more on externalities today: positive externalities highway congestion problems who is this? (answer...
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More on externalities
Today: Positive externalities
Highway congestion
Problems
Who is this? (Answer later)
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
A simple algebraic example
Inefficient equilibrium, P = Q P = 50 Socially optimal quantity, P = Q + 10 P = 55
marginal damage per unit of $10
P = 100 – Q
MPC = Q
MSC = Q + 10
Price C = 50
Price B = 55
Recall E = 45 and F = 50
Graphical analysis of externalities
Net social gain going from Q1 to Q*
Coase theorem
The Coase theorem tells us the conditions needed to guarantee that efficient outcomes can occur People can negotiate costlessly The right can be purchased and sold
Property rights
Given the above conditions, efficient solutions can be negotiated
Ronald Coase
(99 years old)
Public responses to externalities Four public responses
Taxes Also known as emissions fee in markets with pollution
Subsidies Command-and-control
Government dictates standards without regard to cost Cap-and-trade policies
Also known as a permit system
Pigouvian taxes in action
Q per year
$
MB
0
MD
MPC
MSC = MPC + MD
Q1Q*
c
d
(MPC + cd)
Pigouviantax revenues
i
j
Emissions fee in action
0Abatement quantity
MSB of abatement
MC of abatement
e*
f*
$
Inefficiencies of uniform reductionsOverall abatement costs
can be reduced if Homer reduces abatement by 1 unit and Bart increases abatement by 1 unit
$ $
Emissions fees
Bart’spollutionreduction
Homer’spollutionreduction
50 75 90 50 75 90
MCB
MCH
25
f = $50
f = $50
Bart’s TaxPayment Homer’s Tax
Payment
MC is for abatement on these graphs
Cap-and-trade
Bart’spollutionreduction
Homer’spollutionreduction
50 75 90 50 75 90
MCB
MCH
25
f = $50
f = $50
10
a
b
Suppose Bart starts with 80 permits and Homer starts with none (see points a and b)
Bart and Homer will negotiate until they agree on a $50 price for permits
Bart sells 65 permits Homer buys 65 permits
Today: More on externalities
Positive externalities What do we do when externalities are good?
An application Externality problems of highway congestion
More problems
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
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
Positive externality example
Researchper year
$
MPB
MC
MEB
MSB = MPB + MEB
R*R1
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
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
A simple example
Choose between a highway and a bridge
highway
bridge
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
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
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
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)
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
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?
For efficiency, see the right column# on bridge Travel time on
bridgeTotal 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
What is efficient? 5 or 6 on bridge# on bridge Travel time on
bridgeTotal 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
55 1414 7070 500500 570570
66 1515 9090 480480 570570
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
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
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
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
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
Real traffic problems
Los Angeles metro area
Some refer many of these freeways to be parking lots during rush hours
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
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
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
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
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
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
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
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
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
Example: 91 Express Lanes toll schedule
$10.25 toll going eastbound on Fridays, 3 pm hour
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
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
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
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
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
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?
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
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
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
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 + 580Q per year
$
MB
0
MD
MPC
MSC = MPC + MD
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 Q per year
$
MB
0
MD
MPC
MSC = MPC + MD
Q1
Actual output
Another problem on externalities What is the socially
efficient output? Q*
Set MB = MSC 3000 – Q = 1.2Q + 580 Q = 1100
Q per year
$
MB
0
MD
MPC
MSC = MPC + MD
Q*Socially efficient output
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
Q per year
$
MB
0
MD
MPC
MSC = MPC + MDDWL triangle is 13310
How would you solve congestion?