CONGESTION PRICING

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

1

Outline

2

 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

Motivation

3

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

Science in 1968

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 interest for this to happen.

limited resource even when it is clear that it is not in anyone's long-term Examples:  Overgrazing  Congestion Criticized for promoting privatization Used here to encourage “control”

Motivation (cont’d)

5

 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.

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)

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 increase change output by one unit = Δ in total cost TC/ Δ Q → required to d(TC)/d(Q)

$ MC AC Demand Output (Q)

Microeconomic Foundations I:

Demand, Cost, Revenue, and Profit (cont’d)

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 Profit AC P Q MR Demand Output (Q)

Microeconomic Foundations I:

Demand, Cost, Revenue, and Profit (cont’d)

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) marginal external congestion cost and (mecc).

the additional cost (s)he imposes on all other travelers. This additional cost is known as the

$ MC AC

mecc

V Flow

Microeconomic Foundations I:

Demand, Cost, Revenue, and Profit (cont’d)

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:

Travel Time MC AC

   TC = 11,000 *(1.09 min * VOT) AC = TC/Flow = 1.09 min * VOT MC = TC (11,000) –TC (10,999)

1.09

1.07

externality = 10,999* 0.02 min 10,999 11,000

= 11,000 * (1.09 min*VOT) – 10,999 * (1.07 min*VOT) = (1*1.09min*VOT) + 10,999 ((1.09-1.07) min*VOT) = AC + externality cost

Flow

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

Consumer Surplus $ Social Surplus MC P Demand Producer Surplus Q Quantity

Microeconomic Foundations III:

12

Engineers vs. Economists Definition of Congestion 

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.

Flow (veh/hr) Capacity

Economists Traffic Engineers

Cost (1/speed) AC

Breakdown Traffic Engineers Economists

p Critical density Density (veh/km) Capacity (max flow) Flow (veh/hr)

Microeconomic Foundations III:

13

Engineers vs. Economists Definition of Congestion  “Congestion” for traffic engineers is termed “hyper congestion” for economists.

Flow (veh/hr) Normal Congestion Hyper Congestion Uncongested capacity Breakdown

 Hyper-congestion causes a significant drop in capacity (at critical density ).

C ongested capacity

 Eliminating hyper-congestion allows the sustenance of the original capacity.

Critical density Density (veh/km)

Outline

14

 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

15

Static vs. Dynamic Pricing

Congestion Pricing Static 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 Predictive

Profit-Maximizing vs. Social-welfare Maximizing Pricing

16 $ Social-Welfare Maximizing Price Consumer Surplus $ Profit Maximizing ( Consumer Surplus shrinks Monopoly ) Price P * Producer Surplus MC Social Welfare maximized Demand Q * Output

• Set to maximize the social welfare.

• Achieved when the “Demand” equals the MC .

Monopolist maximizes its Producer Surplus MC P m Dead weight loss But total social welfare declines by yellow area “ dead weight loss ” Producer Surplus maximized MR Demand Q m Output

• Set to maximize profits (PS).

• It is the price consistent with the output where the MR equals the MC .

17

Social-Welfare Maximizing Pricing

First-best pricing

• Set to maximize the social welfare.

• No constraints on congestion prices.

• It is often impossible!

Static congestion Dynamic congestion

Second-best pricing

• 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

First-Best Pricing with Static Congestion

    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 $ MC (under demand curve) when Toll Revenue Social Subsidy AC reducing traffic flow from V 0 to V 1 .

MC 1 AC 1 τ = mecc Demand V 1 V 0 Flow (V)

First-Best Pricing with Static Congestion

19 Static models limitations:

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

20

First-Best Pricing from a Dynamic Perspective

 The basic bottleneck model  Alternative dynamic congestion technologies  Chu 1995  Verhoef 2003

The Basic Bottleneck Model

21

   The most widely used conceptual model of dynamic congestion pricing

Cumulative Number

Assumptions: 

of

No delay if inflow is below capacity

vehicles queue entries



Cumulative

Queue exit rate equals capacity (when a queue exists)

(slope: V k )

  Single desired (for all users) queue exit time t*

forms Queue disperses

Total demand for passages Q is inelastic

t q t* t q’ Time

Two costs in un-priced equilibrium:   Travel delay cost c T (t) Schedule delay cost c s (t) ( early and late arrival costs)

Average cost c s (t) c T (t) c(t) c s (t) c s (t) t q t* t q’ Exit time (t)

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

Average cost c s (t) c s (t) c(t) τ(t) c s (t) t q t* t q’ Exit time (t)

Alternative Dynamic Congestion Technologies: Chu 1995

23

 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 .

$ MC

Toll Revenue

AC

MC 1 AC 1

τ = mecc

Demand

Flow

V 1 V 0

Alternative Dynamic Congestion Technologies: Verhoef 2003

24

 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.

Congestion Pricing: a Conclusion

25

   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 static tolls.

( temporal distribution ) from the trip origin, which can produce significant benefits going beyond those produced by

Outline

26

 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

27

International Experience

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

London Congestion Pricing

28

      In service since 2003.

The first congestion pricing program in a major European city.

£10 daily to 6pm) ( cordon fee one ( flat price ) for driving in “Central London Congestion Pricing Zone” during weekdays (from 7am 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)

The Central London Congestion Pricing Zone

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.

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.

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.

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!

Research Vision

34

    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.

Research Vision (cont’d)

35

 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.

Thank You Questions, suggestions and comments are always welcome!

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 #07-2109.

Price Elasticity of Demand

Price elasticity of demand: