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"Aggregate demand for goods is a demand for those goods in terms of money. At least, that's true in a monetary exchange economy, where all goods are bought and sold for money -- the medium of exchange."

I want to see if I can induce any doubt in your mind about the relevance of this. If you just briefly browse The Theory of Money and Credit by Mises, you don't need to pay any attention to the rest.

1. The quantity or supply of money is equal to the sum of the money held by all holders of money at any instant in time. For a given supply of money, this means that everyone is in competition to hold a desired portion of that money.

2. Let's say you are paid $1000 once a month and you spend all of it in a single monthly rent payment. Is it not clear that the degree of your competition for the holding of money depends critically on the relative timing of the two payments? At one end you might make your rent payment the day after you receive your income. In this case, you have a one day demand for holding $1000, with no demand for the rest of the month. At the other end you might make your rent payment the day before your income payment. In this case you have a 29 day demand for holding $1000. In the first case, just $1000 in money supply could satisfy up to 30 people if the timing were carefully adjusted. In the second, just you could be satisfied.

3. You don't actually need to hold money for an extended time to buy goods. You could hold even non-checkable MMF's up until the point where you would need to convert them to actual money for making a purchase.

I'll stop there.

Regards, Don

Hi Don: It's a long time since I read von Mises Money and Credit, but I don't think I say anything here that would contradict Mises' view. True, there is the demand for money conceived as a stock, and the demand for money conceived as a flow. I was not explicit on the stock/flow distinction (I expect I was implicitly thinking in discrete time terms, where everything is a stock), but I don't think I say anything that could not be re-said making it explicitly consistent with that distinction. Money is the medium of exchange. That's what's key.


The number one take-away from Mises is that all demand for money is a demand to hold and that the need for holding money would approach zero if it weren't for the fact that the future is uncertain. Otherwise you could invest all your money for interest with a maturity that returns it in the nick of time for a payment.

When a purchase is made all that happens is that the purchase price is transferred from the buyer to the seller. The supply of money isn't changed or even stressed.

Regards, Don

Nick: "I go to the supermarket with $10 in my pocket planning to buy $10 worth of apples and no pears. Those are notional demands. Excess demand for apples $10, and excess supply of money $10. Walras' Law applies. But when I get to the store there are no apples, so I re-maximise my utility function, including that quantity constraint, and decide to buy $10 of pears. Excess demand for apples $10 (because I still want the apples). Excess demand for pears $10 (because I can't buy apples). Total excess demand for goods (apples plus pears) $20. But what's the excess supply of money corresponding to that excess demand for goods? $20? But I only have $10 in my pocket."

This is all wrong. If I go to the store wanting $10 worth of apples and then, on finding no apples, SUBSTITUTE $10 worth of pears then I no longer demand $10 worth of apples. I do not demand $10 worth of apples AND $10 worth of pears. Once I buy the pears there is no longer an excess demand for apples because I don't have any money left. More generally, if I have $10 I might like to have $20 worth of stuff but I can't afford it, nobody would say that this leaves a $10 excess demand for goods. After all, I'd like a Porsche but I don't have enough money. Does that mean that there's an excess demand for Porsches? I don't think so.

Don Lloyd,
I don't believe your model of the transactional demand for money (not the only demand) is realistic. Most people like to have money in their pocket, not just because the world is uncertain (regarding supply and demand) but because they don't know what they want. People LIKE to be able to impulse shop. The idea that they plan all purchases is a fable.

Don Lloyd,
besides which, what is the point of the story? There is a demand for money that varies according to income and interest rates (of money and near substitutes) stochastically. Is anything else relevant?

Don Lloyd,
I think your post does however illustrate the problem the monetary theorist has today. Just what EXACTLY is money? Mises thought it was clear, I'm not so sure.

Just continuing from my last comment, the problem with the example is that you haven't said anything about prices. Thus you can't say if we are in or out of equilibrium.

Let's suppose that apples and pears both cost $2 a piece and I have $10. I show up at the store planning to buy 5 apples but only 2 are there. What happens next? In the Walrasian market with flexible prices I bid up the price of apples. Do I bid the price all the way to $5? Probably not, apparently I consider pears a substitute for apples, even though I prefer apples when the price are the same. As the price of apples rises the pears start looking like a better deal, I probably start substituting away from apples and towards pears before the price of an apple hits $5. Of course, in the proper Walrasian market sellers of apples don't have to post a price before the market opens. The prices and quantities are all jointly determined, and all determined at the same time.

Now, if the prices of apples can't change then I buy the 2 apples that are there and, at the posted price, would like to buy 3 more. This sure sounds like an excess demand for apples but I think it's an illusion. If there really is no way to get more apples then no matter how much money anyone offers the vendor he won't sell them another apple because he can't, there are no more. This sounds to me like an infinite price. You can insist that we are out of equilibrium by saying that apples are still priced at $2 but does it really make sense to insist that there is a fixed, finite price for something that isn't on the market?

reason, money is anything that the government accepts as tax payment.

Adam P: Walras' Law is supposed to hold true at any vector of prices, whether it is an equilibrium or a disequilibrium vector. Since I was unable to buy all the apples I wanted to buy, there must have been an excess demand for apples, so I was assuming a disequilibrium price vector in my example. In Walrasian equilibrium theory, the Walrasian auctioneer calls out a price vector at random (prix criee au hazard if I remember the French), collects demand and supply information, and then adjusts prices if there is excess demand or supply (tatonnement), *but does not allow trade to take place until all markets are clearing*. All offers to buy and sell are provisional, and are only binding if the price vector turns out to be the equilibrium one (tatonnement with Edgworthian recontracting). The Walrasian auction is conducted outside of time, not in real time, so no actual trade takes place at disequilibrium prices. The whole point of the "disequilibrium macro" approach (which could also be called "Non-Walrasian general equilibrium (or disequilibrium) theory" is to ask what happens when we drop the assumption of Edgworthian recontracting, and to allow trade to begin at disequilibrium prices, before the auctioneer has finished his tatonnement.

If trade takes place at disequilibrium prices, some markets will be in excess demand, and so buyers will be quantity-constrained, and some will be in excess supply, so sellers will be quantity-constrained. In each case, actual quantity traded = min{quantity supplied, quantity demanded} (the short side of the market rules). We then analyse how those quantity constraints will spill over into demands and supplies in other markets, which affects quantity constraints in those other markets. The Keynesian multiplier process is interpreted as one example of such spillovers. There is excess supply for output, so firms are quantity-constrained in their sales. This spills over to affect firms' demand for labour and other inputs (why hire extra labour if you can't sell the extra output?) so firms' demand curve for labour is no longer the value marginal product curve for labour. (The constrained demand curve for labour will be a very different beast than the notional demand curve for labour; for example, if labour is the only variable input the constrained demand curve for labour will be vertical -- not affected by the real wage -- even if the notional demand curve is downward-sloping). And then workers find themselves even more constrained in thei ability to sell labour, which spills over into their demand for consumption, etc.. Which is just the Keynesian multiplier, analysed formally.

You could say that it assumes quantities adjust more quickly than prices, reversing the standard Walrasian assumption, so you get a tatonnement on quantities first, and then a tatonnement on prices second.

For simplicity, suppose we are at the Walrasian equilibrium price vector, then the government passes a law to lower the price of apples, and hold all other prices constant temporarily. What happens? There is an excess demand for apples, so some buyers (including me) cannot buy as many apples as we demand. Faced with a quantity constraint in the market for apples, I revise my demand for pears. *But this does not mean that the excess demand for apples goes away*. I still try to buy apples. What you are saying, when you say "This sure sounds like an excess demand for apples but I think it's an illusion." is putting forward the "discouraged apple-buyer hypothesis" (analagous to the "discouraged worker hypothesis" -- which says that when there is an excess supply of labour the unemployed workers get discouraged from looking for work, since they know there isn't any, and so the excess supply of labour -- unemployment -- disappears). Dreze retained the "unified decision hypothesis" by adopting this same assumption. But it has the bizarre implication, if carried through to its logical conclusion, that markets will clear at *any* price vector, since discouraged buyers or sellers just give up, so excess demands or supplies just disappear. If so, why would the price vector adjust to the true Walrasian equilibrium? Now, there might/must be *something* to the discouraged worker/apple buyer effect, but it can't be 100% true.

Now the Porsche example is different. With apples, I WOULD buy one if one were offered for sale; with Porsches, I WOULD NOT buy one if one were offered for sale. In other words, the ONLY thing preventing me buying an apples is the lack of a willing seller. [Parenthetically, the precise definition of "quantity demanded" (and supplied) is hard to get right, but only teachers of ECON1000, like me, are forced to try to get it right. The US edition of Greg Mankiw's intro text defines it as "the amount of a good that buyers are willing and able to purchase", but this definition gets into a logical contradiction in the rent control example, where he says there is an excess demand for apartments, but buyers are *unable* to buy any more than Qs. So for the Canadian edition I changed it, to drop the "and able". But then I face the Porsche problem. A precise definition would be "would buy, if it were offered for sale".]

The strange thing is, there is a lot of talk in the econ blogosphere about the "resurgence of Keynesian macro", general disequilibrium, and "Dark Age" etc., but I have seen no reference to the one literature that analysed this stuff properly (except, by implication, when Barro said he had actually done research in macro, and was probably talking about his stuff with Grossman in this area). No reference to constrained vs. notional demand and supplies etc. Admittedly you have to be "of a certain age" (50's, comme moi) to have been exposed to this literature, because it flowered briefly, then died with the New-Classical resurgence. The New-Keynesians never mention it, even though it is implicit in all New-Keynesian macro-models, since prices are sticky.

Must go to all-day meeting for First-Year profs. Back later.

Don: on re-reading my post, I definitely have not been as clear as I should have been on the stock/flow distinction. What I was trying to talk about was the excess flow demand for money. It got fudged because I was thinking in discrete time. So you (understandably, and my fault) missed the main import of what I was trying to say, and have gone off in a different direction. I will think about this and try to clarify later.

Nice post
Proves by example why algebra took over as medium of exchange
For the science


Means of payment
Ie credit adds yet another janus head
Facilitating the
Velocity of a given money stock
But creating defaults and crises of confidence etc

Maybe, Say's Law is false, because there are markets that do not reach a market-clearing equilibrium price.

If aggregate demand made effective by current stock/flow of money is inadequate to fully employ available resources, can unemployed resources show up before Walras' auctioneer and bid their way back into the money economy? The answer, in the presence of non-clearing markets and "sticky" prices might be, "no".

If the answer is no, can monetary policy, without fiscal policy support, bring the economy to a full-employment equilibrium? Could monetary policy induce inflation in the money economy without drawing into the economy the involuntarily unemployed?

Fiscal stimulus spending has the advantage that it can forcibly increase employment. Is this a distinctive advantage in some circumstances, of non-transitory involuntary unemployment?

Bruce: If all markets were always clearing, then Say's Law (and Walras' Law) would be trivially true. The real question of their truth or falsity only arises when some (or all) markets do not clear (prices are not at equilibrium). In that case, will it be true that the excess supplies for some goods must be balanced by an equal value of excess demands? Or can everything be in excess supply (where "everything" may or may not include money)?

Say's Law says that if there is excess supply of some goods, there must be excess demand for other goods (excluding money). Walras' Law says the same thing, only including money as one of the goods.

For your second paragraph, I agree.

Third and fourth paragraphs: I am feeling my way towards saying that anything fiscal policy can do to cure deficient aggregate demand, so can monetary policy.

paine: thanks. I think of credit as the same as bonds. When I give someone credit, I get an IOU (or some sort of record, even if just oral, or electronic). A bond is just a bit of paper with "IOU" written on it.


Just going back to my original comments on the apples/pears example. I was not putting forth a "discouraged apple-buyer hypothesis". The problem in the example is that you allow me to demand $20 worth of stuff when I only have $10. Even notional demands have to satisfy budget constraints or the whole thing becomes meaningless, the Porsche example was meant to illustrate that more starkly.

Thus, if I show up with $10 and try to buy $10 worth of apples but can't and I'm not willing to substitute anything else, I only want apples, then I agree that, at the posted price, there is an excess demand for apples. But that's not what happens, instead I spend the money on pears. Now I have no money left so you can't say I still have a demand for $10 worth of apples any more than you can say I have a demand for a Porsche and a Gulfstream jet.

Adam P: Let me change the example slightly, both to make the stock/flow distinction (as I should have done for Don), and to make it clearer what I am saying in the apples and pears example.

I earn $10 per week. I go to the farmer's market once a week with my $10. There is a stall selling apples (the apple market) and a stall selling pears (the pear market). I go first to the apple market, try to buy $10 worth of apples, and fail. So I visit the pear market, and buy $10 worth of pears (successfully). Next week the same thing happens, assuming prices don't change, and nothing else changes. So we can have a situation (I want to call it an "equilibrium", but it isn't a market-clearing equilibrium) in which the market for apples is in excess demand, but all other markets are clearing. The apple market gets the signal "produce more apples, raise the price of apples", and the pear market gets the signal "we are in market-clearing equilibrium". And at the end of the week, after I have visited the farmer's market, I don't have any undesired excess of the weekly flow of money sitting in my wallet.

To the auctioneer at the apple market, it will sure look like an excess demand for apples. And I think it is an excess demand for apples. The apple auctioneer is getting the right signal. It's the auctioneer in the pear market who is getting the false signal, because it looks like the pear market is in equilibrium, with a clearing market, and it is in equilibrium, but only because the apple market is out of equilibrium. If the apple market cleared, so I was no longer quantity-constrained, my demand for pears would drop, and the pear market would go into excess supply.

My decision at the apple market ("buy $10 of apples, and no pears") respects my budget constraint. My decision in the pear market ("buy $10 of pears, no apples. because there aren't any") also respects my budget constraint. But my decision in the pear market respects my constraint on apple buying as well as my budget constraint, while my decision in the apple market ignores the constraint on buying apples.

In Walrasian GE theory, we model consumers as choosing all demands and supplies simultaneously, subject only to the budget constraint. In non-Walrasian general disequilibrium theory, with a monetary exchange economy, and N markets, we need to model the consumer as making N decisions, each one subject to the budget constraint, plus potentially binding N-1 quantity constraints in all the other N-1 markets.

I taught this in Cuba, where the economy was in repressed inflation with generalised excess demand, and shortages everywhere. You take your monthly 200 pesos, try to buy $200 of one good, fail, try to buy $200 of a second good, fail, try to buy $200 of a third good, fail, and eventually get lucky and buy $200 of a fourth good. $800 monthly demand for goods, with only $200 monthly income. The Cuban consumption function (consumption demand as a function of income) is a very weird beast, with an average propensity to consume of 4.0. Now of course, you can say that 3/4 of that demand is a "false signal" to markets, but it is nevertheless a true signal in each market, *given the quantity constraints in other markets*. The quantity constraints in the Cuban output market also spillover to affect labour supply. "Why work, when you can't buy anything with your wages?". Which creates a repressed inflation multiplier effect, reducing the production and supply of goods still further.

Our problem is the opposite. Generalised excess supply. Firms get a "false signal" in the output market. People want to buy goods, but don't, because they can't sell their labour.

Don: I have now cleared my head. Let me fix the stock flow problem.

When we write a budget constraint, we have to be careful not to have stocks and flows in the same equation (I was not careful). Since we normally think of the demand for goods and the supply of labour as flows, we must make sure that we also think of the demand for money and bonds (and everything else) as a flow too. So when I say "my demand for money is $10" for example, I mean (or should mean) that I want to *increase* my stock of money by $10 *per week* (or per day, or whatever). I was talking (or should have been talking) about the *flow* demand/supply for money -- the rate at which I want to increase or decrease the stock of money in my pocket.

“When we write a budget constraint, we have to be careful not to have stocks and flows in the same equation (I was not careful). Since we normally think of the demand for goods and the supply of labour as flows, we must make sure that we also think of the demand for money and bonds (and everything else) as a flow too.”

This seem extraordinarily fundamental, Nick.

Personally, I find consistent visualization of the stock/flow distinction for money particularly challenging. For some reason, I get derivatively blurred.

It would be interesting to see you do a post constructing an algebra of stocks and flows as it relates to goods and services, real assets, financial assets, and money (to the degree that money is a unique kind of financial asset). It would be informative to develop some sort of framework that ties together stocks, flows, and velocity. E.g. financial assets including money have velocity; flows can recur using the same stock. Goods and services aren’t driven by the same notion of velocity. Flows can’t recur using the same output. Thinking about such a post reminds me of the kinds of conceptual posts you were doing on debt (gross and net stuff, etc.) It would be very interesting. You might get another headache, though, particularly so soon after vacation. And maybe what I’m suggesting is closer to a 600 page textbook than a post.

JKH: I'm not sure whether I can do a good job on that. But I will have a think about it, and may give it a try.

The simplest (but unsatisfactory) way to do it is like this:

There is a flow budget constraint:

p.c = w.l - d(m+b)/dt + i.b (a person plans to finance his continuous flow of nominal consumption demand (p is price of consumption goods and c is quantity demanded per unit of time): by selling a flow of labour (w is the wage and l the flow of labour supplied; by running down his stock of money and bonds (m is the stock of money, b is the stock of bonds, so (m+b) is his wealth, and d(m+b)/dt is the rate at which that stock of wealth is increasing per second); and interest earnings on bonds i.b.

And there is a separate stock budget constraint (portfolio balance constraint) which allows him to make jump-changes in the composition of his portfolio: md + bd = m + b (where md is stock demand for money, bd is stock demand for bonds, and m and b are the existing stocks).

But it's unsatisfactory because if you had perfectly smooth continuous flows of income and expenditures, with flows of pennies coming into and going out of your pocket every second, it is hard to see why we would hold a stock of money. We hold stocks of money because income and expenditure flows are discrete and lumpy, not smooth continuous flows over time.


I imagine your flow and stock budget constraints are fairly standard items in the economist’s toolkit. The framework makes sense.

I’d be interested in your thoughts about how the Federal Reserve’s balance sheet expansion fits into the flow/stock budget constraint framework. It seems that with its credit asset expansion, the Fed has responded to an increased demand for money in the stock sense. It’s substituting for those who no longer want to hold risky bonds, for example. But the Fed’s credit asset expansion has created an increased stock of money, which should respond to an increased demand for money in the flow sense as well.

The terminology “demand for money” still seems awkward. If people choose to hold money rather than buy goods or bonds, that would seem to be an increase in the demand for money. But if the velocity of money is high, more people are using the same stock of money to support more transactions, which seems like an increased demand for money as well, even though it’s effectively the converse idea to the standard definition.

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