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In the early 1960s, a few economists at the University of Virginia wrote the two most insightful articles on externalities. The first, Coase’s article on The Problem of Social Cost, became a bedrock of modern economics. The second? Not so much.

I’m talking about James Buchanan and William Craig Stubblebine’s 1962 paper with the giga-chad title: “Externality”. Gotta love one-word titles.

As I did with my newsletter on Alchian’s “Costs and Outputs,” in today’s newsletter I want to explain their insights and encourage readers to go back to the original, especially section 2 which explains their point without any derivatives.

To illustrate the subtle nature of externalities, Buchanan and Stubblebine give a wonderful example of two people who own neighboring properties. Let me give them my favorite A/B names: Armen and Bengt. While they must share any fence that is built between the properties, they have different preferences over its height.

Bengt values privacy. His utility increases with the height of the fence up to keep out snoopy neighbors. While Bengt values privacy he doesn’t want an infinitely high fence because he must also bear the cost of building the fence.

Armen has more complex preferences. Like Bengt, he values privacy. Unlike Bengt, he only values privacy over some range, say up to 8 feet. Above 8 feet, Armen doesn’t care about any more privacy. In the jargon of preferences, he is “satiated.” However, beyond 10 feet, the fence is blocking Armen’s view of the mountains, so Armen’s utility declines with the height of the fence.

Translating this example into the language of externalities, Bengt’s choice of the height of a fence generates a positive marginal externality for a fence up to 8 feet (since Armen values privacy). Above 8 feet, there is zero marginal externality. Buchanan and Stubblebine call this an inframarginal externality, since Bengt’s behavior does affect Armen, and so is an externality, but not on the margin. Finally, above 10 feet, Bengt’s choice generates a negative marginal externality, since he is blocking Armen’s view.

Suppose that the joint welfare-maximizing height would be 11 feet. Let me just call this “socially optimal” and ignore complications of multiple Pareto optimal heights. After all, this is a newsletter, not a textbook.

However, the fence is Bengt’s private choice and for him, the optimal fence is 12 feet. Don’t judge him and his 12 foot fence! We are left with the normal divergence between private behavior and the socially optimal outcome since Bengt doesn’t consider that the fence is blocking Armen’s view.

The simple fence example highlights a few subtleties of externalities that are important to remember and often ignored in the Econ 101 explanation.

First, we need to verify if the externality is inframarginal. Even if Bengt’s height choice affects Armen’s utility, the optimal Pigovian tax may still be zero. As always in economics, it’s the marginal effect that we need to focus in on, not the existence of an externality.

Second, even at the socially optimal height, the marginal externality is not zero and never will be. I didn’t just pick a random optimal height; the socially optimal height will always have an externality (for any non-trivial cases). If the externality is zero/inframarginal at the socially optimal height, then that means that the private marginal value to Bengt is also zero. In that case, there’s no externality and Bengt chooses the socially optimal height. Is that really an externality in any interesting sense? No. Let’s ignore that.

Going back to the interesting case where the socially optimal externality is strictly negative, Bengt must have a positive “internal” benefit from the fence. By definition, at the optimum, the cost to Armen must be directly offset by the benefit to Bengt. In Buchanan and Stubblebine’s language, Bengt’s “external effect” (which is negative) combined with Bengt’s “internal effect” (which is positive) must add up to zero.

We cannot simply look at whether the external effects remain and decide whether we need a Pigovian tax. Buchanan and Stubblebine explain:

This point has significant policy implications for it suggests that the observation of external effects, taken alone, cannot provide a basis for judgment concerning the desirability of some modification in an existing state of affairs. There is not a

prima faciecase for intervention in all cases where an externality is observed to exist. The internal benefits from carrying out the activity, net of costs, may be greater than the external damage that is imposed on other parties.

Perhaps Armen and Bengt already came to some agreement among themselves and struck a Coasean bargain. The possibility of private agreements between Armen and Bengt leads to the third key insight from the article: a simple Pigovian tax on Bengt will not achieve the socially optimal height.

To see this, suppose a benevolent public economist successfully secures, through the power of the state, a tax on Bengt’s fence height. Suppose it is a correct tax in the Pigovian sense, equal to the marginal externality on Armen. The tax increases the marginal cost of the fence and will reduce the height chosen.

However, if Armen doesn’t directly receive the proceeds from the Pigovian tax and instead it goes to a general slush fund as often assumed, Armen will still want to pay Bengt to further reduce the height of the fence. After all, he is hurt by the fence. So the combination of the cost of building the fence, the Pigovian tax, and the payment from Armen push Bengt to lower the fence BELOW the optimal height.

In the face of the simple Pigovian tax, Coasean bargaining would push them *away* from the socially optimal outcome. As David Friedman explains it, “Coase plus Pigou is too much of a good thing.” The Econ 101 explanation ignores this problem by ruling out the possibility of bargaining but we need to be careful when it is possible or not.

There is still a lot that goes over my head. I’m left wondering what their argument tells us about Coase’s insight that Armen is imposing a reciprocal externality on Bengt? I’m not sure. But I would encourage any students of economics to go through Section 2 of the article with the Edgeworth boxes and graphs, which really drive home the results. Then help me make sense of it all.

## One Word: Externality

Mahalos for such great articles.

Can you help me get this part concrete?

"Suppose it is a correct tax in the Pigovian sense, equal to the marginal externality on Armen. The tax increases the marginal cost of the fence and will reduce the height chosen... However, if Armen doesn’t directly receive the proceeds from the Pigovian tax and instead it goes to a general slush fund as often assumed, Armen will still want to pay Bengt to further reduce the height of the fence. After all, he is hurt by the fence. So the combination of the cost of building the fence, the Pigovian tax, and the payment from Armen push Bengt to lower the fence BELOW the optimal height."

I think I'm just missing an assumption but wanted to clarify - is it assumed that the Pigovian tax reduces the fence height but that it's still higher than the socially optimal, so Armen still wants to bargain with Bengt to get the height into inframarginal externality range? Or that the tax reduces height below 11 ft, but Armen would still bargain to get the height down to 10?

How much of this is genuine insight vs a bunch of really smart ideological people trying their hardest to play down the possibility of an efficient tax? FWIW, I do agree that a Coasian solution is probably best for height building externalities - a market for air rights. But how representative is that when you think about all the externalities that abound? Carbon emissions being one big example. And even when an a Pigovian tax is imperfect, it still raises revenue and reduces a 'bad' - which you can use to reduce taxes that are even worse.