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.

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.

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.

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.