A "proof" of Say's Law; and why money is weird

For a whole economy, does planned expenditure on newly-produced goods necessarily equal planned income from the sale of newly-produced goods? That's what I mean by "Say's Law" in this context.

Say's Law is wrong, and the fact that it is wrong is really important for macroeconomics. But it's not obvious why Say's Law is wrong. And you have to get right inside the minds of those who think Say's Law is right if you want to change their minds. That's what I'm trying to do here.

It is money (qua medium of exchange) and only money, that makes Say's Law wrong. And those Keynesians who reject Say's Law but who also reject the uniqueness of money are as wrong as those who accept Say's Law.

Let me start out by "proving" Say's Law.

There are n goods, and each individual has a budget constraint which says his planned purchases of goods must have the same value as his planned sales of goods, summed over all n goods. If we add up all the individuals' budget constraints we see that the value of the excess demands must equal the value of the excess supplies (aka Walras Law).

(So far, things are not looking good for Say's Law, because there could be an excess supply of newly-produced goods matched by an equal excess demand for, say, bonds, if everyone wants to save part of their income rather than spend it on newly-produced goods. But wait a minute.)

What determines the actual quantity traded in a market where there is excess demand or excess supply? The standard assumption is that the short side of the market determines quantity traded, since you can't force people to buy more than they want to, or sell more than they want to. Exchange is voluntary. For goods in excess demand, quantity traded is determined by supply. For goods in excess supply, quantity traded is determined by demand.

With some markets not clearing, people are forced to revise their plans, since for some goods they cannot sell all they want; and for other goods they cannot buy all they want. These revised plans must also be consistent with the individuals' budget constraints, which means a constraint on an individual's purchases or sales for one good must spillover to affect his planned purchases and/or sales of some other goods.

For example, suppose people were initially planning an excess demand of $100 worth of bonds financed by an excess supply of $100 worth of newly-produced goods. But if you realise you can't actually sell an excess supply of $100 worth of newly-produced goods (and you can't, given the short-side rule) you realise you can't finance an excess demand of bonds with the proceeds. Equivalently, if you realise you can't actually buy an excess demand of $100 worth of bonds (and you can't) you realise that selling an excess supply of $100 worth of newly-produced goods would violate your budget constraint.

Therefore there cannot be an excess supply of $100 worth of newly-produced goods. Say's Law is right. In aggregate, people must plan to buy newly-produced goods of a value exactly equal in value to what they expect to sell and earn as income. They would violate their budget constraints otherwise.

(Just translate the above into math, and write "QED" underneath.)

What's wrong with the above "proof" of Say's Law? (Apart from the fact that it "proves" that no market can have an excess demand or supply?)

In a word: money. Money, qua medium of exchange, is weird. Every other good has one market, which is either in excess demand or in excess supply. But money is in every market.

For every other good, an individual is either a buyer, or a seller, but not both. An individual is either on the short side, or the long side, but not both. But for money, every individual is both a buyer and a seller.

Suppose initially there is an excess supply of newly-produced goods matched by an equal excess demand for money. If money were like bonds, people wanting to buy money would be on the long side of the money market, and would be unable to buy more money and so would stop trying to sell more goods. But money is not like bonds. Every individual is on the long side of the money market when he tries to earn income by selling newly-produced goods, but on the short side of the money market when he tries to spend income by buying newly-produced goods. If you can't get more money by selling more newly-produced goods, you can still get more money by buying less newly-produced goods.

(And if newly-produced goods are initially in excess demand, and money in excess supply, you can't get rid of money by buying more goods, but you can still get rid of money by selling less goods).

If there are n goods including money, there are n-1 excess demands or supplies for the n-1 non-money goods, and also n-1 excess demands or supplies for money, giving 2(n-1) excess demands or supplies in total. Any "proof" of Say's Law that counts only n excess demands or supplies must be wrong (except when n=2, but then money would be redundant anyway, if there were only one non-money good). The most we can say is that in each of the n-1 markets, the excess demand or supply of the non-money good in that market must equal the excess supply or demand for money in that market. (And a true barter economy where everything can be traded for anything else has (n-1)n/2 markets, not the n markets of my "proof").

Brad DeLong interprets John Cochrane as implicitly assuming that velocity is fixed. I interpret John Cochrane as implicitly assuming a non-monetary economy. Both interpretations make sense. But I think (hope?) mine is more fruitful. It is not obvious that my "proof" of Say's Law is wrong, and that it is only the weirdness of money that makes Say's Law wrong.

I don't think there's anything very original in what I have written above. Take a bit of Clower and Yeager and stir.

Keynesians take disequilibrium seriously, and monetarists take money seriously. This post belongs in the somewhat narrow intersection of those two sets.

Perhaps what's wrong with macroeconomics is that fundamental issues like Say's Law need to be debated in blogs. Does it get debated anywhere else nowadays?

Comments

[Too Much Fed]

Does a medium of exchange introduce time differences into an economy?

Hopefully something similar to Say's Law. Can AD and AS BOTH be "infected" with debt (loans denominated in currency)?

[Jon]

Well I think JC is particularly recognizing that velocity is variable. Lets consider one of your claims:

If you can't get more money by selling more newly-produced goods, you can still get more money by buying less newly-produced goods.

Hmm, sounds like velocity is falling. As the objective exchange value of money shifts upwards the desire to hold more money is satisfied without necessitating an actual reduction in expenditure or an increase in goods sold. i.e., the manifestation of the situation you describe depends on prices being sticky.

I think we all agree that Say's law is violated when prices are sticky. Indeed even Say says this himself.

DeLong makes a common mistake of assuming a technological connection to velocity. This is false; it is nothing more than a fitting parameter that reflects that the price-level is decoupled from the stock of money itself.

To put this into your framework. There initially exist n constraints and n variables (the price in each market). Introduction of cross-markets is irrelevant: as I charge those constraints are not independent supports. Your market develops a 'problem' because you then impose an N+1 constraint; i.e., the desire to hold monetary balances. The fallacy is then to neglect that your introduction of monetary balances created a new price 'v'. i.e., the unit price of money.

[Bruce Wilder]

NR: "Perhaps what's wrong with macroeconomics is that fundamental issues like Say's Law need to be debated in blogs. Does it get debated anywhere else nowadays?"

Maybe. It is something I've been trying to think about.

John Cochrane can be a pretty smart guy, but also a deeply prejudiced one.

In physics, they use laws of conservation, to be sure that they know an analysis is complete in the sense of having correctly and exhaustively identified the necessary and sufficient factors. An analysis of aerodynamic force, for example, might make use of conservation of momentum, or conservation of energy, or of mass. http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html

Says' Law, for Cochrane, may be a gambit in lieu of a conservation law. Cochrane ventures Barro's Ricardian Equivalence as another conservation principle, and pretty much makes a hash of it, as well. And, I think Brad is right: Cochrane also believes in the conservation principle of constant velocity: "the money has to come from somewhere".

Cochrane is pretty smart, and I doubt that he is simply mistaken. I think he believes that all these conservation principles work well enough, in practice, to allow a systematic identification of the necessary and sufficient elements for analysis. As he says of Ricardian Equivalence, "This theorem says that debt-financed spending can’t have any effect because people, seeing the higher future taxes that must pay off the debt, will simply save more. They will buy the new government debt and leave all spending decisions unaltered. Is this theorem true? It’s a logical connection from a set of “if” to a set of “therefore.” Not even Paul can object to the connection.
Therefore, we have to examine the “ifs.” And those ifs are, as usual, obviously not true. . . ." Ignoring the misstatement of Ricardian Equivalence, notice that Cochrane thinks the purpose is analysis.

Cochrane wrote: "The impact of Ricardian equivalence is not that this simple abstract benchmark is literally true. The impact is that in its wake, if you want to understand the effects of government spending, you have to specify why it is false. Doing so does not lead you anywhere near old-fashioned Keynesian economics. It leads you to consider distorting taxes, estate taxes, how much people care about their children, how many people would like to borrow more to finance today’s consumption and so on. And when you find “market failures” that might justify a multiplier, that analysis quickly suggests direct fixes for the market failures, not their exploitation along the lines Keynes suggested."

I don't want to put words in Cochrane's mouth, but I suspect that he has the same attitude toward Says' Law: not that it is "literally true", but that it usefully forces you to identify the necessary and sufficient conditions for analysis, even if it is in the act of specifying why a presumption of clearing markets is not true.

The broad question for economics might be, which conservation principles, if any, work, as a foundation for analysis. You use Walras. The full employment limit in the present moment is sometimes used as a constraint functioning as a conservation principle to motivate analysis.

I think using a false principle of conservation implies a false analysis, but I don't know what the formal proof of such a proposition would look like.

[fourthtimeanon]

You’ve said nothing you didn’t say before, and I still disagree.

Say’s Law is easily proven wrong in a monetary economy as a result of the ability to leverage. I borrow from the bank to spend more than my income. If there are slack resources in the economy, my additional demand induces more output. That results in income that nobody planned on.

It’s equally wrong in a barter economy. I exchange my production of 1 banana for yours of 1 apple. I want to borrow to buy an additional apple. I borrow the banana back from you, and offer to spend it in exchange for an additional apple. You increase your output by an additional apple. You thereby increase your income to two bananas. You’ve saved one banana and consumed one. That’s additional income that nobody planned on. GDP (GDF) has increased.

You can only prove Say’s Law correct in a barter economy if you prohibit borrowing. But that’s a specification that is completely independent of the assumption of a barter economy.

BTW, Cochrane doesn’t need to assume a constant velocity of money in order to be wrong. He needs to assume a constant product of the stock and the velocity of money.

Seeing the comments, I wish Krugman had included physics envy in his list of lamentations for the economics profession.

[Ian Lippert]

I always wonder why when people start talking about Say's law they rarely actually quote or analyse anything Say said. Keynes did it, Brad DeLong did it, and you are doing it here.

Your version of Says law: "planned expenditure on newly-produced goods necessarily equals planned income from the sale of newly-produced goods". Other versions are "Supply creates it own demand" and "The market always clears". The critics often then go on to show that markets actually dont always clear and then claim to have refuted all of classical economics. This is what Keynes did and it seems like every economist after that simply took Keynes word for it.

Luckily, with the internet, we can easily get our hands on the original text (http://www.econlib.org/library/Say/sayT15.html#Bk.I,Ch.XV) and find what Say really said.

"I.XV.3
A man who applies his labour to the investing of objects with value by the creation of utility of some sort, can not expect such a value to be appreciated and paid for, unless where other men have the means of purchasing it. Now, of what do these means consist? Of other values of other products, likewise the fruits of industry, capital, and land. Which leads us to a conclusion that may at first sight appear paradoxical, namely, that it is production which opens a demand for products. "

"Production opens a demand for product" is subtly different then "production creates a demand for products". As he says you cannot expect your production to be appreciated and paid for unless others have produced something that you appreciate and pay for. Production is a neccessary but not sufficient condition for creating demand. Its not that Supply equals Demand but that Demand can never be greater then Supply. This leaves more then enough room for there to be numerous supply gluts.

Say continues to argue that this doesnt change in a monetary economy:
"I.XV.7
This observation is applicable to all cases, where there is a supply of commodities or of services in the market. They will universally find the most extensive demand in those places, where the most of values are produced; because in no other places are the sole means of purchase created, that is, values. Money performs but a momentary function in this double exchange; and when the transaction is finally closed, it will always be found, that one kind of commodity has been exchanged for another."

Acknowledges the existance of gluts and argues for their cause:
"I.XV.10
But it may be asked, if this be so, how does it happen, that there is at times so great a glut of commodities in the market, and so much difficulty in finding a vent for them? Why cannot one of these superabundant commodities be exchanged for another? I answer that the glut of a particular commodity arises from its having outrun the total demand for it in one or two ways; either because it has been produced in excessive abundance, or because the production of other commodities has fallen short. ."

And lays out what can and cannot lead to the resolution of a supply glut:
"I.XV.15
1. That, in every community the more numerous are the producers, and the more various their productions, the more prompt, numerous, and extensive are the markets for those productions; and, by a natural consequence, the more profitable are they to the producers; for price rises with the demand. But this advantage is to be derived from real production alone, and not from a forced circulation of products; for a value once created is not augmented in its passage from one hand to another, nor by being seized and expended by the government, instead of by an individual. The man, that lives upon the productions of other people, originates no demand for those productions; he merely puts himself in the place of the producer, to the great injury of production, as we shall presently see. "

"I.XV.20
4. The same principle leads to the conclusion, that the encouragement of mere consumption is no benefit to commerce; for the difficulty lies in supplying the means, not in stimulating the desire of consumption; and we have seen that production alone, furnishes those means. Thus, it is the aim of good government to stimulate production, of bad government to encourage consumption. "

The whole of Says arguement is an arguement to those writers who were precoursors to Keynes work (Sismondi, I think) and its obvious why Keynes had to create a strawman of Says law so that future economists wouldnt bother with those old "outdated" ideas.

[Ian Lippert]

Just to clarify, Says law is a refutation of the idea that gluts can be solved by government expenditure (forced circulation of products) and monetary policy (encouragement of mere consumption). Now I think Says arguements are much to simplistic compared to todays work, but I just wanted to make this post to actually get people to argue about what Say actually said and not what Keynes said Say said.

[Jon]

Ian: Say does deserve respect for explicitly qualifying his claim as being made under the condition that there are no money balances held.

Indeed, my 'rebuttal' to Nick does exactly the same--except that I argue, that if prices float there is a solution wherein the objective exchange value of ones existing money balances can arise and so meet ones increased demand without changing production. i.e., that an accumulation of money balances is never required.

THIS is the uniqueness of money. When you draw the Supply and Demand curves of the zero-maturity market for 'money'--money appears on both axises but with its real and nominal denotations respectively.

[Bill Woolsey]

I use the term "Say's Law" interchangebly with "walras' law" and use the both of them to argue that an excess demand for money is the only plausible reasons for falling nominal expenditure on currently produced goods and services.

Treating "Say's Law" as ignoring that there could be excess demands for something other than currently produced goods, so that the sum of the excess demands for currently produced output must equal zero.. well, it looks like a strawman.

Say's actual notions about how growing productive capacity raises demand are plausible enough, but of little interest in monetary theory. (Though some of the quotes here do look like a straw man could be constructed readily.)

That changes in the price level adjust the real quantity of money to equal the demand, and so clear that market are true, but that _is_ a change in nominal expenditure. Changes in nominal expenditure are of interest because of the associated changes in output and prices, which are because prices are sticky.

I would suggest avoiding the word "leverage" and just stick to borrowing and lending. Where does the lender get the money to lend? What are you assuming would have been done with the money if it hadn't been lent? I think the assumption is always--it would have been held, and the story is about a reduction in the demand for money. When lenders don't want to lend for some reason, what do they do with the money? I think the assumption is that it is held. In other words, an increase in the demand for money.

In previous writing Cochrane has been clearer. Sometimes he explicitly assumes that velocity is constant. Given real output, that is equivalent to the demand for money being constant. If the quantity of money is equal to that demand initially, then there is no excess demand for money as assumed in the story. And so, he tells some Ricardian eqivalence story assuming velocity/money demand is constant. The Keynesians are, supposedly, proposing that things not add up.

Then, he sensibly enough, notes that velocity can change. In other words, the monetary disquilibrium described above is possible. Perhaps bond financed government spending can reduce money demand. And certainly, government spending financed by newly created money can impact nominal expenditure.

Bill Woolsey
http://monetaryfreedom-billwoolsey.blogspot.com/

Anyway, the point is that the problem of inadequate nominal expenditure is fudamentally monetary.

Cochrane also grants that "conventional" monetary policy, which he, like Krugman, see has open market operations with T-bills, might not work. When there is an excess demand for both of these things, how will changing their relative quantities help?

Bill Woolsey
http://monetaryfreedom-billwoolsey.blogspot.com/

[Nick Rowe]

I probably shouldn't post things at 3.00 am. Oh well. I still think I'm onto something.

Too much: I don't understand what you mean by "time differences" in this context. Yes, debt probably affects AD, and AS too. So does almost everything.

Jon: yes, velocity (or desired velocity) is changing when people plan to spend more or less than their income (unless the supply of money changes proportionately, of course). So I'm not saying anything inconsistent with Brad DeLong, just coming at it from a different angle.

Say's Law is moot when prices are perfectly flexible, so markets always clear. Say's Law is only relevant when prices don't adjust instantly, and markets don't clear. And I don't think we do all agree on whether it's right or wrong when prices are sticky (which is the only time it matters).

I don't think Brad DeLong was assuming a technological connection to velocity; more saying that John Cochrane was implicitly assuming this.

You lost me on the last paragraph. Sorry.

Bruce: So that was your comment (on Mark Toma's blog?) asking why discussions like this only happen on blogs? I went looking for your comment again, couldn't find it, and didn't trust my memory. It's a good question. I don't have any answers.

Yes, Say's Law/Walras' Law etc. is like Conservation Laws in physics, or some sort of adding up constraint where you check the consistency of your theory. And they are absolutely fundamental. It's not just an obscure area of macro; it's micro too. And they ought to follow directly from max U() subject to the budget constraint, which is about as basic as you can get. But a quick and dirty web search last night on "Says Law" seemed to pull up only: historians of thought; Austrians; and Post-Keynesians. Not exactly mainstream theory (no offence intended to those groups).

fourthtimeanon: but I did allow bonds to be one of the goods. Hence loans and leverage are not excluded from my "proof". I agree on constant MV.

Ian: I plead guilty as charged. Extenuating circumstances: everyone else does it; words change their meaning over time (not just Say's Law, but also Classical, Ricardian Equivalence, Real Bills doctrine; Sunspot theory) and after a bit it's just easier to go with the flow. But thanks for posting the real Say.

[fourthtimeanon]

"Anyway, the point is that the problem of inadequate nominal expenditure is fundamentally monetary."

I would certainly agree with that in a (real world) monetary economy.

But that's not the same as arguing that it can't happen in an imagined barter economy.

[fourthtimeanon]

"Hence loans and leverage are not excluded from my "proof""

They are in the sense that you don't allow for the effect of new debt issuance. You model trading in stocks, but not the creation of new flows, of loans and leverage.

[Stephen Gordon]

I probably shouldn't post things at 3.00 am.

I nominate this for the motto of the yet-to-be-established Society of Bloggers.

[bob mcmanus]

I am certainly about to embarrass myself, but simply to address the question as to whether Says Law is discussed outside of blogs, this is from Peter Flaschel's Macrodynamics of Capitalism (1993, 2009) Please assume sub and superscripts in the math at the end. Endnotes removed. Everything below is from Flaschel

We are now in the position to describe in detail the type of Say’s Law that we have introduced by our above completion of Ackley’s Classical model. Following Mill (1965, pp. 571/2) we have modeled the following two statements:

1) The Supply of Commodities In General Cannot Exceed the Power of Purchase

2) The Supply of Commodities in General Never Does Exceed The Inclination to Consume

Aggregate demand Yd is made equal to aggregate supply Ys
if Y ≡Ys(assertion I)holds and if the rate of interest performs its job to equilibrate the demand and the supply for loans [Bd =Bs; note here that Mill – in trying to prove the above phrase – restricts his attention to the case S ≡ Idirect, while his discussion of loans and the rate of interest is confined to a later chapter of his “Principles”]. In our view, therefore, the formulation of Say’s Law which is consistent with Ackley’s (standard) version of Classical Macroeconomics should be

p(Yd −Y) ≡ 1/r(Bs−Bd)

Y ≡ Ys

Bs(r0) ≡ Bd(r0)

it consists of two macroeconomic identities [the first of which relates the desire and the ability to purchase with what is happening in the market for loans, while the second claims that planned income should equal planned output under all circumstances] and an equilibrating mechanism [which – via the market for loans – creates as much desire to spend as there is ability to purchase].

since aggregate demand Y has already been determined by Y ≡ I + C ≡ Y +I −
S.

The quantity theory cannot be used consistently for a description of aggregate demand in a Classical model in which the above elaborate form of Say’s Law is assumed to be valid. Yet, though the quantity theory and Say’s Law must be carefully distinguished with regard to their meaning and range of applicability, we shall see in the next section that they stand and fall together if the distinction between saving and lending is developed further.

[bob mcmanus]

"Jon: yes, velocity (or desired velocity) is changing when people plan to spend more or less than their income (unless the supply of money changes proportionately, of course). So I'm not saying anything inconsistent with Brad DeLong, just coming at it from a different angle.

Say's Law is moot when prices are perfectly flexible, so markets always clear. Say's Law is only relevant when prices don't adjust instantly, and markets don't clear. And I don't think we do all agree on whether it's right or wrong when prices are sticky (which is the only time it matters)."

Part of the reason I commented is that I think Flaschel above tries to address both of these. Changes in demand and sticky prices will cause changes in savings and lending, the quantity and prices of loans.

Flaschel is eclectic, but I think closer to Post- than New Keynesian.

[bob mcmanus]

"It is money (qua medium of exchange) and only money, that makes Say's Law wrong."

It is money, and only money, that makes Say's Law right.

[Lord]

Cochrane writes too sloppily to pin down, but my best guess is he believes monetary policy can create money to ease the crisis but has difficulty doing so at the zero bound, but fiscal policy only redistributes money either currently or inter temporally and only makes us poorer. Stimulus falls into the second category. Absent from his writing is that monetary policy takes on aspects of fiscal policy and vice versa at times like these or that there is any way out. Unhelpful, they seem at a loss for what to do since they apparently gave it no thought.

[Too Much Fed]

Nick said: "Too much: I don't understand what you mean by "time differences" in this context. Yes, debt probably affects AD, and AS too. So does almost everything."

Bill Woolsey said: "Anyway, the point is that the problem of inadequate nominal expenditure is fudamentally monetary."

Let's assume there needs to be more spending in the present and enough supply in the present. Does the economy need savings to be spent (past demand brought to the present), more present spending in the present, or more debt (loans denominated in currency and future demand brought to the present)?

If there were no medium of exchange(s), would there be no savings and no debt and therefore no "time differences"?

When there is a third world currency crisis, what do people in those countries look for? Something that holds its value and does not "expire"?

What if debt (loans denominated in currency) is overwhelmingly dominating both AD and AS so that an economy is mostly responding to changes in debt (loans denominated in currency) levels?

[Too Much Fed]

fourthtimeanon's post said: "'Hence loans and leverage are not excluded from my "proof'"

They are in the sense that you don't allow for the effect of new debt issuance. You model trading in stocks, but not the creation of new flows, of loans and leverage."

Can both supply and debt issuance both grow in a barter economy?

[Kevin Donoghue]

Nick,

You ask “What's wrong with the above ‘proof’ of Say's Law?” and you answer “money”. But there is at least one other objection to the ‘proof’ if you seek to refute “those Keynesians who reject Say's Law but who also reject the uniqueness of money”. (Since one of those Keynesians was Keynes himself, you certainly can’t be accused of attacking a straw man.) The trouble starts with the first sentence: “each individual has a budget constraint which says his planned purchases of goods must have the same value as his planned sales of goods.” In the world according to Keynes, a worker faces an additional constraint: the quantity of labour sold cannot exceed the quantity which employers demand based on their price expectations.

When the optimisation problem is formulated in this way, there is no assurance that there will be an excess demand for goods or bonds corresponding to the excess supply of labour. There is a notional excess demand in the sense that workers would demand more if they were fully employed, but that’s not effective demand. So I don’t need to accept a unique role for money to reject this version of Say’s Law (or James Mill’s Law if we want to remedy the injustice to J-B Say at this late stage). All I need is that extra constraint.

Perhaps what's wrong with macroeconomics is that fundamental issues like Say's Law need to be debated in blogs. Does it get debated anywhere else nowadays?

As you noted, Clower, Yeager and several others debated it decades ago. The trouble is that this work doesn’t seem to get the coverage it deserves. Part of the problem I think is that it falls between micro and macro. To get it right one needs to be interested in both.

[Nick Rowe]

fourthtime anon @4.00: ""Hence loans and leverage are not excluded from my "proof""
They are in the sense that you don't allow for the effect of new debt issuance. You model trading in stocks, but not the creation of new flows, of loans and leverage."

I thought my "proof" did allow for new debt issuance. I can start out with an endowment of zero debt, and then plan to sell some, which is like my issuing debt.

bob: It does indeed seem (from the passages you quoted) that Peter Flaschel is some sort of Post Keynesian. His writing doesn't look very mainstream. Again, no offence intended to peter Flaschel; I'm just repeating my guess that this sort of discussion gets ignored in the mainstream.

"It is money, and only money, that makes Say's Law right." You lost me there. Sorry.

Lord: That's my take on him too.

Too much Fed: you can have debt in a barter economy.

Kevin: I agree with your interpretation of Keynes' (through the lens of Clower), and I agree with your/Keynes' refutation of my "proof" of Say's Law. But, your/Keynes' refutation only makes sense in a monetary exchange economy. So, at root, your/Keynes' refutation is the same as mine.

Here's why:

You/Keynes are (quite correctly) implicitly assuming a monetary exchange economy. There is a market in which money exchanges for labour. And a market in which money exchanges for goods. In the first ("labour") market, there is an excess supply of labour matched by an excess demand for money. In the second ("goods") market there is zero (constrained) excess demand for goods matched by zero excess supply of money. So there are two different excess demands/supplies for money: one for each of the two markets in which money appears. (More generally, there are n-1 different excess demands/supplies for money). In my "proof", there is only 1 excess demand/supply for each of the n goods. My "proof" is total rubbish because it assumes there is one excess demand/supply for money; but there are really n-1.

In a true barter economy, there would be a market in which labour is swapped directly for goods.

(I suppressed the labour market for simplicity, thinking of people as being self-employed worker/producers who work, produce, and sell their output. I don't think this makes any difference in this context.)

[Patrick]

"There is a market in which money exchanges for labour. And a market in which money exchanges for goods....

I think this is a helpful way to visualize it. If, for whatever reason, labour decides to hoard money - i.e. instead of buying 5 bananas, people make do with 3. Bananas are now rotting. Seeing this, the banana producer decides to lower prices. But what if people REALLY want to hoard money. So much so that there is essentially no price for bananas low enough to induce people to give up some of their hoard for an additional 2 bananas.

If prices are sticky, I think it just gets worse. And so would some typical irrational behaviours - for example I suspect at some point a producer would be inclined to just let the bananas rot rather than lower the price and sell it at a huge loss.

[Too Much Fed]

Nick said: "Too much Fed: you can have debt in a barter economy."

Are there interest payments on the debt in the barter economy? It seems to me the barter economy you describe is more like a "futures exchange market".

[Jon]

Say's Law is moot when prices are perfectly flexible, so markets always clear. Say's Law is only relevant when prices don't adjust instantly, and markets don't clear. And I don't think we do all agree on whether it's right or wrong when prices are sticky (which is the only time it matters).

Nick: "when prices are flexible, markets always clear"--that is an instance of Says law. Remember the GT sets out to advance the claim that recessions are not due to sticky-prices but a rather a lack of animus.

You haven't responded to my statement that the n*(n-1)/2 markets of the barter economy do not represent unique constraints--they are not independent supports and therefore do not create a distinction between the two economies. What makes money different is that it is not produced (has a vertical supply curve) but it is desired, which is why 'producing' more money to mirror the change in preferences solves the problem.

When you write, deus ex machina: "With some markets not clearing" your analysis has already gone off the rails. You've begged the question.

[JP Koning]

Hi Nick - some questions about the weirdness of money.

"For every other good, an individual is either a buyer, or a seller, but not both."

How about a grocery store owner? He/she is both a buyer and seller of groceries. A used car lot owner is both a buyer and seller of old cars. Money doesn't seem weird to me given these other goods for which individuals are both buyers and sellers.

"But money is in every market."

Depends on what kind of money. Some of the items we call money trade in only a few markets. For instance, try using Swiss Francs to buy a Big Mac in Canada. Nor does domestic cash trade in every domestic market - you can't buy a house with paper bank notes, nor pay for a massive corporate takeover with them. Ditto for chequeable deposits - no grocery store will take a cheque to pay for a gummy bear. A given money need not be bought and sold in every market.

I guess I still need more convincing that there is something inherently peculiar about those items we call money.

[criticontropus]

Say's Law is right.
By definition no excess supply is possible...neither excess demand.
Think please on the supply/demand Robinson Crusoe's.
Add to that model Friday's demand and supply.
There is no incentive for any of them to oversupply because reduces everybodies wealth by reducing bargaining power of oversupplyer.
And because may produce overcrowding effects on resources (including labor).
Say's law, at the end, canno't be wrong because is tautological...is silogistical.
Metaphorical uses of it might be wrong because of interpretation losses.

[Nick Rowe]

Hi JP: you're right. I thought about traders/middlemen/market makers while I was writing that, but couldn't get my head around them, so ignored them. And if we have multiple monies, some accepted in some markets, and others in others, it gets even more complicated. Since this topic is complicated enough with just one money, I had to ignore that too. All models/theories simplify, and abstract from reality.

Jon: if every market always clears, because prices adjust instantly, then all statements about the sum of the excess demands being zero become trivially true. 0+0+0+...+0=0.

"You haven't responded to my statement that the n*(n-1)/2 markets of the barter economy do not represent unique constraints--they are not independent supports and therefore do not create a distinction between the two economies." Sorry, but I don't really understand you here. I don't know if my later post clarifies anything.

But on money being distinct because it has a vertical supply curve: so does land, but the existence of land shouldn't violate Say's Law.

[JP Koning]

Thanks for the response Nick. On a totally different note, are you ever going to blog about the CD Howe Monetary Policy Council? I've always wondered how and what you guys do, and how effective you think it is in influencing the BoC.

[Jon]

Nick:

1) You've got the causality backwards. Says law is that if prices adjust, all markets clear.

2) What I mean is that you can write a series of equations representing the relative value of every good versus every other good. But these equations are not linearly independent. You can always reduce to a basis identical to your monetary economy.

3) I think you have me there. It cannot be the supply curve that matters. Let me try again then, it must then simply be the conflict between the unit-of-account (price-stickiness) and store-of-value role of money (cash balances). When people demand to hold more money, implicitly they are raising its value versus all goods. But when people are price sticky, they are also trying to hold the value of each good with respect to money. The result is over-constrained. Perhaps this what you've meant to say all along.

I think #1 is why we weren't communicating though.