Transpn. Res.-A. Vol. 29A, No. 2, pp. 141-156,1995                                                                        ...
142                              E.   VERHOEF, NIJKAMP P. RIETVELD                                            P.       and...
Regulatory parking policies                                         143      A first important matter in the evaluation of...
144                               E. VERHOEF, NIJKAMP                                            P.       andP. RIETVELDex...
Regulatory parking policies                                       145we can concentrate on the fundamental relations that ...
146                                E. VERHOEF,P. NIJKAMPand P. RIETVELDthe TMSC curves) is at its maximum.’ The regulator’...
Regulatory parking policies                                     147maximum bid for parking spaces. This bid consists of th...
148                           E. VERHOEF, P. NIJKAMP andP. RIETVELD               Fig. 2. Regulatory parking policies for ...
Regulatory parking policies                                     149Of course, parking fees and physical restrictions are n...
150                             E. VERHOEF,P. NIJKAMPand P. RIETVELDas a result of these policies). Hence, such policies o...
Regulatory parking policies                                   151                       Fig. 3. The privately and socially...
152                              E. VERHOEF,P. NIJKAMPand P. RIETVELDFinally, if hi > 0, the Ti curve is decreasing in r:,...
Regulatory parking policies                                                      153and set up the following Lagrangian:  ...
154                         E. VERHOEF,P. NIJKAMPand P. RIETVELD                                         .- f%(*)      d  ...
Regulatory parking policies                                      155                              s(r)      =             ...
156                                E.   VERHOEF, P. NIJKAMP   and P.   RIETVELDwill be able to escape the parking policies...
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  1. 1. Transpn. Res.-A. Vol. 29A, No. 2, pp. 141-156,1995 Copyright 0 1995ElsevierScienceLtd Pergamon Printed in Great Britain. All rights reserved 0965~8564/95 $9.50 + .OO 09658564(94)EOO14-Z 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. INTRODUCTIONOne of the most serious and apparent challenges facing urbanized areas nowadays is thehandling of the urban transportation problem. The term nowadu_y~ is perhaps slightlysuperfluous, as transport has traditionally generated various social costs-which havealways led to more stress in urban areas for reasons of density. For instance, with theintroduction of the automobile in the beginning of this century, it was hoped that finallya 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 pastdecades, it is increasingly recognized that, although mobility as such is an important sideto 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 maydistinguish problems associated with increasing environmental disruption (including noiseannoyance), growing congestion, severe safety problems and expanding use of urban landfor transportation purposes. The realization of socially acceptable (or, ideally, optimal) levels of (road) transportrequires a careful evaluation of the associated social costs and benefits. Due to theexistence of external costs of road transport, this process cannot simply be left to themarket. ’ External costs can loosely be interpreted as the unpriced use of others’- oftenpublic-goods.’ For the external costs of road transport, such goods include a cleanenvironment, silence, time, safety and free access to public space. External costs are animportant 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 shiftedto society instead. Consequently, efficient resource allocation (Pareto efficiency) cannotbe 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, compensatefor its external costs. Road transport’s benefits are usually either internal benefits or pecuniary benefits (seeVerhoef, in press). *The reverse does not hold: Not every free good (or bad) is an external benefit (or cost). See Verhoef (inpress) for a more thorough discussion on the definition of external effects. 141
  2. 2. 142 E. VERHOEF, NIJKAMP P. RIETVELD P. andcongestion) 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 roadpricing. 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 toexternal effects. Currently popular concepts such as optimal road prices and optimaleco-taxes are in fact Pigouvian taxes. The key characteristic of such a fee is that theactivity is taxed for the marginal external costs in the social optimum. Thus, it correctsfor 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 regardroad pricing as the first-best instrument for traffic regulation. However, although theHong 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, certainlyin the short run. The main objections usually raised against ERP include (a) privacyconsiderations; (b) equity considerations; (c) costs of introduction and operation, possi-bly exceeding the expected welfare benefits; (d) the possibility of car drivers followingescape routes (avoiding toll points and adding to road transport’s external effects in otherareas); (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 anyrate, in many countries plans for introducing ERP seem to be hushed up for the timebeing and attention is focused on alternative instruments for traffic regulation. In TheNetherlands, for instance, such alternatives include the introduction of the spitmignet(peak hour permits) for the Rimcity and a policy change from demand-oriented parkingpolicies toward regulatory parking policies. According to the Dutch government, regula-tory parking policies are an “indispensable part of an integral transport policy aimed atreducing the growth of road traffic” (Tweede Kamer der Staten-Generaal, 1991-1992). Intransport economics, expectations are modest as far as the actual implementation of ERPis 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 welfareeconomic 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 andcontains an economic analysis of the ins and outs of regulatory parking policies. InSection 2, the scope for parking policies in traffic regulation is discussed. Section 3contains 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 regulatoryparking 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 beused to relieve some of the social pressures caused by excessive road traffic. Becausevirtually every car has to be parked at the end of a trip, parking policies may indeed offera 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 forthe regulation of traffic flows. The reason for its superiority is that the regulatory tax canbe differentiated according to various relevant trip-specific characteristics, such as triplength, time of driving, route followed and vehicle used. Because these dimensions to alarge extent determine the (marginal) external costs of a trip, they accordingly determineoptimal Pigouvian taxes (that is, the optimal road prices) (see Verhoef et al., 1993, forthe welfare economic effects of second-best undifferentiated regulatory fees). ‘According Dawsonand Catling(1986), “Results to wereextremely encouraging. . . the Hong Kong systemis accurate, reliable and robust enough to be extended to a full system” (p. 134).
  3. 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 substitutefor this first-best instrument. In general, regulatory parking policies are only apt forinfluencing numbers of trips and cannot differentiate according to trip lengths and routesfollowed, 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 orroute followed is not optimal and may in some (derived) respects-in particular, in termsof associated incentives to change behaviour-even be counterproductive (see Verhoef etal., 1993). In the terminology of Himanen et al. (1992), the risk of government (orresponse) failures is indeed present. For instance, suppose that the emission of a certain pollutant (say, C02) per trip is ina fixed relation to the length of the trip. Using parking levies instead of road pricing forcharging road users for this external cost necessarily means that each individual road userwill be charged some weighted average of the individual marginal external costs generatedrather 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 feesaccording to individual trip lengths. Hence, following such a policy implies a relativeimplicit 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 fordifferentiation 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 neverbe 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 areused for affecting external costs depending on dimensions according to which they cannotdifferentiate. To determine the scope for regulatory parking policies, it is necessary tomap out the dimensions determining the external costs per trip and the dimensions alongwhich effective differentiation can take place using such policies. In Table 1, the mainexternal cost categories of automobile trips are roughly classified according to somerelevant dimensions, where the dimension of route followed is hierarchically split intoroads followed and area of driving (that is, an X in “Roads Followed” necessarily impliesan X in “Area of Driving,” whereas the opposite does not hold). Of course, the table isnot unambiguous and only serves to provide a first impression (for instance, externalcosts of some forms of air pollution actually do depend on the area and/or the time ofdriving, 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 UsedExternal 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 XDifferentiation possible using regulatoryparking policies (X = easily possible;. = hardly possible) X X
  4. 4. 144 E. VERHOEF, NIJKAMP P. andP. RIETVELDexternal 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 fourcolumns for determining the scope of regulatory parking policies given the inherentlimitations concerning trip lengths. First, if well performed, parking policies can differentiate according to the time ofdriving; that is, provided that time-variable parking fees are used. Furthermore, parkingpolicies 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 ofdriving (namely, the area around the parking place). On the other hand, parking policiescannot discriminate according to the actual roads followed. Finally, parking policies seemhardly suitable for adaption according to the type of vehicle parked (except perhaps for arough distinction into private cars, vans, buses and trucks). As a consequence of these limited potentials of regulatory parking policies, they donot 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 thatthe 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 Table1. 4 Simply, the less these criteria are met, the more regulatory parking policies lose theirapplicability. For the sake of argument, however, in the following section we will simplyassume that these criteria are indeed met. In addition, we will assume that each individualcar 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 activityof 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 spacewithout any (efficient) price being charged. Clearly, efficiency requires the parkers to beconfronted with such external costs of parking. This may be the second goal of regulatoryparking policies. ’ The scope for regulatory parking policies is limited, considering the wide range ofexternal costs resulting from road transport. In accordance with the foregoing, we willassume that the regulatory parking policy to be analyzed in the remainder of this articleserves the following two goals: (a) optimizing the level of congestion on an urban roadnetwork, and (b) optimizing the activity of parking itself. In a more comprehensivesetting, regulatory parking policies would preferably be supported by supplementaryinstruments 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 spacesupply. Our basic model of regulatory parking policies is set in a simplified world. Wehave already mentioned the following two assumptions: (a) Each individual car driveruses an equal amount of urban road kilometres for his or her trip, and (b) congestion isequally 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, whichare 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 additionalexternal congestion costs. Under the same assumptions and restrictions, regulatory parking policies may againbe used for coping with such effects. ‘For instance, it has been calculated that the total value of land used for parking in The Netherlandsamounts to 47 billion Dutch guilders, while only a small proportion of this sum is actually paid for by theparkers. For every Dutch car, on average three parking spots are available, which means 190 million squaremeter for the Dutch vehicle stock. Often, the parking spot is more expensive than the car occupying it (TweedeKamer der Staten-Generaal, 1991-92). Assuming that only one third of all parking takes place for free on publicland, 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. 5. Regulatory parking policies 145we can concentrate on the fundamental relations that exist between parking and mobilityand, in particular, on the performance of both types of parking policies just mentionedwithout having to worry about parking policies’ other second-best aspects as discussed inVerhoef 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 themorning peak. Every potential commuter will have a certain willingness to pay for makingthe trip by car, which will depend on the benefits associated with the trip and on theavailability and costs of alternative modes. Ranking the potential commuters accordingto descending willingness to pay yields the aggregate marginal private benefit (MPB)curve- the demand curve (D)- for using the urban road network. The marginal privatecost of using the network is given by the MPC curve. The horizontal part of the curveindicates 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 andwith 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 isthat an individual car driver will experience the average social costs (including congestioncosts) as his or her marginal private cost. It is then straightforward to derive the marginalsocial 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 ofoccupying a parking space during a working day. In this graphical approach, it has to beassumed that all commuters have equal parking duration. The TMSC curve can then befound by shifting the MSC curve upward by the social cost of parking. Hence, the sociallyoptimal number of trips in the morning peak is N*, where the marginal social costs areequal 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 measuredrather than the traditional variable of traffic flow. By doing so, theoretical problems (backward bending costcurves 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. 6. 146 E. VERHOEF,P. NIJKAMPand P. RIETVELDthe TMSC curves) is at its maximum.’ The regulator’s job is therefore to reduce the freemarket 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 optimalroad price, charging the individual car driver for the optimal marginal external costs ofcongestion and the social costs of occupying a parking space and therefore securing theoptimal inflow N* to emerge. Furthermore, one may try to accomplish N* by posingsome sort of a quantitative restriction on the inflow. A practical application of such apolicy can be found in cities like Athens, where cars with even (odd) number plates areallowed to drive on even (odd) days only. However, a somewhat closer inspection of thedemand curve reveals that, if such a policy indeed leads to a number of trips equal to theoptimal 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 themost 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 theworst case, the trips (roughly) between (No - N+) and N, are left over, yielding muchsmaller benefits. It is therefore conceivable that such a policy involves social costs whichlargely exceed the potential benefits and consequently leads to an outcome inferior to thenonintervention outcome. Clearly, the formal equivalence which exists between economicand noneconomic instruments for optimizing external costs in standard textbook, single-producer analyses of externalities breaks down when the number of actors, rather thanthe level of the activity (per actor), becomes the optimization variable. As mentioned inthe foregoing section, this is the case for regulatory parking policies, where not the triplength per actor but merely the number of trips can be affected. Hence, a reduction in thenumber of trips to a level equal to N+ by means of quantitative measures involves merelya 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 numberof trips and the number of parking spaces occupied is 1:l by assumption, as every car isassumed to get parked on publicly managed parking space. This is reflected by thephysical 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 areduction 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 infact 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 tripby car, the potential car drivers have to know whether there will be a parking spaceavailable to them. Otherwise, we run the risk of not realizing the intended reduction intrips. Moreover, an acute shortage of parking spaces may then occur. This may give riseto more instead of less congestion, caused by car drivers driving around in search of aparking space. Such situations indeed occur in cities in which physically restrictive park-ing policies are conducted (see Vleugel et al., 1990). Second, the efficiency problemmentioned in the discussion of purely quantitative measures on car use applies here. Thereis 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 isderived 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 equalto those associated with the inflow during the morning peak. Car drivers can be assumed to be aware of thecosts of outflow. Therefore, the MPE and MSC curves in fact describe the benefits and costs associated withround trips. This has no serious implications for the analysis; shifting all curves simultaneously downward by afactor 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 mostefficient trips indeed remain. In that case, the associated transaction costs are the additional social costs of thesystem. 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 destinationwhile avoiding the zone where the policy is conducted.
  7. 7. Regulatory parking policies 147maximum bid for parking spaces. This bid consists of the willingness to pay for makingthe trip by car minus the private costs of doing so. Hence, the B curve is derived byprojecting the vertical distance between the MPB curve and the MPC curve in Fig. la, viathe geometrical mirror of panel (b), into Fig. lc. The parking fee’ F, depicted along thehorizontal axis, determines the number of parkers according to the B curve and hence theamount of trips via the P curve. With free parking place supply (F = 0), PO parkingspaces will be occupied and an inflow of No cars takes place. Any positive value of F willresult in lower values of P and N because the marginal bid of a certain number of cardrivers will be exceeded. The optimal inflow N* can thus be realized by setting theparking fee equal to F*. In this stylized setting, the optimal parking fee is equivalent to the optimal roadprice. 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 toget parked and to be subject to the parking policy: F* * P* = R* * N*. A comparableresult could be obtained for the optimal toll. In this setting, these instruments only differin the time of levying: before, during or after the trip. The use of parking fees overcomes the two fundamental flaws associated with mererestrictions on parking space supply. First, the use of parking fees involves far lessstringent 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 theoptimal inflow (assuming stable traffic demand). On the other hand, a physical restrictionon parking space supply requires dynamic information flows on the actual occupation ofthe 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 ifwe allow commuters, subject to a scheme of a physical restriction on parking spacesupply, 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 asubstitute for the price mechanism. In the first place, the process of departure timeadaptation may to a certain extent take care of an efficient allocation. The car driverswith the highest utility may, ceteris paribus, be expected to be prepared to make thelargest adaptations in departure times. Furthermore, the information argument may to acertain extent be overcome if car drivers know an expected chance of getting a parkingspace given the time of departure. However, it is crucial to note that this mechanism ofdeparture time adaptation involves important welfare losses. Whereas the revenues ofparking levies can be used for whatever purpose (perhaps even lump-sum compensationsof 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 commutersas considered in Fig. 1 have done so in period C. The new bold demand curve Ds givesthe demand for this second kind of trips. The MPC and MSC curves do not change (theirpositions 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 optimalparking 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. 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 generalobservation that the optimal parking levey for a certain cohort will be higher if theparking duration time is longer and if the optimal level of congestion costs during thetime of driving are higher. Consequently, for the sake of efficiency, regulatory parkingpolicies require fees which are allowed to vary during the day, in particular in accordancewith variations in congestion costs during times of inflow and outflow. The third fundamental flaw of a physical restriction on parking space supply thatbecomes apparent now is that, if the commuters’ inflow is restricted to NE by means of aphysical restriction on parking space supply P $, there will be no parking space left forthe shoppers. This problem might be overcome by distinguishing between parking spacefor commuters and parking space for shoppers. However, because the group of shoppersalso consists of successive cohorts, this does not really solve the problem. Because of thecumulative nature of parking, physical restrictions on parking space supply, aiming atreducing congestion at certain times of day, will in general lead to inefficiently strictrestrictions on parking space supply to successive cohorts. A comparable problem emerges when the total capacity of the parking space is notsufficient to provide the necessary parking space to the (otherwise optimal) traffic flows.For instance, in Fig. 2, the capacity might be somewhere between PE and P$ . It is thennot optimal to allow PE to get parked. Rather, an intertemporal optimum requires anextra mark-up on both fees to divide the capacity constraint efficiently among bothcohorts. Both parking fees need to be raised in such a way that the difference between themarginal private benefits and the total marginal social costs is equal for both cohortswhile 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 earlyparkers 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 parkingspace occupation over the day. This is, in turn, accompanied by a nonoptimal distributionof 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 athird underpinning of our conclusion that regulatory parking policies have the largestpotential efficiency if time-variable parking fees rather than physical restrictions are used.
  9. 9. Regulatory parking policies 149Of course, parking fees and physical restrictions are not mutual exclusive instruments butrather complementary measures. The use of parking fees will make restrictions on parkingspace supply possible and even desirable with regard to efficiency in urban land use. Onthe other hand, physical restrictions on parking space supply will most likely lead tochaotic 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 whichregulatory 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 potentiallystrong features of parking policies is that the fees may be differentiated spatially. In thissection, we will elaborate on this option. In particular, we will see that, under certaincircumstances, it may be possible to overcome the difficulty of regulatory parking policiesnot being capable of differentiation according to distance driven. Congestion is often a spatially differentiated phenomenon. Especially near and inCBDs (central business districts), roads tend to become increasingly congested due torelatively 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 hasaccordingly 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 ofresidential use versus use for transportation is considered in such models, as well asoptimal 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) policiesderived 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, maytake at least decades to materialize. In this section, we develop a short-run counterpart tothese models, in which parking locations are studied. Instead of focusing on locationtaxes, 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 ofspace capacity effects in terms of interactions between parking and road use and allowingfor 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 thedistance 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 numberof households located beyond a distance r from the edge of the CBD, where r = 0 (weignore 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 themorning 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 bycar, they can switch to the alternative mode wherever they like, but of course not afterhaving parked their car. lo Although road usage suffers from congestion, the alternativemode 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 equalamong all individuals (and is fixed in terms of price per unit of distance). All commutersare assumed to be identical, except for their location and the psychological cost theyattach to using the alternative mode. Finally, we assume that regulation of transport doesnot 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) isassumed not to be possible (or relevant).
  10. 10. 150 E. VERHOEF,P. NIJKAMPand P. RIETVELDas a result of these policies). Hence, such policies only affect the modal split and thus thepoint at which the individual car driver switches to the alternative mode. ” Because the overall demand for transport is assumed to be given, we can characterizethe 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; rigives the point at which the individual takes the alternative mode; tA gives the (per unit ofdistance, pud) tariff charged for using the alternative mode; ci gives the (pud) individualcost associated with using the alternative mode in excess of the tariff and therefore reflectsindividual tastes and cc gives the (pud) private cost of road transport, which depends onthe number of road users at that distance NC(r) and (possibly) on the number of carsparked 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 andcommuters who reside at r and start their trip by the alternative mode). This latter effectreflects 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 ofparkers at r and on a road-use dummy 6’: If the commuter travels all the way by thealternative mode (6’ = 0), he or she can leave the car where it is and therefore faces nosearch costs. The restrictions indicate that the optimal point of modal change is naturallybounded 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 beincorporated by adding a term like the one already included. However, because theanalytics remain essentially the same for both models, we will refrain from an explicitdiscussion of two peaks rather than one. Road usage may be expected to be increasingly congested toward the CBD. This isdue 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. (Forinstance, road space decreases quadratically toward the CBD in a circular city with afixed share of infrastructure in total land use). Figure 3 illustrates the resulting trade-offthat 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 heor she causes an external congestion cost, however, the social cost of driving an additionalunit of distance by car (denoted see) are larger than the private cost cc, and rz gives thesocially optimal point of modal change (assuming optimal pricing for the alternativemode). We can be more precise about the individual optimization problem by solving theLagrangian implied by eqn 1: “Given our interest in parking policies, N(r) merely includes commuters who possess a car that might beused for commuting. Other commuters by definition travel by the uncongested alternative mode and aretherefore not of any relevance to this model.
  11. 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 thesecond-order conditions are fulfilled). There are three regimes in which the commuter canfind himself or herself. First, if Xi = 0 (and hence 6’ = 1) and r; > 0, the relevant TLcurve is the one labelled “Multi-modal trip”: The commuter makes a multi-modal trip andfinds the optimal point of modal change by putting the first inequality in eqn 3 equal tozero. 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 makesthe 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 AFig. 4. Total individual transport costs as a function of the point of modal change for three types of commuters.
  12. 12. 152 E. VERHOEF,P. NIJKAMPand P. RIETVELDFinally, 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 commutermakes the trip entirely by the alternative mode. To find the optimal spatial distribution of parking fees, the features of individualoptimization as implied by eqns 3 through 5 should be compared to the conditions forminimization of the social (total) transport cost T. This problem can be formulated asfollows: + (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 thetotal 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 costassociated with occupying a parking spot during the day. Strictly speaking, through theassumption 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 searchcosts, one might argue that this residual marginal opportunity cost of parking a vehiclewould be zero. However, we may interpret y(r) as a reflection of any additional costcaused by parked cars (such as visual annoyance), or as an exogenous shadow pricereflecting that, in the long run, any acre of land used for parking actually does imply itnot to be available for alternative purposes. However, y(r) does not play a crucial role inthe 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 usersand 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 spatialgrowth (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 carsand all (used) cars have to be parked before the (spaceless) CBD is reached, we also haveNA(0) = P. The second boundary condition simply states that no commuters live beyondthe city fringe rf. Analogous to methods applied in continuous-time optimization problems, we maydefine the continuous-space Hamiltonian as H(NA (rMA (rhrl(r)) = dNA(rh~AW) + rl(r) - (-n,(r)) (7)
  13. 13. Regulatory parking policies 153and 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 thecontrol variable, and T,J the adjoint (or costate) variable. The necessary first-order isconditions 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 marginalvalue 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 thespatial distribution of the optimal parking fees, which, through their impact on individualbehaviour as stated in eqn 3, should ideally induce individual commuters to behave so asto satisfy the first-order conditions. From eqn 3, it follows that individual commutersbase 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 ofeqn 14 with individual optimizing behaviour as implied by eqns 3 through 5 reveals thatoptimality requires the following pricing strategies: tA = CA (13
  14. 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) drwhere 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 easyto see why it was permissible to speak so loosely of the general alternative mode. As longas the (uncongested) alternatives are priced at their marginal cost, individual maximizingbehaviour is efficient. That is, it does not matter that for some commuters r; is the pointat 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 thenearest public transport stop, if we explicitly take account of the fact that public transportusually cannot be used from every distance preferred. Marginal cost pricing ensuresefficiency, and we can leave choices among the alternative modes to the market (as longas the alternatives are indeed uncongested). Equation 16 defines the slope of what we maycall the optimal parking fee gradient. Clearly, in the static setting with given patterns ofland use and given patterns of car ownership, we need not worry about the actual valuesof parking fees, but merely about their spatial distribution. From eqn 16, it follows thatthe slope of the parking fee gradient should exactly reflect the (pud) increase in theexternal part of the three types of congestion considered (parking-road, parking-parkingand 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 toovercome the difficulty of regulatory parking policies not being capable of differentiationaccording to distance driven by specifying the appropriate spatial pattern of parking fees,making individuals respond to (spatial) parking fee differentials. As it stands, the modeleven allows a relaxation of the assumption of each commuter travelling all the way up tothe CBD. As long as they travel in the same direction, optimal parking fee gradients asdescribed by eqn 16 may be derived. However, the scope for such policies will of courseincreasingly be eroded when the actual spatial patterns within the city move away fromthe 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 appliedin urban economics. The fact that only spatial parking fee differentials matter, and not the absolutevalues of parking fees, hinges on the rigidities assumed. In particular, because commutersare assumed not to respond in terms of car ownership or in terms of job, and because neitherhouseholds nor employers are assumed to relocate, the constant term in the actual parkingfee 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 theirexternal 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 onmodal split and points of modal change) to car owners of
  15. 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 theycause, 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 thesubsidies s(r) given by eqn 19. Apart from satisfying some sense of equity, the additional policies of eqns 17 and 19may turn out to provide optimal incentives in terms of car ownership and residentiallocation, 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 forcharging the use of scarce parking space, such levies can only be a second-best alternativeto (electronic) road pricing for the regulation of road transport externalities. The reasonis 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 accordingto 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 optimizingexternal costs which are (relatively) insensitive to individual trip lengths and routes fol-lowed. With this in mind, we considered regulatory parking policies aimed merely atoptimizing congestion on an urban road network and optimizing the activity of parkingitself. In Section 3, a simple diagrammatic analysis was presented, which allowed for acomparison of two basic forms that regulatory parking policies might take: regulatoryparking fees versus physical restrictions on parking space supply. Three reasons why theuse of (time-variable) parking fees is superior to mere physical reductions in parkingspace supply emerged: the information argument, the temporal efficiency argument andthe 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 byspecifying 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 roadpricing, there may be a particular advantage in favour of parking policies. Becauseparking policies are already existent in many cities, the extension to regulatory parkingpolicies as discussed in this article may be easier than the introduction of a completelynew system such as ERP. Apart from the possibility from a technical point of view, thatparking policies may receive broader social acceptance, their introduction may also beeasier than the introduction of ERP. Consequently, parking policies may have a politicaladvantage. However, there are a number of fundamental disadvantages of regulatory parkingpolicies in comparison to a system of road pricing. First, all external costs of roadtransport will to some extent depend on trip length and roads followed. Therefore,regulatory parking policies will always contain some distortive elements and will thereforeremain a second-best option by nature. Second, there are two groups of car drivers that
  16. 16. 156 E. VERHOEF, P. NIJKAMP and P. RIETVELDwill be able to escape the parking policies: those who are parking on private parkingspace, and the so-called through-flow. The first problem might be tackled by additionaltaxation of private parking spots (although the time element in optimal parking fees willprobably have to be given up). The existence of through-flow, however, seems to be aninsoluble problem for regulatory parking policies (see Glazer & Niskanen, 1992). A thirdfundamental 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 outto be much more expensive than the introduction and operation of ERP. Finally, theremay 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 interestingalternative for urban traffic regulation because road pricing is not likely to be introducedon a large scale in the short run. The potential power of regulatory parking policies hasrecently been underlined by several empirical studies (see Small, 1992, pp. 126-128, foran overview).Acknowledgement-The authors would like to thank two anonymous referees for useful comments. REFERENCESButton K. J. (1992). Alternutivesto roudpricing. Paper presented to the OECD/ECMT/NFP/GVF Conference on The Use of Economic Instruments in Urban Travel Management, Basel, Switzerland.Dawson J. A. L. and Catling I. (1986). Electronic road pricing in Hong Kong. Transpn. Res., ZOA, 129-134.Else P. K. (1981). A reformulation of the theory of optimal congestion taxes. J. Trunsport Econom. Policy, IS, 217-232.Else P. K. (1982). A reformulation of the theory of optimal congestion taxes: A rejoinder. J. Trunsport Econom. Policy. 16,299-304.Evans Alan W. (1992). Road congestion: The diagrammatic analysis. J. PoliticulEcon., 100, 21 l-217.Evans Andrew W. (1992). Road congestion pricing: When is it a good policy? J. TransportEconom. Policy, 26, 213-243.Fujita M. (1989). Urban Economic Theory: Land Use and City Size. Cambridge University Press, Cambridge, U.K.Glazer A. and Niskanen E. (1992). Parking fees and congestion. Reg. Sci. Urban Econ., 22, 123-132.Hau T. D. (1991). Economic Fundumentals of Rood Pricing: A Diugrammatic Analysts. Revised draft. The World Bank, Washington, DC.Himanen V., Nijkamp P. and Padjen J. (1992). Environmental quality and transport policy in Europe. Transpn. Res., 26A, 147-157.Kanemoto Y. (1980). Theories of Urbun Externalities. North-Holland, Amsterdam.Knight F. H. (1924). Some fallacies in the interpretation of social cost. Q. J. Economics, 38,582~606.Mohring H. (1989). The role of fuel taxes in controlling congestion. In Transport PO/icy, Munugement and Technology Towurds ZOOI. Proceedings of the Fifth World Conference on Transport Research, Vol. 1, The Role of Public Sector in Transport, pp. 243-257. WCTR, Yokohama.Nash, C. A. (1982). A reformulation of the theory of optimal congestion taxes: A comment. J. Transporr Econom. Policy, 16,295-299.Pigou A. C. (1920). Weulthand Welfare. Macmillan, London.Small K. A. (1992). Urban Transportution Economics. Fundamentals of Pure and Applied Economics, 51, Hanvood, Chur etc.Tweede Kamer der Staten-Generaal (1991-1992). Uitvperingsnotitie Parkeerbeleid. Hoeksteen en Toetssteen van her Verkeers-en Vetvoersbeleid (in Dutch). Vergaderjaar 1991-1992, 22.383, 1 and 2, Sdu, ‘s-Gravenhage.Verhoef E. T. (in press). External effects of road transport: Some theory und u survey of empirical results. TRACE discussion paper TI 93-35, Tinbergen Institute, Amsterdam-Rotterdam.Verhoef E. T., Nijkamp P. and Rietveld P. (in press). Second-best regulation of road transport externalities: The case of regulatory parking policies. TRACE discussion paper TI 93-209, Tinbergen Institute, Am- sterdam-Rotterdam.Vleugel J. A., van Gent H. A. and Nijkamp P. (1990). Transport and environment: Experiences with Dutch policies. In J. P. Barde and K. J. Button (Eds.), Trunsporr Policy and the Environment, pp. 121-156. Earthscan. London.

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