Another Island

Now imagine the people on the island discover that there is another island not so far away. The other island is also populated, and produces the same set of goods. On this island, goods are exchanged against tennis balls. Let's assume for a moment that people on both islands decide to consider tennis balls and golf balls as worth the same. If we assume, in addition, that there are no transportation costs for goods, it is the case that prices of goods are the same on both islands. If the price of a certain good differs from one island to the other, then all who desire the good will buy from the cheapest location, bringing that price up and the other down. Under these assumptions, then, we get a very simplified version of the law of one price.

In our bi-island world, there is now possibility to have excess savings or borrowing: it is possible to lend to foreigners, or to borrow from foreigners. The difference between income and spending in a country is called the current-account balance. It has to be equal to net-foreign investment. If the current-account is in deficit, then the country is spending more than its income, and is a net borrower from abroad. (This is the case with the United States)

So what happens when there are changes in the production function? Well, the existence of an international credit market allows savings and borrowing in the economy to be different. Hence, if we assume that the economy we are looking at is small relative to the rest of the world (which clearly is not the case in our world), then wherever we had changes in the interest rates for the closed (single) economy analysis, now the interest rate doesn't change, but the current-account balance changes. For instance, in the case of a temporary negative shock in our first island, say a harvest failure, at the given interest rate, people want to borrow more, to spread the negative effects of the shock. In our previous analysis, this would push the interest rate upwards, thus making it more costly to borrow, and more attractive to lend, and reconciling borrowing and lending. Now, however, borrowing is going to increase, and the interest rate is going to stay at its level. But the island is going to borrow from the other island, hence pushing its current account balance towards higher deficits. Basically, the island is using foreign funds to finance part of its consumption.

Similarly, if instead of a supply shock we consider a demand shock, say because capital got a lot more productive, inducing an increase in investment demand, in our previous analysis, this would have resulted in an increase of the interest rate. But now, the other island will finance part of the increase in home investment, and the current-account is going to be pushed towards higher deficits.

The analysis above assumes that the country is relatively small, and doesn't weight enough in world borrowing markets. This is the case for countries like Belgium, Austria, Portugal, and Ireland. But it is not the case for each of our islands in our two island world (since each island accounts roughly for half of the influence), and it is not the case for the U.S. If we consider the case in which each island weights a lot in the world borrowing market, then we get a situation that is a mix between the case of a closed economy and the case of a small open economy. The interest rate is going to increase, but by less as in the closed economy case, and current accounts are pushed towards deficits. This is how one significant country can have an impact on the world economy.

Until now, we have assumed that golf balls and tennis balls are exchanged on a one to one basis. Let's relax that assumption in order to introduce exchange rates.

The exchange rate expresses the number of foreign currency units needed to buy one unit of home currency. For instance, it is possible that 2 tennis balls are required to get a golf ball. The exchange rate is then 2. Each island has now a central bank of some sorts, and the central bank's only role is to hold some of the other island's currency in reserve. These reserves will be used to defend the currency is some cases: for instance, if demand for golf balls is going down, so that the value of golf balls relative to tennis balls dips, Robinson's central bank might want to buy golf balls in exchange for tennis balls to keep the exchange rate at a reasonable level. Before we take a look at fixed and flexible exchange rates, let's take a look at the two main propositions in international economics.

First, there is the purchasing-power parity, or PPP. This is a generalization of the law of one price: if there are no transportation costs, the prices, corrected for the level of the exchange rate, should be the same across countries. Second, a similar proposition holds for interest rates: if people can freely borrow and save on both islands, then the interest rates corrected for the level of the exchange rate, should be the same on both islands. This is called the interest-rate parity.

Let's take a look at fixed exchange rate systems. Basically, our two islands decide that the exchange rate is going to remain fixed at 2 tennis balls for a golf ball. The respective central banks commit to exchanging tennis balls for golf balls at that rate and vice-versa, whenever someone requests it. Why would such a system break down? Imagine that because of government policies, people feel that golf balls are worth relatively less than 2 tennis balls…then they will all go and request from Robinson's central bank tennis balls in exchange for their excess golf balls. Although the central bank holds a lot of tennis balls, eventually, it is going to run out of them. Hence if this keeps on for long enough, the system will break, and the exchange rate will have to fluctuate freely. Will it break when the central bank holds zero tennis ball or before? The answer is before: at some point, people will realize that the central bank can't keep giving out tennis balls. If suddenly it runs out of them, then people holding golf balls will have lost, since golf balls will be worth a lot less than 2 tennis balls. Hence many people will go exchange their golf balls, accelerating the process. When the exchange rate is allowed to float, then the exchange rate level is determined by the demand for the currency in the world economy. In this case, the exchange rate just varies whenever people want more or less of the currency relative to other currencies. This allows the 2 tennis balls to a golf ball to change to 2.2, 2.5, 1.8, or whatever, depending on the demand on tennis and golf ball exchanges.