Externalities
Christopher Makler
Stanford University Department of Economics
Econ 51: Lecture 15
pollev.com/chrismakler
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 | Fall 2022 | 15 | Externalities
By Chris Makler
