Externalities

Christopher Makler

Stanford University Department of Economics

Econ 51: Lecture 15

pollev.com/chrismakler

Climate Change

Inequality

COVID-19

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
and allow them to trade:

\(E_K\): 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 \(P - t = PMC\)

Q: Makler, what do you think about taxes?

A:

It depends. What model are we in?

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 revenue from additional fish:

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.

Econ 51 | 15 | Externalities

By Chris Makler

Econ 51 | 15 | Externalities

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