Lecture 3.2 Externalities

ExternalitiesLecture 3.2 – Tom Holden

Intermediate Microeconomics Semester 2

http://micro2.tholden.org/

ECO2051 – Intermediate Microeconomics 1

http://micro2.tholden.org/

Readings

• Varian, Chapter 34

• Morgan, Katz and Rosen, Chapter 18


Externalities questions

• What are externalities?

• How do they affect efficiency and welfare?

• When do private equilibria agree with social ones?

• Does the assignment of property rights (e.g. the right to clean air) solve the problems caused by externalities?

• How else may the problems caused by externalities be solved?

• What is the tragedy of the commons, and where do such problems arise?


Definitions of externalities

• Consumption externality:• When an individual’s utility is affected not just by their own consumption of

goods, but also by the consumption of another individual.

• Examples?

• Production externality:• When the costs faced by a firm are affected by the production of another

firm or the consumption of an individual.

• Examples?

• No market for these external effects.• Missing markets lead to Pareto inefficiency.

ECO 2051 – Intermediate Microeconomics 4

Motivating question

• The ring road around Paris is one of the busiest roads in France.

• Whenever a person takes his or her car onto the road during rush hour, the congestion increases.

• Why is an externality present?

• What market is missing?


Recall: The Edgeworth box


Good A ↑

Good B →Person A

Person B

Endowment

Equilibrium• Which good is in excess

supply at the endowment?

• Which outcomes Pareto dominate the endowment?

The Edgeworth box with externalities & property rights (the right to clean air)


Smoke ↑

Money →Person A(likes smoking)

Person B(likes clean air)

Endowment

Equilibrium

• What would the picture look like if there was a right to smoke?

Externalities and Property Rights

• As with the usual case the final allocation will depend on the initial endowments, which in turn depend on property rights here.• If there is a right to smoke the initial endowment of smoke will be at the

maximum possible level of smoke.

• If there is a right to clean air, the initial endowment will be zero smoke.

• If the agents use the price mechanism to trade this effectively creates a market for smoke and the externality problem is solved. • Utility at the Pareto efficient point will depend on the endowment.

• Problems come about when property rights aren’t defined.


The Coase theorem: efficiency form

• The efficiency form of the Coase Theorem states that:• in the presence of complete competitive markets and

• in the absence of transactions costs,

• an efficient set of inputs to production and outputs from production will be chosen by agents regardless of how property rights over the inputs were assigned to the agents.

• This is basically a tautology.

• As we saw in the previous example the amount of smoke depended on the allocation of property rights although the outcome was always Pareto efficient.


The Coase theorem: indifference form

• The indifference form of the Coase Theorem states that:• in the presence of complete competitive markets and

• in the absence of transactions costs,

• and when all agents have quasi-linear utility,

• the same efficient set of inputs to production and outputs from production will be chosen by agents regardless of how property rights over the inputs were assigned to the agents.

• Quasi-linear utility is a substantial restriction.• Rules out income effects.

• So, given price, demand is independent of income.

• Examples?

• Plausible here?


Quasi-linear preferences


Smoke

MoneyPerson A(likes smoking)

Person B(likes clean air)

Equilibrium amount of smoke is independent of endowment

Production externalities


• Imagine a fish farm and a steel factory.

• The steel firm pollutes (externality).

• Pollution affects fish production.

• Level of pollution out of control of fish farm.

Pollution(x)

Fish farm

Steel factory

Production externalities

• With competitive markets (price taking):• Steel will be produced up to the point where the marginal cost of steel

equals the price.

• Fish will be produced up to the point where the marginal cost of fish equals the price.

• Pollution will be produced by the steelworks as the marginal cost to the steelworks is equal to 0, but socially this is not the case, there is a cost to the fishery.


Technical details (1/2)

• Suppose the cost of producing 𝑠 units of steel is given by 𝐶𝑠 𝑠, 𝑥where 𝑥 is the amount of pollution released at the same time, and:

•𝜕𝐶𝑠

𝜕𝑠> 0 (producing more costs more),

• Suppose the cost of producing 𝑓 units of fish is given by 𝐶𝑓 𝑓, 𝑥 , where:

•𝜕𝐶𝑓

𝜕𝑓> 0 (producing more costs more),

•𝜕𝐶𝑓

𝜕𝑥> 0 (pollution makes producing fish expensive).


Technical details (2/2)

• Suppose that the steel producer takes the price of steel as given as 𝑝𝑠, and the fish producer takes the price of fish as given as 𝑝𝑓.

• What are profits?

• What is the optimal choice of 𝑠 and 𝑥 for the steel producer?

• What is the optimal choice of 𝑓 for the fish producer?

• What levels of 𝑠, 𝑓 and 𝑥 would a social planner choose?

• Details on the board, please take notes.


Internalising production externalities

• Suppose that the steel factory owner bought the fish farm (or vice versa).• What would they maximise then?

• Why is this socially optimal?

• Suppose that the steel factory and the fish farm were both listed on the public stock market.• Would this help with the externality?


Example on private and social optima

• A typical citizen has the utility function• 𝑈 𝑚, 𝑑, ℎ = 13𝑑 − 𝑑2 − 4ℎ +𝑚, where:• 𝑑 is the number of hours per day that she spends driving around,• ℎ is the average number of hours per day spent driving around by other people in

her home town, and • 𝑚 is the amount of money she has left to spend on other stuff besides gasoline

and auto repairs.

• Gas and auto repairs cost $1 per hour of driving.

• All citizens have an income of $40 a day.

• If all citizens believe that their driving will not affect the amount of driving done by others how much will they drive?

• If a social planner was deciding how much people should drive, how much would they choose?

• Details on the board again.


Implications

• The First Theorem of Welfare Economics breaks down: the market outcome is not Pareto efficient.

• That consumers only care about their own consumption is one of the assumptions implicit in the First Theorem.


Solutions to externalitiesPermits

• Firms may vary in their costs of reducing pollution.

• Given a reduction target, firms should shoulder the burden such that the marginal cost of emission control is equal across firms.• Otherwise the total cost of reduction could be lowered by switching units

between different firms.

• This outcome can be achieved by using saleable permits.

• In a free market permits will sell at exactly the price of reducing emissions.

• Downside: how should permits be allocated to firms?


Solutions to externalitiesA Pigouvian tax/subsidy

• If bargaining or merging are not possible, then we can use taxes or subsidies to encourage agents inflicting externalities on others to behave socially optimally.

• E.g. in our steel/fish example, if the tax on pollution is set equal to the marginal cost of pollution on the fishery, then it is as if the steel factory owned the fishery.• Details…

• Difficulty: knowing the optimal level of pollution in order to choose the tax level.• If we knew this info in the steel/fish example we could just regulate (instruct

the steel firm to only pollute so much).• Does this criticism apply to carbon taxes for countering global warming?


Solutions to externalitiesProperty rights and bargaining

• Assume that the two parties can bargain efficiently.• Efficient bargaining means that bargaining will take place and reach an

outcome that maximises the total surplus to be split between the two parties.

• Presumes no significant transaction costs and no asymmetric information.

• Could also think of this as directly solving the missing markets problem.

• In the fish farm example, the “pie” to be bargained over is the gain in total surplus that comes from moving from the private optimum to the social optimum.

• The result of bargaining will generally depend on the initial allocation of property rights.


Missing market interpretation

• Suppose that:• The fishery had the right to clean water.

• Before production took place the steel firm signed a contract with the fish firm entitling it to pollute as long as it paid some price 𝑞 to the fishery per unit of production.

• What are profits now?

• What is the solution?

• What is the fisheries profit maximising choice of 𝑞?


Tragedy of the commons

• Inefficiencies are caused by poorly defined property rights.

• The tragedy of the commons is caused because the land is held ‘in common’.• Price of a cow: 𝑎

• 𝑐 cows in total.

• Total milk yield is 𝑓 𝑐 , so average yield is 𝑓 𝑐

𝑐.

• What is the socially optimal number of cows?

• How many cows will there be under laissez-faire?


Tragedy of the commons graphically


𝑐

Milk

𝑓 𝑐

𝑎𝑐

slope = 𝑓′ 𝑐∗

𝑐∗

𝑓 𝑐∗

𝑓 𝑐∗

𝑐∗> 𝑎

𝑐

𝑓 𝑐

𝑐= 𝑎

Further details

• Intuition:

• When a villager adds one more cow his income rises (by 𝑓 𝑐

𝑐− 𝑎) but every

other villager’s income falls.

• The villager who adds the extra cow takes no account of the cost inflicted upon the rest of the village.

• Modern-day “tragedies of the commons” include• over-fishing

• over-logging forests on public lands

• over-intensive use of public parks; e.g. Yellowstone.

• urban traffic congestion.


Another example (1/2)Solutions in the next lecture

• It takes 45 minutes to go around town on an uncongested road.

• The road through town can get congested. It then takes 20+𝑛

100minutes

to travel the direct route.

• Assume 6000 commuters need to travel from one side of town to the other.

• With no tolls how many will travel through town?

• How many minutes will be spent travelling?


Another example (2/2)

• Suppose a social planner determines the allocation of routes.

• How many people will go a) through town b) around town?

• How many person-minutes would be spent travelling?

• If each commuter values their time at £x per minute what level should a toll on the road through town be set at to minimise commuting time?

• Are commuters better off? By how much?


Conclusions

• Externalities violate one of the assumptions which lead to the First Fundamental Theorem of Welfare Economics.

• With externalities, Pareto efficient outcomes are unlikely in general.

• Solutions involve the state mimicking the price signals that should be provided by the market, or determining property rights to allow missing markets to be created.


Documents

Lecture 3.2 Externalities