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
