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?