Christopher Makler
Stanford University Department of Economics
Econ 51: Lecture 15
pollev.com/chrismakler
Not as much a "one size fits all" model,
but more of an approach:
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
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.
Under certain circumstances, the efficient amount of externality is independent of the original assignment of property rights.
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.
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 \(P - t = PMC\)
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 \(L\)?
Suppose you needed to buy a fishing permit for a fee F.
What value of F would result in the optimal L*?
Suppose the village levied a tax of t per fish caught.
What value of t would result in the optimal L*?
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.