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Externalities
Christopher Makler
Stanford University Department of Economics
Econ 51: Lecture 15
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.
Preferences
Each have preferences over how much Ken smokes (good 1) and money (good 2).
u^K(x_1^K,x_2^K) = k \ln x_1^K + x_2^K
u^C(x_1^C,x_2^C) = c \ln x_1^C + x_2^C
MRS^K = {k \over x_1^K}
MRS^C = {c \over x_1^C}
Preferences
Each have preferences over how much Ken smokes (good 1) and money (good 2).
u^K(s,m^K) = k \ln s + m^K
u^C(s,m^C) = c \ln (10 - s) + m^C
MRS^K = {k \over s}
MRS^C = {c \over 10-s}
Suppose we define property rights over smoking.
This is like an endowment:
Let's assume Chris and Ken each start with $100.
Equilibrium
If we allow them to trade from their endowment, they'll end up on the contract curve — at an efficient allocation!
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 having that person not hunt:
What's the effect of an increase in \(L\)?
10f(L)
400L-10L^2
100(35-L)
3500 - 100L
400-10L
100
100
400-20L
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*?
Externalities
Efficiency in the Edgeworth box comes from everyone
equating their own private marginal benefits and costs.
In the presence of externalities, personal decisions affect others.
If everyone just balances their own personal marginal benefits and costs,
it can have a negative (or positive) external effect on others.
Markets will not, in general, result in a Pareto efficient outcome on their own — there is a role for government intervention.
Game Theory
For the rest of this course, we're going to derive
a general framework for analyzing situations in which
everyone's payoffs are a result of everyone's actions.
Econ 51 | 07 | Externalities
By Chris Makler
