Correct Foresight, Perfect Foresight, and Intertemporal Equilibrium

In my previous post, I discussed Hayek’s path-breaking insight into the meaning of intertemporal equilibrium. His breakthrough was to see that an equilibrium can be understood not as a stationary state in which nothing changes, but as a state in which decentralized plans are both optimal from the point of view of the individuals formulating the plans and mutually consistent, so that the individually optimal plans, at least potentially, could be simultaneously executed. In the simple one-period model, the plans of individuals extending over a single-period time horizon are constrained by the necessary equality for each agent between the value of all planned purchases and the value of all planned sales in that period. A single-period or stationary equilibrium, if it exists, is characterized by a set of prices such that the optimal plans corresponding to that set of prices such that total amount demanded for each product equals the total amount supplied for each product. Thus, an equilibrium price vector has the property that every individual is choosing optimally based on the choice criteria and the constraints governing the decisions for each individual and that those individually optimal choices are mutually consistent, that mutual consistency being manifested in the equality of the total amount demanded and the total amount supplied of each product in that single period.

The problem posed by the concept of intertemporal equilibrium is how to generalize the single-period notion of an equilibrium as a vector of all the observed prices of goods and services actually traded in that single period into a multi-period concept in which the prices on which optimal choices depend include both the actual prices of goods traded in the current period as well as the prices of goods and services that agents plan to buy or sell only in some future time period. In an intertemporal context, the prices on the basis of which optimal plans are chosen cannot be just those prices at which transactions are being executed in the current period; the relevant set of prices must also include those prices at which transactions already being planned in the current period will be executed. Because even choices about transactions today may depend on the prices at which future transactions will take place, future prices can affect not only future demands and supplies they can also affect current demands and supplies.

But because prices in future periods are typically not observable by individuals in the present, it is not observed — but expected — future prices on the basis of which individual agents are making the optimal choices reflected in their intertemporal plans. And insofar as optimal plans depend on expected future prices, those optimal plans can be mutually consistent only if they are based on the same expected future prices, because if their choices are based on different expected future prices, then it is not possible that all expectations are realized. If the expectations of at least one agent, and probably of many agents, will be disappointed, implying that the plans of at least one and probably of many agents will not be optimized and will have to be revised.

The recognition that the mutual consistency of optimal plans requires individuals to accurately foresee the future prices upon which their optimal choices are based suggested that individual agents must be endowed with remarkable capacities to foresee the future. To assume that all individual agents would be endowed with the extraordinary ability to foresee correctly all the future prices relevant to their optimal choices about their intertemporal plans seemed an exceedingly unrealistic assumption on which to premise an economic model.

This dismissive attitude toward the concept of intertemporal equilibrium and the seemingly related assumption of “perfect foresight” necessary for an intertemporal equilibrium to exist was stridently expressed by Oskar Morgenstern in his famous 1935 article “Perfect Foresight and Economic Equilibrium.”

The impossibly high claims which are attributed to the intellectual efficiency of the economic subject immediately indicate that there are included in this equilibrium system not ordinary men, but rather, at least to one another, exactly equal demi-gods, in case the claim of complete foresight is fulfilled. If this is the case, there is, of course, nothing more to be done. If “full” or “perfect” foresight is to provide the basis of the theory of equilibrium in the strictly specified sense, and in the meaning obviously intended by the economic authors, then, a completely meaningless assumption is being considered. If limitations are introduced in such a way that the perfection of foresight is not reached, then these limitations are to be stated very precisely. They would have to be so narrowly drawn that the fundamental aim of producing ostensibly full rationality of the system by means of high, de facto unlimited, foresight, would be lost. For the theoretical economist, there is no way out of this dilemma. ln this discussion, “full” and “perfect” foresight are not only used synonymously, but both are employed, moreover, in the essentialIy more exact sense of limitlessness. This expression would have to be preferred because with the words “perfect” or “imperfect”, there arise superficial valuations which play no role here at all.

Morgenstern then went on to make an even more powerful attack on the idea of perfect foresight: that the idea is itself self-contradictory. Interestingly, he did so by positing an example that would figure in Morgenstern’s later development of game theory with his collaborator John von Neumann (and, as we now know, with his research assistant who in fact was his mathematical guide and mentor, Abraham Wald, fcredited as a co-author of The Theory of Games and Economic Behavior).

Sherlock Holmes, pursued by his opponent, Moriarity, leaves London for Dover. The train stops at a station on the way, and he alights there rather than traveling on to Dover. He has seen Moriarity at the railway station, recognizes that he is very clever and expects that Moriarity will take a faster special train in order to catch him in Dover. Holmes’ anticipation turns out to be correct. But what if Moriarity had been still more clever, had estimated Holmes’ mental abilities better and had foreseen his actions accordingly? Then, obviously, he would have traveled to the intermediate station. Holmes, again, would have had to calculate that, and he himself would have decided to go on to Dover. Whereupon, Moriarity would again have “reacted” differently. Because of so much thinking they might not have been able to act at all or the intellectually weaker of the two would have surrendered to the other in the Victoria Station, since the whole flight would have become unnecessary. Examples of this kind can be drawn from everywhere. However, chess, strategy, etc. presuppose expert knowledge, which encumbers the example unnecessarily.

One may be easily convinced that here lies an insoluble paradox. And the situation is not improved, but, rather, greatly aggravated if we assume that more than two individuals-as, for example, is the case with exchange-are brought together into a position, which would correspond to the one brought forward here. Always, there is exhibited an endless chain of reciprocally conjectural reactions and counter-reactions. This chain can never be broken by an act of knowledge but always only through an arbitrary act-a resolution. This resolution, again, would have to be foreseen by the two or more persons concerned. The paradox still remains no matter how one attempts to twist or turn things around. Unlimited foresight and economic equilibrium are thus irreconcilable with one another. But can equilibrium really take place with a faulty, heterogeneous foresight, however, it may be disposed? This is the question which arises at once when an answer is sought. One can even say this: has foresight been truly introduced at all into the consideration of equilibrium, or, rather, does not the theorem of equilibrium generally stand in no proven connection with the assumptions about foresight, so that a false assumption is being considered?

As Carlo Zappia has shown, it was probably Morgenstern’s attack on the notion of intertemporal equilibrium and perfect foresight that led Hayek to his classic restatement of the idea in his 1937 paper “Economics and Knowledge.” The point that Hayek clarified in his 1937 version, but had not been clear in his earlier expositions of the concept, is that correct foresight is not an assumption from which the existence of an intertemporal equilibrium can be causally deduced; there is no assertion that a state of equilibrium is the result of correct foresight. Rather, correct foresight is the characteristic that defines what is meant when the term “intertemporal equilibrium” is used in economic theory. Morgenstern’s conceptual error was to mistake a tautological statement about what would have to be true if an intertemporal equilibrium were to obtain for a causal statement about what conditions would bring an intertemporal equilibrium into existence.

The idea of correct foresight does not attribute any special powers to the economic agents who might under hypothetical circumstances possess correct expectations of future prices. The term is not meant to be a description of an actual state of affairs, but a description of what would have to be true for a state of affairs to be an equilibrium state of affairs.

As an aside, I would simply mention that many years ago when I met Hayek and had the opportunity to ask him about his 1937 paper and his role in developing the concept of intertemporal equilibrium, he brought my attention to his 1928 paper in which he first described an intertemporal equilibrium as state of affairs in which agents had correct expectations about future prices. My recollection of that conversation is unfortunately rather vague, but I do remember that he expressed some regret for not having had the paper translated into English, which would have established his priority in articulating the intertemporal equilibrium concept. My recollection is that the reason he gave for not having had the paper translated into English was that there was something about the paper about which he felt dissatisfied, but I can no longer remember what it was that he said he was dissatisfied with. However, I would now be inclined to conjecture that he was dissatisfied with not having disambiguated, as he did in the 1937 paper, between correct foresight as a defining characteristic of what intertemporal equilibrium means versus perfect foresight as the cause that brings intertemporal equilibruim into existence.

It is also interesting to note that the subsequent development of game theory in which Morgenstern played a not insubstantial role, shows that under a probabilistic interpretation of the interaction between Holmes and Moriarity, there could be an optimal mixed strategy that would provide an equilibrium solution of repeated Holmes-Moriarity interactions. But if the interaction is treated as a single non-repeatable event with no mixed strategy available to either party, the correct interpretation of the interaction is certainly that there is no equilibrium solution to the interaction. If there is no equilibrium solution, then it is precisely the absence of an equilibrium solution that implies the impossibility of correct foresight, correct foresight and the existence of an equilibrium being logically equivalent concepts.

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25 Responses to “Correct Foresight, Perfect Foresight, and Intertemporal Equilibrium”


  1. 1 Henry May 28, 2017 at 9:45 pm

    I am very glad to see that you now accept that the assumption of perfect foresight is critical to the pure theory of neoclassical equilibrium.

  2. 2 Mark Buchanan May 29, 2017 at 12:46 am

    Thank you for this interesting history. I’m puzzled by the following. You write that…

    “The idea of correct foresight does not attribute any special powers to the economic agents who might under hypothetical circumstances possess correct expectations of future prices. The term is not meant to be a description of an actual state of affairs, but a description of what would have to be true for a state of affairs to be an equilibrium state of affairs.”

    To me, this implies that the equilibrium concept has virtually no relevance to the real world, and to real economies, and is of intellectual or mathematical interest only. We are interested in the actual state of affairs. The only reason economists seem to follow this path in their theories is because of a pre-committment to building theories based on optimal decision making. This is baffling.

  3. 3 David Glasner May 29, 2017 at 6:07 am

    Henry, You have misunderstood me. I accept no such thing.

  4. 4 JKH May 29, 2017 at 3:17 pm

    excellent stuff

    keep it coming

  5. 5 Henry May 29, 2017 at 4:08 pm

    “The term is not meant to be a description of an actual state of affairs, but a description of what would have to be true for a state of affairs to be an equilibrium state of affairs.”

    David,

    Does not your statement shown immediately above say this?

  6. 6 David Glasner May 29, 2017 at 8:34 pm

    Henry, The statement above refers to the term “correct foresight” not to the term “perfect foresight.” The two terms are not synonymous.

  7. 7 Henry May 29, 2017 at 11:15 pm

    David,

    Can you explain the difference? Perhaps I should go back and study the posts more carefully.

  8. 8 Henry May 30, 2017 at 4:45 am

    ” Perfect foresight and rational expectations are assumptions required for finding the solution to a system of equations describing a general equilibrium. They are not essential properties of a system consistent with the basic rationality propositions of microeconomics. ”

    David,

    You made this statement back in December 2012 (“The State We’re In”).

    Here you seem to be saying that the pure theory of neoclassical equilibrium does require these (extreme) assumptions. However, the tenor of the preceeding and proceeding argument in the piece is to the effect that they are unreasonably unrealistic assumptions when the behaviour of the real world and the data of real world economics is considered.

    Is this correct?

  9. 9 Henry May 30, 2017 at 6:11 am

    “If there is no equilibrium solution, then it is precisely the absence of an equilibrium solution that implies the impossibility of correct foresight, correct foresight and the existence of an equilibrium being logically equivalent concepts.”

    David,

    Using the word “impossibility” adds some confusion (at least in my mind) given that you say “correct foresight and the existence of an equilibrium being logically equivalent concepts”. Don’t you mean to say that correct foresight is not present when there is no equilibrium?.

  10. 10 Henry May 30, 2017 at 8:35 pm

    It seems to me that von Hayek’s notion of “correct foresight” is a more or less useless concept. It’s like saying the sun is shining today. What would be of more interest is whether the sun will shine tomorrow.

  11. 11 lambsanger May 31, 2017 at 9:40 am

    Henry, perhaps I don’t get it either, but Glasner’s point here seems simple to me. He just seems to be saying that modern GE models are inconsistent in claiming perfect foresight because economic actors which have simultaneous knowledge of all other actor’s expectations will cause a chicken and the egg problem where people will indefinitely continue to change their expectations in response to other’s expectations which will codetermine other actors to change their optimal plans.

    Glasner then says that if we dial back this perfect foresight condition to simply say that all actors can choose between multiple sets of perceived optimal plans based upon their current amount of knowledge and current expectations that we can then state that there are multiple solutions for optimal equilibrium in the next period which can be achived more or less probably depending on the set of changes in variables that are exogenously introduced by certain actors in the model per each period.

  12. 12 lambsanger May 31, 2017 at 9:42 am

    exogenously introduced in the model per each period*

  13. 13 lambsanger May 31, 2017 at 10:33 am

    Take this with a grain of salt though I know very little about Econ and recently graduated from high school. Love this blog though.

  14. 14 AMV June 1, 2017 at 3:58 am

    My paper may be of some interest for your purpose:

    http://dx.doi.org/10.1080/09672567.2015.108452

  15. 15 Rob Rawlings June 4, 2017 at 8:17 am

    Having got a bit bored with the economic blogsphere recently I was delighted to come across these wonderful; post on inter-temporal equilibrium. I’m interested in what forces might (in theory) exist to move an economy from a one-period equilibrium to a an inter-temporal one.

    One can imagine that an economy could be in a state where all markets in the current period clear, but as people’s expectations about the future don’t align then when we get to the next period then (even if prices get reset to another market clearing equilibrium) people may look back at decisions they made in the first period with regret as if only they had know then what they know now they could have made different decisions that would have led them to have higher utility across the 2 periods than they actually have.

    Now assume that all things (people’s preferences, production techniques, other random factors) stay the same and the only thing that changes is people expectations. In such a world people get repeated chances to get it right. In this case it seems that market participants might through time learn about each others expectations and eventually we might (via actions that were led by market signals) arrive at a lasting inter-temporal equilibrium.

    Of course the assumption that all thing stays the same apart from people’s assumption is unrealistic. Peoples’ tastes, available production techniques, random real-world variables change all the time. This hugely complicates the task not only of getting people’s expectations about the future aligned but makes even the (in comparison) simple task of achieving a single period equilibrium harder to achieve.

    This makes me wonder whether period of fast rates of technological and social change are more likely to lead to economic disequilibrium than period where nothing much changes and people get a chance to learn about each others expectations in a more static environment.

  16. 16 Henry June 4, 2017 at 11:04 am

    Lambsanger,

    My questions relate to a discussion David and I had back in November/December of last year. I was asserting that the pure theory of neoclassical equilibrium depended on the assumption of perfect foresight. David disagreed and as he has reaffirmed, still disagrees. As evidence I brought to David’s attention Morgenstern’s paper which listed a number of theorists that had incorporated the assumption in their explications of the theory. For me, it is an open and shut case that the assumption is necessary for the pure theory of equilibrium, i.e. that there is a unique stable equilibrium as long as utility and production functions don’t change. I was also arguing that Lucas used rational expectations to replace the assumption of perfect foresight, perfect foresight being an entirely unrealistic assumption. (Not that rational expectations is any better, in my opinion.)

    You said:

    “….expectations will cause a chicken and the egg…”

    It seems to me that perfect foresight means that all agents have the same expectations, any other account is absurd. There is no second, third, fourth etc. guessing. And in a sense “expectations” is a superfluous notion when perfect foresight applies. There is nothing expected, it is “known”.

  17. 17 David Glasner June 4, 2017 at 10:20 pm

    Mark, A mental construct may or may not be relevant to the real world. Does plane geometry have relevance to a spherical world? Maybe yes, maybe no. It depends on the problem. You can’t draw inferences directly from a general equilibrium model about the real world, but it does provide a starting point from which to begin an analysis. There are certain principles and certain general characteristics of a general equilibrium model that are useful in thinking about real world problems, but it requires a fairly sophisticated analysis to make the connections between the model and actual problems. I agree that the decisions that people make are not always or even usually optimal, but that doesn’t mean that it isn’t useful to know what the characteristics of an optimal decision are in trying understand how people are actually making decisions. But I totally agree that a macroeconomic theory that takes it as a premise that all economic decisions are optimal is a terrible theory and can lead to horrible policy mistakes.

    JKH, I’m trying. See my latest.

    Henry, You quoted this from my December 2012 post.

    ”Perfect foresight and rational expectations are assumptions required for finding the solution to a system of equations describing a general equilibrium. They are not essential properties of a system consistent with the basic rationality propositions of microeconomics.”

    You then said:

    “Here you seem to be saying that the pure theory of neoclassical equilibrium does require these (extreme) assumptions.”

    Your inference about what I seemed to be saying is not correct.

    The pure theory of neoclassical equilibrium does not assert that just because an equilibrium exists that the model can be solved analytically for a solution. The solution may exist, but we may have no way of solving the system – for one thing we may have too little information even to write down the equations that characterize the system, much less solve them. (See Hayek’s papers on socialist calculation in Individualism and Economic Order.) The rational expectations and perfect foresight assumptions are among the methods that economists can deploy for radically simplifying the actual model sufficiently to be solvable analytically. So your second sentence is more or less on target.

    You ask:

    “Don’t you mean to say that correct foresight is not present when there is no equilibrium?”

    I certainly did not mean to say that. I meant to assert that the Holmes-Moriarity conundrum posed by Morgenstern was a conundrum because there was no equilibrium solution of the non-repeated game that he was describing.

    You said:

    “It seems to me that von Hayek’s notion of “correct foresight” is a more or less useless concept. It’s like saying the sun is shining today. What would be of more interest is whether the sun will shine tomorrow.”

    Saying that the sun will shine tomorrow may or may not be more useful than saying the sun is shining today. But even if I stipulate that it is more useful to say the sun will shine tomorrow than to say the sun will shine today, that still doesn’t imply that saying the sun is shining today is useless. So I really don’t understand what your point is.

    lambsanger, I think you actually were making a slightly stronger, but nevertheless correct, statement than the one I was making. So I think you definitely did get the point. I would only add that the possibility of multiple equilibria does not rule out the possibility of a unique equilibrium. The conditions required for a unique equilibrium are fairly stringent, so that the common assumption of a unique equilibrium is a convenient simplification that is probably not always appropriate. Congratulations on graduating. Good luck on the next leg of your journey.

    AMV, Thanks for the link to your paper. I will try to have a look.

    Rob, You raise many interesting possibilities. We still have a lot of work to do.

    Henry, I am sorry, but what you regard as open and shut is simply a misunderstanding. The existence of a unique equilibrium is a completely separate question from whether the equilibrium is reached. It has been known for over 60 years that the existence of a competitive equilibrium, which does follow from the standard assumptions of the Arrow-Debreu model, does not entail uniqueness. Perfect foresight is a sufficient, but not necessary, condition for reaching an equilibrium if one exists. In the absence of perfect foresight there is no economic theory that proves that any actual equilibrium will be reached. Thus, perfect foresight is a form of question begging. To say that foresight is correct is simply a way of saying that the equilibrium has been found; it doesn’t purport to explain how it was found.

    Lamsanger’s point that improving the powers of foresight can make equilibrium harder not easier to attain is something that Radner proved long ago; improving foresight may cause changes in expectations by some people that induce changes by other people without necessarily causing a convergence on equilibrium.

  18. 18 Henry June 5, 2017 at 3:19 pm

    David,

    All I am saying is that neoclassical equilibrium theorists have in the past called on the perfect foresight assumption. I used Morgenstern’s paper to support this contention. I am not making a case for the nature of the equilibrium that might or might not be entailed. I don’t feel competent to do so given that I don’t fully understand the mathematical logic that has developed around general equilibrium theory. It is a work in progress for me.

    You said:

    ‘To say that foresight is correct is simply a way of saying that the equilibrium has been found; it doesn’t purport to explain how it was found. ”

    and

    “…..saying the sun is shining today is useless. So I really don’t understand what your point is.”

    Knowing the sun is shining today is a fact, it is known. What is of more interest is whether we can determine whether the sun will shine tomorrow and what might be the cause of that. That is a more interesting question. As you say “correct foresight” doesn’t explain how an equilibrium is found. So that’s why I say it is not a very useful concept. It seems to me we agree on this – there may be a difference in emphasis.

    “… improving foresight may cause changes in expectations by some people that induce changes by other people without necessarily causing a convergence on equilibrium.”

    This just doesn’t make sense. When you have perfect foresight you do not have an expectation, you just know. Expectation suggests a lack of knowing. There is no knowing. When there is perfect foresight all agents know the same thing, it can be no other way otherwise it is absurd to say there is perfect knowledge. There is no improving foresight when you have perfect foresight, it is already perfect. Perfect means it cannot be improved upon.

    Can you cite Radner’s paper which deals with question.

  19. 19 David Glasner June 5, 2017 at 5:21 pm

    Henry, Perfect foresight is not, as you suppose, a completely unambiguous term. Just because Morgenstern gave it a particular interpretation – infallible omniscience of the future — that demonstrated that that interpretation was untenable, does not mean that there are no alternative interpretations of perfect foresight that are tenable. We agree that perfect foresight in the sense that Morgenstern used the term is an untenable concept, yet you insist that we must stick with that interpretation and that interpretation alone. I suppose that if you are trying to show what a holy mess neoclassical economics is inasmuch as it is founded on an untenable concept like perfect foresight understood as Divine foreknowledge of the future, then you might be reluctant to concede that a weaker, and therefore tenable, interpretation, like correct, but fallible, foresight, might replace it. But apparently to admit the possibility that there are alternative understandings of perfect foresight would have the drawback of allowing neoclassical economics to be understood in a way that does not render it ridiculous. Otherwise, I don’t understand why you won’t allow Morgenstern’s understanding of the concept of perfect foresight to receive the decent burial that it so richly deserves.

    In writing about Radner I have relied primarily on his 1987 article on Uncertainty and General Equilibrium in the New Palgrave. An updated version is now available online, but I have not seen the updated version. In the 1987 article, he cites his 1979 paper “Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices” in Econometrica. I suspect that the Econometrica paper would be highly technical and mathematically demanding.

  20. 20 Henry June 5, 2017 at 11:15 pm

    David,

    I am happy for you to bury anything you want but it seems the rest of it is just terminology and definitions. Again, define anything you like any way you like. I guess I am just stuck on the words. To me perfect means perfect. And while we are in funereal mood, I am all for burying neoclassical theory (as macro theory).

  21. 21 David Glasner June 6, 2017 at 10:07 am

    Henry, If you are arguing that a theory is nonsensical because it is based on a particular definition of a concept used by that theory, when there are alternative definitions of that concept that do not render the theory nonsensical, you are arguing like a lawyer (in the worst sense of that term).

  22. 22 Henry June 6, 2017 at 2:57 pm

    David,

    I am not sure what you are referring to.

    If you are referring to one of the theories of equilibrium you have been discussing, I accept that one can introduce any variation as desired, I am merely reacting to (quibbling about you would say) the use of certain words (viz. perfect) to describe those variations.

    If you are referring to neoclassical economics in general qua macro theory, then my comment above is not related to the discussion we are having about perfect foresight. In your discourse, in various places, you have referred to neoclassical theory as macro theory. I can’t see how a theory which is concerned with optimization, scarce resource deployment and relative prices has anything much to say about the general level of output and employment. Isolated market imbalances (i.e. over supply or over demand) may impact relative price pressures and edge an economy to equilibrium. Economy wide retrenchment of capital and labour require a different perspective.

    I guess this is off topic and I shouldn’t have raised it here.

  23. 23 David Glasner June 27, 2017 at 9:30 am

    Henry, This reply is a long time coming, but I have been too busy to reply to comments until now. My comment concerns your insistence that perfect foresight must mean certain (i.e., divine) foreknowledge of the future. That may have been how some economists understood the term, and it seems to be the sense in which Morgenstern used the term, but it was not a useful way to think about an economic theory of equilibrium. Hayek showed that there was a weaker sense in which the future could be correctly anticipated than divine foreknowledge of the future that would be consistent with the idea that individuals were optimizing and that the independent optimum plans of individuals could be mutually consistent and simultaneously realized. Hayek’s insight renders the assumption of perfect foresight in the sense of divine foreknowledge a vulgar misinterpretation of what the neoclassical theory of general equilibrium actually entails. I agree that there is a species of neoclassical macrotheory that is premised on something similar to such a vulgar misinterpretation, I disagree that that is the only possible macrotheory consistent with neoclassical economics.


  1. 1 Hayek and Temporary Equilibrium | Uneasy Money Trackback on June 11, 2017 at 7:43 pm
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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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