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 
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.