The Alexandrian

I’ve gotten tired of explaining why supply-side economics — i.e., voodoo economics — don’t actually work. So I’ve decided to write up a quick-and-dirty version that I can just link to as necessary. This is not meant to be a definitive statement on the subject. It’s not even an air-tight argument of the principles being espoused. It’s just me pointing at some pretty fundamental absurdities in voodoo economics and saying, “Hey! Look! Have you even thought about this? It doesn’t make any sense!”

(1) Money is a form of power. Power tends to accumulate more power. Thus, in a capitalist society, wealth tends to flow up, not down. The rich tend to become richer and the poor tend to become poorer. Supplying the wealthy with even more money doesn’t cause that money to flow down to the poor — it just accelerates this natural trend. Which is why, every time supply-side economics have been attempted, the divide between the rich and the poor has grown wider.

The argument has been made that a “rising tide raises all ships”, but the reason this disproportionate distribution of wealth is a problem leads us to…

(2) The modus operandi of capitalism is consumer spending. In a capitalist system you have multiple products available, and those products which have the greatest value to the consumer succeed (because they buy them) and those which have less value fail (because they don’t). In a very real sense, capitalism is a democracy in which you vote with your dollars for the products you like best. And although in practice a capitalist system can become flawed in many ways, capitalism has widely proven itself to be the best system for encouraging quality, efficiency, and innovation.

You need an unequal distribution of wealth for this system to work, but when that inequality becomes sufficiently disproportionate the reduced spending power enjoyed by the majority of your consumers results in a less efficient system. Not only are the quality of decisions which emerge from such a system degraded, but the system’s ability to encourage increased value and quality becomes quashed.

This all leads us to the fundamenal problem with supply-side economics…

(3) If you want to stimulate a capitalist economy, you should be giving tax breaks to the poor, not the rich.

The reason for this is the difference between spending and investing. Republicans argue that giving tax cuts to the rich allow them to invest in business. By investing in business, the argument goes, the economy grows and the workers end up benefitting in the long run.

But while investing is an important part of capitalism, it’s the secondary mechanism of the capitalist system. The primary mechanism of a capitalist system is spending.

If you give money to someone and have them invest it, that money may or may not eventually result in economic activity and capitalist success. (Whether it does or not will depend entirely on how the money is invested. If it’s invested in a better, cheaper product that people want, it will stimulate the economy. If it isn’t, then it won’t.)

But if you give the money to someone and have them spend it, that money immediately results in economic activity and capitalist success. This result is guaranteed.

In other words: If you give the money to an investor, you are injecting that money into the economy in an inefficient manner — that money may or may not end up growing a business producing products that consumers want.

If you give that money to a consumer, on the other hand, you are injecting that money almost directly into the economy — that money will automatically end up growing a business producing products that consumers want (because the consumer will spend it on the products that they want).

(4) The name “trickle down economics” is actually truth in advertising. Money in a capitalist system flows reliably from the consumer to the successful business/investor/capitalist. Movement in the opposite direction, however, is not reliable.

Which actually brings us full circle: In capitalism, wealth tends to flow up and trickle down. If you want to stimulate an economy, you want to make the money flow and, thus, encourage better ideas and more valuable products.

And that means tax cuts for the poor and the middle-class, not the rich.

THE OTHER FALLACY

Of course, this conclusion simply opens the door to the larger question of when such tax cuts are appropriate. The other fallacy of voodoo economics is the claim that lowering taxes will always result in sufficient economic growth to raise overall tax revenues. This is self-evidently not true for several reasons:

(1) If you reduce the tax rate to 0%, it doesn’t matter how much economic growth you enjoy as a result: You still won’t end up with increased tax revenues (since you’re not collecting any).

(2) Even if you replace “no taxes” with “infinitesimal taxes”, the conclusion is still palpably absurd. If you have an average tax rate of 30% and you lower that to an average tax rate of 1%, you’re claiming that the economy will grow to 30 times its current size entirely as a result of the tax cuts. (That means you can’t count inflation or the normal economic growth that would have occurred even if you hadn’t cut taxes.)

The underlying fallacy here is the belief that the social institutions and infrastructure created by our government have no positive role on economic growth. Common sense alone should tell you that a certain degree of social infrastructure (e.g. law and order), physical infrastructure (e.g. roads), and educational infrastructure (e.g. univeral education) is beneficial to the economy (even if one ignores all the other societal benefits). And even the most cursory analysis of history shows this to be true: Anarchy is not conducive to economic growth.

On the other hand, it is equally trivial to demonstrate that the opposite extreme is equally absurd: The benefits brought by government cannot possibly outweigh the problems caused by an average tax rate of 100%.

The inevitable conclusion is that there is a sweet spot in which both the benefits of low taxes and the benefits of the societal infrastructure provided by our government are maximized.

Or to look at it another way: The problem with both extremist libertarians and communists is that they equally fail to appreciate the sweet spot between anarchic liberty and absolute central control.

2 Responses to “Why Voodoo Economics Don’t Work: The Quick and Dirty Version”

  1. Justin Alexander says:

    ARCHIVED HALOSCAN COMMENTS

    Todd
    When I posted my comment, I wasn’t creating conspiracy theory. These are my personal observations from experience working in medical research. The big funding isn’t there for research that will benefit the most people. It’s going towards drugs that will cure high-profile conditions (making quarterly reports look good) or towards treatments that will alleviate symptoms. The more beneficial research just wouldn’t be possible without government funding. Occasionally I have seen companies throw out small grants to PIs, but this is more of an attempt to lure good researchers away from academia than a contribution good enough to buy new research equipment and materials.

    Perhaps my experience is the exception to the rule, but I doubt it.
    Tuesday, August 26, 2008, 7:48:19 PM


    Leland J. Tankersley
    “I must say, I like this latest assertion — that a company will not pursue a cure unless it believes itself to have both the capacity and resources to do so. That sounds very reasonable; thank you.”

    I would add: “…and believes that developing said cure will benefit the company’s bottom line” since I believe there are situations where this would not be the case.

    “The previous version of this statement seemed to be ‘a company will not pursue a cure, no matter its capacity and resources, if it already has a drug that merely relieves the affliction’s symptoms.’ I’m sure you can see why that was objectionable.”

    I think that perhaps you were reading more into my post than I put there.

    “Can I take it that we agree on my point, then? –That developing cures is slow, not because big business is deliberately maintaining a status quo at everyone’s expense, but because progress takes investment and patience?”

    I believe that this is generally true, yes. I was pointing out another potentially confounding factor; namely, that it some cases, what’s good for a particular company may not necessarily be good for “the rest of us,” and that companies make decisions based on what they perceive as being good for themselves.
    Monday, August 25, 2008, 8:48:06 AM


    Richard
    I must say, I like this latest assertion — that a company will not pursue a cure unless it believes itself to have both the capacity and resources to do so. That sounds very reasonable; thank you. The previous version of this statement seemed to be “a company will not pursue a cure, no matter its capacity and resources, if it already has a drug that merely relieves the affliction’s symptoms.” I’m sure you can see why that was objectionable.

    Can I take it that we agree on my point, then? –That developing cures is slow, not because big business is deliberately maintaining a status quo at everyone’s expense, but because progress takes investment and patience?
    Monday, August 25, 2008, 6:25:07 AM


    Leland J. Tankersley
    You mistake my observation for vehemence. You also appear to imagine that all of these actors possess perfect information about their relative degree of progress towards various objectives, when actually more often than not they do not know where the “finish line” is.

    “Any halfway intelligent company A would attempt to follow their lead and keep abreast of the cutting edge in research to keep from losing the race.”

    This is based on a gross oversimplification. Even ignoring the issue of not knowing if a given “race for a cure” is even winnable (maybe some condition/disease/whatever will never be cured), and the difficulty in assessing progress toward a goal that is not clearly understood, businesses operate under resource constraints. They must decide what research to fund, and how heavily. These decisions are driven by cost-benefit assessments (also made with limited information). Certainly these companies fund a lot of basic research. That is, by and large, the business they are in. My point is merely that, in some cases, the cost-benefit equation might dictate that identifying a cure for a condition that is currently only “managed” might not fare so well in their prioritization compared with e.g. researching products addressing needs not yet serviced at all (thus creating new markets for their products).
    Sunday, August 24, 2008, 3:32:37 PM


    Still Richard
    Re: profit, if I were a money-blinded pharmaceutical company with a cure to some disease that to that point had only had its symptoms relieved, I would do everything I could make this cure proprietary and become the only company legally able to cure the disease, thus creating a very profitable monopoly that could never be accomplished by mere hostile takeovers, and simultaneously driving my competitors out of the niche we had formerly occupied together when selling the palliative. If a monopoly becomes impossible, I would at least do everything in my power to make my brand name synonymous with the treatment. Cf: Sildenafil citrate. Waiting in the wings for somebody else to do all this would not strike me as the most excellent strategy to keep my business profitable.

    Restated: if company A has even the slightest lead toward curing disease X, then as noted previously it is not only possible but near-inevitable that sooner or later company B, or academic researcher C, or some dude in Switzerland D, will find and follow that lead as well. Any halfway intelligent company A would attempt to follower their lead and keep abreast of the cutting edge in research to keep from losing the race.

    One factor in new medicines coming slowly to the market that nobody seems to be considering is that our understanding of the human body is still incomplete. Why does electroconvulsive therapy work at all, and how, and what are its side effects? We’re still not sure. So even if you did come up with a drug, or combination of drugs, to cure (say) the common cold once and for all, it would probably have to see years of computer modeling and animal testing and clinical trials before coming to market, and perhaps a lawsuit or two from some idiot who got fat or stubbed their toe while taking the drug.

    Aha, says Tankersley, that’s exactly why company A will never spend the resources necessary to develop a cure. No, I reply, by that logic nothing new would ever be developed. What it means is that progress, as noted in a previous comment, is incremental, and that progress, as noted in my original argument, requires investment and patience. (By patience I refer to the fact that things tend to change meaningfully on historical rather than attention-span time scales.)
    Sunday, August 24, 2008, 11:41:27 AM


    Leland J. Tankersley
    Re: pharmaceuticals, while a conspiracy certainly seems far-fetched, it’s worth remembering that corporations are not generally speaking charitable organizations. They have a fiduciary responsibility to make money for their shareholders. If such a company has an existing profitable revenue stream based on the production of a drug that ameliorates the effects of some disease, their motivation to research, discover and produce an actual CURE for the same disease that would render the existing product obsolete is questionable.
    Sunday, August 24, 2008, 8:56:42 AM


    Richard
    Yes, Todd, excellent points. I’m sure that your in-depth knowledge of the pharmaceutical industry is what allows you to know that no doctors anywhere are working on drugs to cure harmful conditions, or that if they are, the companies are simply refusing to sell the cure for cancer, on the grounds that curing cancer isn’t profitable. The telecommunications industry is even worse, with its selfish anti-progress lobbying. If only they would allow us to develop the technology for high-bandwidth internet connections and wireless telephones! Alas, we can only dream of such a day. Truly, the answers to all the technological advances you desire are simple and could already have been accomplished if the tech companies weren’t all in a huge conspiracy to give progress to us slowly.

    As amused as any thinking person must be by the assertion that “certain companies” would rather just shuffle around and buy each other “than to benefit themselves,” it’s probably worth pointing out the fundamental lack of understanding the comment reveals. Progress is not just a magic button you press and a new miracle comes out, despite what the industrial and electronic revolutions may seem to imply. Over the course of history, *all progress* has always been incremental. Even the supposed big leaps have hundreds of smaller steps leading up to them — even Einstein was building on ideas he was exposed to, new advances in mathematics and physics — when he formulated relativity. Quantum mechanics was the work of a number of geniuses, all of whom were in communication with each other, developing their ideas through calculation and argument. The science and technology needed to bring about “game-changers” is a lot more difficult and time-consuming than our friend Todd suspects. What’s more, his beloved iPhone too is incremental. All of the technology for it had been developed over the course of years, step by baby-step, and while it may be a bit of an innovation to combine and package them as Apple did, such a result was all but inevitable given that the pieces were there. (Suggested reading: http://www.gladwell.com/2008/2008_05_12_a_air.html)

    There are times when the discourse on this site has been interesting. This is not one of those times. Here’s a challenge: somebody please design a version of Haloscan that tells me when a comment is thoughtful and thorough, and when it’s knee-jerk conspiracy theory. Now that would be a quantum leap forward, eh?

    And here I thought the point of the original post was to make people think.
    Saturday, August 23, 2008, 8:37:59 PM


    Tetsubo
    Excellent points Todd. But how is this change going to happen? The example industries already have there markets and politicians sewn up tight. The politicians aren’t going to put in regulations that might cut off their bribery money. Without that bribery cash, they might not get re-elected.
    Saturday, August 23, 2008, 3:25:07 PM


    Todd
    It seems that one of the main problems with our current system is that after a certain level of wealth is accumulated, certain businesses tend to use that wealth to maintain their status quo rather than to benefit themselves and consumers. This is evident in the pharmaceutical and telecommunications industry, for example. In the telecommunications industry, certain companies go out of their way to purchase their competitors so as to avoid competing with them. When the competition no longer exists, these companies have no incentive to generate anything beyond incremental advances to communication – no real game-changers. The barriers to entry are so huge that any competitor is usually purchased before it can produce a product that threatens the larger corporation. One of the few ways in which this is able to change is from another type of industry moving into telecommunications, such as Apple producing its iPhone. This type of shakeup tends to re-stimulate the other corporations into innovation rather than incremental advances.

    To the same extent, pharmaceutical companies are at a stage where it has become more beneficial to them to produce incremental advances on medications (i.e. time-release versions of heartburn medication) than to seriously research cures to the most harmful conditions. They also engage in the practice of buying up or merging with close competitors (as in the case of Glaxo-Smithkline).

    Basically, these types of activities, along with surreptitious bribery and influence, allow certain companies to bend the capitalist system to avoid making real progress in favor of short-term growth. The fact that this is able to happen indicates we have gone too far towards the no regulation side and we need to move back towards the side of increased regulation.
    Saturday, August 23, 2008, 1:30:43 PM


    Tetsubo
    Here’s the thing: I don’t think the politicians that are making these policies have any more economic training then Justin. And they aren’t half as well spoken. These politicians are using simplistic, voter friendly language to convince people that benefiting the wealthiest Americans will benefit *all* Americans. Which is of course BS. And the people selling this idea know it is BS. But it keeps the bribery money (campaign contributions) flowing.

    This isn’t really about economics. It’s about one party flim-flamming the American people, again.

    Under what Republican administration has the economy improved? The last budget surplus we had was under Clinton.

    I’ll take “tax & spend” over “borrow & spend” any day.
    Saturday, August 23, 2008, 3:18:45 AM


    Richard
    Right; word limit.

    I’m not such an economist that I know the best way to do that, but speaking purely in terms of tax breaks, it seems you’d want to award them, not on the basis of being rich or poor, but based on whether they will help the economy to continue to develop. Companies, even big ones, that are making new things (say, Apple?) will probably be able to do more good for society over the long term with a given magnitude of tax-break than if you simply allowed the nation’s poor to spend a few dollars more each on their consumer habits.

    Despite this piece’s seemingly terrible opinion of “investing,” I see no difference between buying a car company’s car (thus giving them a certain amount of profit that can be spent on increasing society’s wealth) and investing in the company, which allows them to increase society’s wealth but doesn’t require the middle-men or the physical waste of a car being schlepped around. Better yet, consumer spending is dampened in its effects by the expenditure necessary to sell a product or service; it’s inefficient. Investment needs no such expenditure; the investor merely receives some share of the money generated if the input money does its job. (It may not, but then again it may not even if it comes from consumer spending.)

    In brief, then: I agree that a blind application of “trickle-down economic” principles is a terrible idea. The argument in this piece is, ultimately, right. But the reasons it gives hold no water; they seem to be based on reactionary left-wing clichés rather than on observable phenomena. It may be right, but it’s right for all the wrong reasons.
    Wednesday, August 20, 2008, 1:37:30 AM


    Richard
    First: I don’t disagree with the basic contention that there are better ways to stimulate the economy than just giving big corporations tax breaks… but as is almost admitted, the arguments given in this piece are full of holes, as are some of the premises, and hanging a lampshade on this fact still doesn’t excuse it.

    Pardon my ignorance, but I’m not clear at all by what this piece’s definitions of “spending” or “economic stimulation” are. From reading this piece, it feels as if spending only counts if it’s done by an individual. Somehow, a poor family buying a better, cheaper TV (for which they need a tax break?) than they would have otherwise bought equals economic stimulation, but a company buying a building and machinery and hiring workers… doesn’t.

    The “power” rule presented in point 1 may be generally true, but the assertion that “the poor tend to become poorer” (yes, those are your words) is blatantly false from any sort of historical view. When a century ago your average poor family had to struggle to stay warm and fed in the winter, and now your average poor family is overfed and lives in a heated/air-conditioned home, it’s clear that the accumulation of knowledge and infrastructure over time will tend to make all members of a society richer and better off over time, regardless of the numerical gap between the very richest and the very poorest.

    The repeated assertion that wealth somehow flows from the poor to the rich is easily demonstrated as false: if this were, on average, the case, how could the standard of living among the poor ever increase? And why do they never run out of money from this continuous flow? Even if money really does “flow up,” it clearly doesn’t exhibit that behavior overall, or else the poor (with negative average delta-wealth) would eventually hit zero.

    It seems far more likely to me that history’s processes, whereby the sum of all wealth tends to always increase, is the real culprit, and leads to this false perception of upward flow. Bill Gates is a billionaire, not because he created a fancy mechanism for making money flow from the poor to himself, but because he created those billions of dollars out of nothing more than human brain-power. And it’s through his influence that you have a PC and are able to generate wealth yourself, by typing words (to be made into books) and advertising them [glances to the left] on your website. Is wealth flowing from the poor to you? No; you’re creating something that never existed before and your profits are that new existence translated into monetary form.

    The question then becomes, How does one ensure that this process of wealth-generation continues? Regardless of short-term economic activity or government revenue, a society will become richer and better off if it can develop its knowledge and infrastructure and make new products, and will stagnate otherwise.

    I’m not such an economist that I know the best way to do that, bu
    Wednesday, August 20, 2008, 1:28:42 AM


    Autodidact
    Justin: Just as a question, how much formal economics training do you have?
    Wednesday, August 20, 2008, 12:38:37 AM


    L
    There is nothing but voodoo lying behind the (questionable) premise “lowering taxes always results in higher tax revenues” and the conclusion “therefore we should lower taxes for the richest 1% of society”.

    You are arguing against a straw man while misrepesenting your oponents’ arguments

    First, such a claim would be voodoo (reducing the marginal tax to zero would obviuosly reduce revenue to zero), but no one has made it. Some people claim that at the current levels, and infinitesimal reduction in taxes would give an infinitesimal increase in revenue. This is a complicated economic question. I don’t think you or me are qualified to nnswer this question.

    Secondly, while some libertarians argue that taxes should be greatly reduced, they are not arguing that this would increase government revenue. Quite the opposite: they are arguing that this will greatly reduce government revenue. If you believe that the government itself needs to be greatly reduced, then lowering taxes is an obvious corollary.

    Choosing tax levels in order to optimize government revenue only makes sense if government is an end unto iteslf. Otherwise, government revenue should depend on what the government needs to do.
    Tuesday, August 19, 2008, 7:13:39 PM


    L
    Sorry for the double-post. It seems my broswer had an odd interaction with the site.

    In any case, the following quote also needs some response: “Money is a form of power. Power tends to accumulate more power. Thus, in a capitalist society, wealth tends to flow up, not down”.

    You seem to be thinking of the situation as a zero-sum game: each turn some money grows on the trees, and needs to be allocated among members of society. This allocation is coercive (a function of “power”): those who already have some somehow use force to skew the allocation further their way.

    In the US, this is to some extend the case. But government meddling is the cause of this, not the cure. Wealth is in fact not a zero-sum game, but is rather constantly being created. Wealth is allocated in a very simple way: you own whatever wealth you create. You can exchange this wealth for other goods: I exchange the work I create for the salary I get from my employer, for example. It is true that I can get more for my work than other people get for theirs. But you are somehow claining that this happens because I have “power” — not because what I produce happens to be more desirable. Do you really mean that?

    Money is not a form of power. It is merely a convenient token used for exchange of goods and for keeping traack of our obligations to each other.
    Tuesday, August 19, 2008, 7:01:41 PM


    L
    Justin: in fact rght in the second paragraph you said: “The rich tend to become richer and the poor tend to become poorer.” This is false. It may be true that, say, the top 10% of the population is becoming richer faster than the bottom 10% of the population is becoming richer, but not that the poor are becoming poorer. Moreover, the “poor” and the “rich” you are talking about are not actual people. In the US very few people stay either rich or poor over time.

    Further, those in the low income tax brackets actually pay very little of the total taxes. Thus, reducing their taxes will have a small effect on the economy. This is not to say that it’d be a bad idea.

    Finally, note that changing the taxrules for the “rich” a-la Obama will have a much smaller effect on revenue than you think. The “poor” have mostly income from work, the taxation of which is out of their control. Income from business ownership and investment, on the other hand, can be accounted for and taxed many different ways (do you pull dividends or not? do you incorporate the business or not? how much of the profits remain in which part of the enterprise?).
    Tuesday, August 19, 2008, 6:51:02 PM


    L
    Justin: in fact rght in the second paragraph you said: “The rich tend to become richer and the poor tend to become poorer.” This is false. It may be true that, say, the top 10% of the population is becoming richer faster than the bottom 10% of the population is becoming richer, but not that the poor are becoming poorer. Moreover, the “poor” and the “rich” you are talking about are not actual people. In the US very few people stay either rich or poor over time.

    Further, those in the low income tax brackets actually pay very little of the total taxes. Thus, reducing their taxes will have a small effect on the economy. This is not to say that it’d be a bad idea.

    Finally, note that changing the taxrules for the “rich” a-la Obama will have a much smaller effect on revenue than you think. The “poor” have mostly income from work, the taxation of which is out of their control. Income from business ownership and investment, on the other hand, can be accounted for and taxed many different ways (do you pull dividends or not? do you incorporate the business or not? how much of the profits remain in which part of the enterprise?).
    Tuesday, August 19, 2008, 6:51:02 PM


    Justin Alexander
    Robert wrote: “But nobody implements the strong version; nobody is advocating that we drop the tax rate to 1% and that we’ll get a thirtyfold expansion of the economy.”

    Except, of course, that lots of people do advocate exactly that. And whenever someone — Rush Limbaugh or George W. Bush or the Heritage Foundation for example — says that lowering taxes always results in higher tax revenues, that’s what they’re claiming.

    Robert wrote: “We can’t stimulate the economy with tax breaks for the poor, because the poor don’t pay many taxes.”

    It would be a more accurate characterization of my position to say that we should be cutting taxes on the lowest tax brackets and not the highest. That means tax cuts for the poorest tax payers — which also includes the middle class.

    Robert wrote: “The point of the Laffer curve is that there are points on the revenue curve where a small reduction in tax rates might cause an overall higher rate of collections – like going from 29% to 24% or something. ”

    To some extent, I agree. In fact, you’ll note that I said something very similar: “The inevitable conclusion is that there is a sweet spot in which both the benefits of low taxes and the benefits of the societal infrastructure provided by our government are maximized.”

    However:

    (1) I suspect that John F. Kennedy was a lot closer to identifying that sweet spot than Reagan or Bush or Bush have been.

    (2) The Laffer curve is almost laughably over-simplistic (as demonstrated quite strongly by the neo-Laffner curve among other things). The actual economic effects of taxation policies are far more complex than the Laffer curve takes into account.

    (3) For example, one of the things the Laffer curve doesn’t take into account is who is being taxed, which you’ll note is one of my primary problems with supply-side economics. There is nothing but voodoo lying behind the (questionable) premise “lowering taxes always results in higher tax revenues” and the conclusion “therefore we should lower taxes for the richest 1% of society”.
    Tuesday, August 19, 2008, 4:56:33 PM


    Robert
    As an economist, you’re a great game designer. Wink

    You are right that the strong version of the Laffer curve theory doesn’t really work out in practice. But nobody implements the strong version; nobody is advocating that we drop the tax rate to 1% and that we’ll get a thirtyfold expansion of the economy. The point of the Laffer curve is that there are points on the revenue curve where a small reduction in tax rates might cause an overall higher rate of collections – like going from 29% to 24% or something.

    We can’t stimulate the economy with tax breaks for the poor, because the poor don’t pay many taxes.

    And finally, if the capitalist system makes the rich richer and the poor poorer, who are all these poor people with satellite TV and computers I keep running into? A hundred years ago, rich people lived in mansions and drove fancy cars, while poor people lived in tin shacks and gleaned in the fields. Today’s rich people look pretty much the same (there’s only so much you can consume, after all) while the poor people are a thousand times better off.

    I really liked your takedown of 4E, though Wink
    Tuesday, August 19, 2008, 2:24:04 P

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