A Primer on Equilibrium

After my latest post about rational expectations, Henry from Australia, one of my most prolific commenters, has been engaging me in a conversation about what assumptions are made – or need to be made – for an economic model to have a solution and for that solution to be characterized as an equilibrium, and in particular, a general equilibrium. Equilibrium in economics is not always a clearly defined concept, and it can have a number of different meanings depending on the properties of a given model. But the usual understanding is that the agents in the model (as consumers or producers) are trying to do as well for themselves as they can, given the endowments of resources, skills and technology at their disposal and given their preferences. The conversation was triggered by my assertion that rational expectations must be “compatible with the equilibrium of the model in which those expectations are embedded.”

That was the key insight of John Muth in his paper introducing the rational-expectations assumption into economic modelling. So in any model in which the current and future actions of individuals depend on their expectations of the future, the model cannot arrive at an equilibrium unless those expectations are consistent with the equilibrium of the model. If the expectations of agents are incompatible or inconsistent with the equilibrium of the model, then, since the actions taken or plans made by agents are based on those expectations, the model cannot have an equilibrium solution.

Now Henry thinks that this reasoning is circular. My argument would be circular if I defined an equilibrium to be the same thing as correct expectations. But I am not so defining an equilibrium. I am saying that the correctness of expectations by all agents implies 1) that their expectations are mutually consistent, and 2) that, having made plans, based on their expectations, which, by assumption, agents felt were the best set of choices available to them given those expectations, if the expectations of the agents are realized, then they would not regret the decisions and the choices that they made. Each agent would be as well off as he could have made himself, given his perceived opportunities when the decision were made. That the correctness of expectations implies equilibrium is the consequence of assuming that agents are trying to optimize their decision-making process, given their available and expected opportunities. If all expected opportunities are correctly foreseen, then all decisions will have been the optimal decisions under the circumstances. But nothing has been said that requires all expectations to be correct, or even that it is possible for all expectations to be correct. If an equilibrium does not exist, and just because you can write down an economic model, it does not mean that a solution to the model exists, then the sweet spot where all expectations are consistent and compatible is just a blissful fantasy. So a logical precondition to showing that rational expectations are even possible is to prove that an equilibrium exists. There is nothing circular about the argument.

Now the key to proving the existence of a general equilibrium is to show that the general equilibrium model implies the existence of what mathematicians call a fixed point. A fixed point is said to exist when there is a mapping – a rule or a function – that takes every point in a convex compact set of points and assigns that point to another point in the same set. A convex, compact set has two important properties: 1) the line connecting any two points in the set is entirely contained within the boundaries of the set, and 2) there are no gaps between any two points in set. The set of points in a circle or a rectangle is a convex compact set; the set of points contained in the Star of David is not a convex set. Any two points in the circle will be connected by a line that lies completely within the circle; the points at adjacent edges of a Star of David will be connected by a line that lies entirely outside the Star of David.

If you think of the set of all possible price vectors for an economy, those vectors – each containing a price for each good or service in the economy – could be mapped onto itself in the following way. Given all the equations describing the behavior of each agent in the economy, the quantity demanded and supplied of each good could be calculated, giving us the excess demand (the difference between amount demand and supplied) for each good. Then the price of every good in excess demand would be raised, the price of every good in negative excess demand would be reduced, and the price of every good with zero excess demand would be held constant. To ensure that the mapping was taking a point from a given convex set onto itself, all prices could be normalized so that they would have the property that the sum of all the individual prices would always equal 1. The fixed point theorem ensures that for a mapping from one convex compact set onto itself there must be at least one fixed point, i.e., at least one point in the set that gets mapped onto itself. The price vector corresponding to that point is an equilibrium, because, given how our mapping rule was defined, a point would be mapped onto itself if and only if all excess demands are zero, so that no prices changed. Every fixed point – and there may be one or more fixed points – corresponds to an equilibrium price vector and every equilibrium price vector is associated with a fixed point.

Before going on, I ought to make an important observation that is often ignored. The mathematical proof of the existence of an equilibrium doesn’t prove that the economy operates at an equilibrium, or even that the equilibrium could be identified under the mapping rule described (which is a kind of formalization of the Walrasian tatonnement process). The mapping rule doesn’t guarantee that you would ever discover a fixed point in any finite amount of iterations. Walras thought the price adjustment rule of raising the prices of goods in excess demand and reducing prices of goods in excess supply would converge on the equilibrium price vector. But the conditions under which you can prove that the naïve price-adjustment rule converges to an equilibrium price vector turn out to be very restrictive, so even though we can prove that the competitive model has an equilibrium solution – in other words the behavioral, structural and technological assumptions of the model are coherent, meaning that the model has a solution, the model has no assumptions about how prices are actually determined that would prove that the equilibrium is ever reached. In fact, the problem is even more daunting than the previous sentence suggest, because even Walrasian tatonnement imposes an incredibly powerful restriction, namely that no trading is allowed at non-equilibrium prices. In practice there are almost never recontracting provisions allowing traders to revise the terms of their trades once it becomes clear that the prices at which trades were made were not equilibrium prices.

I now want to show how price expectations fit into all of this, because the original general equilibrium models were either one-period models or formal intertemporal models that were reduced to single-period models by assuming that all trading for future delivery was undertaken in the first period by long-lived agents who would eventually carry out the transactions that were contracted in period 1 for subsequent consumption and production. Time was preserved in a purely formal, technical way, but all economic decision-making was actually concluded in the first period. But even though the early general-equilibrium models did not encompass expectations, one of the extraordinary precursors of modern economics, Augustin Cournot, who was way too advanced for his contemporaries even to comprehend, much less make any use of, what he was saying, had incorporated the idea of expectations into the solution of his famous economic model of oligopolistic price setting.

The key to oligopolistic pricing is that each oligopolist must take into account not just consumer demand for his product, and his own production costs; he must consider as well what actions will be taken by his rivals. This is not a problem for a competitive producer (a price-taker) or a pure monopolist. The price-taker simply compares the price at which he can sell as much as he wants with his production costs and decides how much it is worthwhile to produce by comparing his marginal cost to price ,and increases output until the marginal cost rises to match the price at which he can sell. The pure monopolist, if he knows, as is assumed in such exercises, or thinks he knows the shape of the customer demand curve, selects the price and quantity combination on the demand curve that maximizes total profit (corresponding to the equality of marginal revenue and marginal cost). In oligopolistic situations, each producer must take into account how much his rivals will sell, or what prices they will set.

It was by positing such a situation and finding an analytic solution, that Cournot made a stunning intellectual breakthrough. In the simple duopoly case, Cournot posited that if the duopolists had identical costs, then each could find his optimal price conditional on the output chosen by the other. This is a simple profit-maximization problem for each duopolist, given a demand curve for the combined output of both (assumed to be identical, so that a single price must obtain for the output of both) a cost curve and the output of the other duopolist. Thus, for each duopolist there is a reaction curve showing his optimal output given the output of the other. See the accompanying figure.cournot

If one duopolist produces zero, the optimal output for the other is the monopoly output. Depending on what the level of marginal cost is, there is some output by either of the duopolists that is sufficient to make it unprofitable for the other duopolist to produce anything. That level of output corresponds to the competitive output where price just equals marginal cost. So the slope of the two reaction functions corresponds to the ratio of the monopoly output to the competitive output, which, with constant marginal cost is 2:1. Given identical costs, the two reaction curves are symmetric and the optimal output for each, given the expected output of the other, corresponds to the intersection of the two reaction curves, at which both duopolists produce the same quantity. The combined output of the two duopolists will be greater than the monopoly output, but less than the competitive output at which price equals marginal cost. With constant marginal cost, it turns out that each duopolist produces one-third of the competitive output. In the general case with n oligoplists, the ratio of the combined output of all n firms to the competitive output equals n/(n+1).

Cournot’s solution corresponds to a fixed point where the equilibrium of the model implies that both duopolists have correct expectations of the output of the other. Given the assumptions of the model, if the duopolists both expect the other to produce an output equal to one-third of the competitive output, their expectations will be consistent and will be realized. If either one expects the other to produce a different output, the outcome will not be an equilibrium, and each duopolist will regret his output decision, because the price at which he can sell his output will differ from the price that he had expected. In the Cournot case, you could define a mapping of a vector of the quantities that each duopolist had expected the other to produce and the corresponding planned output of each duopolist. An equilibrium corresponds to a case in which both duopolists expected the output planned by the other. If either duopolist expected a different output from what the other planned, the outcome would not be an equilibrium.

We can now recognize that Cournot’s solution anticipated John Nash’s concept of an equilibrium strategy in which player chooses a strategy that is optimal given his expectation of what the other player’s strategy will be. A Nash equilibrium corresponds to a fixed point in which each player chooses an optimal strategy based on the correct expectation of what the other player’s strategy will be. There may be more than one Nash equilibrium in many games. For example, rather than base their decisions on an expectation of the quantity choice of the other duopolist, the two duopolists could base their decisions on an expectation of what price the other duopolist would set. In the constant-cost case, this choice of strategies would lead to the competitive output because both duopolists would conclude that the optimal strategy of the other duopolist would be to charge a price just sufficient to cover his marginal cost. This was the alternative oligopoly model suggested by another French economist J. L. F. Bertrand. Of course there is a lot more to be said about how oligopolists strategize than just these two models, and the conditions under which one or the other model is the more appropriate. I just want to observe that assumptions about expectations are crucial to how we analyze market equilibrium, and that the importance of these assumptions for understanding market behavior has been recognized for a very long time.

But from a macroeconomic perspective, the important point is that expected prices become the critical equilibrating variable in the theory of general equilibrium and in macroeconomics in general. Single-period models of equilibrium, including general-equilibrium models that are formally intertemporal, but in which all trades are executed in the initial period at known prices in a complete array of markets determining all future economic activity, are completely sterile and useless for macroeconomics except as a stepping stone to analyzing the implications of imperfect forecasts of future prices. If we want to think about general equilibrium in a useful macroeconomic context, we have to think about a general-equilibrium system in which agents make plans about consumption and production over time based on only the vaguest conjectures about what future conditions will be like when the various interconnected stages of their plans will be executed.

Unlike the full Arrow-Debreu system of complete markets, a general-equilibrium system with incomplete markets cannot be equilibrated, even in principle, by price adjustments in the incomplete set of present markets. Equilibration depends on the consistency of expected prices with equilibrium. If equilibrium is characterized by a fixed point, the fixed point must be mapping of a set of vectors of current prices and expected prices on to itself. That means that expected future prices are as much equilibrating variables as current market prices. But expected future prices exist only in the minds of the agents, they are not directly subject to change by market forces in the way that prices in actual markets are. If the equilibrating tendencies of market prices in a system of complete markets are very far from completely effective, the equilibrating tendencies of expected future prices may not only be non-existent, but may even be potentially disequilibrating rather than equilibrating.

The problem of price expectations in an intertemporal general-equilibrium system is central to the understanding of macroeconomics. Hayek, who was the father of intertemporal equilibrium theory, which he was the first to outline in a 1928 paper in German, and who explained the problem with unsurpassed clarity in his 1937 paper “Economics and Knowledge,” unfortunately did not seem to acknowledge its radical consequences for macroeconomic theory, and the potential ineffectiveness of self-equilibrating market forces. My quarrel with rational expectations as a strategy of macroeconomic analysis is its implicit assumption, lacking any analytical support, that prices and price expectations somehow always adjust to equilibrium values. In certain contexts, when there is no apparent basis to question whether a particular market is functioning efficiently, rational expectations may be a reasonable working assumption for modelling observed behavior. However, when there is reason to question whether a given market is operating efficiently or whether an entire economy is operating close to its potential, to insist on principle that the rational-expectations assumption must be made, to assume, in other words, that actual and expected prices adjust rapidly to their equilibrium values allowing an economy to operate at or near its optimal growth path, is simply, as I have often said, an exercise in circular reasoning and question begging.

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16 Responses to “A Primer on Equilibrium”


  1. 1 Nick Rowe December 7, 2016 at 1:39 am

    David: good post.

    Go back to the one-shot Cournot duopoly game. Each firm chooses its quantity not observing the other’s choice (the two choices are made simultaneously). (And set aside the question of who sets the prices if the firms set the quantities). We need to assume not just that each firm knows its own cost curve, and the demand curve, but it needs to know the other firm’s cost curve too, and all this knowledge needs to be Common Knowledge between the two firms, and that they can do the math to solve for the Counot-Nash equilibrium.

    In other words, the rational expectations assumption is baked right into Cournot’s cake, even in a very simple one-period game.

    Now, in a repeated Cournot game, even without that Common Knowledge, it *might* be possible for the two players to learn the Cournot equilibrium by trial-and-error, and will be possible (given that the two reaction curves cross with the right relative slopes) if they use something like adaptive expectations for learning. But in a repeated game it is also possible that each will play Tit-for-Tat and they end up at the joint monopoly solution.

  2. 2 Henry December 7, 2016 at 9:44 am

    David,

    I am not clear what we are talking about here.

    Are we discussing the perfect competition model? I would argue that the REH replaces the perfect rationality/knowledge/foresight assumptions of the perfect competition model. Time does not exist in the perfect competition model so expectations are not necessary and redundant.

    Are we discussing RE in the context of the Muth/Lucas model?

    Are we talking about the REH in the context of imperfect competition (Cournot’s duopoly/Nash Equilibrium)? Because it doesn’t make sense to do this.

    Are we discussing Walrasian tatonnement? Ditto, doesn’t apply. WT imagines an auctioneer allowing buyers and sellers to adjust prices such that quantity supplied is equal to quantity demanded in every market, i.e. prices are set at equilibrium levels. All this happens in an instant – there is no time – no path to equilibrium, no need for expectations.

    It seems to me you have done a “Morgenstern” – where he started talking about perfect foresight and ended up sliding off into arguments about imperfect competition where perfect foresight does not apply and then admits in a perfect competition model, perfect foresight applies.

    Your very last sentence seems to be arguing my point about the circularity of the REH?

    You use the term “correct expectations” – which from what I can see of your discussion, means the RE of the Muth/Lucas type. Then you go on to say you are not defining expectations in that way. If you want to discuss how human beings actually form expectations, then you cannot be talking about the REH – you are making the case as to why REH is unrealistic.

    I was endeavouring to make a case about the REH. I was arguing that its logic is circular. You effectively said its not a matter of logic, it is ASSUMED that expectations allow model equilibrium to pertain. I can accept that, however, I am not entirely certain that that’s what Muth/Lucas were saying. Something I will have a closer look at. I would also say, in this context, that if the model’s outcomes are assumed to be set at equilibrium, then an assumption about expectations is not required – it is redundant.

    If the assumption that the REH makes about expectations doesn’t hold, would you agree that my argument about circularity is valid? You haven’t been entirely clear about that as far as I can see.

  3. 3 Miguel Navascués December 7, 2016 at 10:25 am

    If REH implies that the final result is equilibrium, and if equilibrium necessary is defined by de RE, there is some suspected grade of circularity in the model.
    Because I suppose than a “casual” equilibrium (not obtained by RE) is not acceptable for this master of GE.

  4. 4 Miguel Navascués December 7, 2016 at 10:28 am

    I’m not saying that yupour argument is cicular, I’m saying that the REH is circular.

  5. 5 David Glasner December 7, 2016 at 1:30 pm

    Nick, Thanks. Yes, you are right that the Cournot model assumes that the duopolists have a lot of information about each other, without which reaching the equilibrium solution would be a lot harder than it is with that information. But for two somewhat similarly situated duopolists over the same product, the assumption is not necessarily outlandish even in a one-shot game. But I take the general tenor of your comment to be supportive of my general skepticism that the information available to agents in a general equilibrium is insufficient for agents to form convergent (rational) expectations about future prices. Am I reading you correctly?

    Herny, You said:

    “Are we discussing the perfect competition model? I would argue that the REH replaces the perfect rationality/knowledge/foresight assumptions of the perfect competition model. Time does not exist in the perfect competition model so expectations are not necessary and redundant.”

    I am sorry, I thought that I had already rejected this idea, but I completely disagree that the perfect competition model assumes perfect rationality, knowledge and foresight. I don’t think that there is any basis for that assertion, though it may be popular caricature of what perfect competition assumes or entails that sometimes is propagated by people who wish to reject the model by ridicule rather than argument. Pure competition simply means that transactors are price-takers. Perfect competition adds the condition that (economic as opposed to accounting) profit is zero.

    “Are we discussing RE in the context of the Muth/Lucas model?”

    I don’t think that there is a single model that can be identified as proprietary to Muth and Lucas, but I am talking about Muth’s idea as applied by Lucas (and others) to macroeconomic models.

    ” Are we talking about the REH in the context of imperfect competition (Cournot’s duopoly/Nash Equilibrium)? Because it doesn’t make sense to do this.”

    I don’t know what you mean. REH can apply to models in which competition is imperfect as well as to models with perfect competition. My whole point was that the idea of rational expectations was implicit in the Cournot/Nash and it was precisely that assumption that enables the solution to be characterized with such elegance. Whether the model works empirically is another question. In some cases it may; in others it certainly does not. But it was not my intention to limit the application of REH to just these examples. I thought that was quite obvious. And in all humility, I think that I can say that my discussion of the Cournot model showed that it actually makes perfect sense to talk about REH in the context of imperfect competition.

    “Are we discussing Walrasian tatonnement? Ditto, doesn’t apply. WT imagines an auctioneer allowing buyers and sellers to adjust prices such that quantity supplied is equal to quantity demanded in every market, i.e. prices are set at equilibrium levels. All this happens in an instant – there is no time – no path to equilibrium, no need for expectations.”

    Walrasian tatonnement is a heuristic. It is not part of GE models, it is a device by which Walras attempted to connect his abstract equations to some real world process. Obviously, the heuristic is not even close to being a real world process either, so tatonnement has no actual significance though it may have played a role in motivating the application of the fixed point theorem to prove the existence of a general equilibrium. Again, I must apologize for saying this but your conviction that time and decision-making over time cannot be accommodated in some very simplified and abstract way in a general equilibrium problem is totally unfounded. Have a look at Jack Hirshleifer’s Investment, Interest and Capital or C. J. Bliss’s Capital Theory and the Distribution of Income.

    “It seems to me you have done a “Morgenstern” – where he started talking about perfect foresight and ended up sliding off into arguments about imperfect competition where perfect foresight does not apply and then admits in a perfect competition model, perfect foresight applies.”

    It has been 30 or 40 years since I read Morgenstern’s article. I don’t remember it well, but I think he misunderstood the role of perfect foresight in general equilibrium models. I think that Hayek cleared up the confusion in his 1937 paper, showing that what intertemporal general equilibrium requires is not perfect foresight as Morgenstern thought, but contingently correct (and, therefore, potentially incorrect) foresight. But I really only guessing now, because I have almost no recollection of what Morgenstern was arguing. I concluded that Hayek corrected his misunderstandings a long time ago when I still had a decent recollection of what Morgenstern had written.

    “You use the term “correct expectations” – which from what I can see of your discussion, means the RE of the Muth/Lucas type. Then you go on to say you are not defining expectations in that way. If you want to discuss how human beings actually form expectations, then you cannot be talking about the REH – you are making the case as to why REH is unrealistic.”

    Yes, my use of correct expectations corresponds to what I take Muth to have meant by rational expectations, the expectations that are consistent with the workings of the model in question. When I said that correct expectations was not my definition of equilibrium, I meant to say that the equilibrium of the model could be defined without reference to expectations. If I as the creator of the model can determine the equilibrium in terms of the assumptions that I have made about the model, I know more than the agents in the model know. Because I know more than the agents, I know what the agents can only guess at. And I know that the equilibrium which I can determine with certainty will not be arrived at by the agents unless they, somehow, all manage to form correct expectations. And my further point is that I as creator of the model have no idea how they would actually go about forming correct expectations, I only know that those poor miserable agents will not succeed in reaching equilibrium unless they manage to do so. I wish them luck. So yes, I believe REH is an unrealistic assumption, though empirically, it does work in many, but certainly not all, cases. And agree that REH is circular in asserting that REH must be adopted as a matter of methodological principle by all macro models. It is not circular to say that a condition for equilibrium is that agents’ expectations converge on the equilibrium of the model.

    “I was endeavouring to make a case about the REH. I was arguing that its logic is circular. You effectively said its not a matter of logic, it is ASSUMED that expectations allow model equilibrium to pertain. I can accept that, however, I am not entirely certain that that’s what Muth/Lucas were saying. Something I will have a closer look at. I would also say, in this context, that if the model’s outcomes are assumed to be set at equilibrium, then an assumption about expectations is not required – it is redundant.”

    I think that you are failing to see the difference between what the creator of the model knows and what the agents in the model are allowed to know. And I think that you fail to understand that distinction because of your entirely false belief that perfect knowledge is a necessary assumption of the standard GE model. If you appreciate that distinction you will see that an assumption about expectations is not redundant — it is required.

    “If the assumption that the REH makes about expectations doesn’t hold, would you agree that my argument about circularity is valid? You haven’t been entirely clear about that as far as I can see.”

    Yes, I would agree that REH is making a circular argument, or at least a question-begging argument. And I think I did make that clear. See the last sentence of my post.

    Miguel, I think we agree.

  6. 6 Nick Rowe December 7, 2016 at 1:42 pm

    David: “But I take the general tenor of your comment to be supportive of my general skepticism that the information available to agents in a general equilibrium is insufficient for agents to form convergent (rational) expectations about future prices. Am I reading you correctly?”

    Yes, I think so, though I am not 100% sure where I’m going with this myself 😉

    For example, the “Neo-Fisherian” equilibrium is an RE equilibrium that I wouldn’t trust one inch. It’s like a duopoly equilibrium where the two reaction functions cross the “wrong” way (with the “wrong” relative slopes), so there is no way that individuals could learn that Nash equilibrium by trial and error (tatonnement/groping). It’s what we used to call an “unstable” Nash equilibrium in the olden days. Like in the old Keynesian Cross model, if MPC > 1, where there is no way it would converge to the 45 degree line. It’s not a “learnable” equilibrium.

    But I don’t think this problem is restricted to Hayek/Hicks temporary equilibrium.

  7. 7 Nick Rowe December 7, 2016 at 1:44 pm

    Put it this way: some equilibria are learnable, so RE is reasonable if the distribution of shocks stays roughly the same. Other’s aren’t. And the job of monetary policy is to reduce the amount of learning needed.

  8. 8 Jose Poncela December 8, 2016 at 12:59 am

    Dear Mr Glasner, thank you for this very informative article. Would you mind developing a bit more your sentence “If the equilibrating tendencies of market prices in a system of complete markets are very far from completely effective” and on the possibility of a rational expectations equilibrium holding the economy at one of many possible equilibrium point but which doesn’t need to be optimal in the sense of maximising welfare.
    Thank you again for your article

  9. 9 Henry December 8, 2016 at 2:31 am

    “..all this knowledge needs to be Common Knowledge between the two firms..”

    Nick,

    This sounds like perfect knowledge rather than rational expectations to me.

  10. 10 Henry December 8, 2016 at 3:26 am

    “… but I completely disagree that the perfect competition model assumes perfect rationality, knowledge and foresight..”

    Oskar Morgensten, the contemporary of Hicks and co., thought enough of perfect foresight to write a 15 page paper on the matter. He quotes Hicks, Knight, Fisher and Hayek all of whom make reference to perfect foresight in relation to perfect competition. Then of course he proceeds to attempt to argue that perfect foresight is not required except that he discusses non perfect competitive models, where foresight is not meant to apply. So there are well credentialed economists who disagree with you on perfect foresight. Perfect rationality is required in the formulation of indifference curves.

    “My whole point was that the idea of rational expectations was implicit in the Cournot/Nash and it was precisely that assumption that enables the solution to be characterized with such elegance….”

    As Nick has pointed out, both firms need complete KNOWLEDGE of each other’s production functions for equilibrium to be attained.

    ” Again, I must apologize for saying this but your conviction that time and decision-making over time cannot be accommodated in some very simplified and abstract way in a general equilibrium problem is totally unfounded.”

    Where did I say this? I said there is no time in the perfect competition model and the Walrasian tatonnement model. When various assumptions are relaxed, time becomes an element of the models.

    “It has been 30 or 40 years since I read Morgenstern’s article. I don’t remember it well, but I think he misunderstood the role of perfect foresight in general equilibrium models.”

    I agree – he had himself in a nice tangle – but his paper does highlight that various theorists connected perfect foresight to the perfect competition model.

    ” It is not circular to say that a condition for equilibrium is that agents’ expectations converge on the equilibrium of the model.’

    When it is assumed that agents know the outcome of the model, there is no circularity. Remove the assumption, then I would argue that the REH is based on a circular logic.

    “I think that you are failing to see the difference between what the creator of the model knows and what the agents in the model are allowed to know. And I think that you fail to understand that distinction because of your entirely false belief that perfect knowledge is a necessary assumption of the standard GE model. ”

    The REH says they know the same thing – the equilibrium outcome of the model. I make no reference to perfect knowledge here. This is the assumption that you yourself have said underlies the REH.

    “Yes, I would agree that REH is making a circular argument, or at least a question-begging argument. And I think I did make that clear. ”

    In your previous blog you said there was no circularity. Have I misunderstood you?

  11. 11 Henry December 8, 2016 at 9:00 am

    “A wave of economists in the late 19th century—Francis Edgeworth, William Stanley Jevons, Léon Walras, and Vilfredo Pareto—built mathematical models on these assumptions. In the 20th century, Lionel Robbins’ rational choice theory came to dominate mainstream economics and the term economic man took on a more specific meaning of a person who acted rationally on complete knowledge out of self-interest and the desire for wealth.”

    The above is from the Wiki on Homo Economicus:

    https://en.wikipedia.org/wiki/Homo_economicus

  12. 12 David Glasner December 8, 2016 at 9:44 am

    Henry, “Perfect rationality,” which is a very ambiguous term has a very precise meaning in economic theory: a complete and consistent ordering of preferences over all possible choices. “Perfect foresight,” as I understand it, means the power to predict the future unerringly. I see no connection between those two concepts. I do not deny that perfect foresight was an assumption used by some economists in the early 20th century in describing the conditions for general equilibrium. Another condition for general equilibrium was perfect competition. The two assumptions are parallel but not identical and I deny that either logically entails the other. Your general citation of various economists who mentioned the idea of perfect foresight in their writings establishes nothing except that they may have fully understood what they were talking about. That happens frequently. The problem with perfect foresight (or perfect knowledge) is that it is too strong an assumption. If you assume perfect foresight/perfect knowledge, you have assumed your conclusion. The key point is to recognize that an equilibrium entails the perfect consistency of all independently formulated plans. With complete markets that is accomplished via equilibrium prices in each market. We only know that there is at least one set of equilibrium prices that would support an equilibrium of optimized and mutually consistent plans. So for such an equilibrium to obtain, either the equilibrium price vector must discovered by some process, or it must be anticipated by the agents, i.e., all agents must somehow expect the equilibrium prices that would support the equilibrium. The equilibrium model is not a causal theory of how equilibrium is achieved it is a strictly logical analysis of what conditions would be necessary for an equilibrium to obtain. It was Hayek who made that all clear in his 1937 paper.

    You said:

    “As Nick has pointed out, both firms need complete KNOWLEDGE of each other’s production functions for equilibrium to be attained.”

    I don’t think that’ what Nick meant. He was pointing out that if we are thinking of the Cournot model as a positive theory of pricing, it would require both firms to have considerable knowledge about each other to expect that the Cournot result would be observed in practice. That has nothing to do with what is logically necessary for the Cournot equilibrium to obtain. What is logically necessary is that both duopolists correctly anticipate the output chosen by the other. That says nothing about the likelihood that their expectations will converge.

    You quoted me:

    ”Again, I must apologize for saying this but your conviction that time and decision-making over time cannot be accommodated in some very simplified and abstract way in a general equilibrium problem is totally unfounded.” And then you said:

    “Where did I say this? I said there is no time in the perfect competition model and the Walrasian tatonnement model. When various assumptions are relaxed, time becomes an element of the models.”

    And that is exactly what I am saying is unfounded. You have no basis for saying that there is no time in the perfect competition model. Walrasian tatonnement is not the same as the perfect competition model.

    You said:

    “When it is assumed that agents know the outcome of the model, there is no circularity. Remove the assumption, then I would argue that the REH is based on a circular logic.”

    Assumed by whom? We both agree that RE theorists make this assumption in their models. There may be circumstances in which it is a legitimate assumption, but often it is an illegitimate assumption. I am quarreling with you because you are accepting their assertion that they are simply applying neoclassical assumptions in a routine fashion, that they are just doing regular economics. They aren’t; they misunderstand what regular economics really is.

    You said:

    “The REH says they know the same thing – the equilibrium outcome of the model. I make no reference to perfect knowledge here. This is the assumption that you yourself have said underlies the REH.”

    That’s the gross error of the REH hypothesis. Agents can’t know the outcome of the model. But that doesn’t mean you can’t ask what would happen if agents somehow did expect prices to be what the equilibrium price vector of the model. Unless your model tells you that they get to the equilibrium of the model, there is something very wrong with the model. There is a difference between making a behavioral assumption about what agents actually know and a conditional assumption about what would happen if expectations were such and such.

    You said:

    “In your previous blog you said there was no circularity. Have I misunderstood you?”

    It’s circular if you assume that agents know the equilibrium, it’s not circular if you ask what would happen if they were to expect the equilibrium.

    Your citation of the Wikipedia article on “economic man” referencing Robbins assumption of rationality based on complete knowledge misconstrues the ambiguity in the phrase “complete knowledge.” The completeness of the agents’ knowledge only extends to their knowledge of the current prices at which they could either buy or sell. Aside from that they are clueless as the rest of us.

  13. 13 Maiko December 9, 2016 at 3:31 am

    “If we want to think about general equilibrium in a useful macroeconomic context,”
    “My whole point was that the idea of rational expectations was implicit in the Cournot/Nash and it was precisely that assumption that enables the solution to be characterized with such elegance. Whether the model works empirically is another question.”
    “The equilibrium model is not a causal theory of how equilibrium is achieved it is a strictly logical analysis of what conditions would be necessary for an equilibrium to obtain. It was Hayek who made that all clear in his 1937 paper.”
    “they misunderstand what regular economics really is…That’s the gross error of the REH hypothesis. Agents can’t know the outcome of the model. But that doesn’t mean you can’t ask what would happen if agents somehow did expect prices to be what the equilibrium price vector of the model.”

    Unfortunately what you have produced is a primer on confusion and non sense.
    On the basis of what you imagine economy or capitalism is and of what you imagine reh should be you develop your personal model, which is a legitimate operation, though a diversion and distraction. No doubt Hayek made it clear about metaphysical neoclassical approach but at least he was in his way coherent ending up in mysticism, since his prejudices wouldn’t allow him to understand capitalism.
    The fact that in capitalism you might have sometimes maybe a sort of equilibrium according to your personal meaning it doesn’t mean general equilibrium is of any help.

  14. 14 Henry December 9, 2016 at 10:12 am

    David,

    “Perfect rationality,” …….. “Perfect foresight,” ……… I see no connection between those two concepts.

    I didn’t say there was a connection.

    “I don’t think that’ what Nick meant. ”

    It is what Nick said. And if he meant something else, then it is anybody’s guess. And your logic in this paragraph twists all over the place and is replete with contradiction.

    ” You have no basis for saying that there is no time in the perfect competition model. ”

    When there is perfect knowledge/foresight, equilibrium can only but be instantaneous.

    “Walrasian tatonnement is not the same as the perfect competition model.”

    I agree.

    “There may be circumstances in which it is a legitimate assumption, but often it is an illegitimate assumption.”

    Maybe. But we are talking about Muth and Lucas as best as I can gather – you do range all over the place and can be difficult to follow.

    “…they misunderstand what regular economics really is.”

    What do you mean by regular economics? What is it?

    “That’s the gross error of the REH hypothesis. Agents can’t know the outcome of the model. ”

    It’s an assumption of the model as you have said. If you’re saying it’s not realistic, I would agree with you.

    “There is a difference between making a behavioral assumption about what agents actually know and a conditional assumption about what would happen if expectations were such and such.”

    I agree. In the first case, I would argue, you end up with a circularity and in the second case it’s just an assumption.

    “It’s circular if you assume that agents know the equilibrium, it’s not circular if you ask what would happen if they were to expect the equilibrium.”

    As far as I am concerned, it’s the other way around. Where there’s an assumption there is no logic. If there’s no attempt at logic there can be no circularity.

    “….it’s not circular if you ask what would happen if they were to expect the equilibrium.”

    It is if the equilibrium is dependent on their expectations.

    “Your citation of the Wikipedia article on “economic man” referencing Robbins assumption of rationality based on complete knowledge misconstrues the ambiguity in the phrase “complete knowledge.””

    The point is not about complete knowledge but that economic agents are assumed to be rational. Just endeavouring to show that all the assumptions which you say are not applicable to perfect competition have been used by various economists.

  15. 15 kevinrfoster December 9, 2016 at 6:44 pm

    See also Ingrao & Israel, “The Invisible Hand, Economic Equilibrium in the History of Science,” also Jean Michel Grandmont on learning under rational expectations

  16. 16 David Glasner December 12, 2016 at 12:22 pm

    Maiko, Thanks for your comment.

    Henry, You said:

    “It is what Nick said. And if he meant something else, then it is anybody’s guess.”

    My mistake. Nick is a smart guy, and I was assuming that he understood the difference between assuming that the duopolists expect each other to produce the same quantity and have conclusive reason to expect each other to produce the same quantity. For the Cournot solution to obtain, all that is necessary is that each duopolist expects the other to produce exactly the same quantity that it plans to produce. They could have that expectation because they both know what the other duopolist’s cost is, or they could have that expectation because they simply assume or guess that the other duopolist’s costs are the same as its own. Either assumption would work, but you are correct that I don’t know if that’s what Nick had in mind.

    “And your logic in this paragraph twists all over the place and is replete with contradiction.”

    I agree that that is one possible explanation for your failure to understand what I wrote; I don’t agree that that is the only possible explanation.

    You quoted me:

    ” You have no basis for saying that there is no time in the perfect competition model. ”

    You then responded:

    “When there is perfect knowledge/foresight, equilibrium can only but be instantaneous.”

    Well, I continue to deny that perfect knowledge and foresight is a necessary assumption in the perfect competition model.

    You asked:

    “What do you mean by regular economics? What is it?”

    “Regular economics” is a term used by Robert Barro a few years ago in a Wall Street Journal op-ed in which he compared Keynesian economics to “regular economics” and found Keynesian economics didn’t measure up.

    Kevin, Thanks for the references. I forgot about Grandmont, but he is worth looking at again.


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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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