26  Externalities

For more information on these topics, see Varian Chapter 34: Externalities.

An externality happens when one person’s or company’s actions affect others without any market transaction. Like when your neighbor plays loud music (affecting your wellbeing) or when a factory pollutes a river (affecting fishing companies downstream). There are two types of externalities:

1. Consumption externalities: When one consumer’s actions directly affect another’s utility (e.g., noisy neighbors, smoking)
2. Production externalities: When one firm’s production affects another firm’s production possibilities (e.g., pollution affecting fishing)

26.1 Example: Factory and Fishery

A steel factory produces steel (\(S\)) and pollution (\(X\)). A downstream fishery catches fish (\(F\)), but the fishery’s costs increase the more pollution the factory produces. Let’s analyze their decisionmaking:

The factory’s profit is total revenue minus total costs: \(\pi_S = P_S S - c_S(S,X)\). The fishery’s profit is their total revenue minus their total costs: \(\pi_F = P_F F - c_F(F,X)\).

The factory chooses \(X\) to maximize its own profit, setting: \(\frac{\partial c_S}{\partial X} = 0\).

But the efficient amount of pollution to produce means choosing \(X\) to maximize total profits: \(\pi_{Total} = \pi_S + \pi_F\), which gives us the efficiency condition: \(-\frac{\partial c_S}{\partial X} = \frac{\partial c_F}{\partial X}\)

The interpretation: At the efficient solution, the factory’s marginal savings from polluting should equal the fishery’s marginal cost from that pollution.

Let’s use numbers to understand this clearly:

Say reducing pollution:

• Costs the factory $100/unit (i.e., \(-\frac{\partial c_S}{\partial X} = 100\))
• Saves the fishery $150/unit (i.e., \(\frac{\partial c_F}{\partial X} = 150\))

A mutually beneficial deal might look like:

1. Factory reduces pollution by 1 unit
2. Fishery pays factory $125 to do so
3. Result:
   • Factory: +$125 payment - $100 cost = $25 benefit
   • Fishery: +$150 savings - $125 payment = $25 benefit

They should keep making such deals until the factory’s marginal cost of reducing polluting equals the fishery’s marginal savings from pollution reduction.

Classwork 1) Factory and Farm

If pollution reduction costs a factory $80/unit and saves a farm $120/unit:

1. Is this efficient? Why or why not?

2. Let’s understand why pollution reduction costs change over time. When a factory first starts reducing its pollution, the first marginal dollar goes pretty far because there are (cheap/expensive) solutions available, like fixing leaky pipes or upgrading old equipment. But as the factory reduces pollution further and further, additional reductions become increasingly (cheap/expensive) because they might require completely redesigning production processes or using cutting-edge technology. This pattern explains why the marginal cost of pollution reduction increases as pollution decreases.

3. To increase efficiency, should the factory pollute less, more, or is it polluting the most efficient amount right now?

4. Is there a mutually beneficial amount that the farm could pay the factory to reduce their pollution? If so, what is the range of prices?

Classwork 2) Neighbor’s Parties

Your neighbor often has loud parties that affect your sleep. If they value parties at $150 each and you value quiet nights at $100 each:

1. Is it efficient for your neighbor to party less, or more?

2. Suppose you own the right to a quiet night: that is, if you call the police, they come right away and break up your neighbor’s party. Is there a mutually beneficial amount of money your neighbor could pay you to not call the cops on them?

3. Suppose instead your neighbors own the right to party: the police do not respond to noise disturbance calls. Is there a mutually beneficial amount of money you could pay your neighbor so that they cancel their party?

4. Final analysis: the efficient outcome is for your neighbor to (cancel their party/have their party). It’s an outcome that (is/is not) achieved if police don’t respond to noise complaints, and it (is/is not) achieved if police do respond to noise complaints, as long as your neighbor can offer you money to not call the police.

The neighbor party scenario illustrates the Coase Theorem, developed by economist Ronald Coase in his influential 1960 paper “The Problem of Social Cost.” The theorem suggests that when property rights are well-defined and transaction costs are low, parties will negotiate to reach an efficient outcome regardless of the initial assignment of property rights. In this case, whether the neighbor has the right to party or you have the right to quiet, the efficient outcome (determined by comparing the $150 party value to the $100 quiet value) will be reached through bargaining.

Coase, who later won the 1991 Nobel Prize in Economics for this work, challenged the prevailing view that government intervention was always necessary to correct externalities. His key insight was that if parties can freely negotiate, they will find ways to compensate each other and reach efficient outcomes, regardless of who initially holds the rights. The only difference the initial assignment of rights makes is distributional - it determines who pays whom.

26.2 Example: Tragedy of the Commons

Imagine a village with a shared grazing field that anyone can use (a village commons). Each cow costs $1000 to buy and maintain. Let \(f(c)\) be the total value of milk produced when \(c\) cows graze on the field. As more cows graze:

• The first few cows produce lots of milk (plenty of grass to eat)
• Additional cows produce less milk (they compete for limited grass)

There are two ways this field could be managed:

1. Private Owner. The field could be owned by one person who decides how many cows to allow. They would maximize:
   • Total Profits = Value of milk - Cost of cows
   • In math: \(f(c) - 1000c\)
   • They’ll add cows until the value of milk from one more cow equals its cost
   • In math: \(f'(c^*) = 1000\)
2. Common Access. Anyone can bring cows to graze. People will add cows as long as their cow, eating the same amount of grass as the average cow, produces more value than it costs. So their decision rule has to do with average value, not marginal value:
   • Average value per cow > Cost per cow
   • In math: \(f(c)/c > 1000\)
   • This leads to too many cows because each person only considers their cow’s average production, not how it reduces other cows’ milk production

Let’s solve a numerical example to see this more clearly. Say \(f(c) = 10,000 \sqrt{c}\)

1. Private Owner solution:
   • Marginal value of cow equal to MC: \(f'(c) = \frac{5000}{\sqrt{c}} = 1000\)
   • Solving: \(c^* = 25\) cows
2. Common Access solution:
   • Average value per cow: \(\frac{10000 \sqrt{c}}{c} = 1000\)
   • Solving: \(c = 100\) cows

The common field ends up with 4 times too many cows! This happens because each new cow-owner only considers their own benefit, not the cost they impose on others by reducing available grass.

Classwork 3) Tragedy of the Commons

Say a field produces total milk value of \(f(c) = 1600\sqrt{c}\) when \(c\) cows graze. Each cow costs $200.

1. Under private ownership, how many cows should the owner allow? What will the total profit be?

2. Under common access, how many cows will graze? What will the total profit be for all cow owners?

26.3 Practice Questions

Question 1: Which of the following best illustrates a production externality?

A neighbor playing loud music late at night
A factory’s pollution increasing costs for a downstream fishery
A person smoking in a restaurant
A homeowner’s beautiful garden increasing property values

Question 2: According to the Coase Theorem, when will parties reach an efficient outcome regarding externalities?

Only when the government imposes regulations
Only when the affected party has legal rights
When property rights are well-defined and transaction costs are low
When the party causing the externality has more resources

Question 3: In the “Tragedy of the Commons” scenario, why does common access typically lead to overuse of a resource?

Because private owners are more efficient managers
Because users only consider their own benefits, not costs imposed on others
Because there aren’t enough resources to go around
Because users don’t understand how to manage the resource

Question 4: What determines whether an activity’s externality is positive or negative?

Whether it’s a production or consumption externality
Whether it’s regulated by the government
Whether it increases or decreases others’ welfare
Whether it’s intentional or unintentional

Question 5: What is the economically efficient level of an externality?

Zero - externalities should always be eliminated
Where marginal social benefit equals marginal social cost
Where total benefits are maximized
Where the affected party experiences no harm