metadata: authors: 0: author: Anas,Alexandros
1: author: De Sarkar,Sayan
2: author: Timilsina,Govinda R.
count: Morocco
docna: 0: docna: The optimal mix of pricing and
            infrastructure expansions to alleviate traffic congestion
            and in-bus crowding in grand Casablanca
docty: Policy Research Working Paper
subtopic: Intelligent Transport Systems,Services & Transfers to Poor,Economic Assistance,Access of Poor to Social Services,Disability,Transport Services,Transport in Urban Areas,Urban Transport,Transport Economics Policy & Planning
teratopic: Social Protections and Labor,Urban Development,Macroeconomics and Economic Growth,Poverty Reduction,Transport
abstracts: cdata!: Like in many large cities in developing
            countries, traffic in Grand Casablanca, Morocco, is
            congested and public buses are crowded. These conditions are
            alleviated by a combination of supply-side infrastructure
            expansions, such as more buses and new road capacity, and
            demand-side pricing instruments, such as parking and fuel
            taxes. Using an empirical urban transportation mode choice
            model for Casablanca, this study finds a mix of these
            expansion policies and pricing instruments to alleviate
            congestion and maximize aggregate social welfare. The
            optimal mix is sensitive to the marginal costs of the
            infrastructure expansions. If the city were to spread out in
            its periphery where land constraints do not exist and land
            is available at lower prices, a supply-side instrument,
            particularly the optimal expansion of roads, would be far
            more effective in achieving welfare gains than the use of
            optimal pricing instruments without new roads. By contrast,
            if the city were to densify in already built-up areas, land
            and other physical constraints and the high price of land
            may leave expensive “elevated roads” as the only option. In
            this case, demand-side instruments together with the
            elevated roads would equally contribute to reduce traffic
            congestion and in-bus crowding.
geo_reg_key: 517202,517191
repnme: repnme: The optimal mix of pricing and
            infrastructure expansions to alleviate traffic congestion
            and in-bus crowding in grand Casablanca
display_title: The optimal mix of pricing and
            infrastructure expansions to alleviate traffic congestion
            and in-bus crowding in grand Casablanca
listing_relative_url: /research/2018/06/30218517/optimal-mix-pricing-infrastructure-expansions-alleviate-traffic-congestion-in-bus-crowding-grand-casablanca
topicv3: Transport m1326661 135,Traffic Congestion m1326913 1817,Social Assistance m1327201 1466,Mass Transit m1327372 1726,Traffic Management m1583399 4231
publishtoextweb_dt: 2018-06-28T00:00:00Z
historic_topic: Social Protections and Labor,Urban Development,Macroeconomics and Economic Growth,Poverty Reduction,Transport
no_of_pages: 44
author_keys: 0: author_key: 670534
1: author_key: 940446
model_extractions: WPS8501 Policy Research Working Paper 8501 The Optimal Mix of Pricing and Infrastructure Expansions to Alleviate Traffic Congestion and In-Bus Crowding in Grand Casablanca _Alex Anas Sayan De Sarkar Govinda Timilsina_ Development Economics Development Research Group June 2018
Policy Research Working Paper 8501

# **Abstract**

Like in many large cities in developing countries, traffic in Grand Casablanca, Morocco, is congested and public buses are crowded. These conditions are alleviated by a combination of supply-side infrastructure expansions, such as more buses and new road capacity, and demand-side pricing instruments, such as parking and fuel taxes. Using an empirical urban transportation mode choice model for Casablanca, this study finds a mix of these expansion policies and pricing instruments to alleviate congestion and maximize aggregate social welfare. The optimal mix is sensitive to the marginal costs of the infrastructure expansions. If the city were to spread out in its periphery where land constraints do not exist and land is available at lower prices, a supply-side instrument, particularly the optimal expansion of roads, would be far more effective in achieving welfare gains than the use of optimal pricing instruments without new roads. By contrast, if the city were to densify in already built-up areas, land and other physical constraints and the high price of land may leave expensive “elevated roads” as the only option. In this case, demand-side instruments together with the elevated roads would equally contribute to reduce traffic congestion and in-bus crowding.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at gtimilsina@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **The Optimal Mix of Pricing and Infrastructure Expansions to Alleviate Traffic Congestion and In-Bus Crowding in Grand Casablanca**

Alex Anas, Sayan De Sarkar and Govinda Timilsina<sup>1</sup>

**Keywords** : Traffic congestion, Sustainable urban transportation, Morocco, Casablanca

**JEL Classification** : R13, R41

> 1 Anas and De Sarkar are in the Department of Economics, State University of New York at Buffalo. Timilsina is a Senior Research Economist in the Development Research Group, The World Bank. The research reported here was supported by funding from DFID through the Strategic Research Program Trust Fund. Results reported here and any opinions expressed are those of the authors and not of the World Bank’s. The authors are grateful to Mustafa Kahramane for providing data and feedback to the analysis.
# **The Optimal Mix of Pricing and Infrastructure Expansions to Alleviate Traffic Congestion and In-Bus Crowding in Grand Casablanca**

# **1. Introduction**

How should congestion be alleviated in large and rapidly growing urban areas in developing countries? In practice, policy makers may think and act somewhat narrowly, considering only some instruments that are more politically desirable, and evaluating each instrument in isolation without optimizing an overall objective. Economists have emphasized that congestion should be alleviated by pricing it efficiently, preferably by means of first-best congestion tolls or more feasibly by instruments such as parking fees, fuel taxes or public transit subsidies. This emphasis on demand-side instruments is important, but supply-side policies, particularly expansion of road capacity or adding buses, tram lines and trains, are necessary along with the demand side instruments. We need to know the relative efficiency of each demand and supply-side option, how they interact with each other when they are used jointly, and the mix of instruments that maximizes social welfare.

In this study, our demand-side pricing instruments are a higher fuel tax, a higher parking tax and a higher bus fare subsidy. Our supply-side policies are to add more buses to the existing fleet, to expand the tram system, and to increase road capacity. This study finds the optimal level of each instrument or infrastructure expansion when used by itself and the optimal levels of all when they are used simultaneously. We measure the welfare gain by monetizing annual consumer surplus increases and by adding the annual profits or losses from bus and tram operations plus the public revenues from any tax instruments such as fuel tax or parking tax minus the annualized costs of any bus fleet or road capacity expansions. Social welfare gains are then expressed as a percentage of consumer income.

Greater Casablanca is the largest urban agglomeration in Morocco. It spans 0.6% of the national territory, holds 12% of the population and generates 20% of the national GDP (World Bank, 2017; page 2). It encompasses the Casablanca Municipality, and the Nouaceur, Mohamedia and Mediouna Provinces. Like many large urban areas in developing countries, Greater Casablanca has experienced a population increase caused by economic growth and the rise in urban wages, the emergence of new economic opportunities relative to the rest of Morocco, and the 2
expansion of the city causing increased economic activities and jobs in the urban periphery. All these factors have increased the demand for urban transport services and have put a strain on the existing transportation infrastructure. There has been an under-investment in the urban transport sector and the projected investment in this sector for major cities in Morocco including Greater Casablanca is around 320 billion MAD over a time horizon of 10 years,<sup>2</sup> i.e. 32 billion MAD per year.<sup>3</sup> The public urban transit system remains highly inadequate and overcrowded. Several public and private operators faced bankruptcies in the past decade (World Bank, 2016) and this has exacerbated the poor service quality in public urban transport. New tram lines became operational since 2012, but the market share of this mode was only 2% in 2014 while the cost of its implementation is high. According to World Bank (2016), a Bus Rapid Transit (BRT) option would have incurred only 29% of the tramway cost.

Our model of Grand Casablanca is highly aggregated spatially due to data limitations on geographically detailed land and labor markets. Nevertheless, we calibrate a model of modal split in commuting that explains the user choices among private car, motorcycle, shared taxi service, public bus and tram. The distribution of these choices among the modes determines endogenously the equilibrium road congestion, the travel times by mode and the equilibrium in-bus and in-tram crowding. Out of the five vehicle types, four modes (private car, motorcycle, taxi and bus) share the same aggregate road capacity and impose delays on each other causing congestion which lengthens travel time and increases fuel consumption due to lower speeds. In Greater Casablanca, a taxicab carries 5.5 passengers on average, while the average bus occupancy is reported as106 passengers. In contrast, a motorcycle carries one passenger-driver, and a private car 1.4 passengerdrivers on average. The average tram occupancy is reported as 324 passengers per two connected tram cars and the average capacity (seating and standing) of a tram is 454 passengers. In carequivalent units in our baseline, adjusting for the load caused by the four vehicle types, a persontrip by shared taxi places an almost three times lower load on road capacity than does a persontrip by private car or motorcycle, while a person-trip by bus places a load that is almost 38 times lower than that of a private car.

Travel by bus or tram is more time consuming due to lower speed, passenger aggress-egress times to and from stations and waiting times at stations. Adding buses or trams have several effects.

> 2 The World Bank Report No. 1214332-MA, 2017

> 3 MAD: Moroccan Dirham. The average exchange rate in 2014, our baseline year, was 8.5 MAD per US $.

3
First, a higher frequency of service reduces average waiting times. Second, more buses alleviate road congestion when enough travelers switch to bus from the other modes. Switches from cars to shared taxi and to bus can also increase in-bus crowding unless a sufficiently large number of buses is added to the fleet. While the number of buses and the bus fare are public sector decision variables, we treat the shared-taxi industry as a private sector competitive industry with a perfectly elastic supply of taxis. When the fuel tax, the bus supply or anything else changes, we assume that taxi fares and the supply of taxis adjust so that taxi operators continue to make zero economic profit. In the case of taxis, a higher fuel cost becomes reflected in a higher taxi fare and is shared among the taxi riders, but in the case of bus the higher fuel cost may not be reflected in the fare as the fare is set as a policy instrument, and it is socially optimal to subsidize bus travel as doing so relieves road congestion at the expense of more in-bus crowding. The crowding is optimally alleviated by adding more buses.

A summary of our main results is as follows. Reduction of congestion improves social welfare because it saves travelers’ time which has an opportunity cost. The size of the social welfare gain from the optimal level of the three demand side instruments (fuel tax, the parking fee and the bus fare), when they are implemented simultaneously, amounts to 0.8% of income. The optimal fuel tax rate is 4.7 times the baseline rate, while the optimal parking tax is 7 times the baseline parking tax and the optimal bus fare is zero. The three instruments are policy substitutes. The parking tax is a per-vehicle-trip instrument paid solely by cars and motorcycles. Hence, a higher parking tax induces a switching to shared-taxi, bus and tram because such switching makes it possible to completely avoid the parking tax. The fuel tax is an instrument that is equivalent – in our aggregated model – to a per-kilometer tax and is paid by all modes except tram. The fuel tax also induces a shift towards the higher-occupancy modes of shared-taxi, bus and tram. In the case of switching to tram or to bus completely avoids the fuel tax but the switching to shared-taxi softens the impact of the fuel tax because of the sharing effect. The bus fare subsidy turns out to be a very weak instrument because the baseline fare is already quite low. All three demand-side instruments induce more bus crowding keeping the bus fleet constant. The parking tax and the fuel tax have very similar welfare effects and all three instruments, when used together are strongly sub-additive in their welfare effects because they are policy substitutes. The welfare gain due to the optimal fuel tax when it is used as a single instrument is 0.76% of income, that of the optimal parking tax is 0.77% and that of the optimal bus fare is only 0.04%. When all three are jointly 4
optimized, then the welfare effect is only 0.8%. Hence, they are strongly sub-additive because 0.76% + 0.77% + 0.04% = 1.57% > 0.8%. This confirms that the three instruments are strong policy substitutes.

The social welfare gains from jointly optimizing with respect to the number of buses and the road capacity, depend on whether or not space for road expansion is available. Assuming that the city expands in its peripheral areas, especially towards the south and the southeast, where land is available at cheaper prices and there does not exist a land constraint to expand the city, expansion of the roads into those areas would be the most desirable option to reduce congestion in greater Casablanca. In this case, the social benefits of expanding roads and adding new busses would be 9.17% of income. Achieving this optimum requires increasing the number of buses 2.96 times and expanding road capacity 2.78 times from their baseline values. If the city gets denser and denser with more high-rise buildings in the Casablanca-Mohammedia-Rabat corridor, expanding the existing roads or adding new roads in these areas would be difficult. One solution to this would be building elevated roads (vertical expansion of road capacity) on the existing roads that requires little additional land. In this case, the cost per road kilometer would be much higher and the welfare benefits much smaller when compared to the case of the ground-level (horizontal) expansion of roads in the periphery. We find, however, that the social benefits of building elevated roads would still be higher than using only the demand side instruments. There is also an important difference between expanding the fleet of buses versus expanding the road capacity. The former causes a reduction in waiting times and in congestion by inducing a shift from car, motorcycle and taxi to bus which results in a more efficient use of the existing road capacity and has welfare gains of 0.9% of income. When all policies (demand-side and supply-side) are jointly optimized, the social welfare increases to 1% (with the vertical expansion of roads), or to 9.3% (with the horizontal expansion of roads).

Our results suggest that in trying to achieve social welfare gains it is much more important to expand critical infrastructure than to fine-tune pricing decisions that affect the demand-side directly. But the demand-side instruments are more effective in reducing fuel consumption and carbon emissions. They cut these by 20% while the supply-side policies cut them by 3% to 11% depending on whether roads are optimally expanded vertically or horizontally. Another important difference between demand-side and supply-side optima is that the optimal demand-side instruments have adverse income effects that reduce consumer utility despite the congestion 5
improvements that they induce, but the optimal supply-side expansions can raise utility. But the demand-side instruments raise a great deal of revenue which can defray a large part of the public cost of implementing the supply-side infrastructure expansions, thus reducing the need for supplementary taxation or debt-financing. Hence, there is good reason to jointly implement the demand-side and the supply-side policies. We find that joint optimization of the demand-side instruments and the infrastructure expansions reduces by a third, the public deficit from bus and tram operations and from ground level road construction. We also present a zero public deficit constrained-optimum, in which road construction and the fuel tax are the only policies used. We show that, in this case, the road construction, under the ground level expansion of the road capacity, can be cut back from its optimal level until the fuel tax completely pays for the cost of the new roads, still generating large welfare gains.

Section 2 explains the technical details of the model. Section 3 describes how the model’s parameters are calibrated and includes a table with data and calibration results, some data aspects being relegated to tables and discussions in the Appendix. Section 4 explains how the social welfare analysis is done, and section 5 presents the optimal policy simulation results with accompanying tables. Section 6 concludes and mentions possible extensions.

# **2. The Model**

## **2.1 Commuting preferences, mode choice probabilities and expected utility**

We specify the utility function of a worker-consumer making work trips (commutes) over a year by travel mode _m_ , as follows: where, _Em_ is the utility constant of mode _m_ , _Gm_ is the one-way daily commute time by mode _m_ . _y_ is the annual income of the consumer in MAD, _gm_ is the two-way daily monetary cost of a commute by mode _m_ in MAD and we assume that there are 250 work days per year. _um_ is the random utility of mode _m_ distributed over the population of commuters. The choice of modes available for the consumers are � = 1 (private car), � = 2 (motorcycle), � = 3 (taxi), � = 4 (bus) and � = 5 (tram). We ignore non-motorized modes as they are used for much shorter trips. The monetary cost of the five modes are: 6
(2a) For private car ( _m_  1) and motorcycle ( _m_  2) , the first term of (2a) is the vehicle ownership cost, _Om_ ,that includes vehicle purchase and tax, and insurance and other costs that are annualized and then prorated to a day, and then multiplied by  _m_ , the inverse of the vehicle passenger occupancy which for private car and motorcycle, includes the driver. _t_ is the parking tax. While for private car, motorcycle and taxi, passenger occupancy is taken as exogenous, for bus and tram it is endogenously determined as we shall see. In the second term of (2a), we have the after-tax fuel costs, where _dm_ is the one-way travel distance in kilometers,<sup>_F_</sup> _m_<sup>is the liters of fuel consumed</sup> per kilometer, _p_ is the market price of fuel per liter, and  is the ad valorem fuel tax rate. Fuel is assumed to be perfectly elastically supplied and, hence, we take _p_ as exogenous. Note that the tax factor 1  can be attached to either the fuel price _p_ or to the distance _dm_ without any consequence because the model is aggregated. Hence, because of the aggregation a per liter fuel tax and a per kilometer tax are fully equivalent and not distinguishable. In contrast, the parking tax, _t_ , is a per-trip tax paid only by the private car and motorcycle modes. For taxi ( _m_  3), bus ( _m_  4) and tram ( _m=_ 5) the only cost to the passenger is twice the one-way fare<sup>_f_</sup> _m_<sup>, shown in</sup> (2b).

The coefficient of ln �� in (1) has two parts.  0 0 is common to all the modes and helps calibrate the marginal disutility of commuting time as we shall see; and ����, with  1 0, depends on mode _m_ according to  _m_ , the in-vehicle standing passenger density as a measure of in-vehicle crowding. We set  1   2   3  0 , since for private car, motorcycle and taxi there is no in-vehicle crowding. For bus and tram,  4 and �� are set to be the average standing passenger density which will be endogenously determined as, 7
/ Seat, Sin MUTT, _—= _ ~~~~Yot%1Pm)TM~~ MUDIm ~~K~~ = <u>s552~</u> VOTn VOTm = MRS(DlmTTm) = ~~TopiMUTTm~~ =_ ~~—eo(Yot¥iPm) (y—2509m)~~ VOT = Y)=1Pn X VOT Um Pn = ~~——am~~ AUm m=1Pm = 1 m! =1,..,5 E{max(U;, Uz, U3, U4, Us] = ~~=~~ In(S5.-1 EXP AU)
time. The vehicle fuel efficiency is<sup>_e_</sup> _m_ .<sup>Then fuel consumption in liters per kilometer is according</sup> to Davis and Diegel (2004)<sup>5</sup> , <!-- Start of picture text --> 3.785 0.122619  1.17211  10  2 sm  6.413  10  4 sm 2  1.8732  10  5 sm 3 <br>Fm ( sm , em )  em 1.6093     3  10  7 sm 4  2.4718  10  9 sm 5  8.233  10  12 sm 6  , (6)<br>Figure 1: Fuel consumption and traffic speed<br>Car Motorcycle Taxi Bus<br>0.45<br>0.4<br>0.35<br>0.3<br>0.25<br>0.2<br>0.15<br>0.1<br>0.05<br>0<br>16 26 36 46 56 66 76 86 96 106 116 126 136<br>Fuel consumption (liters/km) Traffic speed (km/hr)<br><!-- End of picture text --> Figure 1 is a plot of the fuel consumption in liters of fuel per kilometer as a function of traffic speed in kilometers per hour, for each vehicle type. Bus is the least and motorcycle the most fuelefficient<sup>6</sup> mode of transport. The fuel consumption per kilometer is similar for private cars and for taxis.

# **2.3 Traffic load**

One-way person-trips are calculated as the expected number of commuters choosing mode _m_ , given that an exogenous total of _N_ workers, each making one trip per day, commute by one of the five modes: _Tm_  _NPm_ . These person-trips by mode are multiplied by the reciprocal of the average vehicle occupancy rates for that mode (that is by person-trips per vehicle) to calculate the total vehicle-trips by that mode. The vehicle-trips are then converted to car-equivalent traffic units by multiplying with, l�, the mode-specific car-equivalence traffic load factors. Finally, these carequivalent units are aggregated over all modes to calculate the total traffic load:

> 5 They calculated fuel use in gallons/mile from speed in miles/hour. We converted the equation to liters/km by making adjustments shown in (6). First, the speed in kilometer/hour is divided by 1.6093 km/mile in order to get the speed in miles/hour. It is then used to predict gas consumption in gallons/mile. Second, the result is multiplied by 3.785 liters/gallon to get fuel use in liters/mile and divided by 1.6093 to get fuel use in liters/km.

> 6 According to the U.S. Department of Energy, the average fuel economy of car and motorcycle are 23.41 and 43.54 miles per gallon respectively. The difference between their average fuel economy is around 46%.

9
# **2.4 The bus and tram occupancy rates**

The bus and tram occupancy rate given by 1/  4 and 1/  5 respectively, which are endogenously determined by supply, the daily number of vehicle journeys and the respective daily person-trips. For the bus, we have bus supply (number of buses), _B_ , the daily number of bus journeys  4 ,<sup>7</sup> and the person-trips by bus<sup>_T_</sup> 4<sup>:</sup> where  0 0 and 0 <<sup></sup> 1<sup>< 1 are parameters we will calibrate. A bus running in a particular route</sup> will travel from one end of the route to the other, completing a bus journey; and such a journey is made by a bus  4 times a day. From (8a), we observe that the bus occupancy rate will increase with �� at a decreasing rate by 0 ��� �1. It is realistic to increase the bus occupancy rate nonlinearly with trips, since eventually there will not be enough space for passengers to stand inside the bus and the occupancy cannot increase any further. Adding buses increases the total traffic load (7) if the additional buses do not fill up much with passengers, but can decrease the traffic load as more people switch to bus from the other modes, if by (8a) the occupancy rate becomes high enough. For tram, we have tram supply (TRAM), and we specified the daily number of tram journeys ��, and the daily person-trips by tram:

# **2.5 Waiting times**

Private car and motorcycle have no waiting times. The waiting time of taxis is taken as exogenous. Relying on simulations by Meignan, Simonin and Koukam (2007), we model the  waiting time for bus as _G_ 4, _wait_  with the parameters   0, 1    0 that we will calibrate. _B_<sup></sup> Note that when a new bus is added to the existing fleet of buses, waiting time is reduced which

> 7 The average daily number of journeys that a taxi, a bus and a tram make are ��, �� and �� respectively.

10
(m = 4) G4 inv m Np:g = —A Ym=1/o + ¥1Pm)Pm(1 — Pn) "P:g -_ ~~_2509m _~~ _ ~~ Ak dim <u>(y-2509m)</u> PrQl Pr): "P:pm = —AY1Pm IN Gm (1 — Pr)
When the cost of operating a taxi rises, as it does in our simulations of an increase in the fuel tax rate,  , assuming no change in the demand function for taxis, some taxi operators would exit the industry and equilibrium would be re-established at higher taxi fares. But the higher fuel tax impacts a car or motorcycle passenger more severely, since the higher fuel cost is shared by fewer co-passengers. Hence, higher fuel taxes, other things constant, cause passengers to switch to taxis which then causes a higher demand for taxis at the higher fuel tax rate. This, as we will see causes more taxi operators to enter the industry while taxi fares rise. Equilibrium taxi fares are calculated by solving (13) for<sup>_f_</sup> 3<sup>.</sup> Buses are operated by a public authority and bus operations in the base case are shown to be subsidized. We treat the fare per bus trip as a policy instrument. Its value can be made positive or zero. So, unlike the case of taxis, when the fuel tax rises buses become more expensive to operate and, with fares unchanged, they become less profitable to operate. When fuel taxes rise, many trips switch to bus. By doing so they escape the impact of higher fuel taxes on their budgets, and reduce road congestion which improves welfare provided the disutility from in-bus crowding is not too severe.

Trams are also a publicly operated mode of transport and tram networks are located in the Casablanca Municipality. The expansion of tram is done by reallocating a portion of the existing road capacity for the tram network. In this situation, half of the road capacity in the relevant roads are allocated for tram expansion. The decrease in road supply is treated as a parameter for tram expansion. A tram expansion makes it easier for a commuter to switch to tram from the other modes of transport.

# **3. Calibration**

The model formulated in section 2 is empirically implemented for Greater Casablanca. Our model approximates the baseline data of 2014 displayed in Table 1, in Table 2 and in column “Base” of Table 3. The targeted share of transportation related expenditure to the average income across all modes is around 0.135.<sup>8</sup> We set the average monthly wage to match this share. We got

> 8 According to the Bureau of Labor Statistics, in the U.S. the average expenditure in 2014 was 13.5% of annual income. <u>https://www.bls.gov/opub/reports/consumer-expenditures/2014/home.htm.</u>

12
an average monthly wage of 7,500 MAD i.e. 45 MAD/hour, assuming 8 hours of work per day and 20.833(=250/12) work days per month<sup>9</sup> . The annual income is _y_ = 90,000 (7,500 x 12) MAD.

The fleet of vehicles in this study are either diesel-fueled (58%) or petrol-fueled (42%). The after-tax consumer price of fuel in the model is taken as the weighted average of the price of diesel and the price of petrol or 9.42 MAD/liter.<sup>10</sup> The supplier fuel price, in the model is _p_ = 6.12 MAD/liter. The excise tax rate on fuel in the base year of 2014 is 0.54 which means that about 35% of the after-tax consumer price of fuel is tax and 65% is the supplier price.

The total road area<sup>11</sup> is 22.7 square kilometers which is used in the denominator of the congestion function (9). The parameter, _A_ , is calibrated to match the base travel times. The average daily number of bus journeys, i.e.<sup></sup> 4<sup>, is 7.8. If we multiply the number of journeys with the average</sup> bus occupancy per journey, i.e. 106 riders, and by the total bus supply, then we get the average daily bus ridership given in the column “Base” of Table 3. In the case of taxi, given the average taxi occupancy of 5.5 riders per journey along with the total number of taxis of 15,000 and the total daily taxi ridership, we calibrate for the total journeys,<sup></sup> 3<sup>, made by a taxi in a day on average,</sup> which comes to 29 daily journeys. For tram, the average capacity of a double tramcar is 454 which includes 118 for seating and 336 for standing. There are 37 tramcars currently operating in Casablanca, and the average number of daily journeys made by a tram i.e. �� �� 10. Given these parameters along with the daily transit ridership information, the average occupancy per tram per trip is 324 passengers calculated from (8b). The standing area of bus, �� is 10.7 square meters. The average seating capacity of a bus is 45. Therefore, 61 out of 106 passengers are standing which gives a high crowding density of 5.75 passengers per meter squared. The bus, as modeled here, is a 12 meter by 2.5 meter vehicle giving a floor area of 30 square meters. Hence the ratio of seating

> 9 From the Survey of Income and Household spending (2006, 2007), the 2007 average monthly household income in Morocco was 6,124 MAD (for cities) and 3,954 (for rural areas). We found no other data, but we think that the imputation of average monthly income from the transportation expenditure share is reasonable.

> 10 The after-tax prices of diesel and petrol are about 9 MAD and 10 MAD per liter respectively.

> 11 The percentage of urbanized land area occupied by roads in developing countries is lower than it is in developed countries. The length of roads by type were available. Assuming widths for the road types, the road area in Grand Casablanca to be around 10% (see Appendix). In Western Europe it would be 15% - 20% and in the U.S. 30% of the urbanized area. <u>https://people.hofstra .edu/geotrans/eng/ch6en/conc6en/ch6c1en.html</u>

13
to standing area for bus is about 2 to 1. Similarly, there are 206 passenger standing inside a double tram in a single journey. The double tram is 65 meter by 2.65 meter which has a standing area of 84 square meters. The average standing passenger density for the double tram is 2.45. The tram has more space for standing relative to seating which makes the ratio of seating to standing to be around 1.

In the calculation of the monetary cost of the fuel for bus, we are using average distance of a bus journey as<sup>_D_</sup> 4<sup>=15.6 km. And the bus rider’s average travel distance is 8 km which corresponds</sup> to an in-vehicle travel time of 32 minutes. A bus rider’s average distance and the in-vehicle travel times are then used to calculate the speed of the bus which is around 15 km/hr. The tram rider’s average distance is 6 km and the reported operational speed of 18 km/hr is used to calculate an average in-vehicle travel time of 20 minutes.

**Table 1:** Mode characteristics and calibrated parameter values (2014 baseline)

|**Mode characteris**<br>|**tics**<br>||||
|---|---|---|---|---|
|Private car|Motorcycle|Taxi|Bus|Tram|
|Modal shares,<br>_m_<sup>_P_</sup><br>33|13|40|12|2|
|Utility constants,<br>_m_<sup>_E_</sup><br>13.6|11|11.8|9.5|0|
|Travel distances,<br>_m_<sup>_d_ (km)</sup><br>13.4|9.6|11.69|8|6|
|Fuelconsumption, ��(liters/km)<br>0.088|0.06|0.09|0.43|0|
|Fuel efficiency factor,<br>_m_<sup>_e_</sup><br>1.09|0.63|1.09|3.26|0|
|Relative slowness,<br>_m_<br><br>0.43|0.60|0.45|1|0|
|Vehicle occupancy,<br>1<br>_m_<sup></sup><br><br>1.4|1|5.5|106|324|
|Car equivalent load of a vehicle,l�<br>1|0.75|1.4|2|0|
|Trip load factor,<br>_m_<br>_m_<br>l<br>0.714|0.75|0.254|0.019|0|
|In-vehicle time/trip,<br>,<br>_m inv_<br>_G_<br>23|23|21|32|20|
|Speed,��(km/hour)<br>35|25|33|15|18|
|Waiting time/trip,<br>,<br>_Gmwait_<br>0|0|5|11.5|6|
|Monetary cost/trip,<br>_m_<sup>_g_</sup><br>42.1|54.1|7.09|3.45|5.7|
|Journeys per taxi, bus and tram:��, ��,��<br>0|0|29|7.8|10|

The congestion parameter values in equation (9) are partially taken from the literature, and the rest are calibrated to provide reasonable congestion estimates. The value of the congestion 14
parameter �� is the inverse of the free flow travel speed, assumed to be 60 km/hour. ��, is set to 0.15, which is a standard value in the literature. The exponential congestion parameter, ��, is important for capturing the convexly increasing effect of traffic volume on travel time. The calibrated value of �� is 1.21. The procedure used to calibrate for �� is explained in Appendix A.1. Given the parameter values of the congestion function, the aggregate road area, _A_ , is calibrated to match the in-vehicle travel time for private car shown in Table 1. The traffic congestion index i.e. the ratio of load to road capacity is 11.9.

The research on public transportation crowding has provided an understanding of the effect of in-vehicle public transit crowding on the travel behavior of its passengers. Li and Hensher (2011) provide a brief literature review on this topic and suggest potential areas for future research. Batarce et. al (2016) have estimated the effect of standing passenger density on the in-vehicle travel time disutility for Santiago de Chile, Chile. This study calculated elasticity values of bus demand for different standing bus passenger densities. A corresponding elasticity formula is (12). The average standing in-bus passenger density considered for this study is 5.75 per square meter. Given this level of passenger density, the calibrated elasticity value for bus is - 0.17.<sup>12</sup> We assume the same in-vehicle travel time disutility parameter, ��, for both bus and tram. Litman (2017) presented a comprehensive analysis of transportation elasticities by year and country. Most of the studies mentioned in Litman (2017) are from middle to high income countries and give travel time elasticities by trip purpose, by peak/off-peak period, by road type (urban/rural), by length of the time period (short term/long term) and by mode. There is a wide variation in these travel time elasticities. SACTRA (1994) concluded that the elasticity with respect to travel time is -0.5 in the short term and -1 in the long run. Anas and Timilsina (2015) used the income-weighted value of -0.60 for Beijing as an average elasticity of the choice probability with respect to travel time. Because Morocco is a low-income country, its travel time elasticity could be similar to Beijing. It will be lower than in high and middle income countries due to the relatively low value of time. We set an average travel time elasticity of -0.68. For travel cost elasticities, we selected from the values mentioned in Dunkerley, Rohr and Daly (2014) and ranging between -0.1 and -0.5. Morocco’s

> 12 In Batarce et. al (2016), the passenger density elasticity is ��������1 � ���. The values of travel time, share of bus and bus-crowding disutility parameters are 28 (min), 0.41 and 0.007 respectively. Given a standing passenger density of 1 per square meter, the elasticity value derived in their study is -0.12. With ln��, �� is matched with the value of passenger density elasticity corresponding to 1 passenger per square meter.

15
population should be more sensitive to the monetary cost of travel compared to the richer developed economies. We set the average elasticity with respect to monetary cost as -0.43.

We fix the value of � to 0.25 and take the value of �� as 0.04. We calibrate �� and � from equations (10) and (11). We use these parameters to derive the value of the marginal utility of income given in Table 2. We then use these parameter values in (3b) to calculate the Value of Time (VOT) as 26 MAD/hour which is around 58% of the hourly wage, and within the range suggested in the empirical literature<sup>13</sup> , that VOT is around one-half of the wage rate for commute trips, highest for business trips and lowest for discretionary leisure travel. In the bus waiting time function, the parameter � is from Meignan, Simonin and Koukam (2007) and the constant, �, is calibrated to match the base data on bus waiting times. The constant parameter for the bus occupancy function, ��, is calibrated from (8). The waiting time for taxi and tram remains invariant to its changes in supply. The average waiting time for taxi, bus and tram are 5, 11.5 and 6 minutes respectively.

**Table 2:** Other calibrated parameter values (2014 baseline)

|Congestion (traffic load to capacity ratio),<br>����<br>�∗����� �����|11.9|
|---|---|
|BPR congestion function parameters:��,��, ��|1/60,0.15,1.21|
|Bus occupancy parameters:��, ��|25.83,0.80|
|Bus waiting time parameters:�, �|110.9,0.335|
|Average seating(seats)for bus and tram:�����|45,118|
|Average standing (sq. met.)capacityof bus tram:��|10.7,84|
|Standing passenger density per square meter for bus and<br>tram: ��|5.75, 2.45|
|Total Number of taxis|15,000|
|Total Number of buses,_B_|866|
|Total Number of tram, TRAM|37|
|Total kilometers of tram lines|31|
|Total tram kilometers traveled (VKT) per day|8500|
|Share of monetary cost of transportation with respect to<br>annual income (probability weighted)|0.135|
|One-way daily person trips by bus|359,829|
|Elasticity with respect to own-mode travel time|-0.68|
|Elasticity with respect to own-mode monetary cost|-0.43|
|Value of time, probability weighted (MAD/hour)|26|
|Fuel tax rate (in the baseline),�|0.54|
|Pre-tax price of fuel,�(MAD/liter)|6.12|
|Lengths of a taxi, bus routes,��,������|11.69,15.60|
|Road Area (sq. km)|22.7|

> 13 See Small and Verhoef (2007).

16
~~<u>eG I775 2 i a</u> CE~~ Oz ds
buses is denoted by the variable, _Bus_ . _O_ 4 is the annualized fixed cost of operating a bus prorated to a day. It includes depreciation, the daily annualized cost of the vehicle, personnel expenses, tires and replacement parts, insurance costs and other service charges. The daily revenue of the bus is the sum of revenues collected from fares and from advertising, _ADR_ being the daily advertising revenue per bus. A bus travels on a pre-determined bus journey of length ��. This will be different from the distance, _d_ 4<sup>,</sup> traveled by a bus rider. The annualized profit or loss from tram operations is given in (14c). which can be positive or negative. �� is the daily cost of tram operation which is the sum of operational and implementation annualized costs of the project per vehicle kilometer traveled (VKT). Appendix Table A.1, Table A.2 and Table A.4 show the different cost components for private car and taxi and for bus and tram operations.

The aggregate fuel tax revenue ( _FTR_ ) is: The aggregate parking tax revenue (PTR) is: The aggregate fuel tax revenue ( _FTR_ ) and parking tax revenue ( _PTR_ ) which are two sources of public revenue considered in this study are given in (15) and (16) respectively. If there is any policy which is related to the construction of new roads, then the annualized road construction cost will be included in the welfare function. Details about the costs of constructing new roads are given in Appendix A.3.

The aggregate welfare per worker given a fixed population of _N_ workers is: �� � � ln�∑���� ������ � ��� � �� ��� ������������������ (17) ��� ~~�~~ � ��� � _MUI_ is the probability-weighted marginal utility of income calculated as _MUI_ is evaluated using the baseline data and is kept constant at that value in the simulations we will be reporting. The first part of (17) is the aggregate expected utility per worker, divided by _MUI_ to get welfare in monetary terms. The second part of (17) is the social operating surplus which 18
is the sum of an aggregate public revenue from the fuel taxes paid, the profit of the taxi operators, and the surplus or deficit of the bus operators.

# **5. Optimal policies**

The results that we report here optimize over the six possible policy instruments as explained in the Introduction. To repeat, our demand side instruments are the fuel tax rate, the parking tax and the bus fare; and our supply side infrastructure policies are expanding the number of buses that are operating, the road supply and the tram network.<sup>14</sup> The full results of the simulations are reported in Tables 3-5. We will discuss the results by focusing on how each policy affects congestion, in-bus crowding, fuel consumption (and CO2 emissions which are strictly proportional to fuel consumption) and the components of social welfare. All simulations are done while keeping the population of worker-commuters of Grand Casablanca fixed at the baseline level.

Table 3 reports what would happen if each demand-side instrument were to achieve its optimal level while all other instruments remained at their baseline values. The optimal level of the fuel tax rate is 554% of the supplier’s price of fuel which is about ten times the baseline fuel tax rate of 53%. This reduces the car-equivalent traffic load and the level of congestion by 14% and fuel consumption by 21%. Fuel tax revenue increases by 715% and parking tax revenue decreases by 23%. Bus occupancy meanwhile increases by 20% while bus fares remain at their baseline values not reflecting the higher fuel costs. Social welfare gains are 0.76% of income. The bus operating deficit increases by about a third its baseline value and the number of taxis increase by 19%. The tram operating deficit improves by 5% since trams run on electricity and are immune to the fuel tax. The changes under the optimal fuel tax occur because riders of the low occupancy vehicles (private car and motorcycle) switch to high occupancy vehicles (taxi, bus and tram) to avoid in part the impact of the higher tax on them. Because these high occupancy vehicles are shared by many, traffic congestion is reduced. At the same time, the disutility of bus and tram passengers increases as the standing passenger density in these modes increases.

> 14 We do a grid search. The fuel tax rate is varied from its base value of 0.538462 in steps of 0.1 (that is 10 percentage points increase), bus fare is varied from 0 to 10 MAD in steps of 1, parking tax is varied from 0 to 100 MAD in steps of 1, the number of buses are increased from 866 to 5966 in steps of 50 buses, road supply (square kilometers) is varied from its base value in steps of 1, and tram expansion is varied from 0.0065 square kilometer (equivalent to 1 km of tram line) to 0.65 square kilometer (equivalent to 100 km of tram line) in steps of 0.0065 . Our code is in MATLAB and solves the model for each grid point in the six dimensional policy space. The search could be refined near the optimum for more accurate pinpointing of the optimum but the benefits of doing so are negligible and the qualitative conclusions do not change.

19
The effects of the parking tax increase are similar, but with some differences stemming from the fact that the fuel tax is equivalent to a per kilometer tax, as explained earlier, while the parking tax is a per-trip tax. The optimal parking tax is about ten times higher. Congestion and fuel consumption decrease by 13% and 18% respectively and the welfare gains are 0.77% of income. Parking tax revenue increases by 691% and fuel tax revenue decreases by18%. Bus occupancy increases by 13%, the number of taxis in operation increases by 22% and the tram is only slightly affected. The bus operating deficit decreases by 58% because of the higher bus ridership.

**Table 3: Demand-side instruments: Optimal fuel tax, optimal parking tax, and optimal bus fare.**

|(**NOTE:**All numbers in MAD are|per commuter.|Percent changes fro|m the baseline in|parentheses.)|
|---|---|---|---|---|
||**Base**|**Fuel tax**|**Parking tax**|**Bus fare**|
|Fuel tax rate(��|0.54|**5.54**|0.54|0.54|
|Bus fare(���|3.45|3.45|3.45|**0**|
|Parkingtax(�)|5|5|**53**|5|
|Bus supply (B)|866|866|866|866|
|Road Area(sq. km)|22.7|22.7|22.7|22.7|
|Tramline(km)|31|31|31|31|
|**Mode Choices (Person-trips)**|||||
|Private Car|989,530|711,615 (-28)|805,911 (-19)|983,966 (-0.56)|
|Motorcycle|389,815|337,067 (-14)|243,162 (-38)|387,652 (-0.55)|
|Taxi|1,199,430|1,431,684 (19)|1465,053 (22)|1,191,166 (-0.69)|
|Bus|359,829|447,391 (24)|418,716 (16)|376,413(4.61)|
|Tram|59,972|70,818 (18)|65,734 (10)|59,377 (-0.99)|
|**Traffic Load(car-equivalent)**|1,301,277|1,125,422 (-14)|1,129,799(-13)|1,293,695(-0.6)|
|**Traffic load-to-capacity**|11.89|10.3 (-14)|10.3(-13)|11.82(-0.6)|
|**Fuel consumption(1,000 liters/year)**|649,129|514,649(-21)|<br>530,624 (-18)|643,975 (-0.8)|
|**Bus waiting time**|11.5|11.5 (0)|11.5(0)|11.5(0)|
|**Bus occupancy**|106|127 (20)|120(13)|110(4)|
|**T**|**ravel time (one**|<br> **-way minutes)**|||
|Private Car|23|20.2 (-12)|20.3 (-12)|22.9 (-0.5)|
|Motorcycle|23|20.2 (-12)|20.3 (-12)|22.9 (-0.5)|
|Taxi|26|23.5 (-10)|23.5 (-10)|25.9 (0.4)|
|Bus|43.5|39.6 (-9)|39.7 (-9)|43.3 (-0.4)|
|Tram|26|26 (0)|26 (0)|26 (0)|
|**Expected utility/MUI(MAD)**|886,951|882,672 (-0.48)|884,599(-0.26)|887,205(0.03)|
|**Social welfare(MAD)**|887,828|888,508 (0.07)|888,516(0.08)|887,865(0.004)|
|**Social welfare increase(%of income**||0.76|0.77|0.04|
|**Fuel tax revenue(MAD)**|714|5820 (715)|583(-18)|708(-0.8)|
|**Park tax revenue(MAD)**|453|349 (-23)|3,582(691)|450(-0.6)|
||**Bus (M**|**AD)**|||
|Annual Profit|-63|-116 (-85)|-26 (58)|-270 (-329)|

20
|Annual Revenue|208|259 (24)|242 (16)|1 (-99)|
|---|---|---|---|---|
|Annual Cost|271|375 (38)|268 (-1)|271 (-0.04)|
||**Taxi (MA**|**D)**|||
|Annual Profit|0|0|0|0|
|Annual Revenue|1,418|3008 (112)|1,712 (21)|1,407 (-0.74)|
|Annual Cost|1,418|3008 (112)|1,712 (21)|1,407 (-0.74)|
|Fare(per trip)|7.09|12.6 (78)|7.01(-1)|7.08(-0.05)|
|Total Taxi|15000|17904 (19)|18,322(22)|14,897(-0.7)|
||,<br>**Tram (M**|,<br>**AD)**|||
|Annual Profit|-227|-217 (5)|-222 (2)|-228 (-0.24)|
|Annual Revenue|57|67 (18)|62 (10)|56 (-1)|
|Annual Cost|284|284 (0)|284 (0)|284 (0)|

Clearly the existing levels of the fuel or parking tax are too low relative to the optimal levels and huge hikes are necessary to achieve efficiency. This is an important result especially because under both of these policies consumer expected utility decreases by 0.48% and 0.26%. This is because the utility gain from congestion alleviation is offset by the increased disutility from bus crowding and more importantly by the income effect of the large fuel or parking tax hikes. These results have strong policy implications. First, increasing the fuel tax and the parking tax by 10 times to reduce congestion would be a tough and unpopular decision for the government because it invites a strong opposition from the general public even though it helps reduce congestion and improves social welfare. Second, demand side instruments alone may not be effective enough if adequate infrastructure is not added to facilitate the switching from private to public transportation. On the other hand, demand side instruments have some desirable distribution implications. For example, not only does the population that relies on public transportation benefit from the congestion reduction, but the revenue collected from the increased fuel or parking taxes could be expended to improve education, health or public transportation. This would be a popular revenue transfer mechanism from the rich, who can afford private automobiles and would be the ones paying the higher fuel and parking taxes, to the poor who rely more heavily on education and health services and on better public transportation.

In order to encourage the use of high occupancy vehicles such as buses, it is optimal that the bus fare be reduced to zero. On the one hand, the lowering of the bus fare improves the expected utility, but on the other hand, the expected utility suffers due to the increased crowding in buses. Overall, there is a small increase in expected utility. But the social welfare increase is only 0.04% 21
of income as the gain in expected utility is followed by a 329% increase in the operating deficit of the bus service, and a slight decrease in fuel and parking tax revenues.

Consider now the results displayed in Table 4 which are for two supply side policies. The optimal increase in the number of buses is from 866 buses in the baseline to 2,466 buses, a 2.84fold increase. This optimal bus supply reduces the waiting time from 11.5 to 8.1 minutes. The bus occupancy drops so that there is almost no one standing in the bus. Enough trips switch to bus from the other modes, and the total car-equivalent traffic load is reduced by 2%. Travel times improve by 2% for other modes and by 9% for bus while aggregate fuel consumption decreases by only 1%. Expected utility increases by 0.15% and social welfare is improved by 0.9%. The bus operational deficit increases by 704% because of the cost of acquisition of the large number of new buses. Tram operations are barely affected and the number of taxis operating falls by 4%.

By far the most beneficial policy is the construction of additional road capacity. However, the social benefits should depend on the availability and price of land for the expansion of roads. We consider two scenarios for the expansion of roads. Ground level or horizontal expansion of roads is possible in the periphery of the urban area, specifically in the south and southeast of Casablanca, where land is both abundant and cheap and there are no physical constraints. The second scenario considers the other extreme where the city may further densify with high-rise buildings especially in the in the Casablanca-Mohammedia-Rabat corridor. Such road capacity expansion is possible only through the construction of elevated roads on top of the existing roads (vertical expansion) because land is not available and existing surface roads in the interior of the urban area cannot be widened due to physical and other constraints prohibiting demolition of buildings.

**Table 4: Supply-side policies: Optimal bus supply and optimal road supply.** <u>(</u> **<u>NOTE:</u>** <u>All numbers in MAD are per commuter. Percent changes from the baseline in parentheses.)</u>

||<br>**Base**|<br>**Bus supply**|<br>**Road supply**<br>**(ground level)**|<br>**Road supply**<br>**(elevated)**|
|---|---|---|---|---|
|Fuel tax rate(��|0.54|0.54|0.54|0.54|
|Bus fare(���|3.45|3.45|3.45|3.45|
|Parkingtax(�)|5|5|5|5|
|Bus supply (B)|866|**2466**|866|866|
|Road Area(sq. km)|22.7|22.7|**65.09**|**25.23**|
|Tramline(km)|31|31|31|31|
|**Mode Choices (Person-trips)**|||||
|Private Car|989,530|956,571 (-3)|1,108,020 (12)|1,002,016 (1.3)|
|Motorcycle|389,815|376,951 (-3)|439,271 (13)|395,266 (1.4)|

22
|Taxi|1,199,430|1,153,366 (-4)|1,094,420 (-9)|1,189,090 (-<br>0.9)|
|---|---|---|---|---|
|Bus|359,829|454,684 (26)|323,021 (-10)|356,248 (-1)|
|Tram|59,972|57,003 (-5)|33,843 (-44)|55,955 (-7)|
|**Traffic Load(car-equivalent)**|1,301,277|1,270,095 (-2)|1,394,939(7)|1,311,514(0.8)|
|**Traffic load-to-capacity**|11.89|11.6 (-2)|4.4(-63)|10.8(-9)|
|**Fuel consumption(1,000 lit/year)**|649,129|<br>642,312(-1)|584,102(-10)|632,772(-3)|
|**Bus waiting time**|11.5|<br>8.1 (-30)|11.5(0)|11.5(0)|
|**Bus occupancy**|106|45.1 (-57)|98(-8)|105.6(-0.8)|
|**Travel time**|**(one-way minu**|**tes)**|||
|Private Car|23|22.5 (-2)|11 (-52)|21.1 (-8)|
|Motorcycle|23|22.5 (-2)|11 (-52)|21.1 (-8)|
|Taxi|26|25.5 (-2)|15 (-42)|24.2 (-7)|
|Bus|43.5|39.4 (-9)|26.8 (-38)|40.8 (-6)|
|Tram|26|26 (0)|26(0)|26 (0)|
|**Expected utility/MUI(MAD)**|886,951|888,243(0.15)|901,191(2)|888,713(0.2)|
|**Social welfare(MAD)**|887,828|888,652 (0.09)|895,493(0.9)|887,950(0.01)|
|**Social welfare increase as a % income**||0.9|8.5|0.13|
|**Fuel tax revenue(MAD)**|714|706 (-1)|642(-10)|696(-3)|
|**Park tax revenue(MAD)**|453|438 (-3)|508(12)|459(1.3)|
|**Annualized Road cost(MAD)**|0|<br>0|6,525|1,624|
|**B**|**us (MAD)**||||
|Annual Profit|-63|-505 (-704)|-71 (-13)|-63 (-0.2)|
|Annual Revenue|208|265 (27)|187 (-10)|206 (-1)|
|Annual Cost|271|770 (184)|258 (-5)|269 (-0.7)|
|**Ta**|**xi (MAD)**||||
|Annual Profit|0|0|0|0|
|Annual Revenue|1,418|1,360 (-4)|1,241 (-12)|1,394(-2)|
|Annual Cost|1,418|1,360 (-4)|1,241(-12)|1,394(-2)|
|Fare(per trip)|7.09|7.07 (-0.2)|6.8(-4)|7.03(-0.8)|
|Total Taxi|15,000|<br>14,424 (-4)|13,687(-9)|14,871(-0.9)|
|**Tr**|<br>**am (MAD)**||||
|Annual Profit|-227|-230 (-1)|-252 (-11)|-231 (2)|
|Annual Revenue|57|54 (-5)|32 (-44)|53 (-7)|
|Annual Cost|284|284 (0)|284 (0)|284(0)|

If adding only ground level roads at the periphery, it is optimal to increase baseline road capacity almost threefold. This reduces travel times by 52% for cars and motorcycles, by 42% for taxi and 38% for buses. Trips by car and motorcycle increase by 12% and 13% respectively as switching in favor of the low occupancy modes occurs. Fuel consumption decreases by 10% mainly because speeds are improved as congestion is alleviated. Bus occupancy decreases by 8% reducing the disutility from standing in the bus. Expected utility improves by 2% and social welfare increases by 8.5% of income which dwarfs many times over the benefits of the demand-side policies. The number of taxis operating decreases by 9%. The bus operations deficit gets worse by 23
13% and the tram deficit by 11%. If instead we assume that only elevated roads can be built because the physical constraints are severe and the cheap and abundant land in the periphery is not used, the baseline road supply changes very little.<sup>15</sup> The optimal length of such elevated roads built would be 195 km and would increase expected utility and welfare much less than the optimal ground level expansion of roads. But the result is still welfare improving relative to the base.

Table 5 presents results when the policies are optimally mixed. In column 1-3 are the results when bus supply, ground level or elevated road supply and the tram line’s length are simultaneously optimized. We find that tram extension does not improve social welfare because of its high marginal (per kilometer) cost (a simulation devoted to showing the sub-optimality of tram extension is relegated to the Appendix). A somewhat smaller number of buses should be added than in the case when bus additions are the only instrument and only somewhat less road capacity should be built than in the case when road expansion is the only instrument. The results are similar to the ground level road expansion case in Table 4. Since the benefits of such road expansion strongly dominates over bus expansion, doing the bus expansion simultaneously with the road expansion does not add much to the welfare gains. The social welfare gains of the two policies are only somewhat sub-additive when they are jointly optimized as was pointed out in the Introduction.

The results of combined supply-side options (optimal mix) when ground level road expansion is replaced with the elevated road expansion are presented in Column 2 of Table 5. Because, the marginal (per kilometer) cost of elevated road expansion is 4.166 times<sup>16</sup> the ground level road expansion, its welfare gains are much smaller and turn out to be comparable in magnitude to those of the optimally combined demand side instruments (Column 3).

In column 3 of Table 5 we see the results of jointly optimizing all the demand side instruments (fuel tax, parking tax and bus fare) while keeping roads and buses at their baseline levels. The results are similar to those of the optimal fuel tax alone in Table 3. The main difference is that

> 15 The cost of an elevated road with 2x2 lanes is MAD 250 million. The total width of the roadway is 4x3.25 m = 13 m i.e. 0.013 km. The area of a 1 km of road is 0.013 km<sup>2</sup> . The annualized cost of construction is MAD 25 million, assuming a long lifespan and an interest rate of 10%.

> 16 The cost of a two-lane ground level road is 30 million MAD/km. The cost of a four-lane elevated road is 250 million MAD/km or 250/2 = 125 million MAD/km for two lanes. Hence, the per-km cost of an elevated road is 125/30 = 4.166 times more than the per km cost of a ground level road.

24
when both fuel and parking tax are optimized, the fuel tax is only quintupled from the baseline and the parking tax is only increased sevenfold, instead of the tenfold increases when they are separately optimized. The reason is that the two instruments are close policy substitutes as we saw in the Introduction, so when they are optimized jointly each instrument does not have be used as intensively as in the cases when each instrument is optimized separately.

Finally, in the last two columns of Table 5 we have the results when all demand-side instruments and all supply-side expansions are simultaneously optimized, when ground level road expansion and elevated road expansion are respectively considered. The results of this allinstrument and all-policies optimum are similar to the “union” of the results of the demand-side and supply-side instrument optimization. Under ground level road expansion (column 4), the optimal fuel tax rate is set at about 3.5 times its baseline value. The optimal parking tax is set at 1.8 times its baseline value, while the optimal bus supply is about 13% higher than in the allsupply-side-policies optimum, but the optimal road capacity expansion is only about 1.5% less.<sup>17</sup> There is almost no in-bus crowding because almost everyone is seated in buses. In interpreting these results, the reader should keep in mind that road expansion and bus supply are policy substitutes for improving road congestion, but that road expansion is the much more effective instrument of the two. On the demand-side, the parking tax and the fuel tax are much closer substitutes and work largely similarly despite the fact that the parking tax is less travel-distance and hence less congestion related than is the parking tax. The two have about the same effectiveness.

> 17 The four panels of Figure A.2 in the Appendix illustrate some aspects of the optimum in the next to last column of Table 5.

25
**Table 5: Optimal all-demand-side instruments, optimal all-supply expansions and optimal all-demand-side instruments and all-supply expansions.**

|(**NOT**|**E:**All numbers in MAD<br>|are per trip. Percent<br>|changes from the base<br>|line in parentheses.)<br>||
|---|---|---|---|---|---|
||**All supply ex**|**pansions**|**All demand-side**<br>**instruments**|**All demand-side i**<br>**and supply ex**|**nstruments**<br>**pansions**|
||**Ground level roads**|**Elevated roads**||**Ground level roads**|**Elevated roads**|
|Fuel tax rate(��|0.54|0.54|**2.54**|**1.9**|**4.40**|
|Bus fare(���|3.45|3.45|**1**|**0**|**0**|
|Parkingtax(�)|5|5|**35**|**9**|**29**|
|Bus supply (B)|**2266**|**2416**|866|**2566**|**3100**|
|Road Area(sq. km)|**64.77**|**24.98**|22.7|**63.07**|**23.2**|
|Tramline(km)|**31**|**31**|31|**31**|**31**|
|**Mode Choices (Person-trips)**||||||
|Private Car|1,074,459 (9)|968,168 (-2)|760,739 (-23)|974,628 (-2)|643,063 (-35)|
|Motorcycle|426,064 (9)|381,993 (-2)|273,174 (-30)|398,027 (2)|257,333 (-34)|
|Taxi|1,057,828 (-12)|1,145,382 (-5)|1,452,102 (21)|1,114,507 (-7)|1,394,118 (16)|
|Bus|407,648 (13)|449,419 (25)|445,223 (24)|476,686 (32)|640,757 (17)|
|Tram|32,576 (-46)|53,613 (-11)|67,337 (12)|34,727 (-42)|63,304 (6)|
|**Traffic Load(car-equivalent)**|1,363,597 (5)|1,279,556(-2)|1,117,287(-14)|1,289,744(-0.9)|1,027,865(-21)|
|**Traffic load -to-capacity**|4.4 (-63)|10.6(-11)|10.2(-14)|4.25(-64)|9.2(-23)|
|**Fuel consumption(1,000 lit/year)**|<br>577,768 (-11)|627,791(-3)|517,832(-20)|542,941(-16)|474,147(-27)|
|**Bus waiting time**|<br>8.3 (-28)|8.2(-29)|11.5|8(-31)|7.5(-35)|
|**Bus occupancy**|<br>45 (-58)|46(-57)|126(19)|45(-58)|47(-56)|
||<br>**Travel time**|**(one-way minutes)**||||
|Private Car|10.9 (-53)|20.8 (-10)|20.1 (-13)|10.7 (-53)|18.4 (-20)|
|Motorcycle|10.9 (-53)|20.8 (-10)|20.1 (-13)|10.7 (-53)|18.4 (-20)|
|Taxi|14.9 (-43)|24 (-8)|23.3 (-10)|14.8 (-43)|21.8 (-16)|
|Bus|23.5 (-46)|37.1 (-15)|39.5 (-9)|22.9 (-47)|33.1 (-24)|
|Tram|26 (0)|26(0)|26 (0)|26 (0)|26 (0)|
|**Expected utility/MUI(MAD)**|902,120 (1.7)|889,794(0.3)|883,978(-0.33)|900,561(1.5)|885,567(-0.2)|
|**Social welfare(MAD)**|896,081 (0.9)|888,748(0.10)|888,567(0.08)|896,208(0.9)|889,774(0.22)|
|**Social welfaregain as % of income**|9.17|1|0.8|9.3|2.2|
|**Fuel tax revenue(MAD)**|635 (-11)|690(-3)|2,684(276)|2,106(195)|4,260(497)|
|**Park tax revenue(MAD)**|<br>493 (9)|443(-2)|2,360(421)|814(80)|1,717(279)|

26
|**Annualized road cost(MAD)**|6,476|1,459|0|6,203|321|
|---|---|---|---|---|---|
||<br>**Bus (**|**MAD)**||||
|Annual Profit|-438 (-597)|-488 (-677)|-235 (-274)|-820 (-1,205)|-1,225 (-1,851)|
|Annual Revenue|237 (14)|262 (26)|75 (-64)|3 (-98)|4 (-98)|
|Annual Cost|675 (149)|750 (177)|310 (15)|823 (204)|1229 (354)|
||<br>**Taxi (**|<br>**MAD)**|||,|
|Annual Profit|0|0|0|0|0|
|Annual Revenue|1,200 (-15)|1,342(-5)|2,236 (58)|1,512 (7)|2,594(83)|
|Annual Cost|1,200 (-15)|1,342(-5)|2,236 (58)|1,512 (7)|2,594(83)|
|Fare(per trip)|6.8 (-4)|7.02(-1)|9.2(30)|8.1(15)|11.2(57)|
|Total Taxi|13,229 (-12)|14,324(-5)|18,160(21)|13,938(-7)|17,435(16)|
||<br>**Tram (**|**MAD)**||||
|Annual Profit|-253 (-11)|-233 (-3)|-220 (3)|-251 (-11)|-224 (1)|
|Annual Revenue|31 (-46)|51 (-11)|64 (12)|33 (-42)|60 (6)|
|Annual Cost|284 (0)|284 (0)|284 (0)|284 (0)|284 (0)|

27
The level of welfare gains of the optimal mix of supply-side policies depend on type of road expansion (ground level vs. elevated). If land is available at relatively cheaper price and roads are optimally expanded at the ground level, the total social welfare gain of the optimal supply side policy mix would be 9.17% of income. This gain would drop to 1% of the income if ground level road expansion is not feasible and only elevated option is available for the optimal road expansion. Adding the demand side optimal instruments contributes a mere 0.13 percentage points to the social welfare gains under the optimal ground level road expansion case and 1.2 percentage points under the elevated optimal road expansion case.

**Table 6:** Fiscal surplus and deficit under the optimal policies ( **NOTE:** All numbers are in MAD per commuter)

||**Baseline**|**All**<br>**demand-side**<br>**instruments**<br>**optimum**|**Supply**<br>**expansions**<br>**optimum**<br>**(Ground level**<br>**roads)**|**Supply**<br>**expansions**<br>**optimum**<br>**(Elevated**<br>**roads)**|**All demand-**<br>**side**<br>**instruments**<br>**& supply**<br>**expansions**<br>**(Ground level**<br>**roads)**|**All demand-**<br>**side**<br>**instruments**<br>**& supply**<br>**expansions**<br>**(Elevated roads)**|
|---|---|---|---|---|---|---|
|**Bus operations**|- 63|-235|-438|-488|-820|-1,225|
|**Tram operations**|-227|-220|-253|-233|-251|-224|
|**New road costs**|0|0|-6,467|-1,459|-6,203|-321|
|**Fuel tax revenue**|+714|+2,684|+635|+690|+2,106|+4,260|
|**Parking tax**<br>**revenue**|+453|+2,360|+493|+443|+814|+1,717|
|**TOTAL surplus**<br>**or deficit**|+1,457|+4,589|-6,039|-1,047|-4,345|+4,207|

The relative strength of demand and supply side options depends on the availability of land for road expansion. If there no land constraint and it is cheaper at very low price or made available freely by the government, ground level expansion of road would be the dominant policy to reduce congestion. In the case of elevated roads, the demand-side instruments and the elevated road expansions are almost equally strong in terms of congestion reduction and the resulting social 28
welfare gains. However, the demand side instruments have some additional merits as reflected in Table 6 which compares the fiscal surplus/deficit under each optimal policy.

The table shows that in the baseline when the instruments are not optimally set, there is a public fiscal surplus of 1,457 MAD per commuter. Under the demand-side optimal policy, the optimal fuel and parking taxes increase this surplus 3.15 times. But under the supply-side optimal policy when roads are built at the ground level, the deficit that emerges is more than four times as large as the baseline surplus. The main cause of this is the high cost of the road building. When the demand side instruments are optimized alongside the supply-side optimal expansions with ground level roads, then the last column of the table shows that the revenue from the demand-side instruments cuts the deficit by a third. Finally, in the last column of Table 6, a substantial fiscal surplus is generated when only elevated roads are built. The reason is that due to the high marginal cost of such roads very few are built at the optimum, congestion remains high, and therefore, the optimal values of the demand instruments are high to price the high congestion.

Naturally, there are also zero-deficit sub-optimal policies to be found if the policy makers could not justify optimal policies with a fiscal deficit. We will refer to the zero-deficit sub-optimal policies as constrained optimal policies since they satisfy the constraint of a balanced public budget. We include only one example here. To construct this example, we limited ourselves to just the fuel tax instrument on the demand-side and the road expansion policy on the supply-side, assuming road expansion at the ground level. We kept the bus supply, the tram system and the parking and bus fare instruments at their baseline values. We start with the all-instruments and allexpansions optimal road supply (Table 5, prior to last column). Decreasing the road supply from this value in steps, we solve for the optimal fuel tax at each step. Continuing in this way, we have less road, less road cost and more road congestion at each step and also have a higher optimal value of the fuel tax instrument to price the higher congestion. Thus, at each step the public deficit becomes smaller since fuel tax revenue increases while road costs decrease. We stop when the public budget is approximately balanced (within about 5%). We then compare this policy to the all-instrument and all-expansions optimum that is reported in the prior to last column of Table 5. The result is shown in Table 7. We see that balancing the budget, reduces the social welfare gain as a percentage of income from 9.3% to 7.4%, still a high percentage of average income. This is accomplished by doubling instead of tripling the baseline road supply and by charging a fuel tax that is 5.7 times the baseline value instead of 3.6 times its base value.

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**Table 7:** A zero public deficit policy in which the fuel tax covers the public budget deficit

||**Base**|**Optimum fuel tax**<br>**given ground level**<br>**road supply**|
|---|---|---|
|Fuel tax rate|0.54|3.04|
|Busfare|3.45|3.45|
|Parkingtax|5|5|
|Bus supply|866|**866**|
|RoadArea(sq.km)|22.7|**44.4**|
|Tramline (km)|31|**31**|
|**Mode Choices (Person-trips)**|||
|Private Car|989,530|937,816(-5)|
|Motorcycle|389,815|405,499 (4)|
|Taxi|1,199,430|1,235,921(3)|
|Bus|359,829|374,702(4)|
|Tram|59,972|44,637 (-26)|
|**Traffic Load (car-equivalent)**|1,301,277|1,285,966(-1.2)|
|**Traffic load-to-capacity**|11.89|6(-49)|
|**Fuel consumption (1,000 lit/year)**|649,129|542,690(-16)|
|**Bus waiting time**|11.5|11.5|
|**Bus occupancy**|106|110(4)|
|**Travel time (one-way minutes)**|||
|Private Car|23|13.3(-42)|
|Motorcycle|23|13.3(-42)|
|Taxi|26|17.1(-34)|
|Bus|43.5|30(-31)|
|Tram|26|26(0)|
|**Expected utility/MUI (MAD)**|886,951|894,381(0.8)|
|**Socialwelfare (MAD)**|887,828|894,528(0.8)|
|**Socialwelfare increase as % of income**||7.4|
|**Fuel tax revenue (MAD)**|714|3,367(372)|
|**Park tax revenue (MAD)**|453|444(-2)|
|**Annualized road cost (MAD)**|0|3,339|
|**Bus (MAD)**|||
|Annual Profit|-63|-85(-35)|
|Annual Revenue|208|217 (4)|
|AnnualCost|271|301(11)|
|**Taxi(MAD)**|||
|Annual Profit|0|0|
|Annual Revenue|1,418|1,932(36)|
|AnnualCost|1,418|1,932(36)|
|Fare (per trip)|7.09|9.38(32)|
|Total Taxi|15,000|15,456(3)|
|**Tram(MAD)**|||
|Annual Profit|-227|-242(-6)|
|Annual Revenue|57|42(-26)|
|AnnualCost|284|284(0)|

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# **6. Conclusion and extensions**

Our main conclusion is that traffic congestion in Grand Casablanca is severely underpriced and there is severe under-investment in alleviating it, as evidenced from the high optimal fuel tax rate and high optimal values for additional bus and road supply that are produced by our model when the various instruments are optimized. Our model also calculates the annualized financial expenditure that has to be incurred for implementing the optimal supply-side policy expansions and the revenue that can be raised from the optimal values of the demand-side instruments. Optimization of the demand–side instruments along with the supply-side expansions obviously provides the highest possible social welfare. The strength of the demand side instruments to reduce congestion depends on the costs of supply-side expansions. If supply-side expansions are cheaper, less in the way of demand-side instruments would be needed; the reverse would be the case when supply-side expansions are expensive and not as much new infrastructure can be supplied. The challenge with demand side instruments is that the required hike in fuel or parking taxes might be too high and might not be acceptable to the general public even if they produce a net gain in social welfare. On the other hand, supply-side expansions require heavy investments, which would crowd out investment from other important sectors of the economy (e.g. healthcare or education) or would create a fiscal deficit. Therefore, mixing the demand-side instruments with the supply-side expansions is desirable because doing so reduces the cost of demand-side instruments to the consumers, while also reducing the fiscal burden of the government to finance supply-side infrastructure expansions.

To reach a more detailed and precise assessment, it would be beneficial to model Grand Casablanca at a higher level of disaggregation by defining several land use zones to include the peripheral centers as well as the traditional center and the bus and road networks connecting these to each other. In such a disaggregated setting, it would be possible to study not only changes in modes induced by an optimal combination of demand and supply side policies but to also model shifts in jobs and population these policies would induce between the core area and the periphery.

31