David R. Henderson  

Greg Mankiw's Deficient Treatment of Negative Externalities

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I was teaching my class Friday on the economics of externalities. I'm using the 5th edition of Greg Mankiw's Principles of Economics. Why the 5th edition? To save my students over $100 a pop. Textbooks rarely get much better after a few editions.

In his treatment of negative externalities, Greg makes a large, and unstated, assumption. He gives an example of aluminum production in which the production process causes pollution. Then he shows the supply curve of aluminum along with the social cost curve of aluminum (which includes private costs and external costs.) He shows that the equilibrium when the externality is not internalized is at a quantity of aluminum that is too high.

But then he jumps to the conclusion that the optimal outcome can be reached by taxing aluminum. That doesn't follow. I'm not making the argument that many libertarians make--that the government can't know the right tax, that it matters where the tax revenues go, etc. I'm sticking within Greg's framework that the optimal outcome can be reached with a tax.

But here's the relevant question: what should be taxed? Greg claims that the tax should be on aluminum. For that to make sense, there would have to be fixed proportions between aluminum production and pollution production. (There would also have to be a constant cost of each unit of pollution to the sufferers from pollution, but put that aside. There's a problem even if that latter assumption is true.)

But what do we know about most production processes? We know that there are various ways to produce. There are probably more-polluting and less-polluting ways to produce aluminum. The problem is that if the government simply taxes per ton of aluminum, it does nothing to give an incentive to the company to use a less-polluting production process.

Remember that the problem is not aluminum per se; the problem is the pollution that comes from the process. So if there is to be a tax, it should be on the pollution, not on aluminum production.

I learned a basic principle early in my economics education. I learned it in a graduate international trade course at UCLA in which we went through Jagadish Bhagwati's proofs that restrictions on trade are almost never first-best solutions to the problems that people want those restrictions to address. The principle is that if your goal is efficiency, the solution should be carefully tailored to aim directly at the problem. Again, the problem is not aluminum production: the problem is pollution.

And it turns out that this error matters for Greg's exposition of his case for taxing gasoline. More on that anon.

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COMMENTS (24 to date)
Thomas Hutcheson writes:

Taxing the product might be a second best solution, but the "correct" solution is to tax the pollution caused by the aluminum itself. This is similar to the sub-optimally of taxing or administratively restricting the use of coal in electricity production instead of levying a CO2 net emissions tax. Of course since there is often political resistance to first best solutions, policy makes are sometimes forced to use second best solutions. Mankiw may have this in mind but has neglected to make this clear.

Mark Bahner writes:
But what do we know about most production processes? We know that there are various ways to produce. There are probably more-polluting and less-polluting ways to produce aluminum.

Absolutely. There is much more pollution from producing aluminum from alumina (aka, aluminum oxide, a process known as primary aluminum production) than there is from remelting aluminum scrap (a process known as secondary aluminum production).

What I notice about this air-pollution discussion is a public space (space being defined in terms of who has power to make what choices, not in terms of 3 dimensions). So that means government created this problem. Government:

  1. gave itself a monopoly on creating and enforcing law, and then
  2. did about as good a job as we would expect from government.
Here is one of my theorems: Any problem which you can describe creates an opportunity for two kinds of entrepreneurs:
  1. real (business) entrepreneurs
  2. political entrepreneurs.
The discussion above seems to consider only the political kind of entrepreneurship.

Here is my paper which may deal most directly with pollution. (I apologize about the broken links to illustrations.) Ostracism works in private space, not in public space. If you see a public problem you are looking, if you pull on my spectacles, at something government has done. Get government out of the way of private entrepreneurship.

mariorossi writes:

I would have thought that such a textbook model would assume identical agents (it must be embedded in the assumptions needed to aggregate demand or in the perfect competition, for example).

With identical agents, you'd get a single optimal tenchnology and the assumption of a direct relationship between production and pollution becomes more reasonable.

In the real world, I agree that low correlation between pollutions and production is a real problem. Or the presence of multiple pollutants for example...

D.W. MacKenzie writes:

"They" could tax the more polluting method of production. Or by Henderson's reasoning "they" could subsidize the less polluting method. Or you could tax the more polluting method a bit and use that revenue to subsidize the other method. Of course, you need to calculate the right dollar amount. You also need to pass tax/subsidy legislation through the political process. Externalities are never solved easily.

David R. Henderson writes:

@mario rossi,
With identical agents, you'd get a single optimal tenchnology
No, you wouldn’t. What’s optimal technology depends on relative prices.

Bahrum Lamehdasht writes:

Why don't you ask the man himself for a definitive answer? Mankiw runs his personal blog addressing questions from students and teachers alike.


Stephen Gradijan writes:

To D.W. MacKenzie:

What is wrong with simply taxing the quantity of pollution emitted during production, regardless of method of pollution?

For example, it is my understanding there are some types of coal that are dirtier than others. Instead of simply taxing coal, or the energy emitted from coal (google for "btu tax" in the early Clinton administration), or regulating which types of coal may be burned, simply tax the Quantity of Coal Pollutants (QCP's). Then simply let market participants in the coal producing and burning industries decide which is more effective via prices, be it cleaning dirty coal or burning cleaner coal or somehow adulterating dirty coal to emit less QCP's.

A single tax on coal seems absurd beyond words; the coal is not the problem in and of itself, it is the QCP's from burning coal that matter.

mariorossi writes:

I don't think I worded it properly.

There might be different technologies at each output level. But all agents would use the same technology for each level, since they solve the same optimization problem. So in terms of allocation of the tax between the different producers, production is still a fair proxy.

In terms of the optimal solution, I would think the social cost function should capture the technology change effect. So if changing output changes pollution per unit, you'd think the social cost would change accordingly. Is that not part of the model? I haven't got the textbook so I am not sure. There will be an optimal level when adding the social cost and we know we can hit that level with an appropiate tax.

David R. Henderson writes:

The problem is not with your wording: it’s with failing to understand that relative prices affect the production method. Mankiw has a tax on aluminum, not on the pollutant. That’s the problem. The problem has nothing to do with different producers. If all producers face the same set of technologies, and if the tax is on aluminum, they will still make the non-optimal choice.

AntiSchiff writes:

Dr. Henderson,

You make a very good point here and Mankiw is not the only textbook author to make this mistake. I seem to recall being taught the same way in my intro class.

mariorossi writes:

I understand what you are saying.

My argument is that in an identical agent model given the level of the tax, you know what technology will be used (as you can find quantity demanded on the demand curve and from that the technology used). Equlibrium quantity is the only thing that can determine technology as far as I can see.

Given that you know what technology will be used, you know how much pollution will be produced and this knoweledge must be included in the social cost of that production level.

What else do you mean by the social cost curve if not the cost of producing a certain amount of aluminium? If for example reducing production amount shifts the optimal technology towards a more polluting version, the unit social cost will increase as production is reduced.

If the relationship is not linear, the demand function will not be parallel to the demand function without externalities, but there will still be an equilibrium (this could be zero if they don't cross I guess). Given an optimal amount, there must be a level of tax that hits that amount.

While this level of knowledge is not available in real life, it's not much different from knowing the full supply function (which in general will also depend on different technologies at different levels of output).

Jim W writes:


My argument is that in an identical agent model given the level of the tax, you know what technology will be used (as you can find quantity demanded on the demand curve and from that the technology used). Equlibrium quantity is the only thing that can determine technology as far as I can see.

Given that you know what technology will be used, you know how much pollution will be produced and this knoweledge must be included in the social cost of that production level.

I think the point is that Equilibrium quantity is not the only thing that can determine technology. There is also the tax. Dr. Henderson (I think) is suggesting that by coupling the tax directly to the negative externality, the efficiency of the system can be increased.

Imagine that there is a process "A" that is more efficient at all quantities, but causes much more pollution than process "B". In your model, process "A" will always be selected, and then taxed accordingly. However, by taxing pollution directly, process "B" becomes more efficient, price drops, and pollution decreases.

In this case, the tax introduces another variable in the model and the extrema change.

Dallas Weaver Ph.D. writes:

Totally agree that externalities should be directly taxed. However, knowing exactly how much tax will always be questionable and we have to include the economic damage created by the tax itself.

However, as all taxes do economic damage along with possible economic good (externalities), revenue-neutral tax shifts from things like payroll taxes (almost all damage inducing) to taxes on externalities is a net economic benefit.

A revenue-neutral carbon tax would be a net economic stimulus and we don't even need to calculate the economic details of a carbon tax.

Mark Bahner writes:
My argument is that in an identical agent model given the level of the tax, you know what technology will be used (as you can find quantity demanded on the demand curve and from that the technology used). Equlibrium quantity is the only thing that can determine technology as far as I can see.

I don't think the real world conforms to the model. :-) You'll have a tougher time changing the real world. :-)

In the real world, aluminum can be produced from bauxite ore. From the bauxite ore, alumina (aluminum oxide) is produced, which is converted into aluminum. That's called primary aluminum production. Aluminum can also be produced by recovering aluminum scrap, and remelting it. That's called secondary aluminum production. Secondary aluminum production (remelting recovered aluminum scrap) emits far less pollution per ton of aluminum produced than primary aluminum production.

David R. Henderson writes:

@Mark Bahner,
Thanks for giving mariorossi and other readers an actual example of different technologies, with different pollution levels, used to produce aluminum.

mariorossi writes:


I think you are breaching the single good assumption in any such model. You are postulating the existance of A good and b good. Usually supply demand models assume that there is no way to distingish between the goods and so way to tax properly along your lines. Of course this is just an assumption to make the math easy, but it's hardly surprising that a 2 goods model has a different solution.

This a problem in the real world as well to be honest...

Rob writes:

I guess Coasean bargaining wasn't considered as an option at all?

Michael Hubbard writes:

What specific work are you referencing on proofs against restriction of trade?

mariorossi writes:


Of course reality is more complicated.

But I would like to highlight one aspect. Taxing the differently produced aluminium is only possible if we can distinguish between the two.

I am not sure if that's the case in this specific instance (I think recycled steel is not usuable in certain processes but I have no idea for aluminium).

In order to tax it, we would need to record the production process as well as the production amount. You'd need to certify the production method used to produce the aluminium to determine the tax due (and likely people will cheat on the certification).

Also in real life, the 2 methods require different inputs, scrap aluminium and bauxite. In real life we give subsidies to scrap metal collections, so you actually have another tax that can adjust the relative amounts of the 2 production methods.

As I said above, I think these statements break the single fungible good assumption in the supply/demand model. Which is obviusly not a valid assumption in real life.

It's obviously correct to say we should tax pollutants, but we need to be able to measure them. If we cannot measure the pollutants or the production method or whatever else you mention, we cannot tax them.

David Seltzer writes:

"The government can't know the right tax." Why not address the emissions externality problem via market approach. It seems a market pricing mechanism gets around the free rider problem and the search for the "right tax." the EU Emissions Trading System is an attempt to solve the issue.
BTW. The Coase solution works if transactions costs are zero.

D.W. MacKenzie writes:

Mr. Seltzer,

The Coase Solution works if the transactions costs of the market are less than the administrative and procedural costs of governmental corrective policies. Transactions costs are never zero- Coase was quite clear about that. The zero transaction cost issue was just a hypothetical case that Coase mentioned in passing- a fiction that he said should be ignored. The idea that Coase took the case of zero transactions costs seriously is a myth, an enduring myth but still just a myth. Externalities should be thought of in terms of comparing imperfect private and public institutions.

D.W. MacKenzie

David Seltzer writes:

Mr. MacKenzie,fair point. I remember a student in the Law School asking Coase how the theorem holds when T/C are zero. He suggested it holds IFF current and future resources were known by all. Of course no one knows the future perfectly.

Mark Bahner writes:

@David Henderson (May 15, 12:55 PM)

You're welcome. This happens to be precisely something I've done as part of my job. I've provided inputs to a MARKet ALlocation (MARKAL) model that calculates energy use and air pollution emissions in the United States for various future scenarios.

One thing I’ve learned from my research is how incredibly complicated and nuanced the real world is. For example, this discussion is about "pollution," but as has I think already been mentioned, there are many types of "pollution." Here are estimates of various air pollutants from primary aluminum production (P) and secondary aluminum (S) production, in units of kilograms of pollutant per megagram of aluminum produced. Note that these numbers for primary aluminum do not include the substantial air pollution from producing alumina from bauxite…they only are for producing primary aluminum from alumina. The ratio (R) of the primary aluminum (P) emissions to secondary aluminum (S) emissions is also given for each pollutant.

SO2: P=13.7, S=0.003, R=4600
PM10: P=1.8, S=0.86, R=2.1
NOx: P=0.53, S=0.34, R=1.6
CO2-eq: P=2300, S=350, R=6.6
CO: p=91, S =0.19, R=480.

Obviously the ratios aren’t the same for all pollutants, so if the tax was on a particular pollutant, it would make a difference which pollutant was chosen.

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