 3 through 5 should be compared to the conditions for
minimization of the social (total) transport cost T. This problem can be formulated as
follows:
+ (N(x) - NA (xl 1 * cc(N(x) - NA (xl, nA (x) )
+ y(x) . rz,.,
(x) + c
ietA(x)
6’ * c,(n, (xl)
1
dx (6)
dNA(r) E NA(r) = -n,(r)
subject to -
dr
N(0) = P = NA (0)
N(r,) = 0 = N._,(r,)
The objective function indicates that the aim is to minimize total transport cost over the
total urban area, which ranges from the CBD (r = 0) to the urban fringe (r = r,); 7(r)
represents the (pud) social transport cost at each distance r. Furthermore, c, gives the
(pud) marginal cost of the alternative mode, and y(r) represents the social land cost
associated with occupying a parking spot during the day. Strictly speaking, through the
assumption of given patterns of land use and by explicitly taking account of the conges-
tion costs of parked cars in terms of both hindering ongoing traffic and increasing search
costs, one might argue that this residual marginal opportunity cost of parking a vehicle
would be zero. However, we may interpret y(r) as a reflection of any additional cost
caused by parked cars (such as visual annoyance), or as an exogenous shadow price
reflecting that, in the long run, any acre of land used for parking actually does imply it
not to be available for alternative purposes. However, y(r) does not play a crucial role in
the subsequent analysis and may therefore be omitted without loss of generality. Finally,
note that the identity equating the total number of commuters to the sum of road users
and users of the alternative mode is substituted into the objective.
The first constraint defines the number of cars parked at r as nA(r), being the spatial
growth (i.e., the change) in the number of users of the alternative mode dN,(r)/dr =
k,.,(r). Furthermore, the first boundary condition specifies that all commuters (N(0) =
P) are travelling at the edge of the CBD; but because n, represents the parking of cars
and all (used) cars have to be parked before the (spaceless) CBD is reached, we also have
NA(0) = P. The second boundary condition simply states that no commuters live beyond
the city fringe rf.
Analogous to methods applied in continuous-time optimization problems, we may
define the continuous-space Hamiltonian as
H(NA (rMA (rhrl(r)) = dNA(rh~AW) + rl(r) - (-n,(r)) (7)

13. Regulatory parking policies 153
and set up the following Lagrangian:
d:=
s
o’ [Ht.) + i * NA (x)1 dx - h(r,) * NA(r,) - ~(0) - NA(0)] (8)
Maintaining the analogy with optimal control methods, NA is the state variable, nA is the
control variable, and T,J the adjoint (or costate) variable. The necessary first-order
is
conditions for a minimum are
(9)
d c c:
iENA
(r)
dlv, (r)
- cc(.) - (N(r) - NA(r)) -- (10)
aNAo-1
1
aH( * )
=-z-n
fiA A (11)
h(r)
NA (0) = P = N(0) (12)
NA (r,) = 0 = N(q) (13)
Because r) gives the shadow price for the state variable NA , it actually gives the marginal
value of keeping a commuter an additional unit of distance in the alternative mode
(measured outward from the CBD). Therefore, this value has a close relationship to the
spatial distribution of the optimal parking fees, which, through their impact on individual
behaviour as stated in eqn 3, should ideally induce individual commuters to behave so as
to satisfy the first-order conditions. From eqn 3, it follows that individual commuters
base their behaviour on the spatial pattern of the respective cost components of commut-
ing. Taking the space derivative of eqn 9, and after substitution of eqn 10, we obtain
(N(r) - NA (d) --
acm d C 6, . dcp(-)
anA (r) 1 + dy(r) + da’cp(-) + icnA (I) d% (r)
dr dr dr dr
d cc:
+ CA +
ieNA (r)
dlv, (r)
- cc(-) - (N(r) - NA(r))
aw)
*-
aNA (r)
=
o
(14)
as a necessary condition for the optimal spatial allocation of parking. A comparison of
eqn 14 with individual optimizing behaviour as implied by eqns 3 through 5 reveals that
optimality requires the following pricing strategies:
tA = CA (13

14. 154 E. VERHOEF,P. NIJKAMPand P. RIETVELD
.- f%(*) d c 6i.s
d&(r) = dNc(r) anA(r) + hn” (I) A
dr dr dr
. &(*) ; h(r) (16)
+ NC(r)
aN,(r) dr
where N,(r) is substituted back for N(r) - NA(r). Equation 15 simply implies that the
(pud) tariff for the alternative mode should equal its (pud) marginal cost. It is now easy
to see why it was permissible to speak so loosely of the general alternative mode. As long
as the (uncongested) alternatives are priced at their marginal cost, individual maximizing
behaviour is efficient. That is, it does not matter that for some commuters r; is the point
at which they for instance start walking (and presumably CA = 0 and only CL matters),
whereas for others it may be the point at which they take public transport (and presum-
ably both c, and CL matter). It may also be the point at which they start walking to the
nearest public transport stop, if we explicitly take account of the fact that public transport
usually cannot be used from every distance preferred. Marginal cost pricing ensures
efficiency, and we can leave choices among the alternative modes to the market (as long
as the alternatives are indeed uncongested). Equation 16 defines the slope of what we may
call the optimal parking fee gradient. Clearly, in the static setting with given patterns of
land use and given patterns of car ownership, we need not worry about the actual values
of parking fees, but merely about their spatial distribution. From eqn 16, it follows that
the slope of the parking fee gradient should exactly reflect the (pud) increase in the
external part of the three types of congestion considered (parking-road, parking-parking
and road-road, respectively) as well as the increase in the residual parking cost.
One of the most interesting aspects of eqn 16 is that it is apparently possible to
overcome the difficulty of regulatory parking policies not being capable of differentiation
according to distance driven by specifying the appropriate spatial pattern of parking fees,
making individuals respond to (spatial) parking fee differentials. As it stands, the model
even allows a relaxation of the assumption of each commuter travelling all the way up to
the CBD. As long as they travel in the same direction, optimal parking fee gradients as
described by eqn 16 may be derived. However, the scope for such policies will of course
increasingly be eroded when the actual spatial patterns within the city move away from
the monocentric, unidirectional (i.e., linear or at least radial) city shape assumed earlier.
Clearly, the same objection can be raised against many other concentric models applied
in urban economics.
The fact that only spatial parking fee differentials matter, and not the absolute
values of parking fees, hinges on the rigidities assumed. In particular, because commuters
are assumed not to respond in terms of car ownership or in terms of job, and because neither
households nor employers are assumed to relocate, the constant term in the actual parking
fee gradient chosen is nothing more than a lump-sum tax to which commuters cannot re-
spond. Without explicit relaxation of these assumptions, we note that a choice of
(17)
implies that commuters living at rf (and owning a car) are charged exactly for their
external costs because the relevant feepY(rAi) they face then always amounts to
+
s7
ri
ac,(.)
NC(X) - -dx
aNc (x)
+ y(rfi,)
Additionally, spatially differentiated lump-sum subsidies (i.e., independent of choices on
modal split and points of modal change) to car owners of

15. Regulatory parking policies 155
s(r) =
sI
‘f
NC(X) *
*
a&(x) x (19)
imply that all car-owning commuters face a budget effect equal to the external costs they
cause, because then we find
s(r’) = Nc(r>)
act(*)
f,(rL) - -
an,
0-A)
+ C
bnA (r)
6’. dcP(‘) +
dn, (r-2) s ri
r:
NC (x) - *x
C
+ -f(r>) (20)
Clearly, as commuters without a car do not pay parking fees, nor should they receive the
subsidies s(r) given by eqn 19.
Apart from satisfying some sense of equity, the additional policies of eqns 17 and 19
may turn out to provide optimal incentives in terms of car ownership and residential
location, issues that were left aside in this model.
5. CONCLUSION
This article presented an economic analysis of the possibilities and effects of regula-
tory parking policies. Although parking levies are the first-best payment vehicle for
charging the use of scarce parking space, such levies can only be a second-best alternative
to (electronic) road pricing for the regulation of road transport externalities. The reason
is that parking policies take place at the end of a trip, which generally rules out differenti-
ation according to trip length or roads followed. Furthermore, differentiation according
to vehicle specific externalities also seems only to be possible to a limited extent. There-
fore, regulatory parking policies can only serve as a satisfactory instrument for optimizing
external costs which are (relatively) insensitive to individual trip lengths and routes fol-
lowed. With this in mind, we considered regulatory parking policies aimed merely at
optimizing congestion on an urban road network and optimizing the activity of parking
itself.
In Section 3, a simple diagrammatic analysis was presented, which allowed for a
comparison of two basic forms that regulatory parking policies might take: regulatory
parking fees versus physical restrictions on parking space supply. Three reasons why the
use of (time-variable) parking fees is superior to mere physical reductions in parking
space supply emerged: the information argument, the temporal efficiency argument and
the inter-temporal efficiency argument. Section 4 contained a spatial parking model, indi-
cating that under certain assumptions it is possible to overcome the difficulty of regula-
tory parking policies not being capable of differentiation according to distance driven by
specifying the appropriate spatial pattern of parking fees, making individuals respond to
(spatial) parking fee differentials.
Although regulatory parking policies are merely a second-best alternative to road
pricing, there may be a particular advantage in favour of parking policies. Because
parking policies are already existent in many cities, the extension to regulatory parking
policies as discussed in this article may be easier than the introduction of a completely
new system such as ERP. Apart from the possibility from a technical point of view, that
parking policies may receive broader social acceptance, their introduction may also be
easier than the introduction of ERP. Consequently, parking policies may have a political
advantage.
However, there are a number of fundamental disadvantages of regulatory parking
policies in comparison to a system of road pricing. First, all external costs of road
transport will to some extent depend on trip length and roads followed. Therefore,
regulatory parking policies will always contain some distortive elements and will therefore
remain a second-best option by nature. Second, there are two groups of car drivers that

16. 156 E. VERHOEF, P. NIJKAMP and P. RIETVELD
will be able to escape the parking policies: those who are parking on private parking
space, and the so-called through-flow. The first problem might be tackled by additional
taxation of private parking spots (although the time element in optimal parking fees will
probably have to be given up). The existence of through-flow, however, seems to be an
insoluble problem for regulatory parking policies (see Glazer & Niskanen, 1992). A third
fundamental drawback of parking policies is the risk of adverse spillover effects to adja-
cent areas. Fourth, enforcement of the policy is crucial but may in the long run turn out
to be much more expensive than the introduction and operation of ERP. Finally, there
may be unwarranted effects on the firms and population in the area under the regime.
Despite these fundamental objections, regulatory parking policies -preferably sup-
ported by supplementary instruments such as fuel taxes -are likely to offer an interesting
alternative for urban traffic regulation because road pricing is not likely to be introduced
on a large scale in the short run. The potential power of regulatory parking policies has
recently been underlined by several empirical studies (see Small, 1992, pp. 126-128, for
an overview).
Acknowledgement-The authors would like to thank two anonymous referees for useful comments.
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