# 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 \(P - t = PMC\)

## 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 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.

By Chris Makler

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