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I hope I never do get into a fistfight over mathematical syntax...

Exactly, Nick! If you let the supply of the unit of account vary, you have to create a horizontal demand curve, Diocletian style. If you let the demand of the unit of account vary, you have to create a horizontal supply curve, Canada style.

Either way, the unit of account is simply the monetary regime. Either the demand or the supply is infinitely elastic, so talking about their interaction in the market as if they were independent curves is not correct.

Here is an alternative version of my model, that I think *might* capture what Ritwik is thinking:

1,2,3 the same, except that G and S are not fixed.

4. G+S = some fixed number.

5. Diocletion adjust has a horizontal supply curve of G in terms of S at Ps=1.


If are bothered enough about math syntax, then before obsessing about measure-theoretically correct representations of straight lines, perhaps you should read about the great sleight of mind that occurs when economists draw Walrasian (P,Q) demand curves in Marshallian (Q,P) space. Read Leijonhufvud on that.

Ritwik - Nick has been talking about price controls. There are finite quantities of gold and silver. You are still wrong.

Good night. And Happy Halloween.

Ritwik: "Either way, the unit of account is simply the monetary regime."

No. The unit of account is the units of the good that people choose to post prices in. That is different from the exchange rate regime chosen by the central bank. Most Canadian prices are posted in CAD. A few are posted in USD. The Bank of Canada can fix the exchange rate or not, and the government can ban trade in forex except at a controlled price or not.

Money has two defining functions: it is the medium of account (all prices are quoted in terms of money); it is the medium of exchange (all other goods are only bought or sold for money). ("Store of value" is not a defining function of money, because my canoe is a store of value too.)

Sorry Nick, but medium of exchange is not a defining function of money. People swap everything from land to cattle to wives, all the time. Because land, cattle, or wives are a medium of exchange, also, for the same reason that canoe mean that money is not a store of value, land, cattle, and wives means that "medium of exchange" is a not a defining function of money.

In lay speak, you are just making it up as you go along.

You have no more idea what money is than any other economist. Hint money is short hand for a Coarsen activity in the same way we use corporation, firm, business. In other words money is a legal construct, nothing more. We could do away with money and what would happen. We would need more lawyers to write the complex contracts that would replace money. Go read the new book on Debt. Learn!


The Bank of Canada wants to deliver 2% inflation. If it is indeed credible and successful, then the unit of account will be depreciate by 2% in Canada, whether prices are denominated in USD or CAD. Assuming no change in relative prices - or immaculate inflation - those prices that are denominated in CAD will go up by 2%, and those that are denominated in USD will go up by 2% over the depreciation of CAD vs USD.

If the BoC loses all control and Canada suffers hyper-inflation, then CAD will fall against USD and a combination of the following might happen :

1) Prices will start getting denominated in USD but will be nominally more or less stable.
2) Prices will continue to be denominated in CAD but sticker prices will start jumping, roughly in line with the fall in CAD vs USD

Even if for some reason effect 2 dominates, it is no longer correct to say that the CAD is the unit of account. The *social* unit of account has shifted to USD, whether prices are denominated in CAD or USD.

During the gold standard, prices were not denominated in gold. The unit of account was still gold. And, as many historians and economists have pointed out, since convertibility was often changed or suspended without causing a price collapse, what the gold standard really was, was price level targeting + fixed exchange rates.


"It's just that the authority here has to have commercial legitimacy - a credible monetary regime, rather than simply (or mostly) dispute-resolution legitimacy as you earlier seemed to imply."

Dispute resolution can be a form of commerce. As long as market participants agree that a third party (a legal authority) is required to settle disputes and as long as market participants are willing to accept the medium of account as compensation for the settlement of the dispute, then you have a form of non-market commercial activity.

Ok, I will weigh into the “Medium of Account” definition, because I think it is very important. To make things clear, let’s have a talk of something else first, like physics. Let’s have a thing called “Energy” measured by unit called “Joule”. What is the definition of joule? It is an energy expended in applying force of 1 Newton through a distance of 1 metre. Ok, not helpful. Let’s tie it to something useful, like something from the real world. So let’s define 1 Joule as energy of a tennis ball moving at 23 km/h. This is our “nominal anchor”, and since we know that in real world there are “relative energy levels” of things, we can for instance calculate that an ammount energy required to ionize atomic hydrogen is approximately 21,76 x 10^-19 Joule. The point is that in objective reality, we may say that unit of energy is anchored by an actual energy of anything that we can measure. Once we have it, we can calculate anything else because we know “relative energies” of various things around us thanks to physical laws and observation.

So let’s say that our unit of account is “Valor”. How much value lies in 1 Valor? Let's say that one Valor has the value of 10 "Sumners" applied for 1 second. Ok, not helpful. Let’s define it by tying it to something useful, like to a value of something from real world. Lets say that 1 Valor has identical value to the market value of 1 ounce of gold. If we know this, and if we know relative prices of various goods we can assign gold value to any other good or service. It would be nice to have an objective world like in Physics, but economic reality is complicated by the fact that relative prices change over time. So what, it does not make this unit of account inherently invalid. In this implementation of unit of account, we merged “valor” with “ounces of gold”. To prevent confusion, we could as well rename “Valor” with “Goldounces” for this is its definition. Since gold is something physical and not abstract – like “Valor” we may even promote “Goldounces” to “Medium of Account”. Everyone knows what gold is, it can therefore serve as “medium”, or tangible, physical representation of unit of value.

But the point is, that this is not the only possible implementation of an unit of account. We can further complicate thing not only by having constantly changing relative prices, but also by constantly changing "value" of our unit of account. Let’s say, that emperor Diocletian decides, that he no longer likes “Goldounce” as unit and medium of account and he will establish a following rule – every day that “ounce” part will be multiplied by random positive real number. So every day the price level changes randomly. Is this a problem? Only for people who were carrying gold coins in their wallets and were happy about having exactly one price unit in their possession. But this will not change relative prices. One day, you will have price of 0.0125 of yesterdays “Goldounces” and tomorrow it could be 1,459,585.2145 of todays Goldounces. Or to have a different view, and you really like nominal numbers, it is as if there is different good as a medium of account every day.

So to sum it up:

Unit of account is inverse of price level. It is “dimensionless” number or “abstract” concept if you wish. The only thing that gives it any meaning is a system of relative prices, or so called “monetary regime”
Medium of account is potentially any market good. This is just more convenient representation of unit of value that somebody can actually hold in his hand.

The most important part:

Relative prices (and therefore unit/medium of account) is not determined out of thin air. It is determined by people exchanging goods on the market. In current world, where we do not have extensive IT network mapping demands and supply of real goods and delivering those to people, we use monetary exchange determining the relative prices. Medium of exchange is a technology that gives rise to a system of relative prices and therefore it is necessary condition for existence of any medium of account.

And back to real world - my country just recently experienced quite drastic change. On day we changed our money and adopted Euro. Everybody had to multiply any number on contracts, price tags or anything that contained price by conversion exchange rate and he had to change the name of unit of account to "Euro". I do not recall anybody being constrained by "supply" of this new "Medium of Account" named Euro when changing contracts. How come that nobody was afraid of this drastic change that should have created recession? Aren't nominal prices sticky? My answer is - no as long as people credibly believe that there will be no change in relative prices.

John: "People swap everything from land to cattle to wives, all the time. Because land, cattle, or wives are a medium of exchange,..."

So people swap cattle for land, not because they want the land, but because they want to swap that land for a wife? OK, in that case, the people who do that really are using land as a medium of exchange. If everybody uses land as a medium of exchange in your country, I would say that land is money in your country.

Nick: Just another thought. If Scott Sumner assumes continuously clearing medium of account / medium of exchange market why not model that case by actually dropping gold altogether and using haircuts as medium of account? Then the price of one haircut will be by definition "one haircut" and since silver/haircut market is constantly in equilibrium by assumption, we are golden - no recession and everybody will be happy ever after.

If this is what Scott believes, I wonder why don't we cut the whole NGDP part since our salvation really is just establishing the most sticky "good" (like laborhour) as medium of account and there go all our problems.

Nick - You need to read Feavearyear's "The Pound Sterling" (1930s?) and Nicola Oresme's "De Monetas" c. 1350.
Both on web, someplace

1. Take half the silver away, people would just cut their coins in half. Too much has gone down under bimetallism for quick summaries to be encompassing.

2. In Oresme, we find 4 qualities of money. Symbolic, Exchange, Account, and Storage values. Subsequent scholarship of various types over 650 years since De Monetas was "published" has found ways each of these varies deterministically under diverse nomenclatures. Modern economists know little of this because money is taught as the "numeraire."

For example in usage, nobody would present their accounts in "ounces" - ounces of what fineness? Instead, over the centuries, one or another money has been used in accounts, multinationally. Venetian Ducat, Dutch Guilder/Spanish"Dollar", British Pound, U.S. Dollar. There are levels of spatial variation in accounting money over history, but domination of the money of account market has been an especially important component in conventional multinational economic activity.

One can't just hawk and spit and declare one or another quality of money as primary. 1, 2, 3, 4, aren't going to be impacted!

With a medium of exchange, a velocity is implied:
M1 * V1 = P * Q

If we say that P * Q is all goods produced and purchased either with income or new money
M1 * V1 = Income * (1 - Liquidity Preference) + dM1/dt
M1 * V1 = I * (1 - LP) + dM1/dt

But, income is simply all money received in the sale of goods or I = P * Q = M1 * V1
M1 * V1 = M1 * V * (1 - LP) + dM1/dt

M1 * V1 * LP = dM1 / dt

Letting M1 = exp ( f(t) ) where f(t) is a medium of exchange demand function
V1 * LP = f'(t) or
V1 = f'(t) / LP

And so the velocity of circulation is simply the ratio of how quickly the demand for a medium of exchange rises with respect to the liquidity preference.
With a medium of account, there is no velocity. Instead there is a rate of issuance.

dM2/dt = P * Q = M1 * V1 = M1 * f'(t) / LP
M2 = M1 / LP
M2 / M1 = 1 / LP

A recession happens when liquidity preference rises faster than medium of exchange demand or medium of exchange demand falls faster than liquidity preference.

A legal authority can try to fight a recession by changing the value of the medium of account in relation to the value of the medium of exchange, but it may not be successful.

A legal authority can change liquidity preference by the increasing the value of the medium of account relative to the medium of exchange, but it cannot also change the demand for the medium of exchange. And so liquidity preference could fall but demand for the medium of exchange could fall by just a much.

Stupid question but: "annual income from haircuts is Y haircuts." means what? The units don't make sense to me. I tried thinking of it like this: "annual income from cars is 5 cars". Can someone please clarify this?

I'm a noob at economics and I'm just trying to understand this issue.

Let's tell a fairy story that is actual history. People trade, tax, collect rent and so on. At some point their various measures for what is owed by way of trade, tax etc drift towards a common measure. Let's call this measure the cow (in honour of old Ireland, where the value of fines and rents was given in cows). this is the common unit of account. Bear in mind that an actual cow is usually worth more or less than a notional cow. People say - "you owe three and half cows in rent every quarter", or "I will sell you this shirt for a quarter-cow" and so on. In such a system, it makes no sense to ask "what's the worth of a cow?" in general - it's worth what people are selling things for at one cow. Nor does it make sense to ask how many cows are in circulation, or how fast they move - that would be like asking how many inches there are (this story has the virtue of being the actual situation over large parts of the world up until quite recently, and the documented case for the several thousand years before coins came into general use).

What might cause a recession in such a world? One is that, obviously, any interval in payment will be covered by promises. One can see that a failure to meet a promise might well set off a chain reaction, should some significant fraction of outstanding promises prove unexpectedly weak, or the creditors simply unable to be meet the shift in desired time of redemption (Cathal owes Liam 15 cows; Cathal defaults; Liam therefore demands that Conall pay the 8 cows he owes immediately; Conall is unable to meet the new timeframe; Liam therefore delays payment to Sinead and so on...soon everyone is reluctant to trade except for immediate delivery; conversely, in good years people pay earlier, trade more and so on). In other words, shifts in timing and sentiment will affect the system. You don't need a unit of exchange to have booms or recessions - you don't even really need a unit of account (although I can see that having one will amplify movements in sentiment and allow changes in preferred timing to ripple through faster). It's enough to simply put time and uncertainty into the system.

yebin: If the economy consisted of just you making 5 cars a year, then your annual income would be 5 cars.

This is not a thread for noobs, by the way. Sorry to leave you out, but it's a response to one of the world's best monetary economists getting confused about a basic point of monetary economics...

Calitri: Feaveryear's is from 1963. I used it in a term paper in the middle 70's. Brilliant book. At the time, (1978) I was the first personn to have checked it out of the LAval U. Library.
Not sure sur if it will help the thread but a fascinating read.

This from Feveryear's The Pound Sterling: A History of english money, chap 11:

"Peel and the Bank Charter Act

WHILE the Bank Charter Bill was still before the House of Commons Sir Robert Peel received a letter from John Horsley Palmer warning him that the proposed strict limitation of the note issue would make it difficult, if not impossible, for the Bank to render that assistance during a crisis which it had rendered in 1825, 1836, and 1839 and which had come to be expected of it. A few days later he received a similar letter from Henry Bosanquet, a director of the London and Westminster Bank, who, without entering into the question of the meaning of 'currency',"...

The quote from


Jacques, yes, similarly, Feavearyear's was an eye-opener. Generally speaking economic historians don't pay much attention to the numbers of interests involved in monetary questions. Beyond that, NYU's catalog system fails me for the most plangent, but there are a number of numismatic studies of Roman coinage successions out of the 1950s and 60s illustrating from hoard coin weight distributions the reasons for successive coinages.

None of this will help the thread. Even if they know the qualities of money, they must not stray from their wedding vows to the numeraire.

By the way, I could have mentioned previously. There is no better explication of the nature of money and variables needing calculation in assessing its role and that of the quasi-moneys than Keynes GT, chapter 17.

How about doing the example this way? Start in some kind of "equilibrium".

Let gold grow 1% per year.

Let silver grow 2% per year.

Let haircuts grow 3% per year.

Demand and supply of the medium of account determine the equilibrium price level.

Is this like demand and supply for the meter?

There is no such thing as demand and supply for a unit of measurement.

I think Nick is trying to be sneaky here.

I think Keynes would say this:

The other set of fallacies, of which I fear the influence, arises out of a crude economic doctrine commonly known as the Quantity Theory of Money. Rising output and rising incomes will suffer a set-back sooner or later if the quantity of money is rigidly fixed. Some people seem to infer from this that output and income can be raised by increasing the quantity of money. But this is like trying to get fat by buying a larger belt. In the United States to-day your belt is plenty big enough for your belly. It is a most misleading thing to stress the quantity of money, which is only a limiting factor, rather than the volume of expenditure, which is the operative factor.

Letter to Roosevelt, February, 1938

To clarify the 12:52 comment,

In the non-financial sector, people transact in deposits, or in bonds, or any number of credit instruments.

Those instruments may be *denominated* in dollars, but the supply and demand is for payment in some instrument denominated in dollars, but not actually consisting of dollars.

The quantity of bank reserves or CB liabilities is not a constraining factor that would either hinder payment or raise or lower prices, provided that, as Keynes said, enough CB liabilities are present in order to allow the financial sector to create as many deposits or credit instruments as the non-financial sector needs in order to execute the desired purchases.

rsj: "Is this like demand and supply for the meter?"

It's more like demand and supply for meter rulers.

And, yes, Keynes is right, velocity matters too.

rsj: that's why I was very precise in my terminology. Gold is the medium of account. An ounce of gold is the unit of account. It's the demand and supply of gold, not the demand and supply of ounces, that determines the equilibrium price level.

But in that case, we make room for Brad DeLong's argument, that it is safe bonds, which are denominated in dollars, that are in short supply, rather than the dollars themselves, because the non-financial sector is able to transact with these bonds, and the financial system will take care of the conversion of the bonds into dollars behind the scenes.

Nick: You (or better to say Scott) are too focused on the "Price Level". When Slovakia changed Slovak Crowns to Euro, everything got less expensive by exactly 30.126 times because the conversion exchange rate of Slovak Crown to Euro was 30.126. The mysterious "Price Level" decreased 30.126 times for people who forgot how the unit of account is called and everybody was quite happy about it, there was even fireworks in most cities. Unions did not protest nominal salary cuts, everything was as it was before. Why? Because conversion did not bring any change in any relative price. One hour of work day before conversion could buy you approximately the same amount of goods day after the conversion. Price level determined by medium of account does not matter at all. It is the expectation that change in price level could distort relative prices in some specific way that is important. And medium of exchange plays the key role here.

The biggest problem with Scott's example is that he actually did not separate medium of account from medium of exchange. If everybody could sell their gold for silver at any time they wish, if the silver/gold market always clears then you just promoted gold to medium of exchange. If all shop owners could have real-time feed from gold/silver commodity exchange so that they could at all times charge the gold price of goods they sell, then what is the difference for them to say: "In my shop all silver is gold. I only change prices every second". This medium of account "always clears" assumption is basically equivalent to a condition that medium of account is medium of exchange.


“Scott: If the price of the MOE is perfectly flexible, and adjusts to clear the market for the MOA, then an excess demand for the MOA can cause a recession. But only because an excess demand for MOA causes the price of the MOE to fall, which causes the real stock of the MOE to fall, and creates an excess demand for the MOE, which causes a recession.”



And later:

Ritwik: in my model, the MOA is a thing. And there is a supply of that thing and there is a demand for that thing (to wear as jewelry). And so there is an equilibrium relative price of that thing. If the MOA is not a thing with a demand and supply, that is a very different model.

I think this is very succinct.

I interpret the first as the idea that a medium of account valuation adjustment can cause a recession, but only because such an adjustment forces a knock-on adjustment in terms of the medium of exchange. And it’s the medium of exchange adjustment that is where the action is – in terms of the recession dynamic.

And the second is important as clarification of a logical distinction:

- The medium of account (gold) is not the account itself (haircut in gold terms)
- There is supply and demand for both the medium of account and the account expressed in terms of the medium of account
- But there is no supply and demand for the choice of the medium of account: i.e. there is no market (that is relevant to this problem) as to whether the medium of account should be gold or silver
- A haircut is not gold; nor vice versa

rsj: "...that it is safe bonds, which are denominated in dollars,..."

A bond is a promise to pay something, e.g. dollars, at some future dates. The current price of those bonds is not fixed in terms of dollars. Those bonds are not the medium of account nor the medium of exchange, though they may be used as collateral to support media of exchange. Such as when banks hold bonds as assets against demand deposits, or shadow banks do repos.

JV: in that case I would say that the medium of account switched from Crowns to Euros. And because it was a coordinated switch, where the government announced the new focal point, and so all prices changed at once in the same proportion, it was neutral.

(Slightly off-topic, but did anyone else noticed how the governor of New Jersey just changed the date of Halloween by simply saying the date had changed? Zero concrete steps at all. But all the kids will go out trick-or-treating on a different day, which is a real effect.)

JKH: I think we are on the same page here.

"Gold is the medium of account"

Ok, English is not my language. And philosophy is not my uni subject.

How does the usage of ounces of gold in measurements translate into demand and supply of gold? If the number of measurements or measured ounces change, does it mean that supply and demand changes as well? In what relationship? Thank you.

Sergei: if we suddenly switched to measuring gold in pounds, rather than ounces (16 ounces in a pound), all prices would switch too, so that "32 ounces of gold per haircut" becomes "2 pounds of gold per haircut". Nothing real changes. It wouldn't affect the demand or supply of gold. (Or, both supply and demand and price would be divided by 16, if you prefer.) It would be like switching from Canadian dollars to Canadian cents.

The medium of account is not a thing even when it is a thing. :)

If something is allowed to be a medium of account despite being a thing, all that means is that the medium of account setter has placed a floor on real rates which limits its ability to counter deflationary pressures.

You could replicate the gold standard by requiring that all bank deposits must pay a minimum of 200 basis points above the benchmark inflation rate, calculated every month. You wouldn't even need gold.


"Slightly off-topic, but did anyone else noticed how the governor of New Jersey just changed the date of Halloween by simply saying the date had changed? Zero concrete steps at all. But all the kids will go out trick-or-treating on a different day, which is a real effect."

No I don't think that is off topic. I think that is spot on. The governor of New Jersey (having a legal authority) changed the value of two days. Prior to his action, October 31 was a day when both agents (kids in costumes and parents) had the incentive to engage in an economic activity - parents get entertainment value and kids get candy. Now that value is bestowed on a another day of the calendar.

I think that is what is missing from the example. A medium of account has a "bestowed" value. The example makes reference to a gold as a Veblen good.

"It's a Veblen-good, where what counts is not the physical quantity of gold worn, but the value of that gold in terms of haircuts. Look at me! I'm wearing 10 haircuts' worth of gold around my neck!"

What the example does not say is how that 10 haircuts worth of gold is calculated. There is no market to set the value of gold with respect to haircuts because gold is not accepted as payment for haircuts. A legal authority is one means upon which value is bestowed.

Suppose instead of gold and silver, the two are replaced with E-Coins and A-Coins. Both are made of the same base metal, but the value of one is determined in a market place and the value of another is bestowed upon it by a legal authority. Where E-Coins have a value based upon the demand for current and future haircuts, A-Coins have a value by decree.

Frank: glad you see the relevance. But notice: there is absolutely nothing the Governor of New Jersey did to *force* people to change the day they go trick-or-treating. But they do all change. Because each person expects everyone else to change.

"Frank: glad you see the relevance. But notice: there is absolutely nothing the Governor of New Jersey did to *force* people to change the day they go trick-or-treating. But they do all change. Because each person expects everyone else to change."

Which is not to say that the Governor of New Jersey can't enforce the change. Many cities and towns have curfew laws - especially in high crime areas. And so if certain towns in New Jersey suspend curfew laws for Halloween, and if the Governor changes the day that Halloween is celebrated, he has in fact change the day on which curfew laws will not be enforced.

And so the Governor did not force people to change, he may have changed the day upon which a person could be outside after dark without threat of detainment or arrest. And so the people could ignore the Governor's decree and engage in an positive economic activity (candy for kids and entertainment for parents) at risk of a negative externality.

Wow, 136 comments.

Nick, it seems to me that you and Scott (and Bill W) are roughly on the same page, given that you've recognized your respective differences in assumptions and ignoring differences you might have on the definition of money. Is that fair?

JP: I *think* so. (But I bet this argument crops up again!)

Note: Price inflation in the medium of account (relative to the inputs and outputs of a company) causes companies to misunderstand their profits and losses in real terms. This hides misallocations of resources.

More on E-Coins and A-Coins.

Suppose that the legal authority accepts both E-Coins and A-Coins as payment for taxes at a fixed rate of exchange - 1 A-Coin is equivalent to 10 E-Coins. Thus the value of an A-Coin with respect to an E-Coin is established through a non-market activity (payment of taxes). Suppose also that the going tax rate is 10% of a person's E-Coin income. Now suppose that during a recession, the legal authority wants to change its tax structure to spur economic growth. It could either cut the tax rate OR change the relative value of A-Coins to E-Coins.

Hi Stephen. You are correct. It is obvious that equations 1 and 3 alone determine the equilibrium price of haircuts Ph. The only role of equation 2 is to help determine the equilibrium price of silver Ps.

From Miles Kimball



What Miles Kimball (and apparently Greg Mankiw) are advocating is imbuing the medium of exchange with equity type risk. If they want government sponsored equity, they should just come out and say - the federal government should sell equity.

We have already convinced people that pension should be invested in equity. Maybe having an equity money is the last step...


"We have already convinced people that pension should be invested in equity."

Here in the US, former President George Bush and former Treasury Secretary Paul O'Neill tried privatizing Social Security so that taxes paid would be diverted to private equity markets. Private equity markets depend on profitability to derive their value. Government equity depends on productivity to derive its value. Profitability and productivity are not the same thing.

"Maybe having an equity money is the last step..."

Having an equity medium of exchange makes no sense whatsoever. Miles is arguing for an equity medium of exchange because people have the wrongheaded idea that money is a store of value. Miles is correct that money is not a store of value, it gets its value through use as a medium of exchange. But Miles tries to address the investment demand for a store of value by devaluing the medium of exchange rather than having the federal government sell liabilities that have a high future value.

Frank: as a teacher, I nudge my students to give me the answers. Spot on, Frank.

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