MOE vs MOA: the battle of the paintings

I used to think that whoever controlled production of the Medium of Account controlled the price level. Now I think that's wrong. Unless the Medium of Account is also the Medium of Exchange.

In an economy with a single MOA, and with n goods, there are only n-1 prices. (And in an economy with a single MOE, and with n goods, there are only n-1 markets.)  The producer of every other good sets the price of his good, and can lower his price if he wants to sell more of his good. But the producer of the MOA cannot lower his price to sell more MOA. Because there are only n-1 prices. He can only sell more MOA if the demand curve for MOA happens to shift to the right.

But if the MOA is also the MOE, the producer of the MOE/MOA doesn't need to lower his price to sell more MOE/MOA; he just buys more of any of the n-1 other goods. The producers of those n-1 other goods will eventually choose to raise their prices, because the quantity of the MOE/MOA has increased.

Money really is weird.

I hold a monopoly on the production of paintings signed by Nick Rowe.

The Bank of Canada holds a monopoly on the production of paintings signed by the Bank of Canada.

Assume the police equally prosecute counterfeiters both of my paintings and of Bank of Canada paintings.

In the real world, Bank of Canada paintings are used as a medium of exchange (MOE) -- every other good is bought and sold for Bank of Canada paintings. And Bank of Canada paintings are used as a medium of account (MOA) -- people set prices of all other goods in Bank of Canada paintings.

Nick Rowe paintings are neither MOE nor MOA. But assume that my paintings are a valuable asset, because people want to hang them on their walls. Simply because they've got my signature on them.

Suppose, for some unknown reason, I wanted to lower the equilibrium price of my paintings, relative to all other goods. That would be very easy for me to do. I simply lower my asking price for new paintings, so the quantity demanded increases, so I sell more, and so the stock of my paintings in public hands increases.

Now suppose my paintings were the MOA. All other goods, including the MOE produced by the Bank of Canada, are priced in terms of my paintings. The Bank of Canada promises to exchange a $20 Bank of Canada note for 20 of my paintings. Canadian supermarkets advertise prices in terms of the number of my paintings, but only accept Bank of Canada paintings in payment. Canadian firms and workers negotiate wage contracts in terms of the number of my paintings per hour of labour, but pay wages in Bank of Canada paintings.

Suppose again, for some unknown reason, I wanted to lower the equilibrium price of my paintings, relative to all other goods.

Can I do it? The Bank of Canada sets the price of my paintings in terms of the medium of exchange. Canadian supermarkets set the price of my paintings in terms of apples and bananas. Canadian firms and workers set the price of my paintings in terms of labour. I don't set the price of my paintings.

To lower the equilibrium price of my paintings, relative to other goods, I need to increase the stock of my paintings in public hands, and to do that I need to sell more paintings, and to do that I need to increase the quantity demanded, and to do that I need to lower the price of my paintings. I'm right back where I started. Can I break out of this circle?

I only sell my paintings for the MOE, because everybody buys and sells everything only for the MOE. What happens if I say my paintings are worth only 50 cents, but the Bank of Canada insists that one of its dollars is worth one of my paintings? People would buy my paintings at 50 cents from me, and sell them to the Bank of Canada for a dollar. Or maybe I could even say my paintings are worth nothing, and simply give them away for free. Helicopter paintings.

Who would win the game of arbitrage: me or the Bank of Canada? Would the Bank of Canada be able to print dollars faster than I could print paintings? Who knows. And if our printing presses are evenly matched, then all that is happening is that my paintings are accumulating in the Bank of Canada's basement, and the Bank of Canada's paintings are accumulating in my basement. The quantitity of MOA in public hands is unchanged.

I control the MOA. The Bank of Canada controls the MOE. Who controls the Canadian price level: me or the Bank of Canada?

It would be really easy for the Bank of Canada to reduce the equilibrium price of its paintings. All it has to do is to cut the price of its paintings in terms of my paintings, to increase the quantity demanded, and sell more of its paintings, and increase the stock of its paintings in public hands. But that doesn't raise the prices of apples in Canadian supermarkets, because those prices are measured in my paintings.

It would be really easy for me to reduce the equilibrium price of my paintings, if I could increase the stock of my paintings in public hands. But can I actually do that? Not unless I can force the Bank of Canada to abandon its fixed exchange rate policy, and devalue its paintings.

Comments

[Nick Edmonds]

If the Bank of Canada promises to exchange a $20 BoC note for 20 of your paintings, presumably in whatever amount is tendered, in what sense do they control the MoE? Surely you do? You can put as many BoC notes into circulation as you want.

[Alex Godofsky]

Nick, in our world case the producer of MOA does get exchange it in a few markets. Not n-1 markets (generally), but in m << (n-1) markets. One of those is the market for bonds. More generally, a lot of financial assets. The producer of MOA has a harder to exchanging it for real goods and services in any large quantities.

The reason MOA is important is because it's nominal (i.e. MOA-denominated) prices that are sticky. If cows were our MOA but we used barter we could still get recessions from a shortage of cows if people did not update their cow-prices properly.

[Mike]

What is n-1 prices? Could someone explain it in a different way?

[Scott Sumner]

Nick does your example involve a dual MOA (in the sense that gold and currency were dual MOA under the gold standard?)

[Benoit Essiambre]

I can offer you ten canadian dollars for a N.Rowe signed portrait of sir John A Macdonald, twenty for a portrait of the Queen.

[Nick Rowe]

Nick Edmonds: Dunno. Maybe, but the Bank of Canada can always take them out of circulation again. Who would win??

Alex: Sure, sticky prices are one reason the MOA may be important. But if I can't control the quantity of the MOA, how can I be powerful?

Let's stick to the assumptions I laid out. There is one MOE and one MOA. This is hard enough already.

Mike: assume n=3. Abel has a monopoly on producing apples, and sets the price of apples in terms of carrots. Betty has a monopoly on producing bananas, and sets the price of bananas in terms of carrots. Carol has a monopoly on the production of carrots, but cannot set the price of carrots. The price of carrots in terms of apples is by definition the reciprocal of the price Abel sets. The price of carrots in terms of bananas is by definition the reciprocal of the price Betty sets. There are only 2 prices. Carol cannot set her price.

This means we cannot logically solve for the 3-player Bertrand-Nash equilibrium to this game. There are 3 goods, but only 2 prices. Carol cannot play Bertrand. She can't even play Cournot, if Abel and Betty play Bertrand.

Scott: I don't think so. I don't want it to. I want my paintings to be the only MOA.

[Nick Rowe]

Put it another way: when we say that the nth good is the MOA, we mean that the producer of the nth good cannot play Bertrand, but that the producers of all the other n-1 goods play Bertrand.

If the MOA is also the MOE, the producer of the nth good can play Cournot.

If the MOA is not the MOE, and the 1st good is the MOE, the producer of the nth good can only play Cournot against the producer of the first good.

When we specify which goods are MOA and MOE, we are also specifying the strategy-space.

[Benoit Essiambre]

There are some semantics at play here because the Bank of Canada act of stockpiling your paintings in their basement means taking control of the MOA not just the MOE.

The way I see it, at some point it's going to be about which party the public trusts more to be able to control prices and if there is too much of a fight between the two parties causing too much uncertainty in the value of the mediums people are going to move to a third option. These can only be imposed to a certain degree.

The problem is reduced to the costs, willingness or physical limits of creating paintings and maintaining a strict exchange rate.

This reminds me of a electrical circuit puzzle with a simple circuit where two capacitors are wired together with a switch in between, one is charged the other is not. When you close the switch the energy flows from the full capacitor to the empty one and they both end up at half the initial voltage of the full one. But since energy is proportional to voltage squared, they each end up holding just of quarter of the initial energy for a total of half the energy. Where did the other half energy go? If you analyse this simple circuit it only leads to paradoxical results. The answer is that the idealized wires between the capacitors you used for the calculation do not exist in the real world. Any real physical wires will have some resistance and inductance however small, in this particular configuration the closing of the switch will make a rather violent current spike which will result in dissipation of the extra energy in the wires. These type of problems boil down to bringing back into the model physical constraint that can't be ignored.

[Scott Sumner]

Nick, In that case the MOE price of MOA will fluctuate. And the MOA market will determine the price level.

[Nick Edmonds]

"Who would win??"

If you mean who controls the overall price level, then l think the answer is that it depends on the actions of both.

If the BoC prints more MoE and spends in on other (non-MoA) goods, both MoA denominated prices of other goods and demand for MoA will go up (purely because your paintings are now cheaper than other stuff). The BoC will have to supply more MoA to meet demand, draining some MoE (assuming they have sufficient stock of it - otherwise they can't hold the price). We end up with more MoA and higher prices of other goods, but how much of each depends on elasticities.

It's a similar story, but a different starting point, if you printed more MoA and exchanged it for MoE with BoC.

[Nick Rowe]

Scott:

But what is happening in the market where my paintings are traded for Bank of Canada paintings? Who is setting what?

1. If the Bank of Canada does not play Bertrand (if it does not set, at least temporarily, a price of its paintings in terms of my paintings) then can we say that my paintings are the universal MOA? I don't think we can.

2. If I play Bertrand, and set the price of my paintings in terms of Bank of Canada paintings, and lower that price in order to sell more of my paintings, then I have just made Bank of Canada paintings the MOA. Everyone else defines their prices in terms of my paintings, but I define the price of my paintings in terms of Bank of Canada paintings, then by transitivity shouldn't Bank of Canada paintings be the MOA?

3. If both the Bank of Canada and I play Cournot, so I announce the quantity of my paintings I will sell for Bank of Canada paintings, and the Bank of Canada announces the quantity of its paintings it will sell for my paintings, then the public will be either buying or selling the difference, and the price will presumably be set by some Walrasian auctioneer.

Dunno.

[Nick Edmonds]

"And in an economy with a single MOE, and with n goods, there are only n-1 markets."

How does that work then if you want to look at more than one medium of exchange? Like, if you want to separately consider demand and supply for cash and for the balance of checking accounts. How many markets are there then?

[Nick Rowe]

Nick Edmonds: 2(n-2)+1 markets. But let's not go there. This is hard enough already.

[Philippe]

"Suppose, for some unknown reason, I wanted to lower the equilibrium price of my paintings, relative to all other goods. That would be very easy for me to do. I simply lower my asking price for new paintings, so the quantity demanded increases, so I sell more"

I'm not sure it works like that in the art market. Higher prices seem to create more demand.

[Philippe]

"Suppose, for some unknown reason, I wanted to lower the equilibrium price of my paintings, relative to all other goods. That would be very easy for me to do. I simply lower my asking price for new paintings, so the quantity demanded increases, so I sell more"

I'm not sure it works like that in the art market. Higher prices seem to create more demand in certain cases, whilst price cuts can reduce demand.

[Nick Rowe]

Scott: let me try it this way:

If the real world Bank of Canada has a fixed exchange rate against the USD, then it is the Fed that determines the Canadian price level. In a useful sense (as JP Koning I think argued once) we can say therefore that the USD is the Canadian MOA, because it is the Fed, as producer of the USD, that controls the Canadian price level.

Similarly, in my imaginary world, if all other Canadians set their prices in terms of my paintings, but I set the price of my paintings in terms of Bank of Canada paintings, then we can usefully say that Bank of Canada paintings are the MOA, because the Bank of Canada, as producer of Bank of Canada paintings, controls the price level.

(I know I'm on the scent of something, but I don't know what it is.)

Philippe: that may be true of other people's paintings, but isn't true of my paintings, by assumption.

[notsneaky]

assume n=3. Abel has a monopoly on producing apples, and sets the price of apples in terms of carrots. Betty has a monopoly on producing bananas, and sets the price of bananas in terms of carrots. Carol has a monopoly on the production of carrots, but cannot set the price of carrots. The price of carrots in terms of apples is by definition the reciprocal of the price Abel sets. The price of carrots in terms of bananas is by definition the reciprocal of the price Betty sets. There are only 2 prices. Carol cannot set her price.

This means we cannot logically solve for the 3-player Bertrand-Nash equilibrium to this game. There are 3 goods, but only 2 prices. Carol cannot play Bertrand. She can't even play Cournot, if Abel and Betty play Bertrand.

Hm, let's put some production in here. Constant returns, one primary factor, labor (and let's call "bananas" "corn" instead). Then there's also a market for labor so the MOA... oh oh, that way lies madness.

[Nick Rowe]

notsneaky: you lost me. Was that a subtle Sraffa reference? (I didn't think there was either a MOA or MOE in his models. The modeller could choose a numeraire, but the modeller's choice of numeraire isn't the same as the agents' choice of MOA.)

[JP Koning]

"Similarly, in my imaginary world, if all other Canadians set their prices in terms of my paintings, but I set the price of my paintings in terms of Bank of Canada paintings, then we can usefully say that Bank of Canada paintings are the MOA, because the Bank of Canada, as producer of Bank of Canada paintings, controls the price level."

That makes a lot of sense to me. We can introduce the term unit-of-account to refer to the symbol in which prices are expressed. People could denominate prices in the NR unit of account, short for Nick Rowe. The NR unit is defined in terms of something else (the MOA), namely one Nick Rowe painting... unless Nick in turn sets the price of one of his paintings in terms of X Bank of Canada paintings, in which case the MOA is now X Bank of Canada paintings. Now the NR unit is defined as X BoC paintings and the BoC effectively sets the price level. If the Bank of Canada in turn defines BoC paintings in terms of Fed paintings, then the latter are the MOA and the Fed determines the value of the NR, and therefore the price level.

So when you announce that your paintings are worth only 50 cents, you've changed the medium of account. Same unit of account as before though, the NR. Now my brain is all muddled up, though.

[Ritwik]

JPK

Agree with you, except for one bit. In your NR -> BoC -> Fed chain, the 'true' MoA is actually a function of where in the chain does credibility and independence, and hence fiat, reside. The rest is just arithmetic.

So for example if Nick has the ability to change 1NR from X BoC dollars to Y BoC dollars over a relatively short time with relatively few shocks, the act of pegging 1NR to X BoC $ does not actually make the BoC$ the MoA.

But of course you understand that, given your terrific posts on the actual implementation of the gold standard.

[Nick Edmonds]

"To lower the equilibrium price of my paintings, relative to other goods, I need to increase the stock of my paintings in public hands, and to do that I need to sell more paintings, and to do that I need to increase the quantity demanded, and to do that I need to lower the price of my paintings. I'm right back where I started. Can I break out of this circle?"

How about this? You print more paintings. You exchange them one for one with BoC for their notes. You spend their notes on other goods. If you do that in sufficient quantity, everyone adjusts their prices upwards. The only price that hasn't gone up is the price of your paintings, as this is fixed. As your paintings are now relatively cheap, people buy more (from you or BoC). You have reduced the price (at least relative to everything else) and sold more paintings.

[PeterN]

Nick Edmonds,

"how about this? You print more paintings. You exchange them one for one with BoC for their notes. You spend their notes on other goods. If you do that in sufficient quantity, everyone adjusts their prices upwards. The only price that hasn't gone up is the price of your paintings, as this is fixed. As your paintings are now relatively cheap, people buy more (from you or BoC). You have reduced the price (at least relative to everything else) and sold more paintings."

The BoC will start selling NR denominated bonds. If there is a demand for safe assets and the bank is buying up all the NR paintings, these bonds will soak up the money for a while unless and until the public doubts the bank's ability to service the debt or the demand is sated.

If Nick can outpaint the bank he'll eventually win, His cost is 0, the bank's isn't, merely small. A bank loss is currency revulsion and search for other media of exchange. The bank's rate is the "official" rate, and we've seen this movie before.

[Nick Rowe]

Peter N: "If Nick can outpaint the bank he'll eventually win, His cost is 0, the bank's isn't, merely small."

I think that can go the other way too. If the Bank can outpaint Nick, the Bank will eventually win.

What we have here is two players (me and the Bank), both trying to play Bertrand (set a price) where our two prices are contradictory. Each of us is trying to make the other's good the MOA. If I win, the Bank's paintings are now the MOA. If the Bank wins, my paintings are still the MOA. (It's a bit like two central banks, both trying to set contradictory fixed exchange rates, each trying to devalue against the other. Or two firms, each promising "we will not be undersold".)

[Scott Sumner]

When you have a fixed price between two monies, then both are in a sense MOAs. Thus in 1929 the US$ and gold were both MOA for the US. In that case it's an entirely pragmatic question; can we best understand what's going on with US NGDP by looking at the US currency stock or the global gold market. Most economists would say the US money stock, although I argued the global gold market is more informative. But there is no right or wrong answer.

If the price of the MOE and MOA are not pegged, then I definitely think the MOA is the dog and the MOE is the tail.

[Nick Rowe]

Scott: "When you have a fixed price between two monies, then both are in a sense MOAs."

I can see the sense in that. But I think it matters who does the pegging. There's a difference between the Bank of Canada pegging the Loonie to the USD, and the Fed pegging the USD to the Loonie. For example, the Bank of Montreal pegs its dollar to the Bank of Canada dollar, which makes the Bank of Montreal the tail wagged by the Bank of Canada dog, even if the Bank of Canada dog is much smaller than its many tails.

[JP Koning]

Ritwik, that makes sense.

Nick, your example of warring media-of-account makes me think of the bimetallic period of monetary history. The pound was described as a certain amount of gold or silver, but when silver was officially undervalued relative to gold in the late 1600s, silver was quickly exported elsewhere so that only gold circulated in Britain. I'm wondering if the BoC painting/NR painting story isn't similar to bimetallism.

[apt]

Can you actually say there are (n-1) markets? Is not there a market for the MOE itself, and therefore n markets?

[Nick Rowe]

JP: Interesting point. Was there an "official" exchange rate between gold and silver, where the BoE stood ready to trade gold and silver at that fixed exchange rate?

apt: There is the apple market, in which apples are traded for the MOE; there is the banana market, where bananas are traded for the MOE;...etc.; and there is the MOA market, where the MOA is traded for the MOE. That's n-1 in total. ALL markets are markets for the MOE. All n-1 other goods have 1 market each. The MOE has n-1 markets.

[JP Koning]

The mint, not the BoE, was the key institution back then. It would mint fixed weights of gold or silver into coin. Since both gold and silver coins defined the shilling unit in the 1690s (prior to that it was silver that stood as the MOA), you could say that the mint set an exchange rate between the two. However, if this rate deviated from the market's gold:silver exchange rate then everyone would bring the overvalued metal to the mint, and the undervalued mint would be exported elsewhere.

Perhaps one thing missing in your story is the equivalent to the medieval free market gold:silver ratio -- the market exchange rate between BoC paintings and NR paintings.

[JP Koning]

I think my comment from this morning was spam-filed. If you can't find it, I'll try reposting later.