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## More on externalities

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**More on externalities**Today: Positive externalities Highway congestion Problems**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**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**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 • See Figure 5.13, p. 101**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**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?**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**$9.55 toll going eastbound on Thursdays, 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**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 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 Another problem on externalities**What is the socially efficient output? Q***Set MB = MSC 3000 – Q = 1.2Q + 580 Q = 1100 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 Another problem on externalities DWL triangle is 13310