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Nick: if we say" store of easily accessible and transformable value", then we are into "liquidity", an essential characteristic of money. Whether we need to specify separately that the ideal medium of exchange is very liquid may be open to discussion but for most people ( and presumably our brothers-in-arms in economics) that,s what they have in mind.

"People want to sell some of their silver for gold, but they can't, because nobody wants to take the other side of the trade"
Are you asusming a fixed gold/silver rate?
What if we throw in some gold/silver noise traders?

My own view is here: https://www.themoneyillusion.com/?p=17368#comment-200887

"Demand and supply of the medium of account determine the equilibrium price level." Ok, I don't think I understand that. What does demand (or supply) for a medium of account even mean?

does there exist a demand (or supply) for kilograms, or inches, or pounds or kilometers?? i don't get the concept

I think the question --- for you and Scott Sumner --- is why on earth people are using a medium of exchange that doesn't have a fixed nominal value, fixed either by being identical to the medium of account or by some agency committing itself to exchanging the medium of exchange for the medium of account at a fixed rate.

As for your thought experiment 2, I think that rather than a recession you would see a switch to a different medium of exchange.

Just to confirm this: Emperor Diocletian's edict does not apply to Ps.

Nick: Great blog as usual - I think nobody in the blogosphere can compete with you in the stile. I think that this is how old Nobelist Krugman had to think like - during times when he was able to think in terms of simple models like babysitting Co-Op and less in terms of "Reinhart & Rogoff proved on data that financial crises cause slow recoveries".

Anyways, I still think that there there is more to the confusion then it is shown in your story, I just cannot put my finger on it. When I was trying to analyze where Scott was coming from I think that he has a very strong assumption that price of gold in terms of silver always clears. So any condition for disequilibrium analysis such as "Start in equilibrium, hold all prices fixed" is immediately disqualified. So the only effect of halving the stock of silver is that the price of gold in terms of silver doubles, which is then (using smart system of automatic price tags updated by cell phone from central gold market in Harare) - displayed as halving the silver price of the haircut.

PS: I will just add that I agree with JCE. It feels weird to speak about "medium of account" alone. The word medium itself strongly suggests some exchange function. For instance, energy is measured in "units" such as Joules and it can be exchanged utilizing various "media" - such as energy of chemical bonds, kinetic energy, energy of physical bonds etc.

Jacques Rene: liquiditity is empirically a very important property of money, but it is not a *defining* property of money. I could imagine an economy, full of very stupid people, who use used cars as medium of exchange and medium of account. Very unlikely, but not logically impossible.

Or maybe dollars used to be liquid, but became less liquid because there are lots of counterfeits in circulation, and it takes a long time to check if the dollar is good or bad. But people keep on using dollars because they have always used dollars, and no individual can easily switch unless lots of others switch at the same time.

123: "Are you asusming a fixed gold/silver rate?"

Yes. Diocletian fixes all (both) prices: Ph and Ps.

"What if we throw in some gold/silver noise traders?"

It doesn't make any/much difference in aggregate. One individual decides to sell some gold, another lucky individual buys it, the first has more silver and so buys more haircuts, and the second has less silver and so buys fewer haircuts.

JCE: the *medium* of account (in my model) is gold. The *unit* of account is (say) one ounce of gold. Prices are measured in ounces of gold. There is a demand for gold to wear as jewelry.

Jonathan: It is unlikely, but there are cases where the MOE and MOA are different, and have fluctuating prices. Hyperinflations, where menus specify prices in a foreign currency but payment is made in domestic currency (because it's too expensive to keep changing the prices), and stores on the Canadian/US border, which post prices in CAD but accept USD too.

"As for your thought experiment 2, I think that rather than a recession you would see a switch to a different medium of exchange."

Agreed, it does create a big incentive to switch to barter or some alternative MOE. But it's not easy for individuals to do that. I think the fact that we do observe some local MOEs being used in big recessions confirms the MOE theory of recessions. I've done a couple of posts on that topic.

primed: I have edited the post. BOTH Ph AND Ps are fixed.

JV: Thanks!

"When I was trying to analyze where Scott was coming from I think that he has a very strong assumption that price of gold in terms of silver always clears [the market where gold is traded for silver]" [added by NR]

I think you might be right. If, in my first thought-experiment, some central bank halved the supply of silver in order to keep Ps the same when the supply of gold halved, we would get a recession. Because that would mean an excess demand for gold causes an excess supply of silver that causes a recession.

Yep, there's the *medium* of account and the *unit* of account. Maybe I should have made that clear.

Ed Dolan gives another example-Russia, where the MOA and MOE were different.

Where your account differs from Scott's: you have introduced a consumption demand for the medium of account. In his version, there does not need to be a gold-silver market.

Gold/silver market is a financial market, so the sticky price assumption is extremely unrealistic. Diocletian will be ignored/circumvented etc.

And the global MoA (dollar) shortage did cause a lot of damage to Russia in 1997-98.

Thank God for math! (Or perhaps just the integers, as some would have it.)

If Scott still doesn't get it now... well I don't know what I'll do. Perhaps I'll simply have to shoot myself. (Like the guy from the Cheese Shop.)

According to your own model though, Nick, doesn't the demand for holding silver-balances (or the velocity of silver) also determine the price level, when prices are flexible? Similarly couldn't a decrease in the supply of gold, when Ps is flexible but Ph isn't, also cause a recession? (I brought these points up in the comments on Scott's blog, too - indeed I believe I brought up every conceivable point.)

Phil: If silver is the medium of exchange, how can there not be a gold/silver market? How else can people buy or sell gold?

123. OK. Let's suppose Ph is fixed, but now suppose Diocletian goes soft and lets Ps adjust when he sees what happens.

Thought-experiment 1. Ps falls because there's an excess demand for gold, which from equation 2 reduces the real value (in terms of haircuts) of the stock of silver, which creates an excess demand for silver in terms of haircuts, which causes a recession.

Thought-experiment 2. Ps rises because there's an excess demand for silver in terms of gold, which increases the real stock of silver in terms of haircuts, which eliminates the excess demand for silver, which ends the recession.

I'm still not convinced that the concept of a "medium of account" is well enough specified. "Unit of account" is fairly straightforward; we measure everything in units (inches, kilograms, minutes, etc.) What is the "medium of account" in the current U.S. monetary system, analogous to the role that gold plays in your simple model? If your answer is "dollars" then I think you may have a very serious specification problem. This is very subtle and difficult.

Nick: all prices are quoted in terms of money

Why is that so? It is all purely voluntary. You can quote your prices in whatever you want as long as you believe in the private sector and freedom. Noone can force you to quote prices "in terms of money". Like car trade-ins: your car dealer can quote you the price of the a car in terms of your used cars. So 1 new car for your 2 used cars plus back massages during next year.

However, what is really true is that liabilities are (very typically) quoted in terms of money. And what is also very true is that this is (very typically) the money of the respective legal jurisdiction.

Saturos: Thanks for very ably defending my POV on Scott's blog!

"According to your own model though, Nick, doesn't the demand for holding silver-balances (or the velocity of silver) also determine the price level, when prices are flexible?"

No. Look at my 3 equations. 1 and 3 determine Ph. You don't need 2. You only need 2, in addition to 1 and 3, to determine Ps.

"Similarly couldn't a decrease in the supply of gold, when Ps is flexible but Ph isn't, also cause a recession?"

Yes. See my comment above in reply to 123.

MR: OK, but the unit of account (in my model) isn't "ounces", it is ounces of gold, as opposed to ounces of silver or ounces of hair.

Medium of account in the US? Hmm. Fed liabilities?

Nick, suppose you have fiat MoA, and fiat MoE, sticky wages and consumer prices, flexible MoA/MoE exchange rate, and MoA and MoE managed by different institutions. Would you rather be a governor of Bank of MoA, or a governor of Bank of MoE?

Nick: I just think, that what Scott Sumner used in his example is basically that he got rid of the money. If you fully embrace his approach, then everything with sufficiently thick markets can serve as money. For instance workers could be paid in Stock options of companies they work for, you can use "oil" credit card that is a at all times contains the value of some set future oil contract.

Scott's mobile price system can be something like unitless Walrasian auctioneer. It really is just a system that contains information about all relative prices using inputs from cash registers and markets all around the world. You can have a mobile app, or something like "Google Glasses" but instead of seeing Google Maps or Google Translation of the text you see, if you look at any price, it will automatically translate it to the preferred "money" you like to use (hold) - Dollars, Euros, barrels of oil, ounces of gold or average price of land on the moon.

But then we will probably need some different monetary ecnonomy in the same way we will need a new international trade models if and when interstellar travel is made possible. My point being, that as long as we live in our world where unit of account and unit of exchange is the same thing, and it is more or less just one thing, it is the property of money as medium of exchange that is crucial for our understanding of business cycle.

Nick, I don't like your gold/silver analogy, because in the US the general medium of exchange (bank deposits) are completely defined in terms of the medium of account (reserves), and that same medium of account is also a medium of exchange for some purposes.

In particular, in your example it shouldn't really be possible to hold Ps fixed.

Of course money is a store of value. When the return on money exceeds the return on real investment we go into recession/deflation. When people (agents??) sense this will happen they will hold on to (not spend) their money.

In the real world with constant shifts in price relations -- including price relations across time -- between different kinds of money substitutes and production goods of differing production times and outputs, there is no "given" equilibrium 'price level' -- there is a constantly contested struggle between different constantly updating approaches to various rival sets of near-but-never-at equilibriums. Don't mistake you math model for the real world .....

Nick writes,

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

How about doing an example where currency plus demand deposits are the unit of account, medium of exchange, and a store of value?

Nick: " I could imagine an economy, full of very stupid people, who use used cars as medium of exchange and medium of account. Very unlikely, but not logically impossible."
You could envision a perfectly spherical hen but no architect or farmer would think about one. They'd go bankrupt.
If economics is a science and not a metaphysics, it must stick to empirical facts. Otherwise, as a french general opined while watching the charge of the Light Brigade: " It is magnificent but it's not war."

See Alfred Eichner
https://www.jstor.org/discover/10.2307/4225324?uid=3739464&uid=2129&uid=2&uid=70&uid=3737720&uid=4&sid=21101324241681

or
https://www.amazon.com/Why-Economics-Not-Yet-Science/dp/0873322657

The economy is never in any fully coherent 'equilibrium' -- and the supply and demand & changing liquidity of money substitutes imperfectly coordinated across time and causally intertwined with the supply and demand of different production goods with different production times and priced across time -- all of that are part of what determine the never-perfect 'equilibrium price level'.

Nick writes,

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

Our job is to understand the word, our job is not to pretend a piece of math is the world, and constantly struggle to make sense of that piece of math, and then claim that our understanding of that bit of math is equivalent to an understanding of the actual world. Physicists don't mistake understanding a bit of math for understanding the mathematically intractable problem of fluid dynamics involving turbulence ....

Jacques Rene: sure. But we also need to distinguish between facts that are true by definition and those that are empirical, contingent, facts.

Ed: "Of course money is a store of value."

And of course canoes are a store of value too. If people think that canoes will rise in value, nobody will want to sell their canoes.

But that isn't what *defines* a canoe.

So, when bank deposits are the medium of exchange and state money is the medium of account then excess demand for deposits causes recessions?

Nick: if canoes were the preferred store of value and after some time people would think of canoes as primarily a store of value, then store of value would be part of the definition of a canoe.
The BoC Museum is full of things that are not obviously either store of value or medium of exchange nor units of account. And yet it was perfectly obvious to their owners that they were such things and that such attributes defined them.

If deposits are money and government currency is the medium of account, an excess demand for deposits will cause a recession.

However, because banks accept currency for deposit, if there is no shortage of currency initally, and a shortage of deposits, it is likely that currency will be deposited until there is a shortage of both types of money.

If the government creates enough currency to make sure there is no shortage of currency, and people deposit currency when there is a shortage of deposits and no shortage of currency, then the government will create enough currency so there is no shortage of deposits either.

But really, the most likely way that shortages or surpluses of deposits impact the demand for currency is through their effect on spending on nominal output and income.

Jacques Rene: sure. But we also need to distinguish between facts that are true by definition and those that are empirical, contingent, facts.

True by definition means it is proved by axiom or hypothesis. Axioms can be falsified by empirical facts, that's the whole point of the scientific method. Persisting in advancing axioms contradicted by empirical results means you are engaging in a fallacy.

Bill: Sure, but aren't you really just introducing currency as a medium of exchange? And could there be enough currency for this to have any significant effect? Also, how does the government get the newly created money to the people if not via new bank deposits?

'Store of value,' to me, just means that it holds its value fairly consistently over time. This is a requirement for money so I don't understand why you exclude it.

The medium of account is a mathematical function, with no necessary physical consequence.

The medium of exchange is a physical presence (albeit mostly an electronic presence), with physical consequence through economic action.

Money involves the second.

The medium of account is optional. The optionality is fully determined by math. That’s why it doesn’t connect to recessions.

The medium of exchange isn’t optional, by physical construction. That’s why it connects to recessions.

Nick wins, IMO.

Again

Unlearning: people continue to use the same money even in hyperinflations, even when it holds its value far worse than canoes and cars and chairs. Empirically, an existing money has to be a really terrible store of value before people stop using it as money. Millions of different goods are stores of value. That doesn't mean they are used as money.

It's a bit like defining chairs as: things you use for sitting on; things that don't float away. Sure, if a thing floated away in the slightest breeze, people would probably stop using it as a chair. But just because a thing doesn't float away doesn't mean it's a chair.

You don't define a thing by a property it shares with millions of other things.

Jeez, you guys who are so hung up on sticking to the textbook orthodoxy! ;-)

HJC said: "So, when bank deposits are the medium of exchange and state money is the medium of account then excess demand for deposits causes recessions?"

Bill Woolsey said: "If deposits are money and government currency is the medium of account, an excess demand for deposits will cause a recession."

I don't understand why currency and demand deposits can't be the medium of account and the medium of exchange as long as there is 1 to 1 redeemability.

1) The 'medium of account' is not a market with demand and supply, it is a convenient shortcut for an entire price/monetary regime. Prices are usually quoted in the medium of account. But this is not necessary.

2) Currency is not a medium of account, it is one particular medium of exchange. A relatively unimportant one at that, until interest rates start hitting zero.

3) The price level is the inverse of the purchasing power of 1 unit of the medium of account. This is a definition, so it's simply not correct to say that the price level is 'determined' by the medium of account. This is true when the unit of account is gold, it's true when the unit of account is the consumer basket, and its true when the unit of account is a foreign currency. In your thought experiment 1, a haircut worth 10 yesterday-golds is now worth 5 today-golds. Yesterday-Golds and today-golds are not the same. The monetary regime has not changed. The unit of account has not changed.

4) Recessions, booms, inflations, deflations are phenomena concerned with the medium of exchange. It is not entirely correct to say that a recession is caused by an excess demand for the medium of exchange, but a variety of factors that do cause recessions - troubles of inter-temporal coordination, loss of trust & net wealth, etc. - ultimately result in an excess demand for the medium of exchange along the way to causing output and employment shortfalls. So purely from a proximate-cause perspective, one could say that an excess demand for the medium of exchange causes the recession.

5) Monetary inflexibility, however, is typically the result of the choice of the unit of account, or equivalently the monetary regime. Commodity units of account tend to demonstrate this inflexibility rather obviously, but they can be easily replicated in fiat monetary standards. The gold standard was basically price level targeting + fixed exchange rates. An increase in the demand for a commodity unit of account is a rise in the real interest rate.

6) Hyperinflations, however, are repudiations of the unit of account. They are indeed be preceded by an acceleration in the measured medium of exchange - a standard feature of a Howitt-Wicksell collapse - but they can typically be stopped only through a change in the unit of account as well as the implied monetary regime.

Ritwik: "3) The price level is the inverse of the purchasing power of 1 unit of the medium of account. This is a definition, so it's simply not correct to say that the price level is 'determined' by the medium of account."

It is not true *by definition* that the price of eggs is determined by the demand and supply of eggs. That's a theory of the price of eggs. It is also not true *by definition* that the price level is determined by the demand and supply of the medium of account. That's a theory. But yes, not a very surprising theory, when you restate it like that!

Nick

But there's no *market* for the medium of account, because there's no supply and demand for the medium of account. The medium of account logically precedes demand and supply curves. Can you draw a locus of points in (P,Q) space without first defining P?

Are you saying currency determines the price level?

I'm actually saying something very much in line with your *we live in the CPI standard* point of view, i.e the price level determines the price level. Or, the monetary regime(+ history) determines the price level.

Ritwik,

"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)."

"An excess demand for the medium of account does not cause a recession."
"An excess demand for the medium of exchange causes a recession."

The defining characteristic of any unit of account is a legal authority that maintains that unit of account. This comes into play via legal proceedings. For a governing body to determine compensatory damages when one party in an exchange is not satisfied with what he / she received, then that governing body needs control over some aspect of that unit of account to make amends. That control could be the cost, supply, or demand for that unit of account.

Suppose in your example that the person exchanging silver for a haircut is dissatisfied with the haircut. He goes before a legal proceeding and makes his / her case that the haircut was substandard. Recognizing that a time delay has occurred between the filing of suit and the awarding of compensation, how is the legal authority to proceed with award without some control over the supply and demand for gold?

Now suppose that a lot of bad haircuts have been given to the point that the suit reaches class action status. If all people are compensated for bad hair cuts with gold, they exchange that gold for silver and go get better hair cuts. If all people are not compensated for bad hair cuts, they end up getting fewer hair cuts and a recession ensues.

Nick,

"But there's no market for the medium of account"

But there is a demand for a governing body that functions as a legal intermediary between buyers and sellers - aka a referee for markets. And because that intermediary must have some control over the value of compensation, a medium of account is required that can be different than the medium of exchange.

The supply and demand for a medium of exchange can fluctuate with markets. The supply and demand for a medium of account is regulated by a legal authority.

Just to clarity. In Ritwik's example the price of haircuts is fixed relative to gold. Which means that the price of haircuts can float with respect to silver. In my class action lawsuit example, all claimants would be paid in gold at a fixed rate, even if they paid differing amounts of silver for the same haircut.

I think the important thing is how people think about prices.

Say workers started valuing everything in terms of the price of coal but dollars are still used for all transactions. The demand for coal increases. Workers ask for a pay rise in dollar terms to bring their coal salary back up to where it was but employees can't meet these demands because of some fixed price contracts (in dollars) that they have in place with buyers. Some workers quit as a result of this drop in their coal wages and RGDP falls. A rise in the demand for the workers MoA has caused a recession.

Nick, I'm trying to understand where you and Scott diverge.

Your assumption is that Emperor Diocletian has issued an edict forbidding any price changes. Ph and Ps are fixed. But Scott seems to be assuming that Ps quickly moves while Ph is fixed. I'm taking this from his initial Zimbabwe example.

Scott: "...suppose that Zimbabwe was on the gold standard at the same time that soaring gold demand in Asia was pushing its value up, relative to other goods and services. Zimbabwe would experience deflation. If the wages of Zimbabwe gold miners were sticky in gold terms, then the diamond mine would have to lay some of them off."

Does that make sense? I don't have a horse in this race. Just trying to isolate the differences.

Ok. Just read Scott's second. You two have seem to cleared it up in the comments.

"Thought-experiment 2. Start in equilibrium, hold all prices (update: both Ph and Ps) fixed, then halve the stock of silver (medium of exchange). What happens?"

Flip that! Double haircuts then "temporarily" double medium of exchange (currency plus demand deposits). "Stable". Next, halve medium of exchange (currency plus demand deposits). What happens?

This is not about the legal authority. This is not about any further complications to the model.

Within Nick's model, with gold as the unit of account, what does the *market* for gold looks like?

In (Q,P) space:

Demand curve : P = 1.
Supply curve : P = 1.
Equilibrium price level: 1
Equilibrium quantity : indeterminate.

I dare anyone to create demand and supply curves for the unit of account that differ from mine and are not logically absurd. In any state of the world.

You could say that hence, we can see that the supply and demand of gold have cleared the market for gold at price = 1. That would be a very weird of looking at things.

In a world where only haircuts are traded and gold is the unit of account, when 1 haircut = 10 golds, what is the price of gold? It is 0.1 haircuts. When 1 haircut = 5 golds, what is the price of gold? It is 0.2 haircuts. Do we need supply and demand curves to understand this? No.

The unit of account is the reciprocal of the price level. This is a definition. It is defined, not determined in some market.

I don't know if I can explain this any better.

Nick, your model is missing an equation:

1.5 G = Ps.S

(with the velocity of circulation of S in the gold market fixed at 1)

Your system, on the other hand, makes it look as though gold is traded directly for Y. Holding Ph constant and halving G, equilibrium would be restored as follows:

excess demand for gold -> cleared by halving Y in the gold market
-> resulting excess supply of silver -> cleared by halving Ps (?)
-> Y = Y*/2

Your k function also ignores demand for silver, except as a proxy for demanding gold. (What about holding inventories of the medium of exchange?) In your model, people can't hold bigger silver-balances, unless they also want to buy more gold in exchange for Y.

I would distinguish between the velocity of spending silver on gold, and the velocity of spending silver on goods.

Suppose the the circulation of silver in the gold market increases, without increasing the price of haircuts. This would drive up the silver price of gold.

But there is a gold price peg. So the quantity of silver has to be reduced to restore the original price of gold.

Anticipating this, the market increases demand for holding S, via asset prices and bond yields (the Chuck-Norris self-fulfilling prophecy). This time, reduced velocity of circulation of S reduces the price in terms of silver in both the gold market and the haircuts market. The silver price of gold comes back down to the pegged level. There is deflation and recession in the market where silver is traded for haircuts. (And the quantity of silver does not have to be reduced after all.)

The silver stock remains constant, as does the silver price of gold - but the "real demand for gold" can be said to have increased (because of the initial burst of silver-velocity in the gold market, pushing up the implicit exchange rate between haircuts and gold).

Isn't this something like what happened in the US Great Depression?

"The market where haircuts are traded using silver".

Ritwik, there is a market where gold is exchanged for silver. The demand for gold, in terms of silver, is Dg(S,1/Ps). The demand for silver, in terms of gold, is Ds(G,Ps). In each of these markets the supply curve is a vertical line at the fixed gold/silver stock (times its velocity of circulation in that market). The quantity of gold people want to buy with silver, is a function of the number of silver-units you have to pay for one unit of gold. This determines the gold-price of silver, and the silver-price of gold. It also implicitly determines the gold-price of everything else, which are what is posted on the stickers in the shops.

Saturos

Sorry, your comment is not clear. Silver is not the unit of account. You cannot denote prices in terms of silver. The (Q, P) space for EVERY market is (# of units, golds).

Ps is a price. 1/Ps is not a price.

But even if you're allowed to write the demand for gold in terms of silver prices, halving the fixed stock of gold does nothing in Nick's model because the demand for silver does not depend on the gold-price of silver, it only depends on the relative price of haircuts and silver. The silver/gold market is neutered by construction in Nick's model. In the real world, it does not exist. The real world has the same conclusion as Nick's model, but his model is still incomplete/ incoherent.

What Nick says is an *excess demand for gold* which is ineffective in doing anything can be parsed differently - you could say, Emperor Diclotian has reduced the demand for gold by fiat and made the excess gold disappear through magic.

The independent gold demand and gold supply that Nick pretends to have in his model simply doesn't exist. The price of gold is defined as one, not determined in some market to be one.

Ritwik: "Ps is a price. 1/Ps is not a price."

Yes it is. It is the price of gold in terms of silver.

Take a simple non-monetary model, with 2 goods: apples and bananas. We can draw a supply and demand curve diagram for apples with the price of apples in terms of bananas on the vertical axis, and the quantity of apples on the horizontal. Or we can draw a supply and demand curve diagram for bananas with the price of bananas in terms of apples on the vertical axis, and quantity of bananas on the horizontal. There is only one price in this model, but there are two ways of writing it. One is just the inverse of the other.

Saturos: "Nick, your model is missing an equation:

1.5 G = Ps.S

(with the velocity of circulation of S in the gold market fixed at 1)"

You lost me there. But yes, I was making an implicit assumption that people are identical so that gold is not traded in equilibrium, so we can ignore gold transactions when we talk about the demand for silver money.

Nick

Sorry, I think we're just talking past each other. 1/Ps = 1/ (Ps). I get that. It is a tautology, not an independent determination in a separate market. That was my original point.

Let's focus on the silver-gold market, since that seems to be the critical point of difference.

1. What is the demand curve of gold in this market? Give us the equation. Any equation. Not the equilibrium demand-supply condition. Just the demand curve.

Nick, to me this notion of a medium of account just introduces a layer of confusion. It can't possibly be "what matters" in monetary analysis, since it seems entirely possible for a monetary system to exist in which there is a medium of exchange and a unit of account, but in which the units are not units of some substantive medium for which there can be any supply or demand. We could have an economy in which prices are conventionally posted in some abstract unit - say "valors" - and in which bits of several substances like silver, gold, platinum and bronze are used as the media of exchange, but where it is impossible to obtain a valor. Market forces determine the exchange rates of of gold, silver, platinum and bronze among themselves, and all four metals are universally accepted in exchange. Market forces (or something else if we have a command economy that establishes prices) also concurrently determine the number of valors represented by each of the metals, consistent with the aforementioned exchange rates and the valor price of any haircut, apple, etc. But there is no demand for valors in themselves, because you can't have one. You can have 10 valors worth of gold and give ten valors worth of haircuts, but that's it.

Ritwik: Gd = k.Ph.Y is the desired stock of gold in equilibrium (i.e. when the desired stock of silver equals the actual stock). I would have to do some work to figure out the demand function when the economy is out of equilibrium.

The indirect utility function would be something like U(G/Ph , S.(Ps/Ph) , haircuts consumed, haircuts produced).

(I have stuck money in the utility function because holding more money means less disutility from running around the forest faster trying to find a customer more quickly.)

But I'm not feeling up to doing the math. It would be like Barro and grossman 1971, except for the gold jewelry.

Nick, The key difference is that I assume the gold market is always in equilibrium (when traded for silver). If it isn't, it no longer serves as the medium of account in any meaningful sense.

Scott, what if there were no silver? Then if the gold market is always in equilibrium, then there are no recessions, as the price level is also perfectly flexible.

Suppose prices adjusted only partially to the excess demand for gold. The rising value of gold lowers the price level. So gold is still working as a MoA. But the remaining excess demand for gold, which doesn't clear, does not cause a recession. If there is no MoE.

Nick, my fourth equation was:

G = Ps.S

(I shouldn't have tried to number it, it came out bad.)

Assuming that gold and silver have the same velocity of circulation in that market. Then the gold-price of silver equals G/S. (Similarly, MV = PY means that the price level P equals the money/gold stock times its circulation, divided by the supply of real output (each bought once).)

"But yes, I was making an implicit assumption that people are identical so that gold is not traded in equilibrium, so we can ignore gold transactions when we talk about the demand for silver money."

Nick -

Gold must still be traded in comparative statics, as you move to the new equilibrium. How else would Ps adjust? You need an equation for the gold - silver market. If I were writing the model, I would make it correspond more closely to reality. I would have an equation for the G-S market. I would have an equation for the S-Y market. And I would have the Y-Y* equation. I would not calculate Ph directly; I would impute it from G-S <-> S-Y.

Then you would also be reminded that there are two (relevant) demands for silver. The demand for silver in terms of gold. And the demand for silver in terms of Y.

And the demand for silver in terms of Y is also split in two: the demand to buy silver with Y (haircuts), but only to immediately turn to the gold market and sell silver for gold. And then there is the demand to hold larger silver-balances.

Because silver, unlike gold, is a MoE, and is subject to a HPE, and a reverse-HPE. Which affects the silver-price of Y, and the silver-price of gold. If the two are effectively, then there is no net effect on Ph (the gold-price of Y). But if silver increases circulation in one market more than another, perhaps to increase the real demand for gold - then silver velocity affects both the silver-price of haircuts, AND the gold-price of haircuts, Ph.

Nick

I wasn't asking for anything that complicated or an equilibrium condition. Just the demand curve. An equation like y = ax + b, if you will. (I'm using y throughout to express an equation, not in terms of the haircuts produced and consumed Y)

Don't you always remind people that the demand curve is not quantity demanded - locus of points, not a single point?

Here's my equation for the set of constraints you mention in your model - with or without jewelry.

Demand curve for gold in (x,y ) = (quantity, price in terms of silver) space is:

y = 1/Ps. True for any Ps.

It's an infinitely elastic demand curve. In other words, it isn't a demand curve at all. It's Emperor Diclotian's monetary regime.

The unit of account is not a market. It is the inverse of the price level. In every market.

The silver-gold market in your model is irrelevant if the price of silver in gold terms is not allowed to change. If it is allowed to change - i.e the demand curve is not infinitely elastic or fixed by fiat - then a halving of the gold stock will drop the price of silver- relative to both gold and haircuts - increasing its demand relative to haircuts and effects similar to your thought experiment 2 will result. (There's no reason why the price of haircuts should respond to a halving of the stock of gold,since there's no gold-haircuts market)

A central bank that raised its gold demand in a gold standard world is hiking the real short rate. This is true whether it raises the bank rate to attract more gold (as in the Bank of England) or engages in outright purchases that cause deflation (Bank of France).

In other words, an action on the unit of account is essentially a modification of the monetary/price regime. This is very similar to your gold standard = CPI standard point. I'm not sure why you insist on creating a *market* for the unit of account. This market does not exist. And even when it existed under a commodity standard, it wasn't relevant any more than what it conveyed about the monetary regime.

"If the two are equally affected, then there is no net effect on Ph (the gold-price of Y)"

is what I meant.

Scott: If the price of the MOE is perfectly flexible, and adusts 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.

Even if Ps is fixed, and you cannot buy gold, it is still possible to use gold as a MOA. Suppose US visitors to Canada were not allowed to buy Canadian dollars, and had to pay with USD. Canadian stores could still post prices in CAD.

Ritwik, the demand for buying gold with silver is a function which is:

Positively related to the stock of silver S (one-for-one)
Negatively related to the demand for holding silver-balances (and positively related to the demand to exchange haircuts for gold)
Positively related to Ps, the gold price of silver (negatively related to 1/Ps, the silver price of gold). But not necessarily one-for-one, as there could be substitution effects.

So Dg = S * F(-k(S), Ps)

But a polynomial expression would be arbitrary and spurious.

Ritwik, the MoA does have a market. Suppose the price level is 100. If you found a commodity in the consumption basket, in GDP, whose price was actually 100, this commodity would have a direct exchange rate with the MoA of 1/100. One MoA buys 1/100 of that commodity.

OTOH a unit of account need not actually be a commodity on a market. You could take a barter economy and arbitrarily decide that its price level was 8625897. You could than assign common prices to each commodity by calculating the relationship between every relative price and the price level.

Dan: IIRC, a guy called Eunadia? wrote a book on imaginary monies, ages ago. About imaginary media of account. They usually occur when the coins are all very bad, so the value of each coin has to be assessed against some perfect coin, but there are no perfect coins. I can't decide if that's a genuine case of a truly imaginary MOA.

University grades are an example of an imaginary MOA. What does "B" really mean? We know it's less than A and more than C, but what pins down the absolute values of the whole set of grades? "Custom" seems to be the only answer.

Same with languages. What pins down the meanings of words? Again, custom.

The problem with imaginary MOAs is that there are multiple (a continuum of) equilibria. Double all prices in terms of venus dust (Peter Howitt's example) and nothing changes. There is no nominal anchor to the system.

The Wickseelian POV is that monetary systems evolve towards an imaginary MOA.

Fascinating topic, but one I want to stay away from in this post. Because it's fairies, all the way down.

"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."

Yes. But I think you mean the nominal stock of MoE. Or the effective stock.

Saturos

Ok, this is getting a bit exasperating. Why is the distinction between definition and derivation so hard to explain?

"Suppose the price level is 100. If you found a commodity in the consumption basket, in GDP, whose price was actually 100, this commodity would have a direct exchange rate with the MoA of 1/100. One MoA buys 1/100 of that commodity."

This the definition of MoA. It's the inverse of the price level. Price level is the inverse of one unit of MoA. Twist, rinse and repeat, in as many permutations as you'd like to. You aren't saying anything new. If you want to explain to me that 0.2 = 1/5 and that 10 = 1/0.1 in many different ways, sure, go ahead, but that's not interesting and does not even begin to address my challenge. Nick's commodity model is half-interesting because there exists a hypothetical market there in which we could talk about the *demand for the medium of account* and I was showing that this demand does not really exist, it is simply a way of expressing the monetary regime.

Don't believe my polynomial expression. Draw a new one. Just make it conform to Nick's model above and see what happens. Btw, there's no demand to exchange haircuts for gold, because haircuts can't be exchanged for gold.

Somewhere, deep inside, you have the intuition that the medium of account is a thing, like currency notes. It isn't. Under a gold standard, it was a real thing, but as Nick showed, the thing-ness of it doesn't really matter. All that matters is the implied monetary regime.

Ritwik,

"This is not about the legal authority. This is not about any further complications to the model."

Uh, yes it is because of this statement from above:

"All prices are quoted in ounces of gold. Just because that's the custom (and I can't think up a silly story to motivate it.)"

Here is the not so silly story to explain why prices are quoted in ounces of gold - the legal authority is a price setting mechanism in terms of the medium of account.

Any unit of account (pound, ounce, kilogram, meter) has some authority figure behind so how you know when you have a pound of something or have traveled a distance of one meter.

"This is not about any further complications to the model."

A legal authority standing behind the definition of a unit of account is not a complication, it is a requirement.

"The unit of account is the reciprocal of the price level. This is a definition. It is defined, not determined in some market."

Defined by who - a legal authority?

Frank

With that, I can agree. 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. Legal authorities are often efficient solutions for questions of commercial legitimacy, but sometimes they aren't.

So apart from stressing on the commercial legitimacy bit, I think we're in agreement.

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.

Ok Nick.

But where do you disagree with my y = 1/Ps demand curve for gold demand in your model?

Nick, I'm not sure that the concept of an imaginary medium of account helps here. I suppose there could be such a thing as an imaginary medium that is exchanged by convention, and the imaginary possession of which is tracked with careful bookkeeping. But in the example of valors, the valor is not a unit portion of any kind of medium, real or imaginary. It's a coordinating unit of measure which is applied both to commodities and the media of exchange. You can obtain, demand and exchange haircuts, gold, silver, etc. But you can't obtain a pure valor. You can only obtain a valor's worth of other stuff.

I'm not saying there can't be such a thing as a medium of account in addition to a unit of account. But it seems to me that you can also have perfectly understandable monetary systems in which there is a unit of account that is not a unit of some medium, real or imaginary. And if that is possible, the concept of the medium of account can't be fundamental.

Ritwik, your equation appears to be saying that the quantity of gold demanded equals the silver price of gold... I disagree with that...

Saturos, the equation says that any amount of gold can be demanded at the fixed silver price of gold. A necessary implication of Emperor Diclotian's edict that Ps is fixed. It's all there in Nick's model.

"Btw, there's no demand to exchange haircuts for gold, because haircuts can't be exchanged for gold."

Yes, I made that criticism too. It's an implied demand, of course, but he shouldn't model it that way.

Ritwik, now that you agree that the MoA is a real thing exchanged on a market (gold, in this hypothetical scenario), why can't you see a demand curve for it, just like the actual demand curve for gold in our world?

In fact, if we got everyone in the world to agree, we could do it right now. Everybody keeps using the same media of exchange. But from today onwards, the price of everything is quoted in terms of its implicit exchange rate with gold. Gold then becomes the medium of account.

Would gold then cease to exist? Or would it cease to have a demand curve?

Dan: I'm not at all sure if we are agreeing or disagreeing here.

Think back to my old unobtainium post. We could imagine a world in which all prices were quoted in ounces of unobtainium. If all prices were perfectly flexible, that would make the price level indeterminate. But the fact that there is an excess demand for unobtainium doesn't cause a recession. If prices were sticky, the central bank could cause a recession by reducing the supply of the MOE.

Ritwik: "But where do you disagree with my y = 1/Ps demand curve for gold demand in your model?"

Do you mean Gd = 1/Ps ?? If so, that's a very strange demand curve. It slopes up. It says the quantity of gold people want to hold is proportional to the price of gold in terms of silver. I can imagine a demand curve Gd = Ps. It says that people want to wear a quantity of gold worth one ounce of silver. That wouldn't change my model much, except you would now need equation 2 as well as 1 and 3 to determine Ph.

I'm probably still not getting it.

Nick

It's a horizontal demand curve. It's drawn in (quantity of gold, price of gold in silver) space. The y axis is the price of gold, not the price of silver - surely the only y axis that is sensible if we want to draw a demand curve of gold.

Saturos, the equation says that any amount of gold can be demanded at the fixed silver price of gold. A necessary implication of Emperor Diclotian's edict that Ps is fixed.

It most certainly is not. Ignore Nick's model; it's badly put. I think you have the same problem with it that I do; it doesn't actually determine the endogenous variable Ps, he simply assumes the appropriate changes.

The demand for gold in terms of silver is a function of the size of the stock of silver, and how often that stock circulates in the gold market. It is not infinite, even at a fixed disequilbrium price of gold.

It's Diocletian, btw. (But at least you get my handle right.)

Ritwik: "Saturos, the equation says that any amount of gold can be demanded at the fixed silver price of gold. A necessary implication of Emperor Diclotian's edict that Ps is fixed. It's all there in Nick's model."

No! The fact that Diocletian fixes the price does not mean that people who hold gold are forced to sell to anyone who wants to buy. They can just say "no". Diocletian doesn't force them to sell gold. He just says that *if* they choose to sell, it must be at the price Ps in the edict.

Nick: yes, you do need equation 2 to determine Ph, as well as a demand curve for gold in terms of silver, such as my fourth equation. (Not Ritwik's, though.)

Otherwise you "determine" Ph whilst leaving Ps undetermined.

Ritwik: If you put 1/Ps (or 1/Ph) on the vertical axis, the demand curve for gold would not be horizontal. It would only be horizontal if gold were a perfect substitute for silver 9or haircuts). It isn't.

Ritwik: Ah, I understand your equation now. You are saying that y, the price of gold in terms of silver, equals 1/Ps, the price of silver in terms of gold.

I don't know where you learned economics, but THAT IS NOT A DEMAND CURVE.

If gold and silver were perfect substitutes, I would replace my 1 and 2 with:

G + S.Ps = 2k.Ph.Y ("We want to hold 2k haircuts' worth of precious metals, but don't care if it's gold or silver")

Saturos

I'm not *agreeing* it's a thing. I'm going along to humour Nick's model.

Nick

What does a demand curve have to do with people being forced to sell??!!

Horizontal demand curve. Y-intercept at 1/Ps. No x-intercept. Has the property that when the supply (or stock) of gold changes, the price doesn't change.

And my model would then leave Ps and Ph indeterminate.

No Ritwik. No no no.

Your equation does NOT say that. Your equation does not have a term for "quantity demanded".

Your equation says that the price of gold (the inverse of the price of silver, as we already knew) is equal to itself.

Ther could be any sort of relationship between the price of gold and the quantity of it demanded. And your equation would still be true.

We have a regular Math Olympian here.

Saturos

1/Ps is the price of gold in terms of silver. You've got it the wrong way round. Calm down, and draw the curve.

Nick

You can build a standard downward sloping demand curve. And then impose a price control at 1/Ps. Doesn't matter. The Emperor-Diocletian-compensated-demand-curve is horizontal. The excess demand for gold when its stock is halved is an artifact of the model, visible only to the model builder. To us mere observers of the model, the demand curve is simply horizontal.

Saturos

Indeed my equation says that the price of gold is equal to the price of gold. Quantity is indeterminate, determined completely by quantity supplied. The demand curve is horizontal. Any 'true' downward sloping demand curve is only visible to Nick (and perhaps you). I cannot observe them because of Emperor Diocletian's edict.

Ritwik: What does Y represent? The price of gold in silver terms? And x is the quantity demanded?

You say that the y-intercept (when 0 gold is demanded) is 1/Ps.

Now, Ps, is by definition, 1/Y. Depending on whatever Y is.

Where shall I draw your Y intercept?

If I drew a downward sloping straight curve, slope -1, then at every point on that curve Y would be equal to 1/Ps.

Your equation is, for lack of a better word, stupid.

Oh dear god. Ps is the exact price at which Diocletian has fixed the price of silver. Let's say that price is 1 gold = 2 silver.

The demand curve is y = 1/2.

When Emperor Diocletian changes the price to 1 gold = 3 silvers, the demand curve drops to y = 1/3.

The demand curve for gold is the Emperor's monetary regime. Nothing more. Nothing less.

Ritwik: If your equation says that the price of gold is equal to the price of gold, then it does not say that quantity is indeterminate. It doesn't say anything about the quantity at all.

Otherwise Newton's Law of Gravity would state that the length of my middle finger is indeterminate.

Stop pretending that what you said wasn't idiotic.

Okay, I'm sorry. I may have gone too far there. I've been posting comments non-stop for three days trying to get Scott Sumner to see reason. I'm a little bleary. And I just can't stand the abuse of mathematics.

Ritwik: there are two ways to fix an exchange rate:

1. The Canadian way. The Bank of Canada offers to buy or sell unlimited quantities of CAD for USD at a price of 1. It adjusts the supplies S and G to make sure that Pg/Ps=1 is always the equilibrium price

2. The Cuban way. The Bank of Cuba makes it illegal to sell pesos for dollars except at a price of 1.

In my model, Diocletian uses the Cuban way. G and S are fixed. Diocletion doesn't trade G and S.

"The demand curve is y = 1/2."

OK. I see what you're saying. There is no relationship between the quantity demanded and the fixed price of gold. If Ps is an exogenous constant.

Why on earth would that be true? How on earth would people demand 10000000000000000000 ounces of gold, with only 1000000 available units of silver, circulating a handful of times? And yet your demand curve says it is possible.

The Canadian way creates a horizontal supply curve for gold in terms of silver, that intersects the downward-sloping demand curve. In my model, both supply curves are vertical. S and G are exogenous.

Saturos

It's alright. But just step back for a moment, and draw a horizontal demand curve.

In period 1, Diocletian decides that the gold price of silver is 5 silvers/ gold. The gold demand curve of that period is y =0.2

In period 2, Diocletian decides that the gold price of silver is 10 silvers/ gold. The demand curve of taht period is y = 0.1

In period 3 Diocletian decides to let the prices of period 2 remain. The demand curve of that period continues to be y = 0.1

For every given monetary regime of Emperor Diocletian, there exists a demand curve for gold that corresponds to his regime. Each of those demand curves is horizontal.

A demand curve with slope -1 does not have the property that the price remains constant when the supply changes. It does not conform to Nick's model.

It's far easier to abuse words than it is to abuse mathematics. *demand and supply of medium of account* is precisely such an abuse.

Saturos: "Okay, I'm sorry. I may have gone too far there."

You did. But you apologised. Take it easy. Rome wasn't argued for in a day.

Actually Ritwik, your old equation was still meaningless. With a normal demand curve and fixed price, Y = 1/Ps is still true - within the domain c - 0.0001 < x < c +0.0001. Your statement required you to specify the infinite domain

Nick, yes, I know. I need to calm down. I hope I haven't offended Ritwik too much. I'm going to get some sleep now.

Please read the other comments I left you though.

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