More on externalities

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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

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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

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Today More on externalities

• Positive externalities
• What do we do when externalities are good?
• An application
• Externality problems of highway congestion
• More problems

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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

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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
• Lets examine the problem and potential solutions

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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

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A simple example

• Choose between a highway and a bridge

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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

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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

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Why charging a toll is useful

• Without tolls, the bridge and highway have the
  same travel times in equilibrium
• Take away the bridge and nobodys travel time
  changes ? No social value to the bridge
• With tolls, some people can have shorter travel
  times
• Lower overall travel time improves efficiency

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Arent 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)

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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

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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?

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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 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 90 480 570
7 16 112 460 572
8 17 136 440 576
9 18 162 420 582
10 19 190 400 590
11 20 220 380 600
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What is efficient? 5 or 6 on bridge
on bridge Travel time on bridge Total minutes for bridge travelers Total minutes for highway travelers Total minutes for all drivers
1 10 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 90 480 570
7 16 112 460 572
8 17 136 440 576
9 18 162 420 582
10 19 190 400 590
11 20 220 380 600
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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
• 11 2T 0
• T 5.5
• Is this a minimum or maximum?
• Try second order condition

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The above example with calculus

• Second order condition to check that this is a
  minimum
• 2 gt 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

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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

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One possible solution Private highways

• Lets 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

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Real traffic problems

• Los Angeles metro area
• Some refer many of these freeways to be parking
  lots during rush hours

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Can we build our way out?

• Some people believe that we can build our way out
  of congestion
• Lets examine this problem in the context of our
  example

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Increased capacity on bridge

• New technology leads to bridge travel time at 9
  0.733T
• Equilibrium without tolls T 15, 20 minute
  travel times for all once again

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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?

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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 100 500 Q ? Q 200
• Next, find P P 500 200 300

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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 150 500 Q ? Q 175

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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

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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

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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

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Another problem on externalities

• What is the socially efficient output? Q
• Set MB MSC
• 3000 Q 1.2Q 580
• Q 1100

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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
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How would you solve congestion?