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CONGESTION PRICING ECONOMIC MODELS AND INTERNATIONAL EXPERIENCE Aya Aboudina, PhD Student Civil Engineering Dept, University of Toronto 1.

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Presentation on theme: "CONGESTION PRICING ECONOMIC MODELS AND INTERNATIONAL EXPERIENCE Aya Aboudina, PhD Student Civil Engineering Dept, University of Toronto 1."— Presentation transcript:

1 CONGESTION PRICING ECONOMIC MODELS AND INTERNATIONAL EXPERIENCE Aya Aboudina, PhD Student Civil Engineering Dept, University of Toronto 1

2 Outline  Introduction  Motivation  Microeconomic foundations  Congestion Pricing Models  Static vs. dynamic pricing  Profit-maximizing vs. social-welfare maximizing pricing  Social-welfare maximizing pricing  Congestion pricing models: a conclusion  International Experience and Research Vision 2

3 Motivation  Users/consumers should pay the full cost of whatever they consume  Otherwise, they are subsidized  Therefore, they unnecessarily consume more to the detriment of all i.e. “Tragedy of the Commons” Garrett Hardin, journal Garrett Hardin, journal Science in

4 Tragedy of the Commons 4  A dilemma arising from the situation in which multiple individuals, acting independently and rationally consulting their own self-interest, will ultimately deplete a shared limited resource even when it is clear that it is not in anyone's long-term interest for this to happen.  Examples:  Overgrazing  Congestion  Criticized for promoting privatization  Used here to encourage “control”

5 Motivation (cont’d)  Recent research conducted at UofT eliminates both capacity expansions and extensions to public transit as policies to combat traffic congestion. On the other hand, it indicates that vkt (vehicle kilometres travelled) is quite responsive to price.  Together these findings strengthen the case for congestion pricing as a policy response to traffic congestion. 5

6 Microeconomic Foundations I: Demand, Cost, Revenue, and Profit 6  Demand (aka Marginal Benefit)  The change in the quantity purchased to the price.  Downward slopping curve Demand Output (Q) $

7 Microeconomic Foundations I: Demand, Cost, Revenue, and Profit (cont’d) 7  Costs  Average Cost (AC) = Total Cost (TC)/Total Production (Q)  Marginal Cost (MC): the change in total cost required to increase output by one unit = Δ TC/ Δ Q → d(TC)/d(Q) MC AC Demand Output (Q) $

8 8  Revenue  Total Revenue (TR) = Price (p) * Total Production (Q)  Marginal Revenue (MR) = Δ TR/ Δ Q → d(TR)/d(Q)  Profit = TR – TC (maximized when MR = MC) MC AC Demand MR Output (Q) P Q $ Profit Microeconomic Foundations I: Demand, Cost, Revenue, and Profit (cont’d)

9 9 In Transportation  AC = Monetary Expenses + VOT * Travel Time  The AC increases with the level of road use. This implies that the MC exceeds the AC. This is because the MC includes both the cost incurred by the traveler himself (AC) and the additional cost (s)he imposes on all other travelers. This additional cost is known as the marginal external congestion cost (mecc). MC AC Flow $ V mecc

10 10 Numerical Example When the flow entering some bridge is 10,999 veh/hr, it takes 1.07 min to cross bridge. Whereas it takes 1.09 min when the flow is 11,000 veh/hr. Then we have the following cost values at flow = 11,000:  TC = 11,000 *(1.09 min * VOT)  AC = TC/Flow = 1.09 min * VOT  MC = TC (11,000) –TC (10,999) = 11,000*(1.09 min*VOT) –10,999 *(1.07 min*VOT) = (1*1.09min*VOT) +10,999 (( )min*VOT) = AC + externality cost Microeconomic Foundations I: Demand, Cost, Revenue, and Profit (cont’d) 10,999 11, MC AC Flow Travel Time externality = 10,999* 0.02 min

11 Microeconomic Foundations II: Consumer,Producer, and Social Surpluses 11  Consumer Surplus (CS) = Total Benefit – Amount Paid  Producer Surplus (PS) = Total Revenue – Total Cost = Profit  Social Surplus (SS) = CS + PS = Total Benefit – Total Cost P Q Consumer Surplus Producer Surplus Demand $ Quantity MC Social Surplus

12 Microeconomic Foundations III: Engineers vs. Economists Definition of Congestion 12  Economists : system is congested if the performance of the system (e.g. travel time) rises with the intensity of use (e.g. flow levels).  Traffic engineers : system is congested when traffic density exceeds the critical density, resulting in traffic breakdown. AC p Cost (1/speed) Flow (veh/hr) Capacity (max flow) Economists Traffic Engineers Economists Traffic Engineers Capacity Critical density Density (veh/km) Flow (veh/hr) Breakdown

13 13  “Congestion” for traffic engineers is termed “hyper- congestion” for economists.  Hyper-congestion causes a significant drop in capacity (at critical density).  Eliminating hyper-congestion allows the sustenance of the original capacity. Critical density Density (veh/km) Flow (veh/hr) Uncongested capacity C ongested capacity Breakdown Normal- Congestion Hyper- Congestion Microeconomic Foundations III: Engineers vs. Economists Definition of Congestion

14 Outline  Introduction  Motivation  Microeconomic foundations  Congestion Pricing Models  Static vs. dynamic pricing  Profit-maximizing vs. social-welfare maximizing pricing  Social-welfare maximizing pricing  Congestion pricing models: a conclusion  International Experience and Research Vision 14

15 Static vs. Dynamic Pricing 15 Dynamic Open Loop Vary according to fixed schedule (based on typical conditions per time of day) Closed Loop vary depending on time of day and level of congestion (based on real-time system state) Reactive Static Congestion Pricing Predictive

16 Profit-Maximizing vs. Social-welfare Maximizing Pricing 16 Dead weight loss But total social welfare declines by yellow area- “ dead weight loss ” Producer Surplus maximized P*P* Q*Q* Consumer Surplus Producer Surplus Demand $ Output MC Social Welfare maximized Social-Welfare Maximizing Price PmPm QmQm Consumer Surplus shrinks Monopolist maximizes its Producer Surplus Demand MR $ Output MC Profit Maximizing (Monopoly) Price Set to maximize the social welfare. Achieved when the “Demand” equals the MC. Set to maximize profits (PS). It is the price consistent with the output where the MR equals the MC.

17 Social-Welfare Maximizing Pricing 17 First-best pricing Second-best pricing Static congestion Dynamic congestion Set to maximize the social welfare. No constraints on congestion prices. It is often impossible! It optimizes welfare given some constraints on policies (e.g. the inability to price all links on a network and the inability to distinguish between classes of users). Rules are more complex. Relative efficiency less than one.

18 18  This is the conventional diagram of optimal congestion pricing.  The un-priced equilibrium occurs at the intersection of demand and AC curves; it involves traffic flow V 0 and cost c 0.  The optimal flow V 1 occurs at the intersection of demand and MC; it can be achieved by imposing a toll τ (marginal-cost pricing).  The gain in the social surplus is depicted by the shaded triangle, which gives the difference between social cost saved (under MC curve) and benefit forgone (under demand curve) when reducing traffic flow from V 0 to V 1. Flow (V) $ AC Toll Revenue MC Social Subsidy MC 1 AC 1 τ = mecc V1V1 V0V0 Demand First-Best Pricing with Static Congestion

19 19 Static models limitations:  Assumes static demand and cost curves for each congested link and time period.  Appropriate when traffic conditions do not change too quickly or when it is sufficient to focus attention on average traffic levels over extended periods.  Cannot explain whether or not hyper-congestion will occur in equilibrium (i.e., whenever demand intersects the AC curve in its hyper-congested segment). First-Best Pricing with Static Congestion

20 First-Best Pricing from a Dynamic Perspective  The basic bottleneck model  Alternative dynamic congestion technologies  Chu 1995  Verhoef

21 The Basic Bottleneck Model 21  The most widely used conceptual model of dynamic congestion pricing  Assumptions:  No delay if inflow is below capacity  Queue exit rate equals capacity (when a queue exists)  Single desired queue exit time t* (for all users)  Total demand for passages Q is inelastic  Two costs in un-priced equilibrium:  Travel delay cost c T (t)  Schedule delay cost c s (t) (early and late arrival costs) Queue forms Time Cumulative queue exits (slope: V k ) Cumulative queue entries Queue disperses Number of vehicles tqtq t q’ t* tqtq t q’ Exit time (t) t* c s (t) c T (t) c s (t) c(t) Average cost

22 The Basic Bottleneck Model (cont’d) 22  The optimum toll τ (t):  Replicates travel delay costs (it has a triangular shape).  Affects the patterns of entries (queue entry rate will equal capacity) (flattening the peak).  Results in the same pattern of schedule-delay cost.  Produces zero travel delay costs.  The main source of efficiency gains from optimal dynamic pricing is the rescheduling of departure times from the trip origin tqtq t q’ Exit time (t) t* c s (t) τ(t) c s (t) c(t) Average cost

23 Alternative Dynamic Congestion Technologies: Chu  Chu extends the same basic logic of (marginal-cost) toll to a dynamic setting in which traffic flow varies with time.  The optimal time-varying toll is a dynamic generalization of the standard toll for static congestion.  Hyper-congestion is absent in this model and both inflow and outflow from the road are assumed to have equal sub-critical value. Flow $ AC Toll Revenue MC MC 1 AC 1 τ = mecc V1V1 V0V0 Demand

24 Alternative Dynamic Congestion Technologies: Verhoef  It uses the car-following model to investigate optimal time-varying tolls on a road with a sudden reduction in the number of lanes by half (which produces hyper- congestion in the un-priced equilibrium).  The study provides a time- and location-specific version of Chu's toll; it extends the basic “marginal-cost" toll to more realistic cases where congestion varies both temporally and spatially in a continuous manner.

25 Congestion Pricing: a Conclusion  Two types of models may be considered to set socially optimal prices, namely, static and dynamic methods.  Static pricing models:  Assume static demand and cost curves and hence come out with static (time-independent) tolls.  The main benefit from static pricing is to force vehicles to pay their full congestion externalities to the road (spatial distribution).  Dynamic pricing models  Take into account the variations of demand (arrival rates) with time (how peak demand evolves then subsides); accordingly they produce dynamic (time-varying) tolls.  A main source of efficiency gains from optimal pricing would be the rescheduling of departure times (temporal distribution) from the trip origin, which can produce significant benefits going beyond those produced by static tolls. 25

26 Outline  Introduction  Motivation  Microeconomic foundations  Congestion Pricing Models  Static vs. dynamic pricing  Profit-maximizing vs. social-welfare maximizing pricing  Social-welfare maximizing pricing  Congestion pricing models: a conclusion  International Experience and Research Vision 26

27 International Experience 27 USA, UK, France, Norway, Sweden, Germany, Switzerland, Singapore, and Australia have implemented major road pricing projects.

28 London Congestion Pricing 28  In service since  The first congestion pricing program in a major European city.  £10 daily cordon fee (flat price) for driving in “Central London Congestion Pricing Zone” during weekdays (from 7am to 6pm) (one time per chargeable day).  Bus and taxi service improved.  Accidents and air pollution declined in city center.  After 1 year of cordon tolls and during charging:  Traffic circulating within the zone decreased by 15%.  Traffic entering the zone decreased by 18%.  Congestion (measured as the actual minus the free-flow travel time per km) decreased by 30% within the zone.

29 London Congestion Pricing (cont’d) 29 The Central London Congestion Pricing Zone

30 I-15 HOT Lanes, San Diego, CA 30  First significant value pricing project.  Implemented in 1996 along the 13-km HOV section of I-15 in San Diego.  Convert HOV to HOT; solo drivers pay a monthly pass ($50 to $70) to use HOV during peak periods.  In 1998, automated and dynamic pricing scheme.

31 I-15 HOT Lanes, San Diego (cont’d) 31  Toll levels determined from congestion level to maintain “free- flow” conditions in the HOV lane.  Tolls updated every 6 minutes ($0.5 to $4) (closed-loop regulator).  Toll level displayed on real-time sign.  48% increase in HOV volumes.  Success in congestion minimization.

32 407 ETR (Express Toll Route) 32  Multi-lane, electronic HYWY running 69 km across the top of the GTA from HYWY 403 (in Oakville) to HYWY 48 (in Markham).  Constructed in a partnership between “Canadian Highways International Corporation” and the Province of Ontario.  Currently owned by 407-ETR International Inc.

33 407 ETR (Express Toll Route) (cont’d) 33  Fees at the regular zone (open-loop regulator):  Monday-Friday: Peak period ( 6-7:30am, 8:30-10am, 3-4pm, 6-7pm ): 22.75¢/km Peak hours ( 7:30-8:30am, 4-6pm ): 22.95¢/km Off-peak rates: 22.95¢/km  Weekends and holidays: 19.35¢/km  Speeds on HYWY 407 ~ double free HYWYs.  High level of user satisfaction.  Monopoly price!

34 Research Vision  The purpose is to develop a comprehensive predictive real- time dynamic congestion pricing model for the GTHA.  The tolls will be set dynamically and adaptively according to location, time-of-day, distance driven (, and if possible, the level of pollution emitted from the vehicle).  The tolling system will target full cost pricing in the case of sub-critical traffic conditions and eliminating hyper-congestion and maintaining flow at the maximum capacity in case of super-critical traffic conditions.  Additionally, this research will attempt an extra step of basing the toll on the predicted (anticipated), rather than the prevailing, traffic conditions. This is to prevent traffic breakdown before it occurs. 34

35 Research Vision (cont’d)  To consider how our envisioned systems will be applied to:  Freeway only with HOT lanes.  Freeway corridor (e.g. Gardiner-lakeshore, where Gardiner would be tolled).  Cordoned network, e.g. downtown Toronto. 35

36 Thank You Questions, suggestions and comments are always welcome!

37 References 37  The Fundamental Law of Road Congestion, Evidence from US Cities (UofT Economists)2009  CIV 1310 Infrastructure Economics lecture notes  Kenneth A. Small and Erik T. Vehoef.The Economics of Urban Transportation.  Jing Dong, Hani S. Mahmassani, Sevgi Erdo ğ an, and Chung-Cheng Lu. “State-Dependent Pricing for Real- Time Freeway Management: Anticipatory versus Reactive Strategies”. TRB Annual Meeting 2007 Paper #

38 Price Elasticity of Demand Price elasticity of demand:


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