Price in Local Exchange Rate Local Price
Price of a Big Mac in
Currency (currency/dollar) Converted to Dollars
Australia A$2.65 1.59 1.66
Canada C$2.99 1.51 1.98
China Yuan 9.90 8.28 1.20
France FFr17.50 6.10 2.87
Germany DM4.95 1.82 2.72
Hong Kong HK$10.2 7.75 1.32
Israel Shekel 13.9 4.04 3.44
Italy Lire4,500 1,799 2.50
Japan Â¥294 120 2.44
Malaysia M$4.52 3.80 1.19
Mexico Peso19.9 9.54 2.09
Poland Zloty5.50 3.98 1.38
Russia Ruble33.5 24.7 1.35
Switzerland SFr5.90 1.48 3.97
United Kingdom Â£1.90 .621 3.07
United States 2.43
Source: Â© 1999 The Economist Newspaper Group, Inc. Reprinted with permission. www.economist.com.
price in New York, the price will be forced down in Mexico and up in New York until
the profit opportunity disappears. This ensures that the dollar price of gold is about the
same in the two countries.2
Gold is a standard and easily transportable commodity, but to some degree you
might expect that the same forces would be acting to equalize the domestic and foreign
prices of other goods. Those goods that can be bought more cheaply abroad will be im-
ported, and that will force down the price of the domestic product. Similarly, those
goods that can be bought more cheaply in the United States will be exported, and that
will force down the price of the foreign product.
This conclusion is often called the law of one price. Just as the price of goods in
LAW OF ONE PRICE
Theory that prices of goods Safeway must be roughly the same as the price of goods in A&P, so the price of goods
in all countries should be in Mexico when converted into dollars must be roughly the same as the price in the
equal when translated to a United States:
peso price of goods in Mexico
Dollar price of goods in USA =
number of pesos per dollar
peso price of gold in Mexico
Price of gold in Mexico = 300 Ã— 9.438 = 2,831 pesos
No one who has compared prices in foreign stores with prices at home really believes
that the law of one price holds exactly. Look at the first column of Table 6.6, which
2Activity of this kind is known as arbitrage. The arbitrageur makes a riskless profit by noticing discrepan-
cies in prices.
604 SECTION SIX
shows the price of a Big Mac in different countries in 1999. Using the exchange rates
at that time (second column), we can convert the local price to dollars (third column).
You can see that the price varies considerably across countries. For example, Big Macs
were 60 percent more expensive in Switzerland than in the United States, but they were
about half the price in Malaysia.3
This suggests a possible way to make a quick buck. Why donâ€™t you buy a hamburger-
to-go in Malaysia for $1.19 and take it for resale to Switzerland where the price in dol-
lars is $3.97? The answer, of course, is that the gain would not cover the costs. The law
of one price works very well for commodities like gold where transportation costs are
relatively small; it works far less well for Big Macs and very badly indeed for haircuts
and appendectomies, which cannot be transported at all.
The Beer Standard
There are very few McDonaldâ€™s branches in Africa, so we canâ€™t use Big Macs to test the
law of one price there. But barley beer is a common and relatively homogeneous prod-
uct throughout Africa. So we can test the law of one price using the beer standard.
Table 6.7 shows the price of a bottle of beer in several African countries expressed
in local currencies and converted into South African rand using the spot exchange rate.
For example, beer in Kenya cost 41.25 shillings; at an exchange rate of 10.27 Kenyan
shillings per rand, this is equivalent to a price of 41.25/10.27 = 4.02 rand. This is 1.75
times the cost of beer in South Africa; for the costs to be equal, the shilling would need
to depreciate by 75 percent to a new exchange rate of 10.27 Ã— 1.75 = 17.9 shillings per
rand. Therefore, we might say that this comparison suggests the shilling is 75 percent
overvalued against the rand.
The price of a beer in
Beer Prices Actual Rand Valuation
In Local In Exchange Rate, against the
Country Currency Rand March 1999 Rand, %
South Africa Rand2.30 2.30
Botswana Pula2.20 2.94 0.75 28
Ghana Cedi1,200 3.17 379.10 38
Kenya Shilling41.25 4.02 10.27 75
Malawi Kwacha18.50 2.66 6.96 16
Mauritius Rupee15.00 3.72 4.03 62
Namibia N$2.50 2.50 1.00 9
Zambia Kwacha1,200 3.52 340.68 53
Zimbabwe Z$9.00 1.46 6.15 â€“36
Source: The Economist, May 8, 1999.
3 Ofcourse, it could also be that Big Macs come with a bigger smile in Switzerland. If the quality of the ham-
burgers or the service differs, we are not comparing like with like.
International Financial Management 605
Countries with high inflation 20
rates tend to see their
Annual relative change in exchange rate, percent
currencies depreciate. States
100 80 60 40 20 20
Annual relative change in purchasing power, percent
A weaker version of the law of one price is known as purchasing power parity, or
PARITY (PPP) Theory PPP. PPP states that although some goods may cost different amounts in different coun-
that the cost of living in tries, the general cost of living should be the same in any two countries.
different countries is equal,
Purchasing power parity implies that the relative costs of living in two
and exchange rates adjust to
countries will not be affected by differences in their inflation rates. Instead,
offset inflation differentials
the different inflation rates in local currencies will be offset by changes in the
exchange rate between the two currencies.
For example, between 1993 and 1998 Russia experienced high inflation. Each year
the purchasing power of the ruble declined by nearly 35 percent compared with other
countriesâ€™ currencies. As prices in Russia increased, Russian exporters would have
found it impossible to sell their goods if the exchange rate had not also changed. But,
of course, the exchange rate did adjust. In fact each year the ruble bought over 33 per-
cent less foreign currency than before. Thus a 35 percent annual decline in purchasing
power was offset by a 33 percent decline in the value of the Russian currency.
In Figure 6.2 we have plotted the relative change in purchasing power for a sample
of countries against the change in the exchange rate. Russia is toward the bottom left-
hand corner; the United States is closer to the top right. You can see that although the
relationship is far from exact, large differences in inflation rates are generally accom-
panied by an offsetting change in the exchange rate. In fact, if you have to make a long-
term forecast of the exchange rate, it is very difficult to do much better than to assume
that it will offset the effect of any differences in the inflation rates.
If purchasing power parity holds, then your forecast of the difference in inflation
rates is also your best forecast of the change in the spot rate of exchange. Thus the ex-
pected difference between inflation rates in Mexico and the United States is given by
the right-hand boxes in Figure 6.1:
606 SECTION SIX
Expected difference Expected change in
in inflation rates spot exchange rate
1 + ipeso E(speso/$)
1 + i$ speso/$
For example, if inflation is 2 percent in the United States and 20 percent in Mexico,
then purchasing power parity implies that the expected spot rate for the peso at the end
of the year is peso11.10/$:
Current expected difference
Ã— = expected spot rate
spot rate in inflation rates
9.438 Ã— = 11.10
Suppose that gold currently costs $330 an ounce in the United States and Â£220 an ounce
in Great Britain.
a. What must be the pound/dollar exchange rate?
b. Suppose that gold prices rise by 2 percent in the United States and by 5 percent in
Great Britain. What will be the price of gold in the two currencies at the end of the
year? What must be the exchange rate at the end of the year?
c. Show that at the end of the year each dollar buys about 3 percent more pounds, as
predicted by PPP.
INFLATION AND INTEREST RATES
Interest rates in Mexico in 1999 were about 25.25 percent. So why didnâ€™t you (and a few
million other investors) put your cash in a Mexican bank deposit where the return
seemed to be so attractive?
The answer lies in the distinction that we made earlier between nominal and real
rates of interest. Bank deposits usually promise you a fixed nominal rate of interest but
they donâ€™t promise what that money will buy. If you invested 100 pesos for a year at an
interest rate of 25.25 percent, you would have 25.25 percent more pesos at the end of
the year than you did at the start. But you wouldnâ€™t be 25.25 percent better off. A good
part of the gain would be needed to compensate for inflation.
The nominal rate of interest in 1999 was much lower in the United States, but then so
was the inflation rate. The real rates of interest were much closer than the nominal rates.
There is a general law at work here. Just as water always flows downhill, so
capital always flows where returns are greatest. But it is the real returns that
concern investors, not the nominal returns. Two countries may have different
nominal interest rates but the same expected real interest rate.
Theory that real interest rates
in all countries should be
Do you remember Irving Fisherâ€™s theory that changes in the expected inflation rate
equal, with differences in
are reflected in the nominal interest rate? We have just described here the international
nominal rates reflecting
Fisher effectâ€”international variations in the expected inflation rate are reflected in the
differences in expected
nominal interest rates:
International Financial Management 607
Difference in Expected differences
interest rates in inflation rates
1 + rpeso 1 + ipeso
1 + r$ 1 + i$
In other words, capital market equilibrium requires that real interest rates be the
same in any two countries.
International Fisher Effect
If the nominal interest rate in Mexico is 25.25 percent and the expected inflation is 20
1 + rpeso 1.2525