In this case, what I want to understand better is cross-country interest rate differentials. And the effects of international trade, and the effects of a common currency, on those interest rate differentials.

Sometimes I like to make assumptions I know are totally false. Not (or not always) for simplicity, but just to see what happens. It helps me understand the world better. For example, sometimes I like to assume a barter economy; it helps me understand monetary exchange better to see what would happen if we didn't have monetary exchange.

Imagine a world with no international trade. Country A produces different varieties of apples. Country B produces different varieties of bananas. The people in country A don't like eating bananas. The people in country B don't like eating apples. There is a massive home bias in consumption preferences that rules out international trade in apples for bananas. Or carrots, or dates, or anything. Also assume zero factor mobility across national boundaries. Would there be international finance in such a world? Would there be international borrowing and lending?

(Think for example of a standard Mundell-Fleming IS-LM-BP-AD-AS model, except that the IS curve is the same IS curve for a closed economy, because NX is always zero. What happens to the BP curve?)

Now lets look at this world under three different assumptions about the monetary system.

1. Barter. Within country A there is trade of one variety of apple for another variety, and there is also intertemporal trade (finance) where people buy and sell apples for promises to pay apples in future. There is both trade and finance within a country.

Suppose the rate of interest on apples in A were above the rate of interest on bananas in B. Because, for examples, the A's are less patient than the B's, so save less. Or because the A's have better investment opportunities than the B's. Would anyone be able to make a profit on the spread? (Would there be any international finance?)

Suppose I expected the exchange rate between apples and bananas to stay constant. I would then borrow bananas, exchange those bananas for apples, lend the apples, then next year exchange my apples for bananas, repay the loan, and pocket the difference. But who would take the other side of the trades in exchanging apples and bananas? Since there is no "natural" market in which apples are exchanged for bananas, the only person who would take the other side of my trades would be someone who expected the exchange rate of apples for bananas to fall. One of us will be wrong. One of us will gain, and the other will lose. Any "international finance" would be gambling on an intrinsically irrelevant event, like the roll of a die.

The market in which apples exchange for bananas would not exist if everyone had the same expectations. Even if people were risk-lovers, and liked to gamble, they would be as likely to create a market in the roll of a die instead. With barter exchange there would be no international finance in a world of no international trade. Except, maybe, sheer gambling.

Each country's interest rate would be independent of any other country's interest rate. There is no tendency for international finance to equalise interest rates across countries. Bonds can't flow from A to B unless some other good flows the other way from B to A in exchange for those bonds. And there is no other good in this case, because the people in country A don't like eating bananas.

2. Monetary exchange with national currencies and freely floating exchange rates. People in country A trade apples for A-bucks, and trade promises to pay future A-bucks for current A-bucks. Suppose the rate of interest on A-bucks in country A were higher than the rate of interest on B-bucks in country B. Would anyone be able to make a profit on the spread? (Would there be any international finance?)

If you expected the exchange rate between A-bucks and B-bucks to remain constant, you would want to borrow B-bucks, take them to the forex market to buy A-bucks, lend the A-bucks, then next year take your A-bucks to the forex market to buy B-bucks, repay your loan, then pocket the difference as pure profit. But who would take the other side of the trades in the forex market?

Again, there is no "natural" market in which A-bucks are exchanged for B-bucks, so the only person who would take the other side of my trades would be someone who expected the exchange rate of A-bucks for B-bucks to fall. One of us will be wrong. One of us will gain, and the other will lose. Any "international finance" would be gambling on an intrinsically irrelevant event, like the roll of a die.

Again, just like in barter, there is no tendency for international finance to equalise interest rates across countries. Bonds can't flow from A to B unless some other good flows the other way from B to A in exchange for those bonds. And there is no other good in this case, because the people in country A don't like eating bananas, and don't use B-bucks.

3. Monetary exchange with a common currency.

Under barter, and under national currencies, bonds could not flow across international boundaries because there were no other goods that could flow the other way in exchange. That all changes when we have a common currency. Everyone uses the same money. So bonds can flow one way and money can flow the other way.

Suppose the (nominal) rate of interest in A were higher than the rate of interest in B. Any individual could then make a profit by borrowing in B and lending in A. Nominal interest rates must be equalised across the two countries. Bonds are flowing from the impatient A's to the more patient B's, and money is flowing the other way, from B to A. But the A's don't borrow the money because they want to hold more money; they borrow the money because they want to spend it on apples and eat the apples. So the price of apples rises. And the price of bananas falls, because there is less money in B.

At this point, David Hume would start talking about the price-specie flow mechanism. He would say that the rise of prices in A, and the fall of prices in B, would mean that A imports more of B's cheaper goods, so that money flows back from A to B to pay for those imports, so we eventually reach an equilibrium. But we have ruled out David Hume's price-specie flow mechanism by assumption. The people in A don't like bananas, so they won't import B's bananas however cheap bananas get relative to apples. So there is nothing to stop the flow of money from B to A continuing forever.

It gets worse. As more of the world's stock of money flows to A, and the price of apples rises, people in A come to expect rising prices. That lowers the real interest rate in A, so the A's want to save less, invest more, and borrow even more. And the real interest rate in B rises with falling prices for bananas, so the B's want to save more, invest less, and lend even more. So even more bonds flow from A to B and even more money flows from B to A.

Lessons. I'm really not sure what lessons to draw from this counterfactual thought experiment.

The easy lesson to draw is that having a common currency is a dangerous thing for monetary stability unless there is high substitutibility between foreign and domestically-produced goods. But that lesson applies equally to provinces within a country like Canada as it does to countries within the Euro.

But there is a harder lesson about money hiding in here somewhere that I still can't quite get my head around. There is a fundamental difference between finance in a monetary exchange economy and finance in a barter economy. The basic purpose of finance is to transfer control of goods across time between people. When I borrow from you then I should eat more fruit now and you should eat more fruit later, and if there's no trade there should be no finance. But in a monetary exchange economy it doesn't seem to have to work like that. (I'm probably going to regret having written that, because it's like issuing an open invitation to all sorts of monetary cranks to parade their own pet confusions, but what the hell.)