Chapter 9 Money: A User’s Guide

The Characteristics of Money

A striking feature of modern developed economies is that people are typically specialists in production and generalists in consumption. By this we mean that most of us work at one or at most two jobs, producing (or, more often, helping to produce) a very small number of things—for example, a cattle farmer produces beef, a software designer produces computer code, and a nurse produces health services. However, we all purchase hundreds of goods and services.

There is no law that says that we have to buy goods and services using money. An alternative is to trade goods or services directly for one another. This is called barterThe exchange of goods and services without money.. We do see some barter in the world. A restaurant may allow its employees free meals at the end of the night, which means that some of the employees’ wages effectively takes the form of food. If a car mechanic and a caterer live next door to each other, they may have an informal arrangement whereby the mechanic repairs the caterer’s truck in exchange for food for a birthday party.

Sometimes we know exactly where to buy the goods and services that we want. At other times, we go looking—perhaps walking or driving from store to store, perhaps searching using a phone book or the Internet. We do this because we don’t know which store has the goods we want in stock; in addition, we might not know the prices that different stores are charging, and we want to hunt around for the best deal.

To understand the role that money plays in an economy, begin by imagining a world where we must search for the goods and services that we want to buy and there is no money, so all trades take place through barter. Imagine, for example, that you are a web designer, and you want to buy a used car. You must look around for someone who has a car for sale. This search takes time: it has an opportunity cost in that you would prefer to spend that time working or enjoying leisure. Eventually, you find someone who has a car that you are interested in buying. But your problems are not over. He has a car for sale, but what can you give him in exchange? You have to hope that he is interested in obtaining some web design services in exchange for the car. Successful barter requires a coincidence of wants: you must have what the other person wants, and they must have what you want.

A world of nothing but barter is hard to imagine. Each time you wanted to buy something from a seller in a store, you would have to exchange some good or service for that good. If you went to a café, you might have to wash the dishes in return for a coffee. Professors of economics wanting a meal would have to go from restaurant to restaurant trying to find a chef who wanted to hear an economics lecture. They would probably go hungry. It is easy to see why all societies find some way of making these transactions easier.

If you can carry some kind of money around with you to make purchases like these, life is much easier. You still have to hunt for the goods and services that you want, but you don’t have to worry about whether the other party in the transaction wants the product that you sell. Money, therefore, plays a key role in ensuring that trades occur. Trades, in turn, create value in our economy. People are not forced to buy or sell things; they do so only if the trade leaves them better off than they were prior to trading. Money therefore plays a critical role in value creation.

The reason that we rarely see exchange without money is that it is so inefficient. Without money, a coincidence of wants is unlikely, so desirable trades do not occur, and value is not created. With money, transactions are much easier. If you want a meal in a restaurant, the owner will always serve it to you if you have money. Likewise, you obtain money by working at your job. You don’t care what good or service your employer produces; as long as your employer pays you in money, you are happy to supply your labor time to them.

Let us think for a moment about what characteristics this money needs to have:

• Money must be portable. If you are going to walk around searching for goods and services, you want to be able to carry money with you. Sacks of coal would not make a very good money.
• Money must be divisible. Different goods have different prices, and the money we use must accommodate that. Watches would not make a very good money.
• Money must be durable. Daffodils would not make a very good money.

It is easy to list many things that are reasonably portable, divisible, and durable: chocolate chip cookies, cigarettes, and printer paper are just a few examples. These are not typically used as money, although they could be. If you went into a fast-food restaurant, asked for a burger, and then offered to pay using chocolate chip cookies, you can be confident that you would not get the food that you want. That is because there is a fourth characteristic of money that is rather different from the other three.

• Money must be acceptable.

Something can function as money only if people are willing to accept it as money. It is not impossible to imagine a world where chocolate chip cookies function as money. If everyone else is willing to accept cookies in payment for goods and services, then you will be willing to do so as well. But if other people accept only printed pieces of paper as money, then you would be foolish to accept chocolate chip cookies for the product that you sell.

The Functions of Money

Thus far, we have thought about money in terms of its characteristics. We can also think about what makes a good or bad money in terms of the functions that it serves.

The Value of Money

The observation that we use money to buy things tells us more about the value of money. Economists often make a distinction between real and nominal values; this distinction can be applied to money as well. First, what is the nominal value of money? This is almost a trick question: we are asking, “How many dollars is a dollar bill worth?” The answer, which does not require a doctorate in economics, is that a dollar bill is worth $1.

Nominal variables—those measured in dollars or other currencies—can be converted into real variables—that is, those measured in units of real gross domestic product (real GDP). To convert a nominal variable to a real variable, we simply divide by the price level. For example, if your nominal wage is $20 per hour and the price level is $10 (meaning that a typical unit of real GDP costs this amount), then your real wage is 2 units of real GDP.

Exactly the same principle can be applied to money itself. The real value of a dollar is obtained by dividing one by the price level. Thus

$$\text{real value of money}=\frac{1}{\text{price level}}\text{.}$$

Think of an economy in which real GDP is measured in pizzas and suppose the price level—the price of a pizza—is $10. Then the value of a dollar bill is 1/10 of a pizza.

Although $1 is always worth $1, you are not guaranteed that the dollar bill in your pocket will buy the same amount of goods and services from one day to the next. If your local café increases the price of a cookie from $1.00 to $1.25, then your $1 will no longer buy you a cookie; its value, measured in cookies, has declined. If the price level increases, then the real value of money decreases. For notes and coins to be a good store of value, it must be the case that prices are not increasing too quickly.We discuss this problem in more detail in Chapter 11 "Inflations Big and Small".

Using Money to Make Money: Arbitrage

An old joke has it that the secret to getting rich is very simple: buy at a low price and sell at a high price. So another use of your $100 would be to buy goods not to consume but to resell—a process known as arbitrageThe act of buying and then selling an asset to take advantage of profit opportunities..

Suppose you discovered that a particular model of digital camera could be bought much more cheaply in Minneapolis, Minnesota, than in Flagstaff, Arizona. Then you could purchase a large number of cameras in Minneapolis, load them into a suitcase, fly to Flagstaff, and sell them for a profit. If the gap in price were large enough to compensate for your time and travel costs, then this would be a money machine. By buying cameras at a low price and selling them at a high price, you could make as much profit as you wished.

This situation would not persist. You, and other entrepreneurs as well, would start to bid up the price of cameras in Minneapolis. Meanwhile, the increased supply of cameras in Flagstaff would cause prices there to decrease. Before too long, your money machine would have dried up: the gap between the Flagstaff price and the Minneapolis price would no longer justify the effort.

Arbitrage ensures that the prices of individual goods do not vary too much across different regions of the United States. Taken to its extreme, it would imply that the price level would be the same throughout the country. Economists call this idea the law of one priceDifferent prices for the same good or service will not persist because arbitrage eliminates such differences.. The law of one price says that different prices for the same good or service cannot persist because arbitrage eliminates such differences. Arbitrageurs would buy the good at the low price and sell it at the high price. Demand would increase in the market where the price was low, causing that price to increase. Supply would increase in the market where the price was high, causing that price to decrease. This process would continue until the prices were equalized across the two markets.

There are, of course, differences in the prices of individual goods and services in different states and different cities. These differences are primarily due to the fact that some items cannot be arbitraged. If cameras are cheaper in Minneapolis than in Flagstaff, then they can be bought and sold as we described. But if apartments in Flagstaff are cheaper than in Minneapolis, it isn’t possible to ship them across the country. Likewise services typically cannot be arbitraged. Thus we do not expect the law of one price to be literally true for every good and service. Nevertheless, the law of one price does lead us to expect that the overall price level will not differ too much in different parts of the country.

It can be difficult to apply the law of one price in practice because we have to be careful about what we mean by the “same” product. An apparently identical shirt at two different retailers might not qualify as the same—perhaps one retailer allows goods to be returned, while the other does not allow returns. Identical goods are not the same if they are in different places: a Toyota on a dealership lot in Kentucky is not the same as the identical model car on a lot in Pretoria, South Africa, and so on. In such situations, the law of one price tells us that we should not expect prices of goods to be “too different,” depending on the costs of transportation and the other costs of arbitrage.

We said earlier that money makes an economy more efficient because it makes transactions easier. Money makes arbitrage easier as well. Arbitrage would be a less certain way of making money in an economy with barter. First, the lack of a clear unit of account would make arbitrage opportunities less transparent. Second, the lack of a reliable medium of exchange would make arbitrage risky: the person in Flagstaff who wants to buy a digital camera from you might not have anything you want, so you might end up giving up something you own and not getting something you want in return.

Foreign Exchange Markets

Imagine a series of three visitors traveling from the United States to Europe. First, we have someone arriving on vacation. Chances are that she will want to exchange dollars for euros to have money to spend on hotels, meals, and so on. She also buys souvenirs in Europe—goods that she imports back to the United States. Our second visitor spends a lot of time in Europe for work purposes. He might open a bank account in, say, Germany. If he wanted, he could use this bank account to keep some of his wealth in Europe. He would buy euros with his dollars, deposit these euros in the bank to earn interest, and then—at some point in the future—he would take his money out of the bank in Germany and exchange the euros for dollars. (Later, we will consider how you can decide if this is a good investment strategy. For now, our point is that this type of financial investment is another source of demand for euros.) Our third visitor to Europe is a professional wine buyer who wants to purchase wine to sell in a US restaurant. She travels to the wine-growing regions of Europe (France, Spain, Italy, Germany, Portugal, etc.) and must exchange dollars for euros to pay for her purchases.

Our three visitors represent a microcosm of the transactions that take place in the foreign exchange market every day. Households and firms buy euros to pay for their imports of goods and services (souvenirs, wine, etc.). Many different goods and services are produced in Europe and sold in the United States. Some are imported by retailers, others by specialist import-export firms, and still others by individuals, but in all cases there is an associated purchase of euros using dollars.

The demand for euros also arises from financial investment by households, firms, and financial institutions. For example, a wealthy private investor in the United States may purchase stock issued by a company in Europe. To buy that stock, the US investor sells dollars and buys euros. In practice, such transactions are typically carried out by financial institutions that undertake trades on behalf of households and firms.

Most exchanges of dollars for euros do not actually entail someone traveling to Europe. Think about the foreign currency needs of a large multinational firm that produces goods and services in Europe but sells its output in the United States. The company naturally needs euros to pay workers and suppliers in Europe. Since it sells goods and thus earns revenues in dollars, the company must convert from dollars to euros very frequently. But you will not see the company’s chief financial officer in an airport line to exchange money. Instead, such currency operations are conducted through financial institutions, such as commercial banks.

Because of all these transactions, there are very active and sophisticated markets in which currencies are traded. We can represent these markets using the familiar supply-and-demand framework. Figure 9.4 "The Market for Euros" shows a picture of the market where euros are bought and sold. Buyers from the United States buy euros with dollars, and European traders sell euros in exchange for dollars.Of course, it is not literally the case that everyone who is buying is from the United States and that everyone selling is from Europe. If you have dollars, you can buy euros; if you have euros, you can sell them for dollars. But it is simpler to explain if we think of Europeans selling euros and Americans buying them. The supply and demand curves refer to the object being traded—euros. Thus the quantity of euros is shown on the horizontal axis. The price on the vertical axis is in dollars.

This market is just like any other you encounter. The demand curve is downward sloping: as the price of euros increases, the quantity of euros demanded decreases. This is the law of demandPeople consume more of a good when its price decreases and less of a good when its price increases. at work. As the price of euros increases, people in the United States will find that goods and services produced in Europe are more expensive. For example, suppose that 1 euro costs $1, and a Mercedes automobile costs EUR 50,000.There is an established set of three-letter symbols for all the currencies in the world. Euros are denoted by EUR, US dollars are denoted by USD, Australian dollars are denoted by AUD, and so forth. In this book we use the familiar $ symbol for US dollars and the three-letter symbols otherwise. A list of the currency codes can be found at http://www.xe.com/iso4217.php. Then its cost in dollars is $50,000. Now imagine that euros become more expensive, so that EUR 1 now costs $2. You now need $100,000 to buy the same Mercedes in Europe. So an increase in the price of euros means that Americans choose to buy fewer goods and services produced in Europe. Exactly the same logic tells us that an increase in the price of the euro makes European assets look less attractive to investors. A German government bond, a piece of real estate in Slovenia, or a share in a Portuguese firm might look like good buys when the euro costs $1 yet seem like a bad idea if each euro costs $2.

The supply curve also has a familiar upward slope. As the price of euros increases, more people in Europe sell their euros in exchange for dollars. They do so because with the higher dollar price of euros, they can obtain more dollars for every euro they sell. This means that they can buy more US goods and services or dollar-denominated financial assets.

The price where supply equals demand is the equilibrium exchange rate. (The market also shows us the equilibrium number of euros traded, but here we are more interested in the price of the euro.)

Arbitrage with Two Currencies

So far, we have talked about buying foreign currencies to purchase either assets or goods and services. Another reason to buy foreign currencies is in the hope that you could make money by trading them. Let us think about how you might try to make money in the foreign exchange market. You might start with some dollars and exchange them for euros. Then you could take those euros and exchange them for dollars again. Is it possible that, by doing this, you could end up with more money than you started with? Could you buy euros cheaply and then sell them at a high price, thus making a profit?

Begin by supposing that dollars and euros are only two currencies in the world, and there are only two economies: the United States and Europe (a shorthand for “those European countries that use the euro”). Imagine that there are two separate markets: in the euro market, the price of 1 euro is $2; in the dollar market, the price of one dollar is EUR 1. With these two prices, there is money to be made by buying and selling currencies. Start with 1 euro. Sell that euro in the market for euros and obtain $2. Use those dollars to buy euros in the market for euros and obtain 2 euros. Now we are talking business: you started with 1 euro, made some trades, and ended up with 2 euros.

There is, of course, a catch. The prices that we just suggested would not be consistent with equilibrium in the foreign exchange markets. As we have just seen, there is a simple recipe for making unlimited profit at these prices, not only for you but also for everyone else in the market. What would happen? Everyone would try to capitalize on the same opportunity that you saw. Those with euros would want either to sell them in the euro market—because euros are valuable—or to use them to buy dollars in the dollar market—because dollars are cheap. Those with dollars, however, would not want to buy expensive euros in the euro market, and they would not want to sell them in the dollar market. Hence, in the euro market, the supply of euros would shift rightward, and the demand for euros would shift leftward. The forces of supply and demand would make the dollar price of euros decrease. In the dollar market, the supply of dollars would shift leftward, and the demand for dollars would shift rightward, causing the euro price of dollars to increase.

The mechanism we just described is arbitrage at work again. The arbitrage possibility between the dollar market for euros and the euro market for dollars disappears when the following equation is satisfied:

price of euro in dollars × price in dollar in euros = 1.

When this condition holds, there is no way to buy and sell currencies in the different markets and make a profit. As an example, suppose that EUR 1 costs $2 and $1 costs EUR 0.5. These prices satisfy the equation because 2 × 0.5 = 1. Imagine you start with $1. If you use it in the dollar market for euros to buy euros, then you will have EUR 0.50. If you then use these in the euro market for dollars to buy dollars, you will get $2 for each euro you supply to the market. Since you have half of a euro, you will end up with $1, which is what you started with. There is no arbitrage opportunity.

By now you have probably realized that there is a close connection between the market for euros and the market for dollars (where dollars are bought and sold using euros). Whenever someone buys euros, they are selling dollars, and whenever someone sells euros, they are buying dollars. In our two-country, two-currency world, the market for euros and the market for dollars are exactly the same market, just looked at from two different angles.

We illustrate this in Figure 9.5 "The Market for Euros and the Market for Dollars". In part (a) of Figure 9.5 "The Market for Euros and the Market for Dollars", we show the market where euros are bought and sold, and in part (b) of Figure 9.5 "The Market for Euros and the Market for Dollars" the market where dollars are bought and sold. The supply curve for dollars is just the demand curve for euros, and the demand curve for dollars is the same as the supply curve for euros. For example, suppose 1 euro costs $2. From part (a), we see that, at this price, people would supply EUR 3,200. In other words, there are individuals who are willing to exchange EUR 3,200 for $6,400. If we think about this from the perspective of the market for dollars, these people would demand $6,400 in the market when $1 costs EUR 0.50—and, indeed, we see that this is a point on the demand curve in part (b). The market is in equilibrium when EUR 1.00 costs $1.25, or equivalently when $1 costs EUR 0.80. At this exchange rate, holders of dollars are willing to give up $2,500, and holders of euros are willing to give up EUR 2,000.

Arbitrage with Many Currencies

We live in a world with many different currencies, not just two. Figure 9.6 "Exchange Rates" shows some exchange rates from http://www.oanda.com, a site that provides current and historical data on exchange rates and that is also an online market where you can trade currencies. So, on March 11, 2007, just after midnight, the price of a euro in dollars was 1.3115. At the same time, the price of a dollar in British pounds was 0.5176.

If you look at the table on the left side of Figure 9.6 "Exchange Rates", you see that it provides both the dollar price of the euro and the euro price of the dollar (and similarly for the other currency pairs). Tables such as this one have already built in the arbitrage condition, so you cannot keep buying and selling the same currency in exchange for dollars and make money.

When there are multiple currencies, we can imagine more complicated trading strategies. As an example, consider the following string of transactions.

1. Take a dollar and use it to buy euros.
2. Take the euros and buy Japanese yen.
3. Take the yen and buy dollars.

If you end up with more than $1, then there are profits to be made buying and selling currencies in the manner outlined here. Can you make a profit this way? The answer, once again, is no. If you could, then the markets for foreign currency would not be in equilibrium: everyone would buy euros with dollars, sell them for yen, and then sell the yen for dollars. Once again, exchange rates would rapidly adjust to remove the arbitrage opportunity.

To verify this, let us go through this series of transactions using Figure 9.6 "Exchange Rates". One dollar will buy you EUR 0.7625. Now take these and use them to buy yen. You will get 0.7625 × 155.1910 = JPY 118.3331. Now, use these yen to buy dollars, and you will get 118.3331 × 0.00845 = $0.9999. You start with $1; you end with $1 (give or take a rounding error).

These calculations assume that there are no costs to trading foreign currencies. In practice, there are costs involved in these exchanges. A traveler arriving at an airport in need of local currency does not see rates posted as in the left-hand table in Figure 9.6 "Exchange Rates". Instead, they see something that looks like the right-hand table, where rates are posted in two columns: bid (buying) and offer (selling). The bid is a statement of how much the currency seller is willing to pay in local currency for the listed currency. The offer column is the price in local currency at which the seller is willing to sell to you. Naturally, the offer price is bigger than the bid: the seller buys currencies at a low price and sells them at a high price. The difference between the bid and offer prices is called the spread. The existence of the spread means that if you try to buy and sell currencies with the dealer, you will actually lose money. At the same time, the spread creates a profit margin for the dealer and thus pays for the service that the dealer provides.

Arbitrage with Goods and Currencies

We have talked about arbitrage with goods and arbitrage with foreign currencies. We can also put the two together to study the prices of goods that are traded across international borders. Arbitrage of goods from one country to another is a bit more complicated because it involves buying and selling currencies as well as goods. To see how this works, imagine you are going on a trip to Europe. You are allowed two suitcases filled with belongings free of charge on the airplane. What about filling a suitcase full of new blue jeans, transporting them to Europe, and then selling them there? Could you make money that way?

Suppose that the dollar price of 1 euro is $1.50. Further, suppose that the price of a pair of blue jeans is $70.00 in the United States and EUR 50.00 in Paris. Consider the following sequence of actions.

1. Take $70 out of your pocket and buy a pair of blue jeans.
2. Travel with these blue jeans to Paris.
3. Sell the jeans for euros.
4. Buy dollars with your euros.

The question is whether you can make money in this way. The answer is given by how many dollars you will have in your pocket at the end of these steps. When you sell the jeans in Paris, you will have EUR 50.00. If the dollar price of euros is $1.50, then by selling the jeans in Paris you will get 50 × $1.50 = $75. This is a profit of $5 for each pair of jeans—you are in business.

Once again, the opportunity for arbitrage suggests that this situation is unlikely to persist. Entrepreneurs will buy jeans in the United States, take them to Paris, and sell them there. Market forces in three different markets will work to eliminate the profit. First, the activity of arbitrageurs will increase the demand for jeans in the United States, causing the US price of jeans to increase. Second, the increased supply of jeans in Paris will cause the price there to decrease. And third, there will be an increased supply of euros in the foreign exchange market, which will cause the euro to depreciate. This is shown in Figure 9.7 "International Arbitrage Restores the Law of One Price".

These price changes continue until there are no profits to be made by arbitrage. Exactly how much of the adjustment will take place in each market depends on the slopes of the supply and demand curves. In Figure 9.7 "International Arbitrage Restores the Law of One Price", we have drawn the new equilibrium as follows: blue jeans cost EUR 49 in Europe and $71.05 in the United States; and the exchange rate is $1.45 per euro. At these prices,

price of blue jeans in dollars = price of blue jeans in euros × price of euro in dollars,

and there is no longer any possibility of arbitrage. This is another illustration of the law of one price. If we were literally talking just about arbitrage in blue jeans, most of the adjustment would take place in the markets for blue jeans in the United States and Europe, and there would be a negligible effect on the exchange rate. But if the same kinds of arbitrage opportunities exist for lots of goods, then there will be an impact on the exchange rate as well.

For tradable goodsGoods that can be easily and cheaply transported from one place to another, which means they can be easily arbitraged., the law of one price says that the

dollar price of good = euro price of good × dollar price of euro.

When this condition holds, there are no arbitrage profits to be gained by purchasing the good with dollars, selling it for euros, and then buying dollars with euros. Likewise, if this condition holds, there are also no arbitrage profits from purchasing the good with euros, selling it for dollars, and then buying euros with dollars. In general, we expect that such arbitrage will occur very quickly. There are no profits to be made from arbitrage when the law of one price holds.

The Economist has kept track of the price of a McDonald’s Big Mac in a number of countries for many years, creating something they call the “the Big Mac index.” Table 9.1 "The " contains some of their data. The last column of Table 9.1 "The " gives the price of a Big Mac in each selected country in July 2011, converted to US dollars at the current exchange rate. That is, the last column is calculated by dividing the local currency price (the second column) by the exchange rate (the third column). A Big Mac costs $4.07 in the United States but more than twice as much in Norway. China is a real deal at only $1.89.

The price differentials in this table violate the law of one price: there is (apparently) profit to be made by buying Big Macs at a low price and selling them at a high price. Applying the principle of arbitrage, we should all be flying to China, buying Big Macs, traveling to Norway, and selling them on the streets of Oslo. Of course, there are a few small problems with this scheme, such as the following:

• It is expensive to fly back and forth between China and Norway.
• There is a limited capacity for transporting Big Macs on the airplane.
• The quality of the Big Mac might deteriorate while it is being transported.
• You might not be permitted to import meat products from China into Norway.
• You might have to pay taxes when you bring Big Macs into Norway.
• It might be tough to open a McDonald’s in Oslo.

This long list easily explains the deviations from the law of one price for Big Macs. Similar considerations explain why the law of one price might not hold for other goods. The law also does not apply to services, such as tattoos, since these cannot be imported and exported. The law of one price is most applicable to goods that are homogeneous and easily traded at low cost. Economists use the law of one price as a guide but certainly do not expect it to hold for all products in all places.

Using the Law of One Price to Understand the Exchange Rate

There is another way to interpret the finding that Big Macs do not cost the same in each country. The Economist uses this information to draw conclusions about the values of different currencies and how these values are likely to change over time.

From this perspective, the Big Mac is more expensive in Europe than in the United States because dollars are cheap in Europe. Put differently, we say that the dollar is undervaluedThe price of a currency is too low compared to the ratio of price levels in the two countries. relative to the euro. If the price of a dollar in euros were 0.85 instead of 0.70, then a Big Mac would cost the same in the United States and Europe. Completely equivalently, we can say that that the euro is overvaluedThe price of a currency is too high compared to the ratio of price levels in the two countries. relative to the dollar. With this in mind, we might expect the undervalued dollar to increase in value relative to the euro. That is, we would expect the price of a dollar in euros to increase. Similarly, we would conclude that the Norwegian kroner is overvalued relative to the dollar, the Chinese yuan is undervalued, and the Czech Koruna is neither overvalued nor undervalued.

To see how this works more generally, look back at our arbitrage condition for blue jeans. If we divide both sides by the price of blue jeans in euros, we get

price of euro in dollars=price of blue jeans in dollarsprice of blue jeans in euros.

This equation says that, according to the law of one price, the dollar price of the euro should equal the dollar price of blue jeans divided by the price of blue jeans in euros. This is exactly the kind of calculation that underlies the Big Mac index, only with blue jeans instead of Big Macs. Equivalently, the law of one price says that the

price of dollar in euros=price of blue jeans in eurosprice of blue jeans in dollars.

Suppose we think about this equation applying (approximately) to all goods and services. We can then get a better prediction of the exchange rate by looking at a general price index in each country:

price of dollar in euros=price of bundle of goods in Europeprice of same bundle of goods in the United States.

Because of all the reasons why the law of one price does not literally hold, economists certainly do not expect this equation to give an exact prediction of the exchange rate. Nevertheless, it can provide a useful indication of whether a currency is undervalued or overvalued.

A currency is undervalued if, following this equation, its price is too low compared to the ratio of price levels in the two countries. A currency is overvalued if, following this equation, its price is too high compared to the ratio of price levels in the two countries. As in our discussion of the euro, if a currency is overvalued, then we would expect its value to decrease over time. This is called a depreciationA decrease in the price of a currency. of the currency. Likewise, we would expect the price of an undervalued currency to increase over time. This is called an appreciationAn increase in the price of a currency. of the currency.

The market forces behind these currency movements come from the buying and selling of currencies for trading purposes. If the Chinese yuan is undervalued, goods produced in China will be relatively cheap in US dollars. The demand for Chinese exports will be high, and this will lead to a large demand for the yuan. Eventually the dollar price of the yuan will increase—that is, the yuan will appreciate, and the dollar will depreciate.

Changes in the Exchange Rate

Even though the law of one price does not literally hold for all goods and services, it reminds us that the value of $1 in the United States is linked to its value in the rest of the world. As a result, we expect that price level changes are likely to lead to changes in the exchange rate. We see this more clearly if we write our previous equation in terms of growth rates. Using the formula for growth rates, we find the following:

growth rate of price of dollar in euros = growth rate of price of European bundle of goods− growth rate of price of US bundle of goods.

If the bundle of goods in each country corresponds roughly to the goods in the Consumer Price Index (CPI)A price index that uses as the bundle of goods the typical purchases of households., then the growth rate of these prices corresponds to the inflation rateThe growth rate of the price index from one year to the next.. The growth rate of the exchange rate is just another term for the percentage appreciation of the currency. Thus we get the following:

percentage appreciation of the dollar ≈ European inflation rate − US inflation rate.

So, if the inflation rate in the United States is higher than it is in Europe, we expect the euro price of the dollar to decrease. We expect depreciation of the dollar if US inflation exceeds European inflation. Inflation reduces the real value of money domestically; it will also tend to reduce the value of money in terms of what it can purchase in the rest of the world. This makes sense. If our currency is becoming less valuable at home, then we should also expect it to become less valuable in the rest of the world.

Arbitrage with Credit and Assets

Suppose you do not want to spend your $100 until next year. You could just put the money under your mattress, but a better option is to find some way of getting more than $100 next year. One way to do this is to lend your money to someone else. For you, this might simply mean taking it to your bank and putting it in your savings account. When you do that, you are making a loan to the bank. Of course, the bank probably will not leave the money in its vault; it will lend that money to someone else. Banks and other financial institutions act as intermediaries between those who want to save and those who want to borrow.

The credit market brings together the suppliers and demanders of credit, and the nominal interest rateThe number of additional dollars that must be repaid for every dollar that is borrowed. is the price that brings demand and supply into balance. The supply of credit increases as the interest rate increases: as the return on saving increases, households will generally save more and thus supply more funds to the credit market. The demand for credit decreases as the interest rate increases: when it is expensive to borrow, households and firms will borrow less. At the equilibrium interest rate, the quantity of credit supplied and the quantity of credit demanded are equal. This is shown in part (a) of Figure 9.9 "The Credit Market and the Asset Market".

There is another way to look at credit markets. Borrowers get money today in exchange for a promise to pay money later. Lenders purchase those promises by giving up money today. Instead of asking how much the interest rate is for a given $100 loan, we could ask what people would be willing to pay today for the right to receive $105 in a year’s time.

The market for the promise to pay $105 in a year is illustrated in part (b) of Figure 9.9 "The Credit Market and the Asset Market". The units on the horizontal axis are $105 payments. These are assets: buyers are purchasing a piece of paper that is a promise to deliver $105 in a year’s time. The price on the vertical axis is the current price of that asset.

The nominal rate of return on an asset is the amount that you obtain, in percentage terms, from holding the asset for a year. In the case of the simple one-year asset we are considering, the return is given as follows:

nominal rate of return on asset=repayment amountprice of asset−1.

We can also rearrange this to give us the price of the asset:

price of asset=repayment amount1+nominal rate of return.

Notice what happens when we look at the market in this way. Buyers have become sellers, and sellers have become buyers. Borrowers are sellers: they sell the promise to pay. Lenders are buyers: they purchase the promise to pay. If we are looking at the same group of buyers and sellers as before, then the current equilibrium price of this asset would be $100.

The nominal interest rate and the nominal rate of return defined through these two markets must be the same. If not, there would be an arbitrage possibility. Imagine, for example, that the interest rate is 5 percent but the price of the asset is $90. In this case, the rate of the return on asset is 11090−1, which is 22.2 percent. So you could make a lot of money by borrowing at a 5 percent interest rate and then purchasing the promises to pay $110 at price of $90.

If you could do this, so also could many major financial institutions—except that they would operate on a much larger scale, perhaps buying millions worth of assets and borrowing a lot in credit markets. So the demand for credit would shift outward, as would the demand for assets. This would cause the interest rate to increase and the asset price to increase, so the rate of return on the asset decreases. This would continue until the arbitrage opportunity disappeared.

In summary, we would say there is no arbitrage opportunity when the

nominal rate of return on asset = nominal interest rate.

The rate of return on the asset, in other words, is equivalent to the interest rate on the asset. Equivalently this means that

price of asset=repayment amount1+nominal interest rate=repayment amountnominal interest factor.

In the second line we replaced (1 + nominal interest rate) with the nominal interest factorA factor, equal to 1 + the nominal interest rate, used to convert dollars today into dollars next year.. The two are equivalent, but sometimes we find it more convenient to work with interest factors rather than interest rates.

The argument that we have just made should seem familiar. It is analogous to the argument for why there cannot be distinct dollar-euro and euro-dollar markets; they are just ways of looking at the same asset. Likewise, we can think of the sale of any asset as equivalent to borrowing, while for any example of credit we can also think of there being an underlying asset.

Different Assets

Very often economists and others talk about “the” interest rate, as if there were just a single asset in the economy. In fact, there are many different assets that you could buy with your $100, each with an associated interest rate. The following are various assets that you might purchase:

• Currency and coin. To begin with, your $100 is itself an asset. If you put the money under a mattress and retrieve it after a year, it is very easy to calculate the nominal interest rate on $100. If you give up $100 today, you will get exactly $100 back next year. The nominal interest rate is zero.
• Bank deposits. Bank deposits are also an asset. If you put your money in the bank, you are extending credit to the bank. Depending on the type of bank account, you may or may not earn interest on your deposits.
• Foreign exchange. The money of other countries is likewise an asset. You can take dollars today and use them to purchase, say, euros or Japanese yen (JPY). Even in this case, there is a rate of return. For example, suppose that today you can buy JPY 100 with $1. Suppose also that in a year’s time, there are JPY 90 to the dollar. Then with your JPY 100, you can buy $1.11 (100/90 = 1.11). You obtained a nominal rate of return of 11 percent.
• Gold and other precious metals. You could take your $100 and use it to buy gold. Unless you are a dentist or a jeweler, you will not have any direct use for the gold; you simply keep it and resell it at some future date. The rate of return on gold is purely a matter of what happens to the price of gold. If the price of gold (in dollars) increases by 10 percent, then you get a 10 percent rate of return.
• Government bonds. A government bond is also a loan contract; if you buy a government bond, you are extending credit to the government. The bond is a promise to pay a certain amount at some future date. Because the loan will be paid off a number of years in the future, it is slightly more complicated to calculate the interest rate.
• Shares. Another example of an asset is a share in a company, such as Dell Inc. If you purchase a Dell share, you have bought the right to a share in Dell’s profits. In this case, you expect not only one payment at a specified future date but also a sequence of payments whenever Dell pays out dividends. Notice that there is also a lot of uncertainty here: you do not know, when you purchase the share, how big these payments will be. The implied interest rate is therefore uncertain as well.
• Real estate. If you purchase a house, you own yet another kind of asset. The value of a house comes from the fact that people can live in it. If you rent your house out, then it gives you a flow of income, much like a share in a company. If you live in your house, then you consume that flow of services, but we still think of the house as an asset because at any time you can sell your house and transfer that flow of services to someone else.

We could list many more assets, but you should be getting the general idea. Most of these assets are more complicated than the simple one-year credit contract with which we began. For one thing, they often involve a whole stream of repayments at different dates, rather than just one repayment. For another, the amounts of these payments may be uncertain.

In Section 9.1 "What Is Money?", we pointed to the different characteristics and functions of money. For most of us, the word money conjures up images of currency and coins. But some of the other assets that we listed also can perform more or less well as money. For example, bank deposits in a checking account or with a linked debit card are portable, durable, divisible, and widely acceptable and serve as a medium of exchange. In general, any asset that performs the functions of money is money. Gold can be used as a store of value and perhaps also as a unit of account, but it is not often used as a medium of exchange. There are many different assets in the world, and they vary in the extent to which they perform these different functions and thus how good they are as money.

Arbitrage with Different Assets: The Term Structure of Interest Rates

We just observed that there are many different assets and thus many interest rates in the economy. But these interest rates are all linked to each other because the same people (particularly banks and other financial institutions) trade in many different markets.

One way in which assets differ is in terms of their maturityThe time when the final payment on a loan is due.. To see how the returns on assets of different maturity are linked, consider two government bonds of different maturities: one-year bonds and two-year bonds. Here are two different ways you could save for two years.

1. Buy a one-year government bond. Collect the payment at the end of the year and then reinvest that money in another one-year bond.
2. Buy a two-year government bond.

There are three interest rates relevant to your choice. The first one is the current interest rate on a one-year bond. The second is the interest rate on a one-year bond next year. The third interest rate is the annualized nominal interest rate on a two-year government bond. An annualized interest rateThe interest rate earned each year on a loan that lasts many years. is the interest rate earned each year on a loan that lasts many years, and the annualized interest factor is (1 + the annualized interest rate). For example, suppose that the annualized rate on a two-year loan is 6 percent. Then you would earn 6 percent per year for two years, and

repayment after two years = $100 × 1.06 × 1.06 = $112.36.

As you might expect, these three interest rates are connected, and we can understand how by again thinking about arbitrage. If you purchase the two-year government bond return, you get

100 × (annualized nominal interest factor on two-year bond)².

Conversely, if you purchase the two one-year bonds, you get

100 × (nominal interest factor this year) × (expected nominal interest factor next year).

Notice that we have referred to next year’s interest factor as “expected.” This is because when you make your decision, you do not know what the interest rate will be.

When

(annualized nominal interest factor on two-year bond)² = nominal interest factor this year× expected nominal interest factor next year,

the two transactions have the same return. Once again, we can appeal to an arbitrage argument to say that we expect this equation to hold. There is one twist, however. When you make this decision, you do not know for sure what the interest rate will be on one-year bonds next year. You have to make a guess. Thus this arbitrage involves some risk.

This relationship is an example of the term structure of interest ratesThe relationship between the actual and expected returns on assets, which are identical except for their maturities., which describes the relationship between the actual and expected returns on assets that are identical except for their maturities. A version of the relationship applies to not only assets of one-year and two-year maturity but also assets of all maturities.

From the term structure of interest rates, we learn something very significant: if the annual one-year interest rate is below the annual rate on a two-year loan, then interest rates are expected to increase in the future. For example, if the annual one-year interest rate is 5 percent and the annual rate on two-year loans is 6 percent, this means both borrowers and lenders expect one-year interest rates to be higher than 6 percent next year. (If desired, you can calculate exactly what the expected rate is by using the previous equation.)

We can see the connection between assets of different maturities by looking at the yield curveThe current annual return for assets of different maturities..For more details and additional graphs, see J. Huston McCulloch, “The US Real Term Structure of Interest Rates: With Implicit Inflation Premium,” updated October 30, 2009, accessed August 22, 2011, http://www.econ.ohio-state.edu/jhm/ts/ts.html. The yield curve shows the current annual return for assets of different maturities. Figure 9.10 "The Yield Curve" shows the yield curve for US Treasury securities in 2011.This is an average of rates in 2011 for US Treasury securities of different maturities from http://www.econstats.com/r/rusa_ew6.htm. On the horizontal axis of the yield curve is the number of years to maturity of the asset. On the vertical axis is the current annual yield on the asset. Notice that the yield curve is upward sloping: the longer the maturity, the higher the annual interest rate. This is generally what we observe, although sometimes the yield curve is inverted, meaning that higher maturity debt has a lower interest rate.

All assets are linked, not just government bonds of different maturities. Suppose that the interest rate on one-year government bonds increases. To buy these bonds, financial institutions will start selling other assets—not only bonds at other maturities but also stocks, holdings of foreign currencies, and so on. As they sell those other assets, their prices will decrease, and their rate of return will increase. An increase in the interest rate on one-year treasuries therefore increases interest rates on other assets. Thus different interest rates typically move together, and it is usually not too misleading, at least for the purposes of macroeconomics, to think about there being a single interest rate in an economy.

Arbitrage with Assets and Goods: The Real Interest Rate

The exchanges we have described so far have all been in terms of dollars. The interest rates paid on such exchanges are nominal interest rates. In a world where prices are increasing, however, the nominal interest rate does not represent the true cost of borrowing and lending.

To see why, begin by recalling that the inflation rate is defined as the percentage change in the price level. This means that the price level next year is equal to the price this year multiplied by (1 + inflation rate).If this is not clear to you, write out the inflation rate as follows:inflation next year=price level next year−price level this yearprice level this year=price level next yearprice level this year−1.Then add one to both sides and multiply by the price level this year. Now imagine that two individuals, Bert and Ernie, want to write a credit contract. Bert wants to borrow some money to buy a pizza. The price of a pizza this year is $10, so Ernie lends Bert $10, and they agree on a nominal interest rate for this credit arrangement. This means that next year he will repay $10 × (1 + nominal interest rate).

We could also imagine that Bert and Ernie decide to write a different kind of contract to guarantee a return in terms of pizzas. Because this rate of return is specified in terms of goods rather than money, it is a real interest rateThe rate of return specified in terms of goods, not money.. Ernie agrees to give Bert (enough dollars to buy) 1 pizza this year in return for being repaid (enough dollars to buy) (1 + real interest rate) pizzas next year. Ernie lends Bert $10 as before (the equivalent of 1 pizza). To repay this loan next year, Bert must give Ernie enough money to buy (1 + real interest rate) pizzas. The price of a pizza has increased to $10 × (1 + inflation rate), so Bert must give Ernie $10 × (1 + real interest rate) × (1 + inflation rate).

If you have worked through this chapter carefully, you probably know what is coming next. Because of arbitrage, we know that these two contracts must be equivalent:

1 + nominal interest rate = (1 + real interest rate) × (1 + inflation rate).

As an approximation, this equation implies that theTo see this, multiply out the right-hand side and subtract $1 from each side to obtain nominal interest rate = real interest rate + inflation rate + real interest rate × inflation rate. Now, if the real interest rate and the inflation rate are small numbers, then when we multiply them together, we get a very small number that can be safely ignored. For example, if the real interest rate is 0.02 and the inflation rate is 0.03, then their product is 0.0006, and our approximation is about 99 percent accurate.

nominal interest rate ≈ real interest rate + inflation rate.

This relationship is called the Fisher equationA formula for converting from nominal interest rates to real interest rates: the real interest rate equals the nominal interest rate minus the inflation rate..

For example, if a loan has a 12 percent interest rate and the inflation rate is 8 percent, then the real return on that loan is 4 percent. Since the nominal interest rate and the inflation rate are easily observed by most of us, we can use the Fisher equation to calculate the real rate of interest. We use the Fisher equation whenever we see a nominal interest rate and wish to convert it to a real interest rate. Just as it is the real exchange rate that matters for people trading goods and assets between countries, so it is the real interest rate that ultimately matters to borrowers and lenders in the economy.

In macroeconomics, we often look at the credit market for the entire economy, where savings and investment are matched in the economy as a whole. The price in this market is the real interest rate. The response of savings and investment to the real interest rate is shown in Figure 9.11 "The Credit Market". Once we know the equilibrium real interest rate, we calculate the implied nominal interest rate using the Fisher equation.

The (net) supply of loans in the domestic credit market comes from three different sources:

1. The private savingsThe net amount saved by households in the economy. of households and firms
2. The savings or borrowing of governments
3. The savings or borrowing of foreigners

Households will generally respond to an increase in the real interest rate by reducing current consumption relative to future consumption. Households that are saving will save more; households that are borrowing will borrow less. Higher interest rates also encourage foreigners to send funds to the domestic economy. Government saving or borrowing is little affected by interest rates.

National savingsThe sum of private and government savings. are defined as private savings plus government savings (or, equivalently, private saving minus the government deficitThe difference between government outlays and revenues.). The total supply of savings is therefore equal to national savings plus the savings of foreigners (that is, borrowing from other countries). The matching of savings and investment in the aggregate economy is described as follows:

investment = national savings + borrowing from other countries or investment = national savings − lending to other countries.

This is the same thing as saying that the flows in and out of the financial sector in the circular flow must balance.

The demand for loans comes from firms who borrow to finance investment. As the real interest rate increases, investment spending decreases. For firms, a high interest rate represents a high cost of funding investment expenditures. This is evident if the firm borrows to purchase capital. It is also true if the firm uses internal funds (retained earnings) to finance investment since the firm could always put those funds in an interest-bearing asset instead.

Arbitrage with Assets and Currencies: Uncovered Interest Parity

If you are like most people, you do not own assets in another country. You may own multiple assets—a savings account that pays you some interest every month, perhaps a certificate of deposit, or shares of some company—but the chances are that all your financial assets are denominated in a single currency. In fact, there is no reason why you should not own assets denominated in other currencies, such as euros, or pesos, or British pounds. You might consider opening a bank account in another country. Or you might even consider other financial investments in another country, such as purchasing a share in an international mutual fund, buying shares of a foreign company, or buying the debt of a foreign government.

Most of us do not know exactly how to go about making such investments. In fact, they are easy to carry out if you make use of the services of professional financial advisers. In any case, we are not really interested in the mechanics of foreign investment here. We want to answer a more fundamental question: how do you know if buying foreign assets would be a good idea? Consider the choice between two investment strategies.

1. Investing in the United States

   • Deposit $100 in a US bank.
   • Wait for a year.

2. Investing in Europe

   • Take $100 and use it to buy euros.
   • Deposit the euros in a European bank.
   • Wait for a year.
   • Withdraw the deposit and interest and use it to buy dollars.

To decide which is the better strategy, you need to determine how much you will earn in each case.

It is straightforward to determine how much you will get with the first option: you will get your $100 plus the interest payments. For example, if the interest rate at the US bank is 10 percent, then after a year you will earn $10 interest for a total of $110.

What about the second strategy? How many dollars will you have if you deposit money in the European bank? This is a bit more complicated. First, you buy euros with your $100. Second, you deposit these euros in a European bank and earn interest. Third, at the end of the year, you withdraw your euros from the bank and sell them for dollars. For example, suppose that the current dollar price of euros is $1.25 and the interest rate paid on deposits in Europe is 5 percent. Suppose you also expect that the price of a dollar in euros will be EUR 0.70 in a year’s time. With the second investment strategy,

• You take your $100 and buy EUR 80.
• You put these EUR 80 in the European bank for a year, giving you EUR 84 at the end of the year.
• You take these EUR 84 and use them to purchase $120.

The second strategy therefore earns you more than the first strategy. It would be better to invest in Europe compared to the United States. Moreover, a slight variation on this strategy seems like it is a money machine. Consider the following.

• Borrow $100 from a US bank for one year.
• Take the $100 and use it to buy euros.
• Deposit the euros in a European bank.
• Wait for a year.
• Withdraw the deposit and interest and use it to buy dollars.
• Repay the dollar loan plus interest.

Using the same interest rates and exchange rates as previously, this transaction works as follows: you borrow $100, obtain $120 at the end of the year, pay back $110 to the bank, and end up with $10 profit.

To evaluate this arbitrage possibility, you need to know (1) the current dollar price of euros, (2) the annual return on deposits in Europe, and (3) the price of a dollar in euros a year from now. Look carefully at the language we used. You need to know “the euro price of dollars a year from now.” But when we went through the example, we said “you expect that the price of dollar in euros will be EUR 0.70 in a year’s time.” As with the term structure of interest rates, there is some risk involved here. You cannot know the future exchange rate with certainty. This strategy entails a gamble about the future exchange rate. Still, if everyone has the same guess about the future exchange rate as you do, then such a situation could not last. Everyone would pursue the same strategy: borrow in the United States, buy euros, invest in Europe, and convert back in a year’s time. What would happen?

• The demand for credit would increase interest rates in the United States.
• The demand for euros would increase the dollar price of euros.
• The extra supply of savings in Europe would drive down the interest rate in Europe.
• Investors might anticipate the extra demand for dollars in a year’s time and expect the euro price of dollars to increase.

These forces would all tend to eliminate the profit opportunity.

So when do we expect this arbitrage opportunity to disappear? It disappears when investors expect to make the same profit whether they invest in Europe or the United States. The condition for this is as follows:

nominal interest factor ($)=(euro price of dollarsexpected euro price of dollars next year)×nominal interest factor (EUR).

The left side is the return on investing in the United States. The terms on the right give the return on investing in Europe. When this condition holds, the returns on deposits in US and European banks are the same. This condition is called uncovered interest parityA relationship between interest rates in two countries and the expected change in the exchange rate that holds when the return earned by investing in assets denominated in different currencies are equal..

Because we do not know the price of euros next year for sure, this equation does not hold exactly when we look at actual data from the past. That is, the actual exchange rates combined with the actual returns on deposits do not quite satisfy this equation. This does not contradict the theory. Hindsight is perfect. The important point is that if people hold similar beliefs, then uncovered interest parity will hold ahead of time.

Using Uncovered Interest Parity to Understand the Exchange Rate

We can rearrange the uncovered interest parity condition as follows:

euro price of dollars=nominal interest factor ($)nominal interest factor (EUR)× expected euro price of dollars next year.

Written this way, the equation tells us that beliefs matter. Suppose everyone in the market believes that the dollar will depreciate relative to the euro in the future: that is, everyone expects a decrease in the euro price of the dollar. This makes investment in euro-denominated assets a better deal since we will get a lot of dollars per euro in the future. Investors will respond by selling dollars now to buy euros. This increase in the supply of dollars will cause the current euro price of dollars to decrease.

Thus we see that if everyone expects the euro price of dollars to decrease in the future, then the euro price of dollars will decrease today. When we talk about the market for currencies, demand and supply today depend on what households and firms think about the future exchange rate.

We can also rearrange the equation to see what it tells us about exchange rate beliefs:

expected euro price of dollars next yeareuro price of dollars=nominal interest factor (EUR) nominal interest factor ($).

If the interest rate in Europe is greater than the interest rate in the United States, then the condition tells us that investors must be expecting the dollar to appreciate.