Real Exchange Rates

The teal exchange rate ts the rate at which a person can trade the goods and services of one country for the goods and services of another. For example, if yon go shopping and find that a pound of Swiss cheese is twice as expensive as a pound of American cheese, tlx- real exchange rate is V: pound of Swiss cheese per pound of American chccse. Notice that, like the nominal exchange rate, we express the real exchange rate as units of the foreign item per unit of the domestic item. But in this instance, the item is a good rather than a currency.

Real and nominal exchange rates are closely related. To sec how, consider an example. Suppose that a bushel of American rice sells for S100, and a bushel of Japanese rice sells for 16,000 yen. What is the real exchange rate between American and Japanese rice? Toanswcr this question, we must first use the nominal exchange rate to convert the prices into a common currency. If the nominal exchange rate is 80 yen per dollar, then a price for American rice of $100 per bushel is equivalent to 8,000 yen per bushel. American rice is half as expensive as Japanese rice The real exchange rate is '/S bushel of Japanese rice per bushel of American rice.

We can summarize this calculation for the real exchange rale with the following formula:

Re-al oxdwngo rate

V--nm.il o dying».- r.'t. • [X-.fii.price foreign price

Using the numbers in our example, the formula applies as follows:

Real exchange rale

(81) yen/dollar) X «lM/buahelof American rice) I6.1XX1 y«n/bu*hel of lapvvwse rk»

tMjOOvcn/biiahel oi American rice - 16X3CO >vn/t*ushi-l <»» JapaiH-e ricv

= Vi buvhcl of Japanese ride/bushel of American rice.

Thus, the real exchange rate depends on the nominal exchange rate and on the prices of goods in the two countries measured in the local currencies.

Why does the real exchange rate matter? As you might guess, the real exchange rate is a key determinant of how much a country exports and imports. When Uncle Ben's, Inc., is deciding whether to buy US. rice or Japanese rice to put into its boxes, for example, it will ask which rice is cheaper. The real exchange rate gives the answer. As another example, imagine that you are deciding whether to take a seaside vacation in Miami, Florida, or in Cancun, Mexico. You might ask your travel agent the price of a hotel room in Miami (measured in dollars), the price of a hotel room in Cancun (measured in pesos), and the exchange rate between pesos and dollars. If you decide where to vacation by comparing costs, you are basing your decision on the real exchange rate.

When studying an economy as a whole, macroeconomists focus on overall prices ratlter than tin- prices of individual items. That is, to measure the real exchange rate, they use prke indexes, such as the consumer prke index, whkh measure the price of a basket of goods and servkes. By using a price index for a US. basket (P), a prke index for a foreign basket (P*), and the nominal exchange rate between the US. dollar and foreign currencies («•), we can compute the overall real exchange rate between tl>e United States and other countries as follows:

This real exchange rate measures the price of a basket of goodsaiul servkes available domestkallv relative to a basket of goods and servkes available abroad.

As we examine more fully in the next chapter, a country's real exchange rate is a key determinant of its net exports of goods and services. A depreciation (fall) in lite US. real exchange rate means that US. goods have become cheaper relative to foreign goods. This cliange encourages consumers both at home and abroad to buy more U.S. goods and fewer goods from other countries. As a result, US. exports rise, and US. imports fall; both of these changes raise U.S. net exports. Conversely, an appreciatkm (rise) in the US. real exchange rate means that US. goods have become more expensive compared to foreign goods, so US. net exports fall.

QUICK QUIZ Defitv» nominal oxclwiv^» rat« and 'oal exdung» ran>, and explain how they are related. • If the nominal exchange rate goes from 100 to 120 yen pet dollar, haj the dollar appreciated or dep'ecated?

How a ¿'eak Dollar Boosts Exports

In 2007 the? U.S. dollar weakened in foreign exchange markets, benefiting shoppers from abroad

With Dollar Low, U.S. Is One Big Outlet; Europeans Arriving in Droves for Bargains

By Jenn Abelson

Hwn tfter her fli/n from Dubln Urdcd in Boston on Ttuntegvna Ake KJnstiU beixfcd in a *bte van *lth a dozen rebwes and frtends to Wfenthjm vllage Premium cutett. II* 36-yeat-okJ has never *sted Boston but she is by^Miiivg the tights for jn eitcrxiid vvK+xrdc/tirgc- shopping for Kinsela and Mhflt Amet-

Ka a one big dsrount fc«n. ttarwi to a weal cHU th« slid tfw *eek to ancthe« recotd knv agansi the ow. At a ifiufe. toulists are spencing thousands to travel to the Unted States to srag Mot* buster bargains cn everything bom to designer tlotbr. and h.ndb.>gs

8/ •» am yesetdar. Ktisella hjd tung up warty $2,000 in ChrrJmos present» and vvrrtrrdothet,inckjdnga leatlvt lacfcet at Guess that she estimated *wA» cos! mute thin $iiO in Matid

The twrfjilns bimw»greet" sad KinvPlai who WW 5t£C0 for a flight and becet but ei peels to uveeven mate on pj> chws tiw

rational tourists w+io scheduled organised sheporg tups yesterday to Wrentfum Vtl tape Pten-ium Oubts— nw then ctouble to,nr. i\r. ulT.

Ibe r».mbci las! year. Ituncfreds mere were expected to com.- on ther own. acccdw»] to Beth Wmboum» the ootids QEnetal marucrr

FoteO" traveters ha»« long visited the United States to get the» IxJtddr, shep ptng Ik. After all many designer brands lile Tommy Hlftger. Ri^ph Lauren, and Goess are cheaper bete because sates ta*es ate losvet trd because thr fciggei mirtet here alt*« ooods to be prtccd mote compettt^V

But now Ameikan wares are even mare ol a turgUn .r. the sbAing US. economy has weakened the dola* Fuithe», as the fedeial ftesetve his tut interest tales to boost the economy, the dciUr bus bvt cvrn more «rt*. and glot»l irt.estots her.e «allied they swn't earn as much wlien they pari thrrr«h(n7wnhttks As.i vwt. ttw •mo K» stwt up by 33 «»cent compared wth the iiJw since 200& so Europeans *ho ercharqe I £00 cvros now get tlote to 1,500 US. dctos And the Canada (Ml* is atxth as much as the US. datai lor the frst time n three decades wnle «me US. shoppers ate tr/iteninj their pu-se stnngt this toldjy season amid Hsng ijjsolne fees, the skimping housing maiktt. and the cunem credt ouxh, the one sit/er Smug tot itmp me«bants a the tidd wa»e of fce+an dolats pourtng no U.S. sicres.

V/lth Amcrcjrrs looking to cut bo:k and ccosctve because of economic urcenan tes. the holy grail this hdiday season ywi tcf wallers are the intomwionil tr».rlers wlio ¿no coming here in ie<crd number^" sad Patncl Mo«antoto, president c! the Gn?aierEo«onCorr.ention4vistors Oxeau Boston is projKtrig a It percent noea« n o/cviMi wsitcrs this month ccmpxed -Ailh Mo-icnibeiofbstyear

Tt* watei dolVii iso 6 promoting tounsm. On Mnndiy, the US. Department of Commerce saw ihls p»st summe» was a recoid-breatfig seinori for inteirutioral tiar.rl to the tinned States. Both the number of traveler, ard overall spending by v.sim surpjssed pressws highs. Ttie wait/ SJO.7 blloo Inn-qn •.tstois spent this summri, whkh Yr.hries pij^hases of Sax!, todging. and gifts, was a 14 percent rcrease over ttie siMTsmetof list >sm>

The pitxrrte ot ba^an shopprg ii a rrufoi draw tot some rternstonal Iras-etets.

■b«- r««n»tionil Counol of 'nop ory Centers «eteased a sw»«y Wedrii diy reposing thit ¿0 percert cf Carodun boiwWds«id a strcrq kwnte |a Ntfciume lot the Caradian dcd*. which has a !oon on ill should lure them to shop n the Urrted States and to fKtcent Hid they pl»rr»xl to pwdiase tiolday ghs by teleotone cr crtlne frcm US. mai-n. Altcad/, U. Bean, the preppy tatatogp- m Fwpon. KWw. •dd It his seen otden Itoni Cmiidi rise more than ,0 percent recently.


Exchange rates vary substantially over time. In 1070, a US. dollar could be used to buy 3.0? German marks or 627 Italian lira. In 1W8, as both Germany and Italy were getting ready to adopt the euro as their common currency, a US. dollar bought 1.76 German marks or 1,737 Italian lira. In other words, over this period, the value of the dollar fell by more than half compared to the mark, while it more than doubled compared to the lira.

What explains these large and opposite changes? Economists have developed many models to explain how exchange rates are determined, each emphasizing just some of the many forces at work. Here we develop the simplest theory of exchange rates, called purchasing-power parity. This theory states that a unit of any given currency should be able to buy the same quantity of goods in all countries. Many economists believe that purchasing-power parity describes the forces that determine exchange rates in the long run. We now consider the logic on which this long-run theory of exchange rates is based, as well as the theory's implications and limitations.

The Basic Logic of Purchasing-Power Parity

The theory of purel»asing-power parity is based on a principle called the law of imc yrice■ This law asserts that a good must sell for the same price in all locations-Otherwise, there would be opportunities for profit left unexpku'ted. For example, suppose that coffee beans sold for less in Seattle than in Boston. A person could buy coffee in Seattle for. say, $4 a pound and then sell it in Boston for $5 a pound, making a profit of SI per pound from the difference in price. The process of taking advantage of price differences for the same item in different markets is called arbitrage. In our example, as people took advantage of this arbitrage opportunity, they would increase tin- demand for coffee in Seattle arid increase the supply in Boston. The price of coffee would rise in Seattle (in response to greater demand) and fall in Boston (in response to greater supply). This process would continue until, eventually, the prices were the same in the two markets.

Now consider how the law of one price applies to the international marketplace. If a dollar (or any other currency) could buy more coffee in the United States than in lapan, international traders could profit by buying coffee in the United States and selling it in Japan. This export of coffee from the United Stales to )apan would drive up the US- price of coffee and drive down the Japanese price. Conversely, if a dollar could buy more coffee in Japan than in the United States, traders could buy coffee in lapan and sell it in the United Stales. This import of coffee into the United States from Japan would drive down the U.S. price of coffee and drive up the Japanese price. In the end, the law of one price tells us that a dollar must buy the same amount of coffee in all countries.

This logic leads us lo the- theory of purchasing-power parity. According to this theory, a currency must have the same purchasing power in all countries. That is. a US. dollar must buy the sime quantity of goods in the United States and Japan, and a la panose yen must buy the same quantity of goods in lapan and the United Stales. Indeed, the name of this theory describes il well. Parity means equality, and purchasing poteer refers to the value of money in terms of the quantity of gocxls purchasing, power parity a theory ol exchanqe rates «hereby a unit ot any given currency should be able to buy the same quantity of goods in all countries

it on buy. Purchasing-pomr parity states that a unit of a currency must have the same real value in every country.

Implications or Purchasing-Power Parity

What does the theory of purchasing-power parity say about exchange rates? It tells us that the nominal exchange rate between the currencies of two countries depends on the price levels in those countries. If a dollar buys the same quantity of goods in the United States (where prices ate measured in dollars) as in Japan (where prices are measured in yen), then the number of yen per dollar must reflect the prices of goods in the United States and Japan. For example, if a pound of coffee costs 500 yen in Japan and $5 in the United States, then the nominal exchange rate must be 101) yen per dollar (500 ven/S5 = 100 yen per dollar). Otherwise, the purchasing power of the dollar would not be the same in the two countries.

To sec more fully how this works, it is helpful to use just a bit of mathematics-Suppose that P is the price of a basket of goods in the United States (measured in dollars), P* is the price of a basket of goods in Japan (measured in yen), and e is the nominal excliange rate (the number of yen a dollar can buy). Now consider the quantity of goods a dollar can buy at home and abroad. At home, the price level is P, so the purchasing power of ¿1 at home is I /P. That is. a dollar can buy 1 /P quantity of goods. Abroad, a dollar can be exchanged into e units of foreign currency, which in turn have purchasing power «7P*. For the purchasing power of a dollar to be the same in the two countries, it must be the case that

Notice that the left side of this equation b a constant, and the right side is the real exchange rate. Thus, if the purchasing power of the dollar is dfauys the same irt home and afnvad, then the teal w^timge rule—the retain* price of domestic and foreign good» cannot change.

To see the implication of this analysis for the nominal exchange rate, we can rearrange the List equation to solve for the nominal exchange rate:

That is, the nominal exchange rate equals the ratio of the foreign price level (measured in units of the foreign currency) to the domestic price level (measured in units of the domestic currencyj. According to the theory of purchasing-power parity, the luminal exchange rate lvuceen the currencies of law countries must reflect the price levdt m Ihose countries.

A key implication of this theory is that nominal exchange rales change when price levels change. As we saw in the preceding chapter, the price level in any country adjusts to bring the quantity of money supplied and the quantity of money demanded into balance- Because the nominal exchange rate depends on the price levels, it also depends on the money supply and money demand in each country. When a central bank in any country increases the money supply and causes the price level to rise, it also causes that country's currency to depreciate relative to

With rearrangement, this equation becomes

other currencies in the world. In other words, ;ohen the central bank prints large quantrtiet of money, thai money to<e* value both in term< of the good* and írmwíí it can buy ami in terms of the amount of other currencies it can buy

We ean now answer the quest »in that began this section: Why did the US. dollar lose value compared to the German mark and gain value compared to the Italian lira? The answer is that Germany pursued a less inflationary monetary policy than the Unit id States, and Italy pursued a more inflationary monetary policy. From 1970 to 1998, inflation in the United States was 53 percent per year. By contrast, inflation was 3.5 percent in Germany and 9.6 percent in Italy. As US. prices rose relative to German prices, the value of the dollar fell relative to the mark. Similarly, as US. prices fell relative to Italian prices, the value of the dollar rose relative to the lira.

Germany and Italy now have a common currency—the euro. This means that the two countries share a single monetary policy and that the inflation rates in the two countries will be ekisely linked. But the historical lessons of the lira and the mark will apply to the euro as well. Whether the US. dollar buys more or fewer euros 20 years from now than it does today depends on whether the European Central Bank produces more or less inflation in Europe lhan the Federal Reseñe does in the United States.

the nominal exchange rate jfotf* during a hyperinflation dLi

Macroeconomists can only rarely conduct controlled experiments. Most often, they must glean what Ihey can from the natural experiments that history gives them. One natural experiment is hyperinflation—lite high inflation tltat arises when a government turns to the printing press to pay for large amounts of government spending. Because hyperinflations are so extreme, Ihey illustrate some basic economic principles with darilv.

Consider the German hyperinflation of the early 192th.. Figure 3 shows the German money supply, the German price level, and the nominal exchange rale (measured as US. cents per German mark) for that period. Noticx' that these series move closely together. When the supply of money starts growing quickly, the prke level also takes off, and the German mark depreciates. When the money supply stabilizes, so do the price level and the exchange rate.

The pattern shown in this figure appears during every hyperinflation. It leaves no doubt that there is a fundamental link among money, prices, and the nominal exchange rate- The quantity theory of money discussed in the previous chapter explains how the money supply affects the price level. The theory of purchasing-power parity discussed hero explains how the price level affects the nominal exchange rate •

Limitations of Purchasing-Power Parity

Purchasing-power parity provides a simple model of how exchange rates are determined. For understanding many ecoriomk phenomena, the theory works well. In particular, it can explain many long-term trends, such as the depreciation of the US. dollar against the German mark and the appreciation of the US. dollar against the Italian lira. It can also explain the major changes in exchange rates that occur during hyperinflations.

Yet Ihe theory of purchasing-power parity is not completely accurate. That is, exchange rates do not always move to ensure that a dollar has the same real value in all countries all the time. There are two reasons the theory of purchasing-power parity does not always hold in practice.

The first reason is that many gixidsare not easily traded. Imagine, for instance, that haircuts are more expensive in I'aris than in New York. International travelers might avoid getting their haircuts in Paris, and some hair cutters might move irons New York to Paris. Yet such arbitrage would be too limited to eliminate the differences in prices. Thus, the deviation from purchasing-power parity might persist, and a dollar (or emro) would continue to buy less of a haircut in Paris than in New York.

The second reason that purchasing-power parity does not always hold is that even tradable goods are not always perfect substitutes when they are pniduced in different countries. For example, some consumers pre-fer German cars, and others prefer American cars. Moreover, consumer tastes can changeover time. If German cars suddenly become more popular, the increase in demand will drive up the price of German cars compares! to American cars. Despite this difference in prices in the two markets, there might be no opportunity for profitable arbitrage because consumers do not view the Iwo cars as equivalent.

Thus, both because some goods are not tradable and because some tradable goods are not perfect substitute» with their foreign counterparts, purchasing-power parity is not a perfect theory of exchange-rate determination. For these reasons, real exchange rate» fluctuate over time. Nonetheless, the theory of purchasing-power parity does provide a useful firs« step in understanding exchange rates. The basic logic is persuasive: As the real exchange rate drifts from the level predicted by purchasing-power parity, people have greater incentive to move goods across national borders- Even if the forces of purchasing-power parity do not completely fix the real exchange rate, they provide a reason to expect that changes in the real exchange rate are most often small or temporary. As a result, large and persistent movements in nominal exchange rates typically re fleet changes in price levels at home and abroad.


When economists apply the theory of pu rchasing-power parity to explain exchange rates, they need data on the prices of a basket of goods available in different countries. One analysis of this sort is conducted by The Economic, an international newsmagazine. The magazine occasionally collects data on a basket of goods consisting of "two all-beef patties, special sauce, lettuce, cheese, pickles, onions, on a sesame seed bun " It's called the "Big Mac" and is sold by McDonald's around the world.

Once we have the prices of Big Macs in two countries denominated in the local currencies, we can compute the exchange rate predicted by the theory of purchasing-power parity The predicted exchange rate is the one that makes the cost of the Big Mac the same in the two countries. For instance, if the price of a Big Mac is S3 in the United States and 3<X> yen in Japan, purchasing-power parity would predict an exchange rate of 100 yen per dollar.

How well dot's purchasing-power parity work when applied using Big Mac-prices? Mere are some examples from July 2007, when the price of a Big Mac was $3.41 in the United States:


Predicted Ewfwig* Rrttn

Actual Exchange RM»

Mfïic-O turc ifti Britain

/.400 bolffj/ 2.900 won 2t0 yen 33 kroner 28 pesos 3.06 e-jros 1.99 poundi

2.17C boivji.'i 850 worV$ 82yerVS 10.1 k/Cr»oi/S 9 7 pesoVS 0.90 aurcxSi 055 pour ft V.

You cam riso a Bo Mac

ft u

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