Home > Macro/Monetary Theory, Uncategorized > Walras’ Law, General Gluts and Zero-Sum Economics

Walras’ Law, General Gluts and Zero-Sum Economics

There is a thread in the blogosphere that seems to have started years ago but which popped back up recently about general gluts and Walras’ law which I have been pondering for a while and have a lot of comments on.  I will take them one at a time.  This will be kind of a deep dive.  Here are the relevant posts going back to 2011.

DeLong [2011]

Dan Kuehn [2011]

DeLong [2014]

Rowe [2014]

[Update: missed the most important one] Rowe

1. Walras’ Law and general gluts

First of all, I think that Nick Rowe, who is becoming my favorite econ blogger, is being a bit too reactionary about Walras’ Law when he says this:

Walras’ Law is the biggest fallacy we are still teaching in economics.

But before I get to why that is, let me agree with what I think are most of his general points.  At the heart of the matter is the question of whether there is such a thing as a general glut.  Some people cite Walras’ Law to argue that such a thing is not possible but this is an abuse of the law.  It reminds me of another similar law (theorem) which is particularly near and dear to my heart: the Coase Theorem .

The Coase Theorem says essentially that if there are no transaction costs, any particular assignment of property rights will result in an efficient outcome.  There are two ways that people commonly abuse this theorem.  One is to say “the Coase theorem proves that property rights don’t matter.”  Another is to say “well we observe inefficient outcomes so clearly the theorem is wrong.”  Both of these entirely miss the point of the theorem.  It is not meant to assert that everything is efficient all the time and property rights don’t matter.  It is to focus our attention on the necessary cause of market inefficiency, namely transaction costs.  If transaction costs are present, you might expect the assignment of property rights to matter.  Similarly, if you have what seems to be a market failure, you aught to be looking for some type of transaction cost (which could be a lot of things) as the culprit.  (Also note, for the record, that there is a big difference between getting an efficient outcome with any distribution of property rights and property rights not mattering.)

The same thing is true of Walras’ Law.  (Though I must say I have never read Walras, so I can’t speak to what he was actually trying to argue but this, I believe, is the proper context in which to view the law.)   Walras’ Law is “true” in the context of the model in which it is derived, the general equilibrium model of an endowment economy with a Walrasian auctioneer, a point which, for the record, Nick acknowledges.  This does not mean that the conclusion reached in the context of that model must be true in the real world, but that doesn’t mean that it is a useless thing to teach.

If your physics teacher told you that the Law of Gravity proves that a bird can’t fly in a vacuum, and you came to the conclusion that therefore, birds can’t fly, you would be mistaken.  However, if you came to the conclusion that, because the Law of Gravity implies that birds can’t fly in a vacuum and birds can, in fact, fly, that the law of Gravity is wrong/useless, you would also be mistaken.  It just so happens that birds don’t exist in a vacuum.  What you should do is notice that air must play some critical role in the process of flight.  This is an important insight into the process which is easier to notice once you have ruled out the possibility of flight in its absence.

Now the “air” in the Walrasian model is money.  In that model, money acts as a “veil over barter.”  If you had a frictionless barter economy, the Law would apply.  And for that matter, if you have an economy where money serves only to replicate a frictionless barter economy, it will apply.  With this in mind, if you think you might be observing a “general glut,” there are two ways of interpreting it.  One is to say that such a thing is not possible so we must actually be observing something else.  This, I think, is the basic idea that Nick is arguing with and he is right to do so.  The other, I think more correct approach, is to say that we don’t appear to live in a frictionless barter economy (or something analogous).  Specifically, I would argue that the role of money is much more important in ways that are not captured by that model.  And this is exactly what Nick is arguing.  So I whole-heartedly agree on that point.  However, I think that rather than proclaiming Walras’ Law “wrong” and saying we shouldn’t teach it, he should be using it to make his point by saying “look, we have this law which says that if money performs its task of making the economy work like a frictionless, barter economy, we wouldn’t have general gluts and yet we have them.  So this should tell us that the root cause of them must be somehow contained in the functioning of the monetary system.”

2. More on the Walrasian model (skippable)

This is kind of in the weeds and a bit beside my main point but I can’t resist going a little deeper.  Take Nick’s example.

An excess demand for bonds cannot cause demand-deficient unemployment. Remember my three women? The hairdresser, manicurist, and masseuse? Suppose they all have an excess demand for bonds. They want to sell their services for bonds. But they can’t, because none of them wants to sell bonds. So do they suffer deficient-demand unemployment? Not if they can barter their way back to full-employment. And Walras’ Law is supposed to be true in all economies, whether barter or monetary.

To me this is playing fast and loose with the model.  Of course, there is a lot of that going on on all sides here, so this is also a criticism of the excess-demand-for-bonds-causes-a-general-glut theory.  In the model, you can’t have an excess demand for money because there is no demand for money because money is acting only as a veil over barter.  People only actually want goods.  Now if you put bonds in as a good, then people are actually willing to trade hair dressing and massages for bonds.  This means that if the Walrasian auctioneer calls out a certain vector of prices for these goods and there is an excess demand for bonds there will be an excess supply of other goods.

However, I don’t think this model was ever intended to be a model of disequilibrium.  Walras’ Law is meant to show that such a frictionless economy will tend toward a general equilibrium.  It is analogous to saying, in an individual market, that supply is upward sloping and demand is downward sloping.  Saying that doesn’t mean that the model is always in equilibrium.  But it does imply that if people are allowed to bid prices up and down, and there are no other funky constraints, that it aught to tend toward an equilibrium and that equilibrium aught to be stable.  If you had both upward sloping or downward sloping or if the process of bidding prices up/down worked differently than hypothesized, prices and/or quantities might shoot off to zero of infinity or something.

By the way, notice that when people say things like “the Walrasian model does not specify any kind of mechanism for determining prices” they are not really being straight.  The mechanism is the process of bidding prices up when there is a shortage and down where there is a surplus.  This is explained in any intro class but then promptly forgotten by professors who like to pooh-pooh classical economics.  The Walrasian  auctioneer is essentially used to represent this mechanism in a simpler way.  Walras’ Law is analogous to this in a general-equilibrium sense in that it tells you that if one market is out of equilibrium for a given vector of prices, then some other market must also be out of equilibrium in such a way that the hypothesized process of bidding prices toward equilibrium in both markets moves you toward a general equilibrium rather than spiraling off into some kind of black hole.

Now, just like you can add in a constraint in the market for a single good, like a price ceiling and find that the market wont then arrive at the Walrasian equilibrium but rather at some other equilibrium, you could do this in the general equilibrium model.  If you said the price of bonds is X but include a constraint limiting the quantity demanded to some amount less than would be demanded at that price, and let every other market clear, you will arrive at some kind of second-best equilibrium in which the prices of every other good clear the markets for those goods given the constraint on bonds.  But in some sense, there will still be an excess supply of those goods relative to bonds given the price X.  People would be willing to trade hair dressing and/or massages for bonds at that price if they could.  What Nick seems to be saying is that this doesn’t matter because they don’t care about bonds, they only care about real goods and the real goods markets are all in equilibrium.  But this is treating bonds like a real good in one sense and then later treating them as if they don’t matter and are just part of the veil.  If nobody cares how many bonds they have, then there isn’t really an excess demand.

The same thing applies to unobtainium.  If you make a model with a price for unobtainium and a constraint setting the quantity equal to zero and let the rest of the markets find a market-clearing equilibrium, you can say that there is excess supply of other goods relative to unobtainium at those prices but that the rest of the market is in a second-best equilibrium given the constraint.  This does not mean that this “excess demand” for unobtainium or bonds causes a general glut or unemployment of course (technically Nick’s point in this context), but I also don’t think it makes Walras’ Law wrong, it’s just playing with definitions in an esoteric and not very helpful way.  So I feel like Nick is  shadow-boxing with an erroneous expression of Walras’ Law crudely repurposed as a theory of recessions (or I guess a couple different theories….or is one an anti-theory?)

I can see why a macro guy would be annoyed by these but I think we should avoid throwing it out all together.  At most, we should let the micro folks keep it but make them promise not to bring it up in discussions of the business cycle at faculty cocktail parties.

3.  Shortage of bonds

Having said the above, I think the whole shortage-of-bonds thing is a silly basis for a theory of recessions because I don’t think I have ever seen a shortage of bonds.  There is a big difference between high demand and excess demand.  If you can go buy a bond at the market price, it’s not excess demand.  A shortage of money is a different story (again, as Nick notes).

4. Zero-sum economics

Dan Kuehn:

You will occasionally hear people say that general gluts can’t happen. That’s zero-sum economics, and it’s been proven wrong empirically and theoretically time and time again. We need more Smithian and Keynesian economics, but I don’t think that means we need less Hayek or Lucas. It simply means that this paradigm shift needs to be more completely integrated and we’ve got to stop this balkanization of the discipline that is always looking for grand ideological fights.

I just want to point out that, even though I am not saying there cannot be a general glut, such a statement does not amount to zer0-sum economics.  I want to do this because I think the single most important thing that we can learn from economics, and probably the thing most commonly forgotten, is that trade is not a zero-sum game.  But there are two ways in which this is the case.  One way is that we can actually get more stuff.  This is what Adam Smith had in mind when he talked about specialization of labor being limited by the extent of the market.  The other is that people have different subjective values of goods.  This means that even if the quantities of goods are fixed, trade can be mutually beneficial.  It’s important not to forget the second one.

Because of this second consideration, saying that a general glut can’t happen is not adopting a sort of zero-sum economics.  It is possible to have a fixed level of output without having an efficient allocation.  It is similarly possible to be on the production possibility frontier without being at the efficient point.  Because of this, there is a place for models of trade that work from a fixed quantity of goods.  And by the way, if you have a PPF that is shifting around endogenously based on the decisions you are trying to model, you haven’t specified it correctly.  [There Is some room for it to evolve endogenously over time but I don’t think that is what we’re talking about here.]

5.  Money: two goods, one price

It’s a notion which is almost as dirty as it sounds.  Here’s Dan Kuehn.

Money is really two products trading at the same price: it’s a medium of exchange and it’s a source of liquidity.

Now here is the most important point relative to the core agenda of this blog.  Money is, in a sense, two things but they are not the two things that DK claims and they do each have their own price (though they are related).  This highlights perfectly the central misconception that nearly everyone seems to be under regarding the nature of money.  Medium of exchange and source of liquidity are not different things.  They are the same thing.  To say that money is “liquid” is only to say that it is a convenient medium of exchange.  Anything can be used as a medium of exchange.  Some things are more convenient than others.  “Liquid” is just a word we use to say that something is particularly convenient for that purpose.

But deep down we know that it makes no sense for something which would be otherwise worthless to be used as a medium of exchange.  We know it has to have two uses.  This becomes paradoxical in the presence of the prevailing theory of fiat money which tells us that money has no other purpose, so we end up saying things that don’t make sense like medium of exchange and source of liquidity are two different things.  To try and sort this out, let’s go back to commodity money where the actual  two things can be easily seen.

If you had a pure barter economy, gold would be valuable.  It has use in various applications, most notably making things look more interesting or impressive than they would otherwise look, which is one of man kind’s greatest aspirations.  In other words, it’s a “real” good.  Of course, barter is complicated and gold is a particularly convenient good to use for trading because it is durable, easily identifiable, divisible, etc. so it makes sense for it to become a common medium of exchange.  This means that it would be highly liquid.

Now, in this case, gold is serving two purposes.  It can be used to make things look cool (and whatever else it can be used for) and it can also be used as a medium of exchange.  If it had no added value as a medium of exchange, it would still be valuable.  It would have some price relative to other goods and that price would change at some rate.  That rate of change in its price would be such that the value of it in terms of other goods would increase as the value of other investments excepting unexpected shocks to the long-run supply and demand.  That rate would be the interest rate (see the Hotelling Rule).

Already, there are two prices of gold, the spot price and the rate of interest (the spot price would really be many prices because there are many other goods but let’s just call it one price).  But of course, the interest rate would not be specific to gold, it would be the same for all assets so it wouldn’t really be the price of holding gold, it would be the price of holding wealth in whatever form and the spot prices of all of those various forms would distinguish their respective values in use.

Now, if we let gold be the common medium of exchange and therefore the most liquid good available to hold as wealth, people will prefer holding it to holding other goods at the same rate of return.  This means that the rate of return on holding it will fall below that of other goods.  And this means that there will be two rates of return.  Let the rate on all other assets (investments), measured in other assets be r and the rate on gold, measured in other assets be d (for “deflation”).  Since this return has to come from the price changing and there is now a differential between the rate at which prices are changing and the real rate of return on other investments, this differential must manifest itself in the form of a third rate which we know as the nominal rate or i.  This nominal rate is the price of liquidity.  (And naturally, the spot price will be higher than it would otherwise be because the price has to fall more slowly, or alternately because the added benefit from liquidity will cause it to be used up at a slower rate.)

So now you have a good with two purposes and two prices.  There is a price paid for the liquidity which is also the price paid for services as a medium of exchange.  This is the nominal rate.  There is also a spot price, let’s call it the price level, which includes both the value of the eventual use and the value of holding for liquidity purposes.  The system is not over-identified.  You just have to look at it as a dynamic system.  Oh, and you have to notice the two reasons that money (gold) is valuable.

Now, if you have gold notes, which are redeemable in gold, you have the same thing.  The notes are valuable because gold is valuable and because they are useful in exchange and gold is valuable because it is useful for other things like making stuff look cool and because it can back notes which are useful in exchange.  That part is pretty straightforward.

Where it goes off the rails is when notes are suddenly not backed by anything, or at least not by anything obvious.  Then we are left trying to say with a straight face that they are valuable only because they can be used for exchange.  The reality, as I have been saying, is that this is not the sole reason.  They still have value for two reasons.  One is that they are nice and liquid and the other is that they are the contractually required payment of debt and defaulting on debt has real consequences.  It’s not that they are not backed by anything, it’s just that the assets backing them are not uniform.  They are our houses, cars, businesses, etc.

Once you realize this, you can start to see why money does not act as a veil over barter, just like gold doesn’t act as a veil over barter.  Gold is a real good and a medium of exchange, money acts as a medium of exchange and a contractual claim on specific real goods.  So in the Walrasian general equilibrium with no money and gold as a good, you can get an excess demand for gold and an excess supply of all other goods.  Similarly, you can get an excess demand for money and an excess supply of all other goods with “fiat” money.  But in order to really grasp what is going on, you have to look at money and credit as a form of trading between periods in a dynamic model.

When you do this, it is clear that the expected rate of inflation and the nominal interest rate make up an important part of the budget constraint.  Since money is “convertible” into peoples’ houses, cars, businesses, etc. at a fixed rate, their willingness to hold money and debt depends on how valuable they expect that money to be in the future.  If they suddenly decide that it might be harder to get money in the future to pay off their debts, they may try to hold less debt and/or more money.  At current pries this is an “excess demand” for money which really represents an “excess demand” for future goods (like keeping their houses) relative to current goods.  But this only happens because their budget constraints across present and future goods shifted inward unexpectedly.  If everyone keeps eating out twice a week, they will all be unable to pay off their mortgages at the new expected rates of interest and inflation so they try to get more money and fewer current goods.  if prices cannot fall, you get a general glut.

So if you want to work at it, I think you can put this into the context of Walras’ law (more or less) if you imagine a dynamic version of it.  But this is only possible once you recognize the true nature of money and abandon the “fiat explanation of value” (it makes sense because we say it makes sense), and the notion of a veil over barter that goes with it.  And in order to do that, it helps to sit around and ponder what Walras’ Law really means and how it relates to what is actually going on for an afternoon or six.  And in order for people to do that, we have to keep teaching the damn law!

  1. August 29, 2014 at 10:28 pm


    I’m coming back to this. But in the meantime, this is what I consider my most thorough post on Walras’ Law: http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/04/walras-law-vs-monetary-disequilibrium-theory.html

    • Free Radical
      August 30, 2014 at 2:41 am

      Yeah, I missed that one thanks. Will put it in, it’s a good one. Also, I will give you credit for basically doing what I said I think you should do (use it to highlight the importance of money). I don’t know if it came across but I essentially agree with everything you’re saying except that Walras’ law is wrong and we shouldn’t teach it. It’s right in it’s own model, if you change the model it isn’t right. We have a lot of things like that. But if you want to throw it out you pretty much have to throw out the whole Walrasian model which I think is a bit extreme [don’t think I’ve ever attempted it but my suspicion is that if you wanted to write down a proof of the existence of a general equilibrium in the model you would have to write some form of Walras’ Law]. It’s kind of like saying “we never go in the basement any more, we should take it out.” But I don’t think it’s meant to be a theory of recessions or the business cycle. It’s an equilibrium model, it’s not supposed to explain how we get stuck out of equilibrium. People who use it for that should tread carefully.

  2. August 30, 2014 at 4:23 am

    FR: OK. I think we are *nearly* in agreement. Let me make two points:

    1. When I say “we shouldn’t teach it”, what I really mean (and what I did say once), is that “we shouldn’t teach it **as gospel truth**”. If you say we should teach it, but remind our students that it is only true in an economy where there is ONE market, where ALL goods are traded for each other, then that is OK. But unless we make that very big caveat very explicitly, students will think (and most economists think) that it is also true in a monetary exchange economy, in the real world, when it isn’t.

    2. You say ” It’s an equilibrium model,…”. Well it isn’t really. Walras Law is supposed to tell us something useful about excess supplies and excess demands. It is supposed to tell us that the values of those excess demands, across all goods, always sum to zero, even if they are not zero for some goods. Walras Law *is about disequilibrium*. Walras Law is supposed to be true for *all* price vectors, not just at the Market clearing price vector. (It would be totally trivial to say that if the excess demand for each good is zero then the sum of the excess demands is also zero. 0+0+0+0=0. Big deal!

    3. OK, a third point. In most markets, only 2 goods are traded. Like apples are traded for money. Or, in a barter economy, apples are traded for bananas. But we can imagine a market where 3 or more goods are traded. Like you can swap any combination of apples and/or bananas and/or carrots for any other combination. Or n goods.

    In any ONE market for n goods, and for any price vector for those n goods, the value of the excess demands for those n goods *in that ONE market* must sum to zero. That is true. Because people plan to pay for stuff, and get paid for stuff. As long as they do their arithmetic right. But in an economy with two or more markets, that tells us nothing whatever about how the excess demands for goods in one market are related to the excess demands for goods in other markets. Only in an economy with a single market, where all goods are traded, does Walras Law apply to all goods in the whole economy.

    • Free Radical
      August 30, 2014 at 5:31 pm


      I agree completely with 1 and 3. I think 2 is mainly a semantic argument. Saying it is an “equilibrium model” and not a “disequilibrium model” may not be the best way to say what I mean but basically what I mean is what you say in 3. Yes, it says something about what happens when the market is not in equilibrium (to some extent any “equilibrium model” has to do that). But it’s talking about being out of equilibrium because of an off-equilibrium price vector in the n-goods market that you’re talking about. I don’t think it is meant to apply when some market is price constrained for example. You can change the model to deal with that but once you change the model, either by putting in a constraint on the quantity of a good or by changing the nature of money or the markets, you get a different kind of “equilibrium” and the Law doesn’t necessarily hold or mean anything useful. So yes, we should be careful to put it in context but that should be the first rule of teaching economics (instead of the popular “it’s where the lines cross.”)

  3. August 30, 2014 at 4:30 am

    For example, suppose there are 7 markets in an economy. Suppose 6 of those markets are in equilibrium where quantity demanded=quantity supplied. Does that mean the 7th market must also be in equilibrium? Nope. For example, in a monetary economy, there can be an excess demand for rent-controlled apartments in the market for apartments (matched by an excess supply of money in that *particular market*), but all the other markets can be clearing.

  4. Ezra Davar
    October 9, 2014 at 8:39 am

    I accidentally saw this discussion which shocked me. First of all, it is not understandable how someone might discuss a work which never did read? Where is responsibility and scientific honesty? Second, the result is that Walras is blamed in theory that he never meant. Because, Walras’ law which was formulated by post-Walras authors and here is discussed is not Walras’s own law. Moreover, Walras’s own laws essentially differ from discussing Walras’ law (see Davar, E. (2012) “Is ‘Walras’ Law’ Really Walras’s Original Law?” World Review of Political Economy, 3(4): 478-500).
    Finally, the central reason for such a situation is that the first group of economists, which are in the minority, who have read Walras’s original works, misunderstood and misinterpreted them, from Pareto through Keynes and Arrow-Debreu; and the second group of economists, which are in the majority, including modern authors who are writing about Walras’s theory, have not read them in the original and have been saturated by the erroneous “Walras’s approach” of the first group of economists. The result is that these two different theories, namely, post-Walras authors’ theory and Walras’s original theory have been identified with each other; and, these terms are used interchangeably as if they aren’t any different from each other; and, these terms are used interchangeably as if they aren’t any different from each other (see Davar, E. (2014) “Walras and Contemporary Financial-Economic Crisis” Modern Economy 5(5): 635-656).
    Ezra Davar

    • Free Radical
      October 9, 2014 at 6:43 pm


      Interesting stuff. I will freely admit that I don’t know what Walras had in mind. What I do know is the model that makes up the foundation of modern economics and the role that what we (the standard micro texts) call “Walras’ Law” plays in that model. My problem is that most people who talk about “Walras Law” as though it proves that a general glut is impossible or that you can’t have an observed shortage in one market, with money, without having an observed surplus in another are not even getting that right, let alone whatever Walras was actually trying to say a hundred and fifty years ago. But that doesn’t mean that what we call “Walras Law” now is wrong, it’s just people misapplying it. I will leave it to historians to debate how great Walras was or wasn’t.

  5. Ezra Davar
    October 12, 2014 at 8:46 am

    Ezra Davar

    Yes, Walras’ law”, formulated by post-Walras authors, is wrong and incompatible with real economics!
    It seems me that there is no chance that you will read my paper ‘Is “Walras’ Law” Really Walras’s Original Law?’; therefore, I decided to post some relevant conclusions:

    Second, in Walras’s approach equilibrium is achieved for each commodity separately connected to equilibrium for other commodities when effective demand is equal to effective supply which is less or equal to available quantities. Therefore, in equilibrium state there might be unutilized quantity for some commodities. In Lange’s approach, however where there is equilibrium the excess supply of commodities is compensated by the excess demand for the money commodity, which is in a state of disequilibrium from the perspective of Walras’s approach.

    Finally, in Walras’s approach, all prices must be strongly positive and their equilibrium magnitude obtained from the framework of the primary demand curves (functions) for goods and the supply curves (functions) for services. Whereas according to Lange’s approach, as well as the post-Walras economists’ approach, the number of prices, but not all prices, might be equal to zero, and might even be negative, because they are only obtained by the technological conditions of the model.

    These two versions of “Walras’ Law” are not only are disconnected from real economics, but also incompatible even with a hypothetical economics; and they differ from Walras’s own system of laws, which are compatible with “a hypothetical regime of perfectly free competition.” Finally, and perhaps most importantly, “Walras’ Law” replaced Walras’s original laws not only in the textbooks but essentially in professional literature and has caused them to become unknown and abandoned and therefore caused huge damage to economic science. The thought of an “alternative” to Newton’s laws coexisting with the original is ludicrous, yet in economics such anomalies are commonplace.

  6. Free Radical
    October 13, 2014 at 6:31 pm

    It is not “wrong,” it is not “incompatible even with a hypothetical economics” and I don’t have any idea what you mean by “real economics.” Given statements like that, I think there is a fundamental disconnect between the way you are looking at this and the way I am looking at it that it is probably not worth trying to reconcile. I have just written many posts trying to carefully explain that statements like that make no sense, so I don’t really feel like going over it all again and you don’t strike me as being very receptive…

  7. Ezra Davar
    October 14, 2014 at 6:37 am

    It is impossible and not useful debate on the scientific topics when one of sides each time changes his/her opinion.

    • Free Radical
      October 14, 2014 at 6:37 pm

      I’m afraid I don’t know what to make of this comment.

  1. October 12, 2014 at 5:48 pm
  2. November 19, 2014 at 2:15 pm

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