Walras' Law vs Monetary Disequilibrium Theory

Walras' Law says that a general glut (excess supply) of newly-produced goods (and services) has to be matched by an excess demand for some other good. But it could be matched by an excess demand of anything that is not a newly-produced good. It could be an excess demand for money. Or it could be an excess demand for: bonds; land; old masters; used furniture; unobtainium; whatever.

Daniel Kuehn calls this the "Whack-a-mole" theory of general gluts. The excess demand that matches the excess supply of newly-produced goods could pop up anywhere.

Monetary Disequilibrium Theory says that a general glut of newly-produced goods can only be matched by an excess demand for money. There's only one mole to whack. Money is special. A general glut is always and everywhere a monetary phenomenon.

In a monetary exchange economy, Walras' Law is wrong; Monetary Disequilibrium Theory is right. We live in a monetary exchange economy. Walras' Law is the worst fallacy currently taught in economics as gospel truth.

Why is Walras' Law wrong? Why is money special? That's what this post is about.

Keynes failed to escape Walras' Law. He said (somewhere) that if Silvio Gesell succeeded in eliminating an excess demand for money by taxing money, people would switch to wanting to hold land instead, and the general glut could continue. The excess demand just pops up somewhere else. Whack-a-mole. But Keynes was wrong; Gesell was right.

New Keynesian (Neo-Wicksellian) models say that a general glut of goods-produced-today is matched by an excess demand for goods-produced-tomorrow, not by an excess demand for money. That's another application of Walras' Law.

Walras' Law is not a zombie theory. It's a poltergeist. It doesn't realise it's dead (Clower killed it decades ago). You have to first understand why it was once alive before you can persuade it to rest in peace.

So first let's recognise the truth in Walras' Law. Instead of an economy with many markets, where only two goods are traded in each market, suppose that all goods are traded simultaneously in one big centralised market. You take apples bananas and carrots to the market, and exchange them directly for dates eggs and figs, in one big exchange. You give your apples bananas and carrots to the auctioneer, and he gives you dates eggs and figs in return. And suppose further that agents never imagine they might be unable to sell or buy as much as they want to in that market. Because there's no "false trading" at disequilibrium prices -- no trade is allowed to take place until the Walrasian auctioneer has found the market-clearing price vector. That's the world of Walrasian general equilibrium theory.

In that world, Walras' Law would be true. Each agent would make one big decision about how much of each good to buy or sell, and that decision would respect the agent's budget constraint. The market value of the goods he planned to buy would equal the value of the goods he planned to sell. Unless agents had fat fingers on their calculators, Walras' Law would be true at the level of each individual agent's planned demands and supplies. Summing across all agents' demands and supplies, Walras' Law would necessarily be true at the aggregate level as well.

We do not live in a world like that.

First, we do have false trading, and agents aren't stupid. They know that if there is an excess supply of apples some of them will be unable to find buyers and so won't be able to sell as many apples as they want to sell. And if there is an excess demand for apples some of them will be unable to find sellers and so won't be able to buy as many apples as they want to buy. They are quantity-constrained. So they revise their planned demands and supplies of other goods taking that constraint into account. The demands and supplies we actually observe in markets are those constrained demands and supplies, not the notional demands and supplies of agents who are stupid enough to think they can buy or sell as much of everything as they wish even at a disequilibrium price vector.

Second, we live in a monetary exchange economy. If there are n goods, including one called "money", we do not have one big market where all n goods are traded with n excess demands whose values must sum to zero. We might call that good "money", but it wouldn't be money. It might be the medium of account, with a price set at one; but it is not the medium of exchange. All goods are means of payment in a world where all goods can be traded against all goods in one big centralised market. You can pay for anything with anything. In a monetary exchange economy, with n goods including money, there are n-1 markets. In each of those markets, there are two goods traded. Money is traded against one of the non-money goods. Each market has two excess demands. The value of the excess demand (supply) for the non-money good must equal the excess supply (demand) for money in that market. That's true for each individual (assuming no fat fingers) and must be true when we sum across individuals in a particular market. Summing across all n-1 markets, the sum of the values of the n-1 excess supplies of the non-money goods must equal the sum of the n-1 excess demands for money.

Walras' Law describes an economy with one market with n goods traded and n excess demands. In a monetary exchange economy there are n-1 markets with 2 goods traded and 2(n-1) excess demands.

OK. So can't we just re-state Walras' Law as saying that the sum of the values of the excess supplies (demands) for the n-1 non-money goods must equal the sum of the n-1 excess demands (supplies) for money?

The short answer is: "No, you can't". Or rather: "You can if you like, but it's a very different beast from the original Walras' Law, and is totally useless". Let me explain why.

Let there be three newly-produced goods: haircuts; manicures; and massages. Let there be one non-money non-produced good: "land". And let there be one medium of exchange: "money". There are four markets: for haircuts; for manicures; for massages; and for land. Money is traded in each of those four markets.

Start in equilibrium. Demand equals supply in each of the four markets. Hold all four prices fixed. Then all of a sudden: the hairdresser decides she wants to buy land instead of a manicure; the manicurist decides she wants to buy land instead of a massage; and the masseuse decides she wants to buy land instead of a haircut. (Substitute "bonds" for "land" and this is the New Keynesian theory of general gluts.)

What does Walras' Law say? Walras' Law says there is an excess demand for land and an offsetting excess supply of newly-produced goods: haircuts, manicures, and massages. A general glut of newly-produced goods, which will cause all three women to be unemployed, because nobody will buy the services they want to produce. WRONG!

Initially, in the market for land there is an excess demand for land matched by an excess supply of money. All three women are trying to buy land with money. And in the markets for newly-produced goods there is an excess supply of haircuts, manicures and massages matched by an excess demand for money. There is one excess supply of money that equals (let's suppose) the three excess demands for money. But what happens next?

Either the price of land adjusts or it doesn't.

If it adjusts, so that all three women stop wanting to buy land at the new higher price, we are back in equilibrium.

If it doesn't adjust, all three women will learn that they cannot buy land, because they can't find a willing seller. They are quantity-constrained in the land market. And being rational utility-maximising agents, they take that new constraint into account and re-formulate their demands and supplies for other goods. What happens next depends on the exact shape of their utility functions. One plausible scenario is that, since they can't buy the land they want, they go back to doing whatever it is they were doing before they suddenly decided they wanted more land. They go back to buying haircuts, manicures, and massages.

Assume my "plausible scenario" is correct. What are the excess demands and supplies we would observe? The hairdresser still drops by the realtor's office, on her way to get a manicure, and asks if they have any land for sale, just in case things have changed. There's still an excess demand for land. She still wants to buy land, even though she might get discouraged from trying to buy some. But then she continues on to buy a manicure. Same for the other two women.

So there's an observed excess demand for land, but no observed excess supply of haircuts, manicures, or massages. Walras' Law fails.

Or does it? Well, you could say that the excess demand for land in the land market is matched by an excess supply of money in the same land market. That's true, totally trivial, and totally useless in explaining general gluts. It tells us what is happening in one market -- an excess demand (supply) of the good must be matched by an equal excess supply (demand) for money in that same market -- but that tells us absolutely nothing about what is happening across markets.

The only true version of Walras' Law in a monetary exchange economy -- the sum of the values of the excess supplies (demands) of the n-1 non-money goods must equal the sum of the n-1 excess demands (supplies) for money -- is totally useless because it imposes no cross-market restrictions on excess demands and supplies. It's just the trivial sum of the individual market restrictions. And imposing cross-market restrictions on excess demands and supplies is precisely what Walras' Law was supposed to do.

Let a be the excess supply of apples, and let A be the excess demand for money in the apple market. Let b be bananas, and c be carrots. If a=A, and b=B, and c=C, then whoopee! a+b+c=A+B+C. But that tells us nothing about the relation between a,b,and c. On the other hand, a+b=C would be useful, but unfortunately it's also false.

Walras' Law is either useful or true. Pick one.

Back to my three women. Start back in equilibrium. Hold prices fixed. Then all of a sudden all three women decide they want to hold more money and less land. Walras' Law says that there's an excess supply of land matched by an excess demand for money. But no excess supply of newly-produced goods like haircuts, manicures, or massages. WRONG!

Initially the three women do plan to sell land and hold the proceeds as money. There's an excess supply of land and an excess demand for money in the land market. But what happens next?

Either the price of land adjusts or it doesn't.

If it adjusts, so that all three women stop wanting to sell land at the new lower price, we are back in equilibrium.

If it doesn't adjust, all three women will learn that they cannot sell land, because they can't find a willing buyer. They are quantity-constrained in the land market. And being rational utility-maximising agents, they take that new constraint into account and re-formulate their demands and supplies for other goods. What happens next depends on the exact shape of their utility functions. One plausible scenario is that, since they can't get extra money by selling land, they try to get extra money by selling more haircuts, manicures, and massages. But that won't work either, since they can't find extra willing buyers.

A second plausible scenario is they they try to get more money by buying less haircuts, manicures, and massages. That's what causes an excess supply of newly-produced goods. That's what causes a general glut.

Nobody can ever stop you buying less other goods.

What makes money different? What makes money special?

In Walrasian General Equilibrium theory, there is one big market in which all n goods are traded. For each good, and for each person, that person is either a buyer of that good or a seller of that good -- not both. If you are a buyer and the good is in excess demand, you won't be able to buy more. If you are a seller, and the good is in excess supply, you won't be able to sell more. You can't always do what you want -- you need to find someone else willing to take the other side of the trade.

Money is different because it is the only good for which every person is both a buyer and a seller. Money comes in one hand when you sell all other goods, and goes out the other hand when you buy all other goods. Each person is only on one side of the market for every other good. Every person is on both sides of the money market. That's because there is no "money market". Or, rather, every market is a money market in a monetary exchange economy. So it doesn't matter if markets are in excess demand or excess supply. The individual can always get more money by buying less other goods even if he can't get more money by selling more other goods.

But while the individual agent can always get more money by buying less other goods, that's not necessarily true in aggregate. And the individuals' attempts to do something which is collectively impossible are what cause the general glut of other goods.

Leave money out of the picture, and it becomes impossible to explain why there should be a general glut of haircuts, manicures, and massages. If all three women are unemployed, why don't they just do a 3-way barter deal? The hairdresser gets a manicure, the manicurist gets a massage, and the masseuse gets a haircut. All three women are better off. Any theory of general gluts which ignores monetary exchange and the excess demand for money assumes the three women are irrational in leaving unexploited gains from trade lying on the table.

Comments

[Daniel Kuehn]

I'm only at the beginning, but I have to say I like the parenthetical "(somewhere)"! Makes citation much easier - I need to do that more.

[anon]

There are general gluts because money is a (rational) option not to buy.

It's an escape chute from Walras' Law.

[david]

In Which Nick Rowe Once Again Banishes the Ghost Of Excess Supply By Stealthily Burying Price Flexibility In His Model, And Is Subsequently Astonished When Prices Adjust

Less snarkily: take the situation where the women desire more land, and all prices adjust. Is there in fact any price vector which would create equilibrium? There doesn't seem to be, since nobody seems to be selling any land. Are you pulling the Unobtanium trick again?

[Curtd]

Am I missing something or are you missing the effect of intertemporal considerations on equilibria?

[Nick Rowe]

anon: OK. But then money is an option that you can *always* buy more of (simply by not buying other things). You don't need to find a willing seller.

david: you lost me a bit there. Simply assume sticky prices, if you like (that's what I am doing to get a general glut). I'm assuming the 3 women are the only people in the economy. (Or, they are representative agents). If everybody wants to buy more land, they won't be able to, because nobody wants to sell.

Curtd: You are coming at this as a New Keynesian? Start in equilibrium. Then suddenly the three women want to consume more tomorrow and less today (Consumption-Euler equation shifts). That's like an excess demand for bonds and excess supply of currently-produced goods. And that's like an excess demand for land and excess supply of currently-produced goods. Which is what I looked at.

[Ken]

"A second plausible scenario is they they try to get more money by buying less haircuts, manicures, and massages. That's what causes an excess supply of newly-produced goods. That's what causes a general glut."

Nick, could you explain whether or not price stickiness is relevant at all to your model and, if so, in what way?

[Daniel Kuehn]

david - I come to much the same conclusion about "burying price adjustment" here: http://factsandotherstubbornthings.blogspot.com/2011/04/nick-rowe-brad-delong-and-me-on-whack.html

Like he says, sticky prices do the trick. It just makes me scratch my head how sticky prices can account for persistent unemployment.

[anon]

Ken, AFAICT, price stickiness _is_ relevant, because if prices were flexible the prices of haircuts, manicures and massages would fall. Eventually, agents will buy these goods again, because they value the goods more than the--now proportionally smaller--decrease in money holdings. Or else, the general price level will fall and the agents will indeed be holding more money (in real terms).

[david]

So it is the Unobtanium again. Regardless of the price of land, and regardless of whether the representative agent wants to hold more or less land at that price, no land is ever traded. It may as well not exist. The part of your examples without money are identical to Unobtanium, and the part of your examples with money hides relative price adjustment in the relative price of money vs. assorted goods.

Applying Walras' Law here was wrong with your earlier Unobtanium essay and it's still wrong. If you allow yourself to define excess demands as, purely, a willing demand for a good at the prevailing price that is unmet, then surely you should define excess supply as a willingness to supply a good at the prevailing price that is not exhausted (which remains wholly true, even though all the women are able to find buyers for their manicures/whatever - if the Prime Mover popped up and offered land for manicures, the women would trade. There is no point at which the women cease to desire to sell more manicures/whatever at the prevailing price vector, which would be immediately observed if land were exogenously introduced). Don't compare notional and constrained excesses.

[Andy Harless]

I'm going to give the same example I always give. Suppose that the prices of haircuts, manicures, and massages are all fixed in terms of land but paid with money, and the price of land in terms of money is allowed to fluctuate. Now if everyone suddenly decides they want to buy land, there will be an excess supply of haircuts, manicures, and massages, despite the fact that noone trades land directly for those things.

In my example, a large landowner has some of the power of a central bank, even though she doesn't produce the medium of exchange. I maintain that something like this happened in the 1970's in the US (and elsewhere). Labor was priced, to a significant extent, in terms of the CPI basket rather than in terms of dollars. OPEC, which controlled a non-trivial part of the CPI basket, was like the large landowner in my example and was able to create an excess supply of labor via a "tight oil" policy.

[anon]

"But then money is an option that you can *always* buy more of (simply by not buying other things). You don't need to find a willing seller."

No. Money is an option not to buy. That's the option, relative to barter, and the cause of the glut.

You already have money by selling. There's no option there.

[Patrick]

Andy: "OPEC, which controlled a non-trivial part of the CPI basket, was like the large landowner in my example and was able to create an excess supply of labor via a "tight oil" policy"

I'm a bit out of my depth here so forgive me if I say something stupid... I think you can explain the OPEC embargo with a simpler story:

Imagine an economy where every job requires a shovel. Also imagine there is a fixed supply of domestic shovel makers (for whatever reason - it doesn't matter). Domestic shovel makers can't supply the domestic demand for shovels, so most shovels are imported from Shovelland . Now imagine that the Shovellanders get mad at us and stop sending us shovels. The price of domestic shovels goes way-up, and some jobs (remember they all require shovels) become uneconomical as the cost of the shovel isn't justified by the MP it'll produce. Unemployment ensues.

[Jon]

Nick,

I'm confused about what you're trying to say here. Personally, I don't see how thinking in terms of Walras' Law is helpful. I think that's the point you're trying to make, but I found it hard to follow.

Walras' Law is basically always true as long as there's local non-satiation of preferences. That's a theorem: Just sum up the budget constraints.

If you want to allow for inflexible prices, then you have to introduce a rationing mechanism. This is in the technology of the economy and is going to act like a price to clear the markets. If you want to make money necessary that's also a change in the technology of the economy.

I don't see how thinking in terms of general gluts, excess supplies and demands, or money markets is helpful. I just find it confusing.

[BSE]

That's a good post. I think I understand now how money acting as a medium of exchange is one cause of a general glut.

I think That's where the disagreement begins, though, because as a wise person once told me all science begins with stamp collecting. I think your problem here is that you seem to be insisting that there is only one way to get a general glut and that's through money as the medium of exchange which has to clear all excess supplies and demands. It seems to me that you still need a coordination failure somewhere to get this to work, but fine.

What you really failed to show is why there can't be other types of general gluts. You keep saying that Walras' Law fails, but nothing you say suggests that it isn't approximately true, so why not imagine Walras' Law holding approximately in the aggregate and model your "disequilibrium" as a search problem? (Which I am sure has been done, don't make me look up the reference) Now, with the economy in approximate equilibrium, let's say there's a glut due to the unit of account function of money because, I don't know, the price of money rises (there is a deflation) and some indebted agent's have too much debt on their balance sheets; call it a "balance sheet recession". Or with the economy in an approximate equilibrium imagine that for whatever reason there is a general glut because the price of future consumption is so high that interest rates would need to be negative to clear that market; but nominal rates can't fall below zero. Call this a "Keynesian recession".

What I'm saying is that "nominal regidity + approximate (or exact!) Walrasian equilibrium = general glut". Walras' Law is still an attractor for the problem, so something needs to come along and kick the problem well away from the equilibrium. Your model suggests that the economy is never in exactly a Walrasian equilibrium, but you still need to find the coordination failure that these other models have (in the form of the nominal rigidity) or else you haven't explained anything.

[beowulf]

"There are general gluts because money is a (rational) option not to buy.
It's an escape chute from Walras' Law."

In Chapter 19 of his General Theory, Keynes specifically stated that his theory of unemployment did not rely on the assumption of wage and/or price rigidities. He claimed that his theory provided a different analysis where the cause of unemployment was related to the operation of financial markets and the public's desire to hold liquid assets.
http://mises.org/daily/3756

[Nick Rowe]

Ken: "Nick, could you explain whether or not price stickiness is relevant at all to your model and, if so, in what way?"

I'm assuming that prices are sticky (or, rather, stuck). Nothing new there. It's the sticky prices that create excess demands and supplies. What I am doing is exploring the relationship between excess supply in some markets and excess demands in other markets. Walras' Law purports to say something about that relationship. I'm saying that what WL says is wrong.

Daniel: "Like he says, sticky prices do the trick. It just makes me scratch my head how sticky prices can account for persistent unemployment."

Depends how sticky they are. And depends how persistent you mean by "persistent". I'm saying nothing new there. (But if prices are sticky then false trading can create its own dynamic that might make it harder to get back to equilibrium. Though I'm not exploring that idea here.)

anon: "AFAICT...." You have got it right. My thinking is the same as yours.

Andy: understood. If prices of haircuts manicures and massages are sticky in terms of land, and the price of money is flexible in terms of land, an increased demand for land, will lower the price of money in terms of land, so reduce the real money supply in terms of haircuts etc., so could create an excess demand for money that way. And that excess demand for money would create a recession.

anon: maybe just a semantic disagreement between us there.

Patrick: yours is more like the standard story. It's not (obviously) stupid. But Andy's story interests me, because it's a bit different.

Jon: "Walras' Law is basically always true as long as there's local non-satiation of preferences. That's a theorem: Just sum up the budget constraints."

That's how we learn Walras' Law. That is how it is normally "proved". And what I am saying is that that "proof" of WL has a couple of implicit assumptions: no false trading or quantity constraints (apart from the BC); a single unified market for all n goods.

"If you want to allow for inflexible prices, then you have to introduce a rationing mechanism. This is in the technology of the economy and is going to act like a price to clear the markets."

Understood. Those quantity constraints will have a shadow-price "Lambda" attached to them, like in linear programming Kuhn-Tucker conditions. And the demands and supplies will be functions of P+lambda, not just of P. You can think of the lambda's as the cost of queuing, for example. I see that as an alternative way of saying what I am saying.

"If you want to make money necessary that's also a change in the technology of the economy."

Agreed, if you want to do it properly. Notice that there's no double-coincidence of wants with my 3 women. And they can't do 3-way direct simultaneous barter, because it's hard to cut someone's hair while you are getting a manicure, etc. Assume all 3 can't ever meet in the same place, or are anonymous, if you want to rule out 3 way barter completely. I just introduced monetary exchange the "quick and dirty" way. I just *assumed* they could only sell haircuts etc for money.

"I don't see how thinking in terms of general gluts, excess supplies and demands, or money markets is helpful. I just find it confusing."

OK. But it is how most people think. "There's an excess supply of labour and newly-produced goods" is how most economists describe a recession. I'm not opposed to some deeper description, in terms of some sort of search/rationing model, like you are talking about. I think it would come to much the same results, just described differently.

BSE: "It seems to me that you still need a coordination failure somewhere to get this to work, but fine."

Agreed. If all 3 women could get together and do a 3-way swap of haircuts, manicures, and massages, they could escape the general glut and unemployment. I'm assuming they can't. They only meet 2 at a time. There is no double-coincidence of wants. That's the coordination problem that monetary exchange solves. But if there's a shortage of money (in real terms), there's not enough of it to solve that coordination failure. So we get a recession.

I think that might also address the points you raise in the rest of your comment. Suppose that real interest rates are stuck too high, as in your example. If the 3 women can do a 3-way barter deal, they can still escape unemployment. It's precisely because they can't do a 3-way barter deal, and have to use money to try to solve that coordination problem, that we get a recession if there's an excess demand for money.

An excess demand for money is like a shortage of trust. There's not enough mutual trust for the 3 women to solve the coordination problem.

[Ken]

I'm a relative beginner, but I don't understand how this post could be written without mentioning wage/price rigidities. I'd love to read a version that includes these concepts -- perhaps just a line that explains why they aren't relevant.

[Nick Rowe]

Ken: I did mention price rigidities. I was talking about what would happen if prices didn't adjust (or, at least, didn't adjust quickly enough to keep all markets clearing continuously). That was something I took for granted -- took as understood. Perhaps I should have been more explicit. But look, this is a hard post. Someone who doesn't have a basic familiarity with Walras' Law and Walrasian General Equilibrium theory may have a hard time with it.

(Wages are just prices -- the price of labour. In my model the wage of the hairdresser is the price of a haircut.)

[Jon]

Nick,

Okay. Maybe this is a generational thing. I'm a current grad student studying macro, and none of my professors talk about Walras' Law and disequilibrium phenomena. They (have taught me to) think about business cycles in terms of introducing frictions (price-stickiness, search, money, imperfect information) into a DSGE framework. Market always clear here.

What do we gain by thinking in terms of disequilibrium? I'm legitimately curious. Also, any good references you can recommend would be appreciated.

[Nick Rowe]

Jon: Yep. It probably is a bit generational. I'm an old guy!

1. I argued in this post: http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/04/excess-supply-excess-demand-and-search.html
that thinking in terms of excess demand/supply is not qualitatively different from thinking about a market with search. If you take the limit of a search model, as it gets easier and easier for buyers and sellers to find each other, you get Q=min{Qd,Qs} in the limit. "Excess demand" is a limiting case where it's very easy for a seller to find a buyer and very hard for a buyer to find a seller. "Excess supply" is a limiting case where it's very easy for a buyer to find a seller and very hard for a seller to find a buyer. It's just simpler to think in terms of limiting cases.

2. A lot of people do talk about there being an excess supply of labour and goods in a recession.

3. You don't ever hear anyone talk about Walras' Law? This post came out of a discussion between Brad DeLong and Daniel Kuehn on Walras' Law. What was causing the excess supply of goods (the general glut)? Was it an excess demand for safe assets?

4. References. God, I'm always bad at references. Have a brain like a sieve. Patinkin's "Money Interest and Prices" is the locus classicus of Walras' Law in an economy with money. This post is sort of a critique of Patinkin through the eyes of Robert Clower and Leland Yeager.

[Lord]

While it is an excess demand for money, and in some cases explicitly that, that is not how the ordinary person would think of it. They don't want money but goods at better price in the future or future goods, and money is just their second best choice.

[david]

Aw, you skipped my reply. :(

@beowulf - if you want to see those, you may like to read the post-Keynesians (and not an Austrian summary of post-Keynesian theory, either). There are at least three Keynes floating around here.

[Jon]

Nick,

Interesting. The generational gap in economics is truly astounding sometimes. I can't think that's good for the discipline.

In undergraduate, I learned Walras' Law in micro as "If all markets but one clear, the last one clears." It was never mentioned in macro (we used Williamson).

In graduate school, I learned Walras' Law in first-year micro when we learned GE theory. It was never mentioned in macro.

I recently taught intro macro using Mankiw. I never mentioned Walras' Law.

I've only seen recessions described as an "excess supply of currently produced goods" on Brad DeLong's blog, and now here. I didn't realize this was a common framework.

I'll have to think about it more.

[William Peterson]

I’m afraid I believe the view expressed here that a general glut can only occur in a monetary economy is yet another zombie theory (except that if we define a general glut as excess supply of all commodities except money it becomes a tautology).
Walrasian economies have two distinctive features. Firstly, the auctioneer does not allow any trade to take place until the auction has revealed the complete vector of market-clearing prices. At these prices, all agents can buy or sell as much as they want (otherwise they would not be market-clearing prices). So no-one has to worry about downward-sloping demand curves and other features of imperfect competition. In Clower’s terminology, notional and effective excess demands coincide. Contrast this with an economy in which trading takes place at ‘false prices’ before markets clear: those on the long side of a market (eg those where the commodity concerned is in excess supply at the prevailing set of prices) can sell more if they cut their price, so they have a degree of market power. In addition, any system where trade occurs before market clears must be a ‘sticky-price’ economy. It is the assumption of full price flexibility, not that of price stickiness, which is a special case. All this was set out in the late 60’s work of Clower and Leijonhufvud.
Secondly, in a Walrasian economy all production processes are characterised by constant returns. This means that there is nothing special about the employment relation, or labour as a commodity. Each individual can employ his own labour to produce goods for sale (or for his own consumption), and he can transform unstorable labour power into storable commodities with no loss of efficiency. In contrast, with increasing returns firms (which are not perfectly competitive) play an essential role in production: and since non-agricultural workers will not usually accept a share of the physical product as wages, they will not hire workers unless they expect to find a profitable market for their product. So there is a coordination problem, since in general firms are specialised and do not produce the wage-goods that the workers desire.
None of this (except possibly the last point about the payment of wages) has much to do with money. The Walrasian auctioneer quotes prices in terms of a numeraire, but the purpose of this is to simplify the calculation of relative commodity prices (which in turn determine excess demand): the auction process would work just as well if prices were quoted in a fictional unit of account, such as the guineas used in English auction rooms. Walrasian monetary models (eg Patinkin) work because real money balances enter the utility function, but this essentially solves the problem by assumption. Where money is useful is in simplifying the process of exchange after market-clearing prices are known, because the existence of money gets round the problems that prospective buyers do not know which other agents wish to sell, and that there is unlikely to be a ‘double coincidence of wants’. But this medium of exchange role is a different issue.
So I would argue that Keynes was right to stress the possibility that excess demand for any non-reproducible commodity (for example, land) could lead to a general glut. Suppose that a shock switches market demand from produced commodities to land. If everyone could wait until the new market-clearing price vector had been found before trading, then the price of land relative to currently-produced commodities would rise until the change in prices, and the resulting higher demand from landlords, was sufficient to clear markets. But if production and trade have to be planned before the auctioneer has found the right prices, it is quite possible that there will be excess supply of all currently produced commodities: and in an economy with production, this will lead firms to cut back output and employment. Workers will find it hard to do much about this, because labour is not fully storable (if they could produce a storable good efficiently, they could maintain production and use their future sales revenue as collateral). So the economy experiences a general glut: but in practice we do not explicitly observe an excess supply of all commodities, because in most markets firms cut back output in response to deficient effective demand. (In a socialist economy, where firms cannot easily dismiss workers, they do end up producing unwanted goods).
Even if in a modern economy it is usually a shift of demand from goods to ‘safe’ financial assets such as money which sets off a crisis, I think it is misleading to see this sort of coordination failure as a direct consequence of the use of money. We would experience similar (or worse) coordination failures if we had to rely on barter. I think this point comes out of some of the examples about manicures etc - but it doesn't quite fit with the opening assertions about 'Whack-a-mole' theories.

[edeast]

Walras still holds in the wider economy, with n goods there are n choose 2 markets, right? Because we are looking at a subset,(n-1 wrt money), able to have the excess supply/demand, but walras still holds overall.

[edeast]

If that statement holds, I think it implies money is not special. Any broadly traded good,( n-whatever), could have a large effect on the economy.

[amv]

@ Nick Rowe,

It's hard for me to grasp your critique of Walras's Law. The following reasoning just refers to this part of your argument:

QUOTE
So first let's recognise the truth in Walras' Law. Instead of an economy with many markets, where only two goods are traded in each market, suppose that all goods are traded simultaneously in one big centralised market. [...] And suppose further that agents never imagine they might be unable to sell or buy as much as they want to in that market. Because there's no "false trading" at disequilibrium prices -- no trade is allowed to take place until the Walrasian auctioneer has found the market-clearing price vector. That's the world of Walrasian general equilibrium theory.

In that world, Walras' Law would be true. Each agent would make one big decision about how much of each good to buy or sell, and that decision would respect the agent's budget constraint. The market value of the goods he planned to buy would equal the value of the goods he planned to sell. Unless agents had fat fingers on their calculators, Walras' Law would be true at the level of each individual agent's planned demands and supplies. Summing across all agents' demands and supplies, Walras' Law would necessarily be true at the aggregate level as well.
END QUOTE

So here is my problem: you seem to suggest that the validity of Walras's Law depends on the equilibrium properties of the Walrasian system. It seems that it is significant part of your argument that markets clear and prices constrain agents to act so that plan consistency exists. You first introduce an equilibrium situation and only afterwards do you sum up over excess demands.

Now, Walras's Law is no equilibrium condition, but a property of the economy. It says that markets are interrelated. Mathematically, it says that the inner product of ANY price system and the excess demand function/correspondence is of zero value. For an arbitrary price vector/system generated by the super auctioneer (aka a system of differential/difference equations and arbitrary initial values), agents signal excess demand functions such that markets may not clear. Nevertheless, Walras's Law holds. It is a necessary condition for convergence (see Franklin Fischer on disequilibrium processes). All in all, if you want to criticize Walras's Law, you cannot do so by referring to it's inability to account for trades at false prices. If money still collides with Walras's Law, in a way the Ostroy/Starr approach to money in GE cannot account for, you may rather focus on why neoclassical trading technologies that allow for bilateral trades cannot cope with "real-world money".

[Paine]

Commodity money ie money with a use value even if only aesthetic
Removes the trust element from what is an inter temporal trade viewed in the whole

[Paine]

I thinkthesemodels replace the use of abstraction with the use of wonderland contrivance
Like the three services toononomy here
Then reification sets in

And the toononomies start to build on themselves not reality

rational speculation is not science
And bizzaro analogy is not modeling

And I'd like some one to show me how political economy is an ahistorical science

Example the historical emergence of money as a commodity that mediated exchange

Here's a story that escapes just so versions only if we review the historic record

Contriving a simplified parallel world is fun maybe even insight giving
But .......
A nice Test can the so called toy models that are non stochastic run in reverse
The walrasian auctioneering system can because there are no real trades until all markets clear simultaneously
Edgeworth recontracting is allowed

Time reversal is possible the auctioneer could call out the prior set of prices and then the prior to the prior etc

This is bogus this is not real markets those social contrivances of millennia of human social development

Notice evolutionary biology never plays these just so games

They look at the record

Trying to comprehend the aspects of our present market system
By removing key elements like credit money and durable goods and debts and etc etc

You pull away from economics int
O moral parables like the ant and the grass hopper

[Paine]

The struggle here I think is to suggest how the money system serves as link
Between the existing asset markets and the product markets
Job markets only complicate the problem

The idiotic macro that is all product no asset leads to missing the minsky moments so to speak

The last 30 years of macro theory with it's elegant wonderland formal structures
headed right for the surprise of 08 09

[Paine]

Btw
Nick great post
In spite of it's redundancy and Lewis carrollite romping

Bravo

[Nick Rowe]

david: sorry. I missed responding to your first comment. But I have read it twice again, and still don't understand it. In competitive equilibrium, there is no excess supply of haircuts. The hairdresser is selling as many haircuts as she wants to at the existing price. She doesn't want to cut more hair and work longer hours at that price.

Lord: you too lost me!

Jon: Yes, there does seem to be a worrisome generational gap. I think this is part of what Paul Krugman and Brad DeLong keep complaining about, in the "Dark Age" meme. But partly I think it's just that we have lost the art of translating between perspectives. (A lot of my posts are attempts to do translation, like my Functional Finance post.)

"I've only seen recessions described as an "excess supply of currently produced goods" on Brad DeLong's blog, and now here. I didn't realize this was a common framework."

It is very much a common framework (outside of RBC and the Lucas' misperceptions model). Sometimes it gets replaced by an "excess supply of labour", but that is really just a slightly different way of saying much the same thing, since labour is a currently-produced service. In New Keynesian models, since they assume firms are imperfectly competitive, so always have an "excess supply of output" in some sense (since P is above MC at the current level of Qd) you can't see it so clearly. But "recessions are an excess supply of goods aka general glut" must go back a couple of centuries at least. The Keynesian Cross model, for example, and the ISLM, assume output is demand-determined, which only makes sense if goods are always in excess supply. Given Q=min{Qd,Qs}.

[Nick Rowe]

William:

1. "All this was set out in the late 60’s work of Clower and Leijonhufvud."
Agreed on that paragraph. I'm just taking that, and throwing in a bit of Yeager.

2. I disagree on the next paragraph, and don't really see its relevance. My model (implicitly) assumes constant returns in any case; the 3 women are self-employed.

3. You lost me a bit on the next paragraph. Agreed the role of money as numeraire in the Walrasian system is irrelevant. The numeraire could be fictional. "But this medium of exchange role is a different issue." Once we allow false trading, so that quantities traded *in a market* are determined by min{Qd,Qs} *in that market*, then it matters very much which markets exist. And an economy with a single medium of exchange has a very different set of markets than an economy where any good can be traded against any other good.

4. "So I would argue that Keynes was right to stress the possibility that excess demand for any non-reproducible commodity (for example, land) could lead to a general glut."

Here I totally disagree. Suppose all prices are fixed (for simplicity). Then people try to buy more land and less haircuts. They immediately find they can't buy more land. As soon as they realise that they can't buy more land, they spend their money income on haircuts instead. Keynes would only be right in that very short interval in which people are accumulating money hoping to buy land; and that's the exception that proves the rule, because the excess demand for land creates a temporary excess demand for money in that case. (BTW, there cannot be an inventory of unsold haircuts, but a hairdresser who is sitting idle for want of customers is an excess supply of haircuts nevertheless.)

5. "...I think it is misleading to see this sort of coordination failure as a direct consequence of the use of money. We would experience similar (or worse) coordination failures if we had to rely on barter."

Agreed. There would be much worse coordination failures under barter. It is not the *use* of money that causes coordination failures; it is the fact that we *need to use* money to overcome even worse coordination failures under barter that causes the coordination failure, if there's a shortage of money. Money resolves that coordination failure when it works well, but only partly resolves it when it works badly.

[Nick Rowe]

edeast: "...with n goods there are n choose 2 markets, right?"

Sorry. You lost me. Typo? "n choose 2"?

amv: "Now, Walras's Law is no equilibrium condition, but a property of the economy. It says that markets are interrelated. Mathematically, it says that the inner product of ANY price system and the excess demand function/correspondence is of zero value. For an arbitrary price vector/system generated by the super auctioneer (aka a system of differential/difference equations and arbitrary initial values), agents signal excess demand functions such that markets may not clear. Nevertheless, Walras's Law holds."

That coincides exactly with my understanding of Walras' Law, as generally understood. I agree with all of it, except the last sentence. I say WL does not hold. And you lost me on the remainder. Sorry.

Paine: "Commodity money ie money with a use value even if only aesthetic
Removes the trust element from what is an inter temporal trade viewed in the whole"

I would say that money replaces trust in the individuals we sell to with trust in money. And a commodity money replaces (to some extent) the trust that people in general will continue to accept that money with trust in the commodity itself. But even here, if a commodity is used as money that will generally increase the demand for that commodity and raise its equilibrium value above its purely non-monetary marginal use-value. (Which is why I say "to some extent".)

"And bizzaro analogy is not modeling"

Yes it is!

"Notice evolutionary biology never plays these just so games
They look at the record"

I thought they did both. Maynard Smith seemed to make a lot of simple models very similar to economists' models.

"Nick great post
In spite of it's redundancy and Lewis carrollite romping"

Thanks! But Lewis carrollite?

[david]

If you define excess demand as an unmet desire to buy at the prevailing price vector, then you must define excess supply as an unexhausted willingness to sell at the prevailing price vector. On the other hand, if you define excess supply as the presence of unsold inventory, then you must define excess demand as the presence of unspent endowment, yes? These two concepts are hardly the same thing. For the sake of consistency, keep them separate.

And so, take this:

"The hairdresser is selling as many haircuts as she wants to at the existing price. She doesn't want to cut more hair and work longer hours at that price."

But this is only the case after you have imposed an adjustment in response to the non-availability of land, so that the representative haircutter has some consumption basket of haircuts, manicures, and massages, bought at the prevailing price (for money from haircuts). But this basket is in excess supply; at the prevailing price vector, our haircutter would prefer to sell rather than consume some of those haircuts, manicures, and massages (for the fourth good, land). There isn't anyone to buy those haircuts, manicures, or massages, so the haircutter settles for consuming them herself - but would prefer to sell if a buyer with land could be found. So, excess demand and excess supply.

[edeast]

it's binomial coefficient. I worked it out on my fingers then on wolfram alpha, for a economy with 4 goods there is 6 two-way trades, 3implies 3, 2 implies 1. n-1 is a subset of all the possible markets.

[Constant returns matters because in a constant returns economy firms are irrelevant. If I can't make the trades I want toi because of coordination failure then I set up a micro-firm and produce it myself.]

Thanks for the detailed response. If I can come back on two issues (using your numbering)

2

[William Peterson]

Sorry - previous comment got submitted before I had finished

Thanks for the detailed response. If I can come back on three issues (using your numbering)

2 Constant returns matters because in a constant returns economy firms (and their sales expectations) are irrelevant. If I can't make the trades I want to because of coordination failure then I set up a micro-firm and produce it myself. This makes it hard to incorporate general glust (or Keynesian unemployment) into a Walras-Arrow-Debreu economy.

3 I was thinking about the Ostroy-Starr argument that the role of money is to facilitate exchange because two agents do not have to exchange commodities of equal value - they can use money to make up the difference. Provided that agents maintain budget balance (over n-1 commodities plus money) over the whole sequence of exchanges any individual exchange need not be balanced in barter terms.

4 I agree that agents cannot in aggregate obtain land (becausde it cannot be reproduced). But they can bid up the price: and if landowners do not immediately respond to the increased price by increasing their demand for reproducible commodities there will be a coordination failure and it will be constrained, rather than notional, demands which matter. Once this happens, WL becomes irrelevant. This is one interpretation of a general glut. I agree that in practice such an outcome is more likely when the excess demand is for money, rather than land, but this is partly because (except under a commodity money system) an excess demand for money does not make the supplier of money feel any wealthier.

[Lord]

Assume the price of land rises to where the hairstylist is still willing to buy, the manicurist now willing to sell, and the masseuse no longer interested in either. The manicurist would have an excess supply of money, but not necessarily any increased desire for haircuts or massages. What she wants is land at a cheaper price or haircuts and massages not now but in the future. An excess demand for money is not really a desire for money at all but for cheaper land or future services which stymied would lead to an excess supply in her hands. The auctioneer can only close the round by lowering everyone's income until she cannot save it or lowering the price of land so she no longer is willing to sell it. What if they had all planned to buy land and were working toward that goal and the equilibrium shifts when they discover they cannot buy any?

[Nick Rowe]

david: "If you define excess demand as an unmet desire to buy at the prevailing price vector, then you must define excess supply as an unexhausted willingness to sell at the prevailing price vector. On the other hand, if you define excess supply as the presence of unsold inventory, then you must define excess demand as the presence of unspent endowment, yes? These two concepts are hardly the same thing. For the sake of consistency, keep them separate."

Agreed. I am using the first pair of definitions only. If you have unsold inventory, or unsold endowment, but don't wish to sell it, it's not excess supply.

Land is available (it exists) but nobody wishes to sell any (in my examples).

"But this basket is in excess supply; at the prevailing price vector, our haircutter would prefer to sell rather than consume some of those haircuts, manicures, and massages (for the fourth good, land)."

But this is the crux of the issue. If there were a market in which haircuts exchanged for land, we would observe a supply of haircuts in that market. But that market does not exist in a monetary exchange economy. We can only observe an excess supply of haircuts in the market where haircuts exchange for money. Because that's the only market where haircuts are traded.

Let's put this another way. Walras' Law is talking about people's wishes to have more of one good and less of another. But we never observe those wishes, except in markets. "Excess demand" and "excess supply" refer to wishes to buy and sell more *in the markets that actually exist.

That, in a nutshell, is what is wrong with Walras' Law. We can only observe excess supplies and demands in the markets that actually exist. We cannot observe the unemployed workers wish to trade his labour for a car, because no market exists where he can express that wish. We can only observe his wish to trade his labour for money. We do not observe his subsequent wish to then trade that money for a car (Clower). Excess demands and supplies are a market phenomenon, not mental states. (I can't express this idea as well as I would like).

edeast: OK. In a barter economy, where any pair of goods can be traded, there are n(n-1)/2 markets. In a monetary economy there are (n-1) markets. If n=2, you can't tell the difference between a monetary exchange and barter economy. You don't need money if there are only 2 goods.

William:

2. OK, I understand you now. There are two reasons for trade: increasing returns, and comparative advantage. I had comparative advantage at the back of my mind. The 3 women can't be self-sufficient because they only have the skills to do the one job. So they need to trade, and they need to use money to trade because of the lack of double-coincidence.

3. OK. The hairdresser gives a haircut to the masseuse, who gives a massage to the manicurist, who gives a manicure to the hairdresser. 3 unequal exchanges, that money transforms into 3 equal exchanges. Provided there's enough money.

4. I was imagining a world in which the 3 women are the only agents. (A representative agent economy). So they currently own all the land. So if they all want to buy more land and buy less services (haircuts etc.) it just can't happen. But unless they decide to hold more money instead, it's impossible for them to buy less services.

Let me put this more provocatively: Say's Law is true -- except when we come to money.

Lord: OK. But if the manicurist chose to sell the land for money, but chooses not to use the money to buy more haircuts (or massages) then she must want to hold the money, at least until the price of land falls.

[Paine]

NR

I'm being to cute contrasting analogy with model

Let me simply agree insight thru a clever bizzaro analogy
Can indeed inform a historical science

But this very discussion using a under specified money
Is dangerously misleading
Nothing here has given any insight into the credit driven economy
In fact this money is so underspecified we can't even understand my it's money and not an iou
That is
As harmless suggests might be tied to a claim on some land
But it must be anchored somewhere
I suggested intrinsic value ie commodity money
And the de monetization u suggest might discount it's value is hardly what one gets when credit money is de monetized
That is analogous to a default on a debt

All this isn't shaving the obvious
Your three service toononomy with
Land and money
U count 4 markets
What no market in money
Of course not that's credit
And that's not possible
Pledge land as collateral
That then becomes the real basis of money value
Toononomies have to start with a genesis
Again economics is intrinsically historical

This disappoints me I need to compress some back ground into tight air balls here

[Paine]

The Patterson scenario is a nice example of the tricks one plays on one's self by elaborating a reification
As does your clarification that our three principals can only produce one product

The personification of sectors here is positively allegorical
Despite the sneaky non self serviceability of the only three useful activities in this market economy

The insights are like paper water buckets

[Paine]

Land is useful because we need some place to stand eh ?

[david]

But this is the crux of the issue. If there were a market in which haircuts exchanged for land, we would observe a supply of haircuts in that market. But that market does not exist in a monetary exchange economy. We can only observe an excess supply of haircuts in the market where haircuts exchange for money. Because that's the only market where haircuts are traded.

That's fine. You can always just observe the single market trading money and land, with a desire to buy land at the prevailing price and a desire to sell money at the prevailing price. Hence excess demand and excess supply. This is because we have gone with the first definition and have already transformed endowments (and any unsold inventory/etc.) into money. By letting people adjust their consumption baskets, the Walrasian allocator has confiscated everyone's stuff and given them their real income M = P.X, and then allowed them to spend that M on the stuff.

Units of money are here just units of claims on real GDP - a unit representative basket of haircuts, manicures, and massages. Since we are not allowing people to not spend money, there is no separate monetary issues here. The result is an excess demand for land, a corresponding excess supply of everything else, but no unemployment and no unspent land savings.

[david]

(an alternative would be to not impose adjustment, as per the second definition, which would immediately allow you to observe excess notional demands for land, excess notional supplies for everything else, and unspent land savings (in idle labor, since labor is the endowment) and unemployment - which would make Walras' Law clear, I presume. As you noted earlier, this is what happens in the very short run. Of course, I say this would be the case with or without a requirement that everything be traded via money, which is where we disagree.)

A point about Unobtanium - suppose there is excess demand for unobtanium, and we discover a desire for a new, desirable, but sadly also nonexistent good, handwavium. For peculiar reasons, the government bans any monetary trade in handwavium; one must sell unobtanium to buy handwavium, and vice versa. People universally desire unobtanium, but desire handwavium more than unobtanium at their prevailing fixed rate, so if people had any unobtanium, they would have excess supply of it and excess demand for handwavium. Is there anything wrong with nonetheless saying that there is excess demand for unobtanium?

The point being that it is not problematic to find money being in excess constrained demand on one market and in excess constrained supply on another market - that's only because we've constrained it, by obliging all agents to spend all their endowment. This prohibits general gluts immediately, of course.

[Edward Lambert]

You have a bubble... prices inflate... balance sheets get vulnerable... there is over-leveraging... then the crash hits... balance sheets are affected... demand for money increases... demand for goods decreases...

simple enough...

but to think that over time this will balance out... is well... what happens...

[Andy Harless]

Nick,

Yes, it all makes sense when you think in terms of real money balances. But treating the medium of exchange in real terms has the troubling implication that, even if one has complete control over the supply of the medium of exchange, one cannot control the quantity. It makes the whole concept of "excess demand for the medium of exchange" seem a bit flimsy to me. If the medium of exchange can spontaneously expand and contract in ways unrelated to its own supply and demand, then the notion of "excess demand" for it is a highly conditional one. To the extent that the medium of exchange and the medium of account are different, the medium of account has the real power, and the medium of exchange is only a figurehead -- perhaps one whose presence is necessary to maintain civil order but still not one with real power. MOE is the Merovingian monarch, and MOA is the majordomo.

[Paine]

Harmless
Artificially extracts MOA which could be considered a tradition or a law
That emerges out of transaction history in a certain trading system

It's perfect that an economist of the modern algebra school
Would make a custom about the unit of measure
It self conventional
more powerful then a medium that is the spontaneous outcome of real exchange history
The two are part of a unholy hyper static entity called money
In our worship system

[david stinson]

Hi Nick. Good post. What I find kind of remarkable though are the comments. Not everyone has had David Laidler as a professor, I guess. Speaking of whom, I have thought for some time now that macroeconomics ought to be renamed "the demand for money (and related matters)".

Back to the substance: You say:

"Money is different because it is the only good for which every person is both a buyer and a seller." That's another way of saying that money is the medium of exchange - i.e., that is what allows people to accumulate money balances by not spending. However, I am wondering if perhaps it is incomplete. In other words, it is not just that money is the medium of exchange but that people, having received it in exchanges, want to hold it. It is ultimately money's status as a reliable (or not) store of value that determines whether people will want to hold a non-zero amount of it. Perhaps that was what Andy Harless was getting at in his comments regarding medium of account. It is the stability of the real value of a currency (against goods) that permits it to remain both a medium of exchange (which may be mandated as per legal tender laws) and a unit of account. Think for example of a situation in which a given currency (not mentioning any names) is still required for transactions but prices are effectively quoted, and savings stored, in another currency [e.g., Swiss francs, gold, loonies (!)].

[JP Koning]

"...thinking in terms of excess demand/supply is not qualitatively different from thinking about a market with search. "

Thanks Nick, that bit of translation makes things much easier.

Steve Horwitz has translated Yeager's monetary disequilibrium theory into Austrian macroeconomics. Is everyone just saying the same thing but with different words? It's as if we're in Babylon, chirping away and no common language.

[Nick Rowe]

Paine: "All this isn't shaving the obvious
Your three service toononomy with
Land and money
U count 4 markets
What no market in money
Of course not that's credit
And that's not possible"

A market in "credit" is really just a market in bonds. You give me money; and I give you an IOU. That IOU is a bond. And my "land market" could easily be replaced by a "bond market" without changing the rest of the story.

david: "The point being that it is not problematic to find money being in excess constrained demand on one market and in excess constrained supply on another market - that's only because we've constrained it, by obliging all agents to spend all their endowment. This prohibits general gluts immediately, of course."

Agreed. We can also imagine that haircuts are in excess supply while massages are in excess demand. And if the excess demands and supplies roughly balanced, we wouldn't talk about a general glut or aggregate-demand-deficient unemployment. We would talk about structural unemployment.

Andy: I disagree. In an old post I sketched a world where bling was the medium of account, and there was a demand for bling that looked exactly like a standard money demand function. We get utility from wearing bling, but it's the real value of bling that we get utility from (because we want to show off our wealth), and the (stock) demand for bling increases with income and decreases with the opportunity cost (interest rate). But it's a barter economy. If prices are sticky in terms of bling, you can get an excess demand for bling, but it doesn't affect the rest of the economy.

david stinson: if you could not hoard money (if the government passed a law saying that all money had to be spent in less than 1 month, so velocity is fixed at 12) then it would be hard to get recessions. (Except people would get around the law).

JP: I think that's a lot of it. But it's hard to disentangle differences of using language from different ways of viewing the world.

[dlr]

Nick (re: your conversation with Andy),

I've read your money-as-bling posts (if only Kocherlakota were that creative he'd have called it "Money for Noting" instead of "Money as Memory" and have groupies), and your rent control analogies, but I still don't understand how you think you can isolate the importance of monetary MOE function as causing these disequilibrium recessions. It seems like both the MOA and MOE roles are inextricably necessary.

If the rate between the MOA and the MOE was not fixed, then changes in demand for the MOE would not cause recessions because it would merely result in a change in the price of the MOE (defined as the MOE/MOA exchange rate) but not the price level (so there would be no reason for stickiness). Prices in the store (quoted in MOA, with the MOA/MOE exchange rate presumably posted) would be unchanged but real MOE balances would change to meet demand. Prices in terms of the MOE would then be presumed flexible since it could change in one market with no change in the price level.

Changes in the demand for the MOA might cause a NK recession (relative price problems, not quite like rent control) as rigid prices tried to move clunkily, but wouldn't cause a monetary disequilibrium recession because people couldn't freeze by refusing to buy anything and instead holding the MOA (because it is not the MOE). This seems true even if barter weren't an option. If prices refused to move upon an excess demand for the MOA, then you'd just have the next best behavior as people gave up on their excess demand for the MOA (like rent control). The bottom line is that they couldn't accumulate the MOA by refusing to spend, so they would surely give up sooner than later.

Only if the MOE=MOA or the MOE/MOA rate is fixed (making them equivalent for this purpose) can you have the unique situation where the price of the very thing that people can decide to hold to avoid spending be expected to fail to clear.

Your money-as-bling post posits money as the MOA (with bling creating a real demand function) with no MOE (barter), merely showing that the MOA can't do the job by itself, but seems to ignore the fact that the MOE also can't do the job by itself (create a disequilibrium recession). It isn't that MOE is more important than the MOA when it comes to causing these kinds of recessions, it's just that barter by definition happens to eliminate an MOE (but not necessarily MOA). But that doesn't make the MOE function any more important than the MOA function. I think you need "money" to be both the MOE and the MOA -- including by fixing the MOE/MOA rate -- to create general gluts. I also don't think it is useful to talk about which of these functions has the "real power" as Andy does, except from a NK perspective where it seems to be plainly the MOA function. But if you believe in the freezing, disequilibrium recession, I can't imagine a helpful answer to which function is more important or which cause more proximate.

[Greg Ransom]

Let's me honest. A stake had already been put through "Walras' Law" by Wicksell & Hayek, decades before Clower. And by all sorts of "classical" economists before them.

Nick writes,

"Walras' Law is not a zombie theory. It's a poltergeist. It doesn't realise it's dead (Clower killed it decades ago)."

Side note: Hayek's argument in _TPTofC_ is that "Say's Law" can be nothing other than the same equilibrium condition specified by "Walras' Law", i.e. an equilibrium condition for a construct which does NOT include money, credit, finance, leverage, and banks ...

[Nick Rowe]

dlr: Hmmm. A thoughtful well-reasoned comment. I was already agreeing with you until the last paragraph. But I now think you are right on that last paragraph too.

Greg: my understanding rests on Clower. I don't remember reading about Walras' Law in Hayek or Wicksell. But that might just be my memory, or my failure to read widely and thoroughly enough.

[Andy Harless]

Nick, re: Bling.

The requirement is that there be a medium of exchange, in order to have recessions, but once the medium of exchange exists, it has no power. As I said in my analogy, the figurehead may be necessary for the maintenance of civil order, but the figurehead has no power. Merovingian France couldn't operate without a monarch, but the particular actions of the monarch were irrelevant to the particular functioning of the kingdom. (Typically, also, the ultimate result of separating the MOE from the MOA would be what happened in France: the old MOE is discarded and replace by the Carolingian MOA.)

[William Peterson]

I don't think I had quite thought things through first time. I hope readers don't mind a second attempt.

Start by considering a simple economy with n goods. There is an auctioneer who only allows trade at market-clearing prices, so the economy is Walrasian. There is a numeraire, and possibly some commodities (eg gold) with money-like characteristics, but no fiat money. The auctioneer starts the process of price discovery by announcing a randomly-chosen vector of prices, and agents respond by revealing their plans to buy and sell at those prices. Since each agent plans to stay on his or her budget constraint, for each individual Sum(i)pEi(p) (the sum of planned transactions Ei(p) at the announced prices) will be zero, regardless of whether these prices clear markets. (I use Sum(i) to mean summing over commodities). Summing over all agents (denoted by Sum(h)) gives Walras' Law - the double summation Sum(h)Sum(i) pEi(p) = 0. This implies that if we define E(p) as market excess demand (a sum over agents), the sum over all commodities Sum(i) pE(p) = 0. Since this is an economy without money, Walras' Law and Say's Law (in one interpretation of Say) are the same proposition: excess supply of all commodities is ruled out. Eventually the auction process converges to a set of market-clearing prices p*. At this point all n components of p*E(p*) are zero.

Now suppose that the auctioneer gives up and goes home before p* has been reached, and individuals start to trade at a set of disequilibrium prices p+. They still plan to stay on their budget constraint, so notional market excess demands (NE(p)) will still obey Walras Law - Sum(i) p+NE(p+) = 0. But since markets don't clear at p+ not all trades will get made, and there will need to be a rationing rule: those who cannot sell their massages will need to cut back on consumption of manicures, and so on. Ultimately (since for all trades which do take place there is both a buyer and seller) it will be true that in each market observed excess demand (OE(p+)) will be zero, so we have a relationship which looks just like Walras' Law, but is actually quite different - the sum, Sum(i) P+OE(p+) is still zero, but individual components are quite different. In addition, each individual is still satisfying a budget constraint: but for an unemployed individual this budget constraint is different from, and 'tighter' than, the notional budget constraint to which he was conforming during the auction.

At this point there are two distinct approaches to the problem. One approach argues that since a general glut should be defined as excess supply (eg E(p) < 0) for all commodities, it can only occur in a monetary economy: in this case (by Walras' Law) it corresponds to an excess demand for money. The alternative, which is what I was trying to get across, says that we have to break down the excess demand terms into demand and supply components (say (D(p) and S(p)). Then notional demands are ND(p), observed demands OD(p). It is quite possible that, for every commodity, OD(p+) is smaller than ND(p+) - all individuals would like to sell more at the current set of (disequilibrium) prices, but cannot actually do so because of coordination failure. It's also possible that OD(p+) is smaller than ND(p*): everyone would willingly trade more if the auctioneer did his job properly rather than leaving early.

So far there's no money. In my view the important thing about money (in addition to its role as medium of exchange) is not that it provides the extra commodity which would permit disequilibrium in all goods markets. Instead, it is that it is the only commodity where individuals know that(ignoring hyperinflation) they will not face rationing. I can 'sell' as much money as I want in return for bread, whereas I may not be able to sell unlimited quantities of my labour if there is unemployment, or bonds if there is a financial crisis. So holding money means that it is less likely that I will be forced off my notional demand curve for consumption goods: and the easier it is for individuals to realise their notional demands, the less the risk of a general glut (or Keynesian unemployment equilibrium). In 'normal' times financial intermediation means that non-money financial instruments ('credit') can play a similar role for an individual, but this will not work if everyone tries to draw on them simultaneously (when there will be a financial crisis). In a crisis only money will do, and will appear to be in excess demand, with excess supply everywhere else. But if the auctioneer did his job properly the crisis would not occur.

[Greg Ransom]

"Walras' Law" is just an equilibrium condition of a math construct -- the central ideas of the construt predated 1960s math economics.

Nick writes,

"Greg: my understanding rests on Clower. I don't remember reading about Walras' Law in Hayek or Wicksell. But that might just be my memory, or my failure to read widely and thoroughly enough."