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.)
Scott Sumner argues that it is the medium of account function that matters. My view is different. Here is my view:
Demand and supply of the medium of account determine the equilibrium price level.
Demand and supply of the medium of exchange determine whether the economy is in a boom or a recession.
[Update: Scott responds.]
Here is a simple model, where one good (gold) serves as medium of account, and another good (silver) serves as medium of exchange.
[Update: just to clarify terminology: in my model, gold is the medium of account; and (say) an ounce of gold is the unit of account.]
The third good is haircuts. Haircuts come in different styles. Styles of haircuts are located on a circle. Each person can only produce one style of haircut, located at one exogenously fixed point on the circle. Each person prefers some other style of haircut, located at some other point on the circle. He gets less utility from a haircut the further away is the style from his most preferred point on the circle.
This silly story does three things: it motivates trade in haircuts (you don't like your own style of cutting hair); it motivates monetary exchange in haircuts (you probably don't like the style of someone who likes your style, so barter won't work unless everybody gets involved); it motivates imperfect competition (so you can get booms as well as recessions, since price will be above marginal cost in equilibrium).
There are two markets: a market (more exactly, a continuum of markets for different styles) in which haircuts are traded for silver; a market in which gold is traded for silver. Nobody trades haircuts for gold, because:
Gold is worn as jewelry. 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!" There is a demand for a real stock of gold, which depends positively on income from selling haircuts.
Silver has no other use except as a medium of exchange. Because people meet at random, they need to keep an inventory of silver in case they suddenly meet someone who can cut their preferred style but don't meet anyone who prefers the style they can produce. There is a demand for a real stock of silver, which depends positively on income from selling haircuts.
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.)
The exogenously fixed physical quantities of gold and silver are G and S, the price of haircuts in terms of gold is Ph, the price of silver in terms of gold is Ps, and annual income from haircuts is Y haircuts.
Full equilibrium is defined by three equations:
1. G = k.Ph.Y (supply of gold = demand for gold)
2. S = k.(Ph/Ps).Y (supply of silver = demand for silver)
3. Y = Y*. A third equation which determines the equilibrium number of haircuts produced, depending on the marginal utility of getting a haircut, the marginal disutility of giving a haircut, and the markup of price over marginal cost, which depends on elasticity of demand for a particular style of haircut.
Note that I have assumed that the demand function for gold is identical to the demand function for silver. The only difference is that Pg=1 by definition.
Note also that I have used the Cambridge "k", rather than the Fisherian "V", approach. Rewriting the equation as S.V=(Ph/Ps).Y makes sense for silver, which circulates as the medium of exchange. It does not make sense for gold.
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.
But what determines Y when we are out of equilibrium, because the Emperor Diocletian has issued an edict forbidding any price changes?
Thought-experiment 1. Start in equilibrium, hold all prices (update: both Ph and Ps) fixed, then halve the stock of gold (medium of account). What happens?
There is an excess demand for gold in the gold market, but nothing else happens. The market for haircuts continues as before. 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. The production and sale of haircuts for silver continues just as before, because there is no change in the relative demands for silver and haircuts. There is no change in the marginal utility of silver, the marginal utility of getting a haircut, or the relative price of haircuts and silver Ph/Ps. So trade of silver for haircuts continues just as before.
An excess demand for the medium of account does not cause a recession.
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?
There is an excess demand for silver. People want to sell some of their gold for silver, but they can't, because nobody wants to take the other side of the trade. People want to sell more haircuts for silver, but can't, because nobody wants to take the other side of the trade. People want to buy fewer haircuts for silver, and they can, because nobody can stop you buying less of something.The quantity of haircuts bought falls, until the marginal utility of haircuts increases by the same proportion that the marginal utility of silver increased when the stock of silver fell. The quantity of haircuts sold will halve.
An excess demand for the medium of exchange causes a recession.
The medium of exchange is different from other goods, because everybody both buys it and sells it. If you want more, and can't buy more, because everybody else wants to do the same thing, you just sell less. And when people sell less medium of exchange, they buy less other goods, which means a recession.
Worthwhile Canadian Initiative 
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: http://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
http://www.jstor.org/discover/10.2307/4225324?uid=3739464&uid=2129&uid=2&uid=70&uid=3737720&uid=4&sid=21101324241681
or
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”.