Larry Summers, writing in the Washington Post, tells us that:
While the recent decline in energy prices is a good thing in that it has, on balance, raised the incomes of Americans, it has also exacerbated the problem of energy overuse. The benefit of imposing carbon taxes is therefore enhanced.
He might have an argument in mind, but he doesn’t seem to have presented it.
The benefit of carbon taxes, as Summers says, comes from “the recognition that those who use carbon-based fuels or products do not bear all the costs of their actions.” In other words, without a tax, people use more oil than they should. I’m with him so far. Now what Summers appears to be thinking is that when the price of oil falls, people use more oil, which increases the gap between what they do use and what they should use. What this overlooks is that when the price of oil falls, there are increases in both the amount people do use and the amount people should use — and hence no particular reason to believe that the gap has grown.
Having made such an argument, one should draw a picture to make sure it’s right. Here are the demand and supply curves for oil. Points on the demand curve show the value to consumers of individual gallons of oil; points on the supply curve show the cost to producers of supplying those individual gallons; points on the social marginal cost curve show the cost to society (including pollution costs) of supplying those individual gallons:
Ideally, oil would be supplied only up to the point where demand crosses social marginal cost and no further. Unfortunately, it’s supplied up to the point where demand crosses supply. Those excess gallons create social losses measured by the skinny rectangles in the left-hand panel (the social loss from a gallon of oil is equal to the social cost of providing that gallon, minus its value to a consumer). These add up to the area labeled X on the right. The value of an appropriate-sized carbon tax is that we’d avoid that social loss. That is, the benefit of a carbon tax is measured by area X.
Now suppose oil becomes available more cheaply. This shifts both the supply curve and the social marginal cost curve vertically downward by the same amount and shifts area X to a new location. As you can see in the picture, there’s no particular reason to think that the area’s gotten any bigger:
So what is Summers thinking? Perhaps he’s focused on the fact that lower oil prices lead to higher incomes and hence a higher demand for oil? No, that won’t work, and for the same reason — a higher demand for oil means both that we will use more and that we should use more, with no expectation that the gap between the two will grow. Here’s the picture:
So what is he thinking? Let’s try this: The fall in oil prices makes us richer, which increases our demand for clean air, which increases the gap between the supply and social marginal cost curves, hence increasing the size of area X. But that’s a pretty weak argument, because the fall in oil prices hasn’t actually made us all that much richer. Besides, it’s an argument that has absolutely nothing to do with the price of oil per se — it’s just an argument that whenever we get richer for any reason, the optimal carbon tax goes up. And similarly whenever we get poorer for any reason — say, for example, that we’re living in the aftermath of an unexpected financial crisis — the optimal carbon tax goes down.
That’s presumably not it either.
There is, as far as I can see, only one way to make Summers’s argument work, and that is to presume that the social marginal cost curve not only lies above the supply curve, but is steeper than the supply curve, so that the size of area X grows as the equilibrium quantity of oil grows. That is, the externality from carbon use is increasing at the margin.
That might be true. It might even be true for reasons that Larry Summers takes for granted because he knows them so well. But since it is absolutely central to his argument — that is, since his argument collapses entirely without this condition — I think it would have been nice if he’d at least mentioned it.
hmmm…wouldn’t increasing demand elasticity for lower quantities at equilibrium for would have a similar effect?
sorry…wouldn’t increasing demand elasticity for lower quantities at equilibrium have a similar effect?***
He is thinking, how can I be a shrewder, more polite Gruber? Summers is not arguing that the rationale for the tax is strengthened, but that there is an opportunity right now to impose the tax at lower political cost.
I suspect I am mis-thinking this but can’t see where….
Assume that the use of 1 gallon of oil causes some units of pollution to be produced. A fall in the price of oil causes an increase in usage ,and also a proportional increase in units of pollution. If one assumes that the cost of a unit of pollution doesn’t fall with the price of oil, won’t that lead to the social cost curve indeed being steeper than the supply curve ?
In any case it does seems likely that the cost of a unit of pollution will rise with additional units as it reaches levels that cross thresholds of increasing harmfulness.
I hear that one of the reasons oil prices are going down is that the OPEC monopoly failed to artificially restrict oil production. I have no idea if that’s really a major cause of falling prices, but let’s assume it is. In that case, while that cartel was functioning, it was causing people to use less oil than they should, offsetting the tendency of people to use more oil than they should due to externalized costs. Perhaps Summers felt the cartel was functioning to bring the amount of oil used closer to the optimum, and now that it’s no longer doing that, people are using even more than they should, making taxes a more attractive policy option.
Ignore the first part of my comment #4. I now see that each price point on the social MC line includes a fixed (not proportional) addition on top of actual supply price.
If the demand curve is constant elasticity, rather than constant slope, I believe Summers would be right. This assumption should be explicit of course
I’m not an expert by any means, but it’s my understanding that assuming convex CO2 damage functions is a common practice in the environmental literature.
I think Summers just didn’t think of it. I don’t think he thought much at all, actually — he just used his intuition, which, in this case, was wrong.
He was probably thinking something like, “The quantity used is rising. Therefore the total negative externality is rising. Therefore, the tax is more urgent because the stakes are higher.”
I suspect he was reacting from his gut like most non-economists: thinking only about the costs and forgetting to offset them with the benefits.
Steve, the flaw in your reasoning is that you assume that Summers is adopting a market-based definition of “overuse”. Admittedly, he seems to give such a definition when he says “That which is not paid for is overused.” But I don’t think he means that at all. He has a liberal mindset that says that consumers are overusing whenever then use more than the socialist planners think that they should be using. The quoted sentence is an empirical fact, not a definition.
Look at the rest of the column. Now is a good time for the tax because it can be more easily politically imposed on poor people.
He says: “What size levy is appropriate? Here there is more danger of doing too little than too much. Once the principle of taxation is accepted, its level can be adjusted.” This is contradictory. If it is so important to accept the principle of taxation, then we should adopt a small tax and raise it later. So the danger is in trying to do too much, and not getting any tax. Better yet, a small tax with the proceeds entirely rebated might get approval, and then the levels can be adjusted later.
After all the talk about a carbon tax making the market work better, in the end he has no interest in using the proceeds to offset those hidden public costs of carbon consumption. He just wants that trillion dollars to fund his pet ideas.
@Professor Landsburg,
I think you are 100% correct here. I also think, like you said there is a good argument to be made for a steeper or kinked social cost curve on the margin. For example, nature may be able to balance a certain level of carbon with minimal to no costs but there may be a tipping point beyond which each additional pound of carbon becomes more costly.
In addition, there may be some dynamics at work in the way competing technologies infrastructures might collapse under the weight of the lower than expected oil prices. Let’s say that competing technologies can compete with oil as long as there are guilt costs for some consumers. These consumers will only buy these new technologies if their price is sufficiently close to oil. In the long run the price of these competing technologies will be lower than oil, but only if a sufficiently large demand for these products allows infrastructure to expand. Therefore the social costs of oil will be small to non-existent when oil prices are high, but will become very large when oil prices fall below some level.
The only thing that’s changed in the last 6 months (presumably what Summers means by “the recent decline in energy prices”) is that oil producers are making less money. Make a graph of that, please.
Great post Steve. I’ve been saying this for months (in reference to people saying “now’s a great time to impose a carbon tax”) but you did it much more carefully, and since you are in principle OK with a carbon tax, it’s stronger coming from you.
From a market equilibrium point of view, a tax on oil now would further destabilize the oil market, but on the positive side, would stabilize the clean(er) energy market.
None of this matters if all you care about is the proverbial long run.
Wait, why would the SC curve move in tandem with supply curve? That doesn’t make sense to me.
The US is having an energy boom, which has forced oil producing countries to be more competitive by producing more oil and increasing their efficiency. This seems like we’re entering the long-run for the energy markets, where all costs are becoming variable. All this means that the marginal cost to produce oil has been reduced, causing the supply curve to look more flat. Also, if there are more people using oil then the external costs are going to be greater since greater production of oil means there are greater external costs falling on individuals other than the producer.
I think it depends on how the marginal social cost curve is derived. If it is derived, as you do, as either a constant or proportional markup to the marginal private cost curve, then yes, Summers’ argument is likely incorrect (or at best indeterminate). But if we believe that the marginal social cost is derived by seeking to impose a *fixed quantity* of output relative to the free-market equilibrium—perhaps because, if one exceeds this quantity, the associated quantity of externalities (say, pollution) would exceed a scientifically-established “safe” amount—then the argument could go through. Sure, we could argue that if this is the case, then the MSC curve should be vertical at the amount, rather than upward sloping throughout; but this is a modeling choice that is not necessary for the basic argument that the amount that *should* be produced remains fixed even as MPC curves shift around.
RJ: I do not understand any part of your comment.
All this means that the marginal cost to produce oil has been reduced, causing the supply curve to look more flat. That’s fine. The Social MC curve then also looks more flat, and there’s no reason to expect a change in area X.
Also, if there are more people using oil then the external costs are going to be greater since greater production of oil means there are greater external costs falling on individuals other than the producer.
You seem to be asserting that the marginal externality is increasing in quantity, but an assertion is not an argument.
There is an oft quoted objective to limit global warming to 2°C. This means that only a certain amount of CO2 can be added in total. Why would this be an objective? Because as Joe Greene at #8 said, the costs start to rise more steeply.
As a crude illustration, imagine a dam filling up. There is no damage at all until a critical level is reached, then total disaster as the dam breaks. Filling the dam with waste is very useful, but if we add too much we flirt with disaster. The social cost of each kg added is zero until the critical point. We would want to add just up to that amount, then no more. If we exceed this, each kg added to the lake contributes the same to the disaster, whether it was the first or the last one added.
Of course, costs of carbon are not quite like that. It stays in the atmosphere for decades, so the eventual social cost of each kg carbon will depend on the final level reached. If we were to limit emissions to cause a 2°C rise, the social cost of each kg would be small (some even say negative). If we allow 5°C rise the cost of each kg will be huge.
However, if we tax it at the 2°C social cost, we are more likely to end up with a 5°C rise, and we will have been under-taxing. If we tax at 5°C level, we are more likely to end up with 2°C rise and we would be over taxing.
Do we tax at current marginal costs? Comparing to our dam, that would be no tax until the dam was full, then an immense tax – effectively a moratorium. Economically, would that be the best way to proceed? There would be no incentive for current dumpers to develop alternatives. But in an ideal world, is that the optimum way to price the dumping? That would mean we currently tax carbon very low, because current costs are low. If the temperature does rise more than 2°C, taxes would then need to be huge, even though the cost of each new molecule added is no greater than the cost of the molecules already there.
Which brings us to discount rates. Anyone planning to dump in the future would need to make plans. They would value the future costs according to some discount rate. Being a commercial concern, they would presumably use market rates.
The Government would also wish to discount future costs to decide how much to spend / tax. The discount rate may not be the same as commercial rates. Pure time preference discounting makes little sense if we are going to different generations. Discounting above GDP growth is impossible long term. The value of unsubstitutable assets will grow in the future. Thus the long term social discount rate will probably be lower than the commercial rate, and a declining discount rate may be best.
If the “correct” social discount rate is lower than the commercial discount rate, then it will be impossible for the market to arrive at the socially optimum solution. Those following the market rates will care nothing for far futures, but those following the social discount rate will.
I don’t think assuming a constant marginal cost is an appropriate in the this case. Harold’s analogy of a dam is more appropriate in this context. The atmosphere is essentially an environmental sink that we can dump a certain amount of CO2 into without any adverse effects, however, at a certain threshold the damages increase steeply.
Steve:
Let me try this again then. I don’t have the luxury of using graphs :/
Marginal Social Cost (MSC) is equal to marginal cost to the producers (MC) plus any external cost. So if marginal cost alone shifts/changes, then so does the MSC curve. Basically, the gap between the the MSC and the supply curve then is the external cost that falls on individuals other than the producers.
What I’m saying is that, given the energy boom, the supply curve ought to look more flat. However, the fact that there is greater production and consumption of oil gives greater rise to external costs, such as global warming, smog, depleted ozone, damage to soil from fracking, tainted water, etc. This is reason enough to suspect that the gap between the supply and MSC curve has increased. This is what you stated in the 2nd to last paragraph of your post.
CO2 has a logarithmic effect, i.e., each unit increase in CO2 has less effect than the previous unit. Thus the effect on climate is concave not convex.
S.C. Schwarz: Assuming you’re correct about this, then the conclusion is that when the price of oil goes down, we should probably care *less* about taxing oil. Is there a place where I can read up on how this effect is known to be logarithmic?
RJ
However, the fact that there is greater production and consumption of oil gives greater rise to external costs, such as global warming, smog, depleted ozone, damage to soil from fracking, tainted water, etc. This is reason enough to suspect that the gap between the supply and MSC curve has increased.
Perhaps I misunderstand you, but it looks to me like you’re confusing total external costs with marginal external costs. Of course if there’s more carbon burned, there will be more external costs in total. But the gap between the supply and SMC curves represented the *marginal* external cost from burning one more gallon of fuel, and there’s no obvious (to me) reason why this should be increasing; in fact, if commenter S.C. Schwarz is correct, it’s exactly the opposite.
@RJ & Joe Green,
Yeah, we get it, you can make a theoretically plausible argument that the per unit social cost of oil consumption [i]increases[/i] with total quantity consumed. But, that’s not the point. The point is, before Larry Summers or whoever, reaches out with their greedy little hands and grabs a big piece of the consumer benefit from reduced oil prices and gives it to hedge fund managers who can afford to buy Teslas, they ought to do us the courtesy of actually making it clear that they are actually arguing the social cost of oil consumption increases with total quantity consumed. Otherwise it seems like they are expecting us to buy into the unsupportable premise that more oil consumption and lower oil prices are everywhere and always a bad thing.
Also interesting is how, at the first hint that cost-benefit analysis might not turn out they way carbon tax proponents want they immediately began arguing that this was the wrong way to think about the problem: http://thinkprogress.org/climate/2014/07/17/3458718/one-metric-cost-climate-change/ (thank you Bob Murphy)
@Capt. J Parker,
Since the title of the post is “What Is Larry Summers Thinking?”, I’m simply answering that question based on my understanding of the literature. I’m not actually trying to defend how he presented his argument in the article at all.
People like Summers can say these things because the ‘social cost’ of carbon is a concept that is poorly determined. Consider:
– At warming below 2 degrees, the additional CO2 in the atmosphere may actually result in a net economic benefit to the globe. In this regime, burning carbon is a positive externality.
– Above 2.5 degrees, the addition of carbon becomes a negative externality. But this point would be reached at some point in the distant future, implying that its present cost should be discounted.
– Estimates for the social cost of carbon require predicting things like economic output and fossil fuel consumption decades into the future, as well as what the multi-generational response of the climate system (a complex adaptive system) will be decades in the future. It also requires that we have enough understanding of all the carbon sinks and feedbacks in the climate system, which we do not.
So since the ‘social cost’ of carbon is ill-defined and ultimately political, people like Larry Summers are free to make all kinds of claims that are outside the bounds of normal economic modeling.
@Capt. J Parker,
Considering its natural for someone’s point of view to be obvious, or seem obvious, to some but not others, then it falls on those who do understand the argument to explain it to those who are confused or have extra questions regarding it. It may be that Steve’s completely correct and that Summer is in the wrong. However, to expect Summer’s article to be perfectly clear to everyone is unfair to the writer, nor is it practical considering the limits or guidelines an editor at the Washington Post may place on its authors. Steve, for example, has NO such constraints on his blog and his argument is constantly in need of explanation to readers.
Finally, arguing about the accuracy of Summer’s point of view is irrelevant to the discussion at hand.
@Steve Landsberg
S.C Schwartz is correct up to a point. The radiative forcing effect of CO2 is logarithmic. But you need to go from forcing to global temp than from global temp to economic cost. Climate models assume big positive feedback effects from global temp rise mainly driven by the fact higher temps mean more water vapor and more water vapor means yet higher temps. I believe, when all is said and done the models predict a roughly linear relationship between global temp and total accumulated atmospheric carbon.
http://wattsupwiththat.com/2010/03/08/the-logarithmic-effect-of-carbon-dioxide/
http://www.skepticalscience.com/C02-emissions-vs-Temperature-growth.html
Steve:
I understand they’re marginal. In much of the environmental literature that I’ve read, most of the marginal costs increase once thresholds are crossed. For example, gold in ingestible, but too much can poison you and thus the marginal cost of consuming gold once a certain threshold is reached is really high. That’s the gist of my argument and what I believe Summer’s is saying, since there are more people consuming and producing oil, these thresholds are being crossed. Thus, we have a greater gap between MSC and the supply curve. Even if S.C. Schwarz is correct, that’s just for CO2 and not the other numerous external costs producing oil imposes.
Harold’s explanation is much more thorough than mine.
@RJ and Joe Green,
Here’s where I’m coming from: Summers, a talented economist and policy wonk, someone who ought to be capable of making a clear and economically supportable policy advocacy statement, chose instead to make a fuzzy and possibly not supportable statement like “the recent decline in energy prices …exacerbated the problem of energy overuse” I don’t think I should have to fill in the blanks for him. You guys are right, it’s not inconceivable that MSC of oil increases with total quantity. But, it’s also not in conceivable that it does not and it’s also not inconceivable that Summers knows he may lose an economic efficiency argument about a carbon tax but still prefers it as a policy and is betting enough people will (incorrectly) fill in the banks for him so that he needn’t have to enter into an efficiency debate he may not win.
Larry Summers states merely that the *benefits* of imposing the carbon taxes increases, not the benefit of a tax of a given size. Although it is implied and not clearly stated by the rest of the op-ed, the reason is that the political and economic factors caused by the plummet in oil prices allow the imposition of a *larger* carbon tax than would otherwise be possible.
In the latter part of the article he invokes that people will feel less pain from a tax imposed now then they would have six months ago.
While perhaps not having the precision demanded by academic economists; that is not the audience of the piece and I think it mostly conveys the message.
Steve:
Richard Tol has written quite a bit on the social cost of carbon (SCC). I think he argues that SCC increases as the atmospheric concentration of CO2 increases. I know Nordhaus makes this argument when he recommends that the carbon tax be increased over time. Also if you believe in ecosystem and atmospheric tipping points (e.g., the fat tails in distribution of climate change damages as argued by Weitzman) then increasing taxes on the margin is warranted. Also look at the AER paper by Mueller and Nordhaus on pollution damage in the US. I believe damages increase in PM2.5 concentrations.
I don’t think I should have to fill in the blanks for him.
I could just as easily say that I, another reader, don’t think he should have to pander to you.
Let me ask you this; how else do you think its even possible when Summers says “The benefit of imposing carbon taxes is therefore enhanced.” after he says “While the recent decline in energy prices is a good thing in that it has, on balance, raised the incomes of Americans, it has also exacerbated the problem of energy overuse.” that he meant anything other than, as Steve puts it, the gap between the MSC curve and supply curve has increased?
The purpose of a carbon tax is to take account of the negative externality of burning gasoline, etc. If lower oil prices lead to greater demand for oil, that would mean that a given carbon tax would bring in more revenue, which means the damage caused in the absence of a carbon tax is greater, and hence the case for a carbon tax is stronger.
Where have I gone wrong?
Steve Landsburg: Here is a helpful, if simplified, discussion of the basic atmospheric physics: http://clivebest.com/blog/?p=1169
The bigger issue if you’re trying to find a rational economic argument for a carbon tax now, is that the recent fall in oil price is not due to unexpected increased supply, but due to reduced demand, relative to prior expectations. I would buy the argument that the marginal external cost (social cost – cost of supply) increases with consumption, that would seem to be generally true of many external costs. But this actually works in reverse here, and argues that the optimal tax is now lower than what it was, say, a year ago.
Worrying that the lower oil price will cause consumption to grow too much is missing the point that the whole reason for the lower oil price is consumption coming in lower than expected.
“presume that the social marginal cost curve not only lies above the supply curve, but is steeper than the supply curve, so that the size of area X grows as the equilibrium quantity of oil grows”
I’m feeling dense. I cannot visualize how a steeper SMC curve increases the size of X in the pictured graphs. When the supply curves shift to the right, the demand curve crosses them where they are closer together. Thus, X should be smaller, not larger. That is assuming the starting points of S and SMC in relation to each other are fixed.
I can visualize it with the second set of graphs, but as you say, this shows a situation in which we are getting wealthier, not just that the price of oil is falling, so that doesn’t help me.
I can also visualize it with a logarithmically shaped SMC curve, which seems to be what Harold is driving at. That is, a marginal externality cost of 0 up to a certain point, then a sharp increase, then tending towards a fixed cost.
On a different note, I read Summers’ argument differently. I imagine a horizontal line cutting through the graphs. This represents the threshold at which the “disproportionately burdened” consumers pay a fair price for their usage. When the demand curve crosses the supply curve at or above this level, the case for a carbon tax is reduced. With the lower price of oil, the demand curve now crosses the supply curve below this point, making room for a carbon tax.
There are problems with this reasoning as well, but I believe that is the point he is trying to make.
@JC 33
I believe what Summers could possibly have meant, and there have been some recent incidents to suggest that progressive economists from prestigious academic institutions in Cambridge, Massachusetts sometimes think this was is:
Josiah Neeley: I think the citation supplied by S.C. Schwarz addresses your question.
A more specific response to what I think you’re saying: When people consume more oil, there is more bad stuff (i.e. pollution) and also more good stuff (i.e. all the stuff people want to use oil for). Because there’s more bad stuff, we want to discourage oil use more than we did previously. Because there’s more good stuff, we want to discourage oil use less than we did previously. Summers presumes the first effect dominates, but makes no argument for that. If Schwarz’s reference is correct, then in fact the second effect dominates, so Summers’s conclusion should be reversed.
#22 – The fact that the climate sensitivity is expressed as temperature rise for a doubling of CO2 indicates not only that it is logarithmic, but that this relationship is absolutely central to our understanding of climate change.
I think RJ has it right. Summers simply said this:
So consider two numbers:
A) The aggregate benefit to society of imposing a carbon tax when oil prices are $100/barrel, and thus consumption is low.
B) The aggregate benefit to society of imposing a carbon tax when oil prices are $50/barrel, and thus consumption is higher.
I understand Summers to argue that B) is larger than A). In short, this isn’t a marginal cost analysis; it’s an aggregate cost analysis.
I notice that your analysis focuses on only static equilibrium. Perhaps Summers had in mind a more dynamic argument. A floor on oil prices would seem to enhance research expenditure on clean energy technologies (at least in a very simple model). Conditioning carbon tax rates on the price of oil serves to stabilize oil prices at a high level, thereby encouraging the development of alternatives
To rephrase: It seems intuitive that the harm of CO2 emissions increases with the amount of CO2 emissions, and thus the benefit of a carbon tax would grow with the amount of carbon demanded. But I struggle with how to cause this conclusion to be reflected on the graph.
To take the extreme example, if the cost of oil became infinite, no one could buy any, so a carbon tax would do no good (and no harm) at all. This prompts me to suspect that, generally, the social benefit of a CO2 tax increases with the amount of CO2 consumed. Yet this general intuition is not reflected in Landsburg’s graph. Yes, arguably the benefit is diminished as the triangle gets compressed into the Y axis. But beyond that point, Landsburg’s graph suggests that the aggregate benefit of a carbon tax of $/unit is uniform, regardless of how much carbon is consumed.
If Landsburg is making the point that the aggregate benefit of a carbon tax of $/unit is uniform, regardless of how much carbon is consumed, that is a powerfully counter-intuitive conclusion.
Maybe we are led astray by assuming that the demand curve is a straight line. Is it reasonable to assume that elasticity of demand grows as quantity grows, and thus the curve would be more asymptotic? If we assume that demand tends to flatten out as price gets lower (that is, if we assume that we would have to supply enormous amounts of oil for free before people will no longer be able to find a use for the stuff), then the size of Landsburg’s Triangle X would grow as demand grows. Similarly, if we assume that price rises disproportionately as quantity falls (that is, some people demand oil almost without regard to cost) then the size of Triangle X would shrink. And this would be consistent with Summers’s statement.
I have the familiar sinking feeling that I’m missing something obvious here….
Does the apparent conflict arise due to the lack of a time component in the curves?
Perhaps thinking in terms of a quota would help. Assume oil is harmful. It is also useful. The amount people should consume is where these balance. As some harm is external, absent a tax, people consume more than this – i.e. the costs are greater than the benefits. A tax is a way to shift the consumption back to where it should be.
A quota is another way to do the same. Ignore the absence of a mechanism, but say we could restrict the amount people used to what they should use (as defined above). Joe Average uses 100 units, he should only use 90 – lets restrict him to 90. This maximises welfare.
Now the price falls. The benefits have grown, so he should use more than 90 now – say he should use 180. Absent a tax, he will use 200. Lets restrict him to 180 units. Welfare is again maximised.
Summers is saying that the benefit is greater in the second instance.
Now in each case we have reduced consumption by 10% In each case we have balanced benefits with harms. In what sense is it more beneficial in the second case? The simple answer is that we have saved more damage from CO2 emissions. This is countered by the fact that we have increased the damage by doubling the amount by which we restrict his use. By definition, we have balanced the harms and benefits. When the same amount of fuel has been used, the harms will be the same in each case.
However, without a tax, the rate of harm is higher in the first case. After time period, the total harm is that produced by 10 units of fuel. In the second case, the harm is that produced by 20 units of fuel. This is not reflected in the price / quantity curves.
nobody.really:
It seems you and I had the same issue with the graphs, except for this:
“If Landsburg is making the point that the aggregate benefit of a carbon tax of $/unit is uniform, regardless of how much carbon is consumed, that is a powerfully counter-intuitive conclusion. ”
My understanding is the graphs show curves for individual units of consumption, not aggregate. I don’t think you can draw conclusions of the aggregate from the graphs.
It’s embarrassing, after all these years, to still struggle with interpreting simple graphs of supply and demand!
That said, I look to Landsburg’s first graph — with rectangles forming a triangle — and conclude that the rectangles are intended to reflect individual units of consumption. The total triangle reflects the aggregate deadweight social loss of misallocated resources – overconsumption of carbon at the expense of other options. Whether this reflects the loss for an individual or for society, Landsburg’s point is that this triangle does not increase just because supply has increased (assuming the demand curve is appropriately reflected by a straight line).
I’m struggling with this insight at the ground floor, just as Landsburg presented it. Forget about the unique dynamics of carbon; I’m struggling with the simple concept of the consequences of taxation – a topic I occasionally opine upon! So this is an enlightening, if somewhat humbling, discussion for me. Landburg is earning every penny I’ve paid for today’s lesson, and then some.
Here’s my new insight/current understanding: The consequences of a tax depend on the slope of supply and demand – but are wholly unaffected by the amount of supply and demand. An incremental tax reduces the quantity demanded by a fixed amount. Later shifts in supply or demand, provided they don’t shift slopes, will have no effect on the reduction in quantity demanded. A tax may reduce consumption of widgets by 10 units. If the entire national market for widgets is 10 units, the tax will reduce the quantity demanded to 0. If supply, demand, or both shift such that the national market for widget expands to 1,000,000,00 units, the tax will reduce the quantity demanded to 999,999,990.
(Or, to re-re-re-phrase, some of my past conclusions about the effects of taxation depended upon an assumption that demand curves tend to be vaguely asymptotic. I still think that’s not a terrible assumption, but one I hadn’t acknowledged before.)
If I am misunderstanding these graphs, please let me know.
Steve, two things:
(1) It is standard in the climate change literature to say that the basic greenhouse effect is logarithmic in units of emissions. So a marginal ton of CO2 will cause a smaller increase in global temperature, as the atmospheric concentration of CO2 increases. However, that’s not the same thing as saying the economic damages (using PDV etc) from a marginal ton of CO2 go down. Most models assume that at some point, additional warming causes rising marginal damages, and that this swamps the physical effect. (There are also possible positive feedback effects even just focusing on the physical processes, like warming above a certain threshold causing permafrost to melt and release methane, etc.)
(2) I’m not sure I get your answer to Josiah. Let me ask it this way: Stipulate that the marginal social damages from an activity are constant. Let’s say there is a $1 negative externality per unit. So a Pigovian tax would be $1. Then the demand for the product goes way up. The gross benefits and gross costs associated with the product go up, but on the margin the Pigovian tax still ought to be $1. I think Josiah is saying that “the case for imposing that tax” is higher once the demand has gone up, because the total amount of negative externality damages is higher. What would you say?
Bob Murphy: On point 1), I was being lazy. I took a quick glance at the reference somebody posted and read it as saying that the economic damage, not the temperature rise, was logarithmic in units of emissions. Of course that’s not what’s relevant.
On point 2), I think the graphs I posted answer this question, no? The “case for imposing the tax” is exactly as strong as the area labeled X is large. Move the demand curve up, and as long as the externality is a fixed $1 per unit, there’s no reason in general to think that area X increases.
nobody.really: I haven’t fully digested your comment, but would like to be helpful, so I hope this speaks to what’s troubling you:
Today, the world should use 100 gallons of oil, but because people dont pay the full social cost of their oil use, we actually use 110 gallons. That’s 10 gallons too many.
Now the price of oil falls (or the demand rises). As a result, the world should use 200 gallons of oil, but because we dont pay the full social cost of our oil use, we use 210. That’s still 10 gallons too many.
I’m not sure why your intuition would tell you that the social problem has gotten any worse.
My intuition tells me that incremental taxation would reduce demand by a percentage (all else being equal but for taxation). If society would consume 110 gallons in the absence of taxation, and a tax would reduce consumption by 9% (down to 100 gallons), then I would expect the same tax to reduce consumption by 9% when social demand would otherwise have been 210 gallons, or 20 gallons, or 200,000 gallons. The idea that the tax would have the same 10 gallon consequence regardless of the size of societal demand is counter-intuitive.
On this basis, the fact that society is starting to consume more carbon lead me to expect that the harm is growing. The fact that a Pigovian tax would ameliorate the harm when society would consume 110 gallons lead me to expect that it would ameliorate the larger harm I would expect to arise when society would consume 210 gallons.
nobody.really: but as you can see from the graphs, the net harm (area X) need not in fact be larger when consumption is higher. And I do not understand why your intuition is telling you otherwise (unless perhaps your intuition is thinking about gross harm, not net harm?).
A comment/question to consider, which partially walks back my previous comment.
In the supply/demand graph, the x-axis is the quantity consumed over some time period, right? The smallest time period over which there’s a reasonably sized oil market is roughly a month, and a month is also the period to which the price of oil commonly quoted in the news refers to.
The temperature rise or economic impact of global warming, however, is expressed as a function of the cumulative oil consumption. Whether this function is logarithmic, linear or some convex function is essentially irrelevant when looking at the time scale of a month. The marginal external cost of each barrel is going to effectively be a constant over such a small time scale.
I see that most (all?) of the comments are still assuming that the supply has grown and consumption is going to be larger — the reality is that there has been no sudden growth in supply, and the growth that has occurred in any case is at marginal costs generally higher than the current market price. The price is falling because demand is not keeping up, it is growing slower than expected — the consumption is not going to take off because prices have fallen, and if it did start rising at a faster rate because of factors unrelated to price, the price will go right back up to where it used to be.
1. I acknowledge that’s what the graph shows — providing me with that classic econ student experience of trying to reconcile my intuition with the model. As to why my intuition would say otherwise, well, that’s the nature of intuition. It’s … intuitive (or, in your case, not).
2. Perhaps my intuition is really telling me that demand curves are better modeled by asymptotes than straight lines. Other than pedagogical ease, is there any special reason to model demand as a straight line?
3. Alternatively (or additionally), perhaps my intuition is telling me that the circumstances that have increased the oil supply have also reduced the slope of the supply curve. This is almost certainly true overall; otherwise we might end up assuming that there is NO incremental cost for producing the first gajillion barrels of oil. But the relevant question addresses the slope of the supply curve (and social marginal cost curve) around where it intersects the demand curve. Is there any special reason to assume the slope has or has not changed? Do you have any intuition about that?
@nivedita
In the supply/demand graph, the x-axis is the quantity consumed over some time period, right?
No, the x-axis represents quantity demanded for the given time period. A change in the time period, for either supply or demand, is represented by a shift in either curve.
I see that most (all?) of the comments are still assuming that the supply has grown and consumption is going to be larger — the reality is that there has been no sudden growth in supply, and the growth that has occurred in any case is at marginal costs generally higher than the current market price.
^That makes no sense whatsoever. If marginal costs are higher than the current market price, suppliers would leave the market and supply would diminish. That may occur, but that’s not what’s currently happening.
The price is falling because demand is not keeping up, it is growing slower than expected — the consumption is not going to take off because prices have fallen, and if it did start rising at a faster rate because of factors unrelated to price, the price will go right back up to where it used to be.
That’s completely contradictory. If demand grows, all else being equal, the price goes up. However, the price of oil is falling, so if, as you say, demand is growing but yet we observe the price is falling, then it must be because supply is increasing much faster than demand.
And yes, consumption will increase if prices fall, this is called the law of demand.
@nobody.really
But the relevant question addresses the slope of the supply curve (and social marginal cost curve) around where it intersects the demand curve. Is there any special reason to assume the slope has or has not changed? Do you have any intuition about that?
In the long-run, the supply curve is flatter because all costs/factors/inputs for the producer are variable.
” If demand grows, all else being equal, the price goes up. ”
But nivedita specifically asserted that demand is falling, at least as compared to expectations.
No, he/she said it was growing slower than expected.
What is the difference between “demand is falling compared to expectations” and “demand is growing slower than expected?”
Falling entails a decrease in demand, whereas growing slower than expected is still an increase.
We are on the same page on that. I was asking for the meaning. It was meant seriously, as what I wrote did not convey the intended meaning.
WTF? I feel like I’m being trolled.
RJ, as a matter of fact, we are seeing suppliers leaving the market. US shale rig count is falling. i.e. shale oil was increasing supply, the recent drop in market price has brought price below shale marginal cost, and those suppliers are starting to exit the market. This is obviously not instantaneous.
I also fail to see what difference you see between “quantity consumed over some time period” and “quantity demanded for the given time period”. The point is that any changes in the quantity for a time period of a month or year are miniscule compared to the cumulative quantity consumed since pre-industrial times, which is the parameter used in the formulas relating temperature rise to fossil fuel consumption.
@nivedita
Fine, then the supply and social cost curve rotate and/or shift appropriately to reflect whatever change in conditions occur as time progresses. Also, note that external costs include every cost and not just global warming. Water pollution, depletion of ozone, deaths on the job from such a dangerous line of work, etc. are all external costs. To say that marginal external costs will be constant is a big leap, for all we know they could have been growing before the oil boom.
Secondly, even if it was true that some suppliers are leaving the market, maybe mostly in shale, that doesn’t entail overall that the price of oil is above marginal cost for the industry as a whole. If this were the case, you’d see prices beginning to rise, yet they’re continuing a downward trend.
RJ:
Water pollution, depletion of ozone, deaths on the job from such a dangerous line of work, etc. are all external costs.
I’m with you on water pollustion and ozone depletion, but what’s external about deaths on the job?
@Steve
I was thinking something along the lines of the death of a worker may entail a potentially lost future spouse, friend, parent, employer, employee, etc. for someone else.
RJ, I agree that other external costs are present and may be increasing on the margin. The point about current consumption vs cumulative consumption was specifically to address the earlier comments by Schwarz and Steve that because temperature rise wrt CO2 is a log function, that means margin external cost is actually declining. It might be declining, but over the time scale of a year or so it should make no difference.
Coming back to the original point of the post/article by Summers. The argument by Summers is that imposing a carbon tax today is more urgent than it was, say, a year ago, because consumption is going to grow due to the lower price.
Consumption pretty much always grows year-on-year (there was a brief blip during 2008/2009, but by 2010 consumption was back up higher than 2007), just as world GDP pretty much always grows. It is generally growing at a slower rate in recent years, as we become more energy-efficient.
Now, current oil supply is a function of investment decisions made in previous periods, on the basis of estimating current oil demand. If current oil demand comes in lower than what it was previously estimated to be, there will be an oversupply, and prices will fall rapidly (oil demand is very inelastic in the short run: note that oil consumption in 2009 actually fell, by ~1.1mm bpd relative to 2008, even with average spot oil prices falling by about 38% in 2009 relative to 2008: that price decline was not enough to offset the shift in the demand curve).
Estimates of oil demand have been falling. At the end of June, the IEA estimated 3Q14 and 4Q14 consumption to be 93.5 and 94 mbd respectively. The most recent estimates are 93.1 and 93.5 respectively. The previous estimates for past consumption were also revised, with the net effect that the estimated consumption growth for 2014 over 2013 went down by about half, from 1.3 mbd to .7 mbd. In July, the EIA estimated 2015 demand growth to be 1.4 mbd, by December, that estimate had fallen to 0.9 mbd.
This is the basis of my argument that consumption is not going to grow because of lower prices, lower prices are the consequence of consumption not growing as much as expected.
If increasing consumption makes carbon taxes more urgent, then it was more urgent to impose carbon taxes by 2015 back in July, than it is now.
Off topic: How basic are integers? Research suggests that infants begin life focusing on ratios, not absolute differences, in quantities. While Western kids are taught to focus on integers, people in other cultures retain a focus on ratios (or the logarithmic scale).
correction to last post, the IEA estimates 2015 demand growth to be 0.9mbd vs 1.4mbd back in July, not the EIA.
As a side point, I think ozone depletion is not very much impacted by fossil fuels, no? They cause ground-level ozone pollution, not stratospheric ozone depletion, I think.
@nivedita
This is the basis of my argument that consumption is not going to grow because of lower prices, lower prices are the consequence of consumption not growing as much as expected.
Again, if both supply and demand increase, then quantity demanded will increase.
You keep citing these numbers and forecasts when I really don’t think you have a clear understanding of how it all ties together. First off, from what I can infer from your post, it sounds like these numbers you’re citing represent a slowdown in growth. However, growth is still growth, which means people are consuming more than before. Second, if oil production forecasts result in an oversupply, then the drop in price causes people to eventually want to consume more. This is the law of demand and you’ll be hard pressed to find any economist who disagrees with it.
If you think the lower price is not going to result in an increase in consumption, then demand is decreasing for some other reason. Fine, but when you make statements like lower prices are the result of “consumption not growing as much as expected”, you’re dead wrong.
nobody.really: On questions about what’s fundamental, I am disinclined to defer to the judgment of infants.
Regardless of the oil price at any moment, most oil expenditure is paid through oil contracts which are gotten into to hedge oil price uncertainty. Even if oil price is quoted low now, contracts would have to be drawn now and if shale companies don’t have the wherewithal to honor them after the cost they incur have to go broke and the price should come back to what’s been expected in due time.
When nivedita says lower prices are the consequence of consumption not growing as much as expected it means prices are lower as oil contracts, which is based on what’s expected, are not drawn up for certain amount of dollar value for which it was drawn the year previously because say a travel related business is not expecting as much volume of business this year.
Ha!
Although when I shared this thought with my engineer friend, he observed that both sight and hearing operate according to logarithmic scales. That is, it’s easy to observe someone on a distant hill lighting a cigarette in the dark, but impossible to observe him doing the same in the light: a change from pitch black to a flame registers more strongly on the eye than a change from full daylight to full daylight + a flame. Similarly, you’ll have a better chance hearing a pin drop in the midst of silence than against a background of heavy metal music. In each case, the absolute different in stimulus is identical, but the relative change in the level of stimulus is not.
RJ, my point is simply this: say, supply and demand (the curves) are both growing, at some rates that keep the price relatively stable from one period to the next.
One period, the demand curve doesn’t shift to the right as much as usual, or, more correctly, as much as expected by the suppliers who were making investments in the past, that are coming to fruition in that period.
The result is that the price in that period will drop. The new lower price, already reflects the new market equilibrium for that period. There is no reason to expect that, simply because the market price is now lower, consumption will increase in the next period.
The law of demand, as I understand it, simply says that the demand curve slopes downwards. I don’t see why it’s obvious that if the market equilibrium in one period is at a lower price than in a prior period, there’s reason to believe that the demand curve will start moving to the right at a higher rate than otherwise.
Also, the reason I “keep citing these numbers and forecasts” is that while it’s all very well to plot some theoretical graphs and try to reason from that, it’s worth taking a look at the estimates made by people who have real numbers, to see if the theory is supported by data, or if it’s missing something.
Larry Summers is worried about overuse because of lower prices, but the EIA, which has real numbers, expects retail gasoline prices in the US to be 23% lower in 2015 vs 2014, GDP growth to be a bit higher, and also expects gasoline consumption to be slightly lower. This might inform us about what the shape of the real supply/demand curves is and how much they’re moving and in what direction.
One period, the demand curve doesn’t shift to the right as much as usual, or, more correctly, as much as expected by the suppliers who were making investments in the past, that are coming to fruition in that period.
The result is that the price in that period will drop. The new lower price, already reflects the new market equilibrium for that period. There is no reason to expect that, simply because the market price is now lower, consumption will increase in the next period.
Okay, now this is better.
As I hear it now, you’re saying firms had rosy predictions about increases in market demand and made future investment decisions to reflect that optimism, resulting in an increase in supply. However, demand didn’t increase by as much as suppliers predicted, so both supply and demand increased, but supply increased much more than demand, resulting in a decrease in the price. This explanation seems at odds with what you stated earlier, but I’ll assume that this is what you meant all along.
Yes, there isn’t any reason to believe that consumption will increase the next period as a result in lower prices, demand increases or decreases as a result of something other than the price. However, quantity demanded this period has increased as a result of the lower price brought about by the increase in supply. More oil than before is being consumed.
The law of demand, as I understand it, simply says that the demand curve slopes downwards.
You’re (correctly) describing what the graph shows, but not what it means. What this means is, given a downward sloping demand curve, as the price of a good decreases then people will consume more units of that specific good, and vice versa. So if you were to draw on a supply and demand graph of how you’re describing the market for oil has played out, with both supply and demand shifting rightward, but with supply shifting rightward by a greater amount than demand, you’ll see that the new equilibrium quantity is much greater than what it was before. Thus, there is a much greater consumption in oil going on until other conditions change.
Also, the reason I “keep citing these numbers and forecasts” is that while it’s all very well to plot some theoretical graphs and try to reason from that, it’s worth taking a look at the estimates made by people who have real numbers, to see if the theory is supported by data, or if it’s missing something.
Yes, but you need to understand what the theory and graphs actually say and mean before you can start comparing the theory to the data.
Larry Summers is worried about overuse because of lower prices, but the EIA, which has real numbers, expects retail gasoline prices in the US to be 23% lower in 2015 vs 2014, GDP growth to be a bit higher, and also expects gasoline consumption to be slightly lower. This might inform us about what the shape of the real supply/demand curves is and how much they’re moving and in what direction.
That’s just gasoline. Oil has a variety of uses, and if it’s cheaper then people may use it in ways that were too costly before.
I’ll tell you, Steve Landsburg, Bob Murphy, etc – what no one has done – as far as I know – they’ve never come up with a simple, elegant maxim for deciding where carbon tax should occur and where it shouldn’t.
RJ,
This explanation seems at odds with what you stated earlier, but I’ll assume that this is what you meant all along.
What are you talking about? From my very first post:
the recent fall in oil price is not due to unexpected increased supply, but due to reduced demand, relative to prior expectations
I think the crux of our confusion is how to state this:
However, quantity demanded this period has increased as a result of the lower price brought about by the increase in supply. More oil than before is being consumed.
The wording that is problematic is “more oil than before is being consumed”. What would you say if the growth in demand wasn’t just smaller than expected, but negative — this is not a theoretical worry, I included the numbers about gasoline because they make sense only if the demand curve for gasoline in 2015 is expected to actually be to the left of the demand curve in 2014 (though the latest EIA outlook has total consumption now expected to increase slightly rather than decrease slightly). Then the quantity consumed can actually drop — surely it doesn’t make sense any more to say that more oil than before is being consumed, or that the lower price has resulted in a greater quantity being demanded. Those statements are only valid if you compare to what the quantity demanded would have been at a higher market price, all else equal, including being the same period, not the prior period.
My statement of this is that the demand curve shifted to the right less than it was expected to (or maybe even shifted to the left), and this has caused the lower price. The lower price itself is just an indicator, it doesn’t cause anything by itself.
The point about the carbon tax is this: six months ago, we thought consumption in 2015 was going to be x, and we had some level of desire to impose a carbon tax in 2015. Today we expect that consumption in 2015 is going to be less than x. I’m arguing that this means our desire to impose a carbon tax in 2015 should be less than before (assume we think it’s more desirable to impose a carbon tax at higher levels of consumption).
Our desire to impose a carbon tax in 2015 may still be higher than our desire was to impose one in 2014, though, but this still has nothing to do with the lower prices — our desire is greater because the expected demand curve didn’t shift to the left so much that 2015 consumption is now expected to be below 2014. The falling price, which is a reflection of the expected demand curve shifting to the left, is a positive indicator in this case.
If, on the contrary, the expected demand curve in 2015 had not shifted to the left, but the price had fallen because of some unexpected supply increase (say someone just found some new oil field with low cost of extraction and a stable political environment, or there was an innovation in drilling technology that made fracking upfront costs much lower), then expected consumption in 2015 would have gone up, and our desire to impose a carbon tax in 2015 would be higher than before, and we could talk about the “lower price making it more urgent”.
nivedita,
I’m not even sure what to make of your posts anymore. You keep repeating the same contradictory statements but have an inability to grasp that they’re contradictory.
1. Saying the demand curve can shift to the right and resulted in a lower price is only true if the supply curve also shifts to the right by more than the demand curve. Saying that it shifted to the right “less than expected” but somehow resulted in a lower price is a complete and utter failure to understand how the graphs work.
2. You narrowly look at statistics to support your claim without considering the larger picture. You started off by only speaking of only global warming as if it were the only external cost, and then moved onto gasoline consumption while ignoring the fact that total consumption of oil is forecasted to rise from your very own EIA sources (I checked).
3. You then go on to say things like this…
Our desire to impose a carbon tax in 2015 may still be higher than our desire was to impose one in 2014, though, but this still has nothing to do with the lower prices — our desire is greater because the expected demand curve didn’t shift to the left so much that 2015 consumption is now expected to be below 2014. The falling price, which is a reflection of the expected demand curve shifting to the left, is a positive indicator in this case.
Nothing in this paragraph makes the slightest bit of sense.
If, on the contrary, the expected demand curve in 2015 had not shifted to the left, but the price had fallen because of some unexpected supply increase (say someone just found some new oil field with low cost of extraction and a stable political environment, or there was an innovation in drilling technology that made fracking upfront costs much lower), then expected consumption in 2015 would have gone up, and our desire to impose a carbon tax in 2015 would be higher than before, and we could talk about the “lower price making it more urgent”.
^This is still not even correct, it misses the entire point of the blog post!
In short, I’m done.
Ahh, html error. Hopefully Steve deletes the one that’s mostly in bold. I’ve also condensed it a bit after giving a more generous reading.
nivedita,
I’m not even sure what to make of your posts anymore. You keep repeating the same contradictory statements but have an inability to grasp that they’re contradictory.
1. Saying the demand curve can shift to the right and resulted in a lower price is only true if the supply curve also shifts to the right by more than the demand curve. Saying that it shifted to the right “less than expected” but somehow resulted in a lower price is a complete and utter failure to understand how the graphs work.
2. You narrowly look at statistics to support your claim without considering the larger picture. You started off by only speaking of only global warming as if it were the only external cost, and then moved onto gasoline consumption while ignoring the fact that total consumption of oil is forecasted to rise from your very own EIA sources (I checked).
3. You then go on to say things like this…
Our desire to impose a carbon tax in 2015 may still be higher than our desire was to impose one in 2014, though, but this still has nothing to do with the lower prices — our desire is greater because the expected demand curve didn’t shift to the left so much that 2015 consumption is now expected to be below 2014. The falling price, which is a reflection of the expected demand curve shifting to the left, is a positive indicator in this case.
Nothing in this paragraph makes the slightest bit of sense. You’re making the same mistakes as before except now you making them in the opposite direction. If demand decreases, ceterus paribus, quantity demanded decreases. If quantity demanded decreases, then our desire to impose a carbon tax, assuming with the decrease the SMC curve is flatter, decreases.
In short, I’m done.
RJ.
1) I’m not sure what your point is here. I’m obviously assuming that the supply curve shifted to the right at the same time, but the demand curve shifted less, or indeed, shifted to the left (the data does not let us determine whether the demand curve shifted to the right less than expected, or shifted to the left). In fact, I have already explicitly made this point, I suppose your response is going to be that I keep repeating myself, but apparently saying it once isn’t enough for you. I understand very well what the graph means, thank you very much.
2) I’ve already explained to you why that particular comment was only about global warming (hint: the original comment wasn’t directed to you), and I’ve even agreed that there are other costs.
I didn’t “move on” to gasoline consumption, that was a specific example given to you in the hope that you would understand that “lower price = higher consumption” is not a truism. I even took the trouble to point out that the latest estimates show gasoline consumption to be slightly higher, and the thanks I get is that I’m accused of cherry-picking the numbers!
3) This paragraph makes perfect sense, if you took the trouble to actually read what is written and try to understand it — you have clearly not grasped what is meant by “expected demand”. Our expectation for consumption for 2015, as of July 2014, was 94.1 mbd. Our expectation for consumption for 2015, as of December 2014, was 93.3 mbd. Our desire to impose a carbon tax in 2015 has declined between July 2014 and December 2014. Our desire to impose a carbon tax in 2015 is still higher than our desire was to impose one in 2014, because 93.3 mbd is still higher than our estimate of consumption in 2014, which was 92.7 mbd in July 2014, 92.4 mbd in December 2014, and coincidentally 92.4 mbd in December 2013.
Steve,
I hope you’re still checking these comments…
I have actually put a lot of thought into why Josiah and I were getting tripped up in reconciling your post with our intuition.
The problem (I think) is that when we imagine an activity that has a negative externality, we tend to think that even the first unit is carrying the bad social cost, and that that only grows with the units.
So if the social external cost of CO2 is $10 per ton, then if the demand for oil goes up and emissions go up by a million tons, then “surely” the negative externality has increased by $10 million.
I realize now that that is not a great way to think about it, for the reason you explain in this post.
If you take requests, I think it would help the blogosphere if you do a First Principles post on Pigovian taxation, and explained that the optimal level of output is *not* zero units, even for something with an admittedly negative externality. It might seem obvious to you, but if both Josiah and I stumbled for a moment when posting off the cuff, it’s probably worth doing. (Especially if it’s your free time that is wasted, rather than mine…)
(To be clear, Steve, I agreed with your post from the get-go, and indeed this is a point I’ve been making all along–that the level of output doesn’t change the case for a carbon tax, at least without some further assumptions. But I could totally see where Josiah was coming from, and your initial answer to him didn’t seem to resolve the confusion in my mind.)
Great discussion, as always. As much as I hate to agree with Larry Summers, you never refuted his original statement. His argument for Pigovian taxes is not based on marginal externalities, but on cumulative.
As you demonstrated, the “per unit” inequality is unchanged, but the greater number of units implies the market inefficiency is greater than before.
Suppose the price of oil declines by 50% and usage doubles (a deliberate over-simplification): As you pointed out, usage “should” have doubled, but this is a marginal argument. If the unfunded externality was $20 billion per day, it is now $40 billion per day.
A market imbalance justifies government intervention based on it’s total size, not the size of the per-unit inefficiency.