# Externalities

Christopher Makler

Stanford University Department of Economics

Econ 51: Lecture 15

pollev.com/chrismakler

## Externalities

• Situations in which the actions of agents affect the payoffs of others
• Often caused by "missing markets"
• Markets (or more generally, everyone acting in their own self interest) will not generally solve the problems — equilibria are inefficient or inequitable

## Externalities

• One agent affecting another:
• Edgeworth Box
• Steel Mill and Fishery
• Many agents affecting each other:
• Market externalities
• Tragedy of the Commons

## Externalities

• One agent affecting another:
• Edgeworth Box
• Steel Mill and Fishery
• Many agents affecting each other:
• Market externalities
• Tragedy of the Commons

Not as much a "one size fits all" model,
but more of an approach:

• identify a "social welfare function" that tell us what the "socially optimal" outcome is
• model the incentives agents face, and understand why the "market equilibrium" outcome differs from the "socially optimal" one.
• try to find a way to adjust the incentives to achieve the socially optimal outcome
• usually involves getting the agents to internalize the externality they are causing others

Classic Example: Smoking

Two roommates, Ken and Chris.

Ken is a smoker who can smoke up to 10 hours per day.

Chris is a non-smoker and dislikes Ken's smoking.

Each have preferences over money (good 1) and how much Ken smokes (good 2).  They each start with \(m = 100\) dollars.

Suppose we define property rights over smoking

\(E_K\): Ken has the right to smoke all 10 hours.

\(E_C\): Chris has the right to a smoke-free environment.

Classic Example: Smoking

Two roommates, Ken and Chris.

Ken is a smoker who can smoke up to 10 hours per day.

Chris is a non-smoker and dislikes Ken's smoking.

Each have preferences over money (good 1) and how much Ken smokes (good 2).  They each start with \(m = 100\) dollars.

Special case: quasilinear preferences

u_C(m_C,s) = m_C + f(10 - s)
u_K(m_K,s) = m_K + g(s)

Two points:

1) Optimal \(s\) is independent of initial allocation

2) Same result as if we had a social planner maximizing
\(W(s) = u_C(m_C, s) + u_K(m_K,s)\)

Classic Example: Smoking

Two roommates, Ken and Chris.

Ken is a smoker who can smoke up to 10 hours per day.

Chris is a non-smoker and dislikes Ken's smoking.

Each have preferences over money (good 1) and how much Ken smokes (good 2).  They each start with \(m = 100\) dollars.

### Coase Theorem

Under certain circumstances, the efficient amount of externality is independent of the original assignment of property rights.

### Steel Mill and Fishery

Base Model: Profit Maximization

Extension: Production choices affect other's profit

Conflict: Steel mill only takes into account its own cost,
not impact on the fishery.

Solution: assign property rights and allow bargaining, or merge.

## Market Externalities

• Individuals solving their own optimization problem
disregard the external effects they have on others
• Social marginal cost (SMC) = private marginal cost (PMC) + marginal external cost (MEC)
• Market equilibrium will occur where MB = PMC
• Social optimum is where MB = SMC

### Pigovian tax:

Internalize the externality so that private marginal cost equals social marginal cost.

Competitive equilibrium:
consumers set \(P = MB\),
producers set \(P = PMC \Rightarrow MB = PMC\)

With a tax: consumers set \(P = MB\),
producers set \(P - t = PMC\)

## Tragedy of the Commons

• Each individual, acting in their own best interest, overuses the common resource
• Possible solutions: regulation (issue permits); taxation (charge for use); privatization (avoid problem by making them not a commons at all)

### Tragedy of the Commons

Village of 35 people who can choose to fish or hunt.
Each fish is worth \$10; each deer is worth \$100. Every hunter gets one deer.

If \(L\) people fish, (and \(35 - L\) people hunt), total fish caught: \(f(L) = 40L - L^2\)

Total revenue from fishing:

Total revenue from hunting:

Average revenue per fisher:

Average revenue per hunter:

Marginal cost of not having that person hunt:

What's the effect of an increase in \(L\)?

### Fees

Suppose you needed to buy a fishing permit for a fee F.

What value of F would result in the optimal L*?

### Taxes

Suppose the village levied a tax of t per fish caught.

What value of t would result in the optimal L*?

### Conclusions and Next Steps

Efficiency in the Edgeworth box comes from everyone equating their marginal benefits and costs.

In the presence of externalities, there is a mismatch between one's personal benefits and costs, and those society feels.

By Chris Makler

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