Congestion Pricing

Congestion Pricing
An Introduction

Prof. David Bernstein
James Madison University

Computer Science Department

bernstdh@jmu.edu

Motivation

Review:
- We've considered an equilibrium model of route choice behavior
What We Didn't Consider:
- Whether the equilibrium is "good" from a societal perspective (i.e., total travel costs)

An Example Revisited

Travel Times (in Minutes) on the Two Routes:
- $t_1(n_1) = 5 + n_1$
- $t_2(n_2) = 10 + 1.5 \cdot n_2$
Value of Time:
- $15.00 per hour (i.e., 25 cents per minute)
Demand:
- 20

An Example Revisited (cont.)

Total Travel Cost:
- $S(n_1,n_2) = c_1(n_1) \cdot n_1 + c_2(n_2) \cdot n_2$
Total Travel Cost in Equilibrium:
- $S(n_1,n_2) = c_1(14) \cdot 14 + c_2(6) \cdot 6 = 19 \cdot 0.25 \cdot 14 + 19 \cdot 0.25 \cdot 6 = 95$
The Question:
- Is this the minimum?

An Example Revisited (cont.)

Total Travel Costs

An Example Revisited (cont.)

An Important Observation:
- Total travel costs are minimized when $n_1 = 13$ and $n_2 = 7$, not at the equilibrium
The Answer to the "Motivating" Question:
- The equilibrium solution is not optimal from a societal perspective

An Explanation

Negative Externalities:
- A cost incurred by a party who had no control over how it was created
In This Case:
- The private cost (i.e., the travel cost incurred by the traveler) does not reflect the social cost (i.e., the cost incurred by other travelers)

An Explanation (cont.)

Getting Started:
- Suppose there are 10 vehicles and there is only one route (route 1)
- The cost incurred by each vehicle is $t_1(10) \cdot 0.25 = 15 \cdot 0.25 = 3.75$ and the total cost incurred is $37.50$
Consider a Change:
- Suppose one more person decides to travel
Continuing the Example:
- That person incurs a cost of $t_1(11) \cdot 0.25 = 16 \cdot 0.25 = 4.00$ but the increase in the total cost is $44.00 - 37.50 = 6.50$
- So, the private cost to the additional person does not reflect the societal cost
- As a result "too many" vehicles will use the route

Changing Behavior

What Do We Want To Change?
- Too many vehicles are using route 1 (i.e., 14 rather than the socially optimal 13)
Can We Order People/Vehicles Around?
- In the two route example, what would happen if we ordered one vehicle on route 1 to use route 2?
Can We Provide An Incentive?
- In the two route example, we could charge a toll on route 1 to make it more expensive and provide an incentive for people/vehicles to voluntarily change routes

Changing Behavior (cont.)

The Route Costs at the Optimal Solution in the Example:
- $c_2(7) = (10 + 1.5 \cdot 7) \cdot 0.25 = 5.125$
- $c_1(13) = (5 + 13) \cdot 0.25 = 4.500$
The Implication:
- We want to make route 1 $5.125 - 4.500 = 0.625$ more expensive

Overcoming Opposition

Electronic Toll Collection:
- Without it, collecting the toll itself can impose costs
Revenue Redistribution:
- Return the toll revenues (e.g., tantamount to some people paying others to change their behvaior)
Disguises:
- For example, HOT lanes charge for the "good" choice
Negative Tolls:
- Make the "bad" choice more attractive rather then the "good" choice less attractive (e.g., reduce tolls during the off-peak rather than raise them during the peak)

Going Beyond Route Choice

Travel Choices:
- The decision to travel
- The origin of the trip (short run vs. long run)
- The destination of the trip (short run vs. long run)
- The mode
- The route
- The departure time
Incentives:
- Different incentive mechanisms (e.g., gasoline taxes, vehicle registration fees, usage fees) may need to be used to influence differen vehaviors

Actual Implementations