1. Today: Positive externalities Highway congestion Problems
More on externalities
Today: Positive externalities
Highway congestion
Problems

2. Previously: Introduction to externalities
Markets are well functioning for most private goods
Many buyers and sellers
Little or no market power by anybody
Example: When demand shifts right for a good, new equilibrium will have higher price and quantity
Some markets do not have good mechanisms to account for everything in a market
Example: Talking on a cell phone in an airplane

3. Previously: Introduction to externalities
A simple algebraic example
Graphical analysis of externalities
Coase Theorem
Public responses to externalities
Pigouvian taxes in action
Emissions fees
Inefficiencies of uniform reductions
Cap-and-trade

4. Today: More on externalities
Positive externalities
What do we do when externalities are good?
An application
Externality problems of highway congestion
More problems

5. Externalities can be positive
Remember that not all externalities are negative
Some consumption leads to external benefits to others
Recall some examples
Planting flowers in your front lawn
Scientific research
Vaccination
Prevents others from getting a disease from you

6. Positive externalities and subsidies
Subsidies can be used to increase efficiency in the presence of positive externalities
Note that this money must be generated from somewhere, probably taxes
Recall that tax money used for subsidies has its own deadweight loss
Compare DWL with efficiency gains from the subsidy
See Figure 5.13, p. 101

7. Moving onto congestion
Although we just talked about positive externalities, highway congestion is one of the worst negative externalities that exists
Let’s examine the problem and potential solutions

8. Congestion externalities
Congestion is a big problem in urban areas
Possible solutions to the problem
Tolls on congested routes
Building our way out of congestion
HOV lanes
Private highways and express lanes
Monopoly power?
Public transit and city design

9. A simple example
Choose between a highway and a bridge

10. More information on this example
Travel time on the highway is 20 minutes, no matter how many other cars travel on this route
The bridge is narrow, and so travel time is dependent on the number of other cars on the bridge
If 1 car is on the bridge, travel time is 10 minutes; 2 cars, 11 minutes; 3 cars, 12 minutes; etc.
Travel time is 9 + T minutes if T represents the number of cars on the bridge

11. Route choice and externalities
Without tolls, equilibrium occurs with equal travel times on both routes
11 cars on the bridge
However, there are negative externalities involved whenever an additional car travels on the bridge
Imposition of a one-minute negative externality to cars already on bridge

12. Why charging a toll is useful
Without tolls, the bridge and highway have the same travel times in equilibrium
Take away the bridge and nobody’s travel time changes  No social value to the bridge
With tolls, some people can have shorter travel times
Lower overall travel time improves efficiency

13. Aren’t tolls costs too?
If bridge tolls go to government, these are just transfers of money
Toll revenue can offset tax money that has to be collected
Remember that taxes have DWL, except in a case like this where negative externalities are present
In this case, an optimal tax (which is a toll in this case) can reduce DWL
Known as double dividend hypothesis (More on this in Chapter 15)

14. Equilibrium with tolls
Suppose each minute has $1 in time costs, and a $5 toll is charged
Cost to travel on HW  $20
Cost to travel on bridge  time cost + $5
What is equilibrium?
Each person on the bridge has $15 in time cost  travel time of 15 minutes  6 cars on the bridge

15. In the following analysis…
…we assume 30 cars that must travel from A to B
How many cars should travel on the bridge to minimize total travel time?

16. For efficiency, see the right column
# on bridge
Travel time on bridge
Total minutes for bridge travelers
Total minutes for highway travelers
Total minutes for all drivers 1 10
580
590 2 11 22
560
582 3 12 36
540
576 4 13 52
520
572 5 14 70
500
570 6 15 90
480 7 16
112
460 8 17
136
440 9 18
162
420 19
190
400 20
220
380
600

17. What is efficient? 5 or 6 on bridge
Travel time on bridge
Total minutes for bridge travelers
Total minutes for highway travelers
Total minutes for all drivers 1 10
580
590 2 11 22
560
582 3 12 36
540
576 4 13 52
520
572 5 14 70
500
570 6 15 90
480 7 16
112
460 8 17
136
440 9 18
162
420 19
190
400 20
220
380
600

18. The above example with calculus
Total travel time for all cars
20 (30 – T) + (9 + T) T
600 – 11T + T2
First order condition to minimize travel time
– T = 0
T = 5.5
Is this a minimum or maximum?
Try second order condition

19. The above example with calculus
Second order condition to check that this is a minimum
2 > 0
Positive second order condition  Minimum
Since fractional numbers of cars cannot travel on a route, we see that 5 or 6 cars minimizes total travel time

20. There are many highways out there
How does this problem generalize to the real world?
Externality problems still exist on congested highways
There are many ways to try to solve this problem

21. One possible solution: Private highways
Let’s look at a short video on LA traffic
WARNING: This video is produced by reason.tv, an organization that advertises “Free minds and free markets”
After the video
I would like your thoughts about whether or not you believe the suggestions in the video will help solve our commuting problems
We will discuss benefits and costs about private highways

22. Real traffic problems Los Angeles metro area
Some refer many of these freeways to be parking lots during rush hours

23. Can we build our way out?
Some people believe that we can build our way out of congestion
Let’s examine this problem in the context of our example

24. Increased capacity on bridge
New technology leads to bridge travel time at T
Equilibrium without tolls: T = 15, 20 minute travel times for all once again

25. Increasing bridge capacity
Increased capacity leads more people to travel on the bridge
Increasing freeway capacity creates its own demand
Some people traveling during non-rush hour periods will travel during rush hour after a freeway is expanded
Freeway expansion often costs billions of dollars to be effective during peak travel periods

26. HOV lanes
HOV lanes attempt to increase the number of people traveling on each lane (per hour)
These attempts have limited success
Benefit of carpool: Decreased travel time, almost like a time subsidy
Cost of carpool: Coordination costs
Problem: Most big cities on the west coast are built “horizontally”  sprawl  limits effective carpooling

27. Private highways Uses prices to control congestion
Private financing would prevent tax money from having to be used
More private highways would decrease demand for free roads

28. Problems with private highways
Monopoly power
Positive economic profits if not regulated
Clauses against increasing capacity on parallel routes
Loss of space for expansion of “free” lanes
Contracts are often long (30-99 years)
Private highways are often built in places with low demand
Tollways in Orange County

29. Public takeover of a private highway
This is what happened on the 91 Express Lanes in Orange County (eventually)
Privately built
Monopoly problems
Public buy-out of the privately-built lanes
With public control, more carpooling has been encouraged

30. Pricing public roads
Pricing based on time of day and day of week can improve efficiency by decreasing congestion
Recall that these measures increase efficiency
Why are these “congestion pricing” practices not used more?
Feasibility
Political resistance

31. Benefits of congestion pricing
Gasoline taxes can be reduced in congested areas to offset congestion pricing
Pricing increases efficiency
Taxes may increase efficiency in this context
Non-commuting traffic has an economic incentive to travel during times of little or no congestion
Trips with little economic value can be avoided
Remember: With externalities, these trips have Social MB lower than Social MC

32. Example: 91 Express Lanes toll schedule
$9.55 toll going eastbound on Thursdays, 3 pm hour

33. Public transit and city design
People often hope that public transit is the solution
However, many people hope that “someone else” takes public transit
Why? Slow, inconvenient, lack of privacy
Public transit can only be a long-term solution if it is faster and less costly than driving
Public transit will almost always be less convenient than driving

34. Public transit and city design
City designs usually make public transit difficult for many people to use effectively
Sprawl leads to people originating travel in many different places
Express buses are difficult to implement
Local buses are slow, used mostly by people with low value of time

35. Public transit and city design
City planners can make public transit more desirable
Increased population density near public transit
Areas with big workplace density, especially near bus routes and rail lines
Designated bus lanes to make bus travel faster than driving solo

36. Public transit and city design
The problem with these potential solutions
People in these cities want their single family homes, low density neighborhoods
People value privacy highly
This leads to the externality problems of congestion

37. Summary: Congestion externalities
Congestion is a major problem in urban areas
Especially in cities built “horizontally”
Congestion pricing has been implemented on a limited basis in recent decades in California
Feasibility and political resistance has limited further implementation
Many other methods are used to try to limit congestion
Mixed success

38. Problem on externalities
Assume the following: Private MC is P = Q + 100; demand is P = 500 – Q; there is an external cost of 50 for each unit produced
What is the equilibrium if there are no market interventions?
What is the efficient outcome?
What is the deadweight loss in this equilibrium?

39. Problem on externalities
Assume the following: Private MC is P = Q + 100; demand is P = 500 – Q; there is an external cost of 50 for each unit produced
What is the equilibrium if there are no market interventions?
Here, the external cost is not accounted for in the equilibrium outcome
Q = 500 – Q  Q = 200
Next, find P: P = 500 – 200 = 300

40. Problem on externalities
Assume the following: Private MC is P = Q + 100; demand is P = 500 – Q; there is an external cost of 50 for each unit produced
What is the efficient outcome?
With the external cost, social MC is (Q + 100) + 50, or
Q + 150
Efficient outcome: Set the right hand sides of the social MC and demand curves equal to each other
Q = 500 – Q  Q = 175

41. Problem on externalities
Assume the following: Private MC is P = Q + 100; demand is P = 500 – Q; there is an external cost of 50 for each unit produced
What is the deadweight loss in this equilibrium?
This is a triangle
Length of triangle is the difference between the quantities in the previous two parts: 200 – 175 = 25
Height of triangle is the external cost: 50
Area is ½  25  50 = 625

42. Another problem on externalities
MB, or demand
MB = 3000 – Q
Marginal Private Cost
MPC = Q + 580
Marginal damage (MD)
MD = 0.2Q
Marginal social cost
MSC = 1.2Q + 580

43. Another problem on externalities
What is Q1?
Output with no negotiation or government control
Set MB = MPC
3000 – Q = Q + 580
Q = 1210
Price is 3000 – Q, or 1790

44. Another problem on externalities
What is the socially efficient output? Q*
Set MB = MSC
3000 – Q = 1.2Q + 580
Q = 1100

45. Another problem on externalities
What is the deadweight loss without controls? See dark red triangle
Length of triangle
Difference of two quantities
1210 – 1100 = 110
Height of triangle
MD at Q1 = 1210
0.2 (1210) = 242
Area of triangle: half of length times height
0.5  110  242 = 13310
DWL triangle is 13310

46. How would you solve congestion?