Exchange rates
Currencies are bought and sold in the foreign
exchange market. The price at which one currency
exchanges for another in the foreign exchange
market is called the exchange rate.
For example, suppose one U.S. dollar buys 0.80
euros, i.e., 80 European cents. Therefore,
$1 = €0.80
which means that
1
€1 = ____
= $1.25.
0.80
Thus the euro exchange rate in terms of dollars is just
the reciprocal of the dollar exchange rate in terms of
euros. Why? 0.80 is the number of euros per dollar,
or €/$. If we want to obtain the number of dollars per
euro, or $/€, then
1
$/€ = ____
=
€/$
1
____
= $1.25.
0.80
The market for currencies is derived from the
international market for goods and services and
assets.
For example, when Americans buy goods or assets
from a foreign country, they must obtain some of the
foreign country’s currency in order to make the
transaction. This gives rise to a supply of dollars
and a demand for the foreign currency in the foreign
exchange market.
Similarly, when foreigners buy American goods or
assets, they must first acquire dollars, which gives
rise to a supply of the foreign currency and a demand
for dollars in the foreign exchange market.
The demand for dollars
The quantity of U.S. dollars demanded in the foreign
exchange market is the amount of dollars that traders
plan to buy during a given time period at a given
exchange rate.
Foreign residents demand dollars because of the U.S.
goods and services (U.S. exports) and assets (bonds,
stocks, bank deposits) the dollars can buy them.
The lower the dollar exchange rate (euros per dollar)
the greater is the quantity of dollars demanded; the
higher the dollar exchange rate, the less is the
quantity of dollars demanded:
A currency depreciation is the fall in the value of one
currency in terms of another currency.
For example, if the dollar falls from €0.80 to €0.75, the
dollar has depreciated against the euro by
approximately 6%.
Vice versa, a currency appreciation is the rise in the
value of one currency in terms of another.
For example, if the dollar falls from €0.80 to €0.75,
this means the euro has appreciated from $1.25 to
$1.33 (1/0.75 = 1.33), which is approximately a 6%
appreciation.
Why is there an inverse relationship between the
quantity of dollars demanded and the price of the
dollar in euros?
The lower the dollar exchange rate, or in other words
the weaker the dollar relative to the euro, the cheaper
are American goods and services to Europeans:
fewer euros are required to buy a dollar, or, in other
words, a euro buys more dollars and therefore more
American goods and services.
Therefore Europeans demand more American goods
and services, and consequently they must buy more
dollars in order to buy these goods and services.
Therefore the quantity of dollars demanded by
Europeans increases.
Factors that shift the demand curve for dollars
interest rates in the U.S. and in other countries
the expected future exchange rate.
Interest rates:
The higher the interest rate on U.S. financial assets
(bonds, bank deposits) compared to foreign assets,
the more U.S. assets will be purchased, both by
Americans and by foreigners.
What matters is not the level of U.S. interest rates
by itself, but the U.S. interest rate minus the foreign
interest rate. This gap is called the U.S. interest
rate differential.
If the U.S. interest rate differential increases, there will
be an increase in the demand for dollars. Foreigners
will be more interested in purchasing U.S. assets (and
less interested in purchasing their own assets) and
therefore, at any given exchange rate, they will be
more interested in purchasing dollars. The demand
curve for dollars will shift to the right.
Expected future exchange rate:
The higher the expected future exchange rate, the
greater is the expected profit from holding dollars and
the greater is the demand for dollars. If people
expect the dollar to be stronger in the future, they will
buy more dollars at any given current exchange rate
and the demand curve for dollars will shift to the right.
The supply of dollars
The quantity of U.S. dollars supplied in the foreign
exchange market is the amount of dollars that traders
plan to sell during a given time period at a given
exchange rate.
U.S. residents supply dollars in exchange for foreign
currency in order to buy foreign goods and services
(U.S. imports) and assets (bonds, stocks, bank
deposits).
The higher the dollar exchange rate (euros per
dollar) the greater is the quantity of dollars supplied;
the lower the dollar exchange rate, the less is the
quantity of dollars supplied:
Why is there a positive relationship between the
quantity of dollars supplied and the price of the dollar
in euros?
The higher the dollar exchange rate, or in other words
the stronger the dollar relative to the euro, the
cheaper are European goods and services to
Americans: fewer dollars are required to buy a euro,
or, in other words, a dollar buys more euros and
therefore more European goods and services.
Therefore Americans demand more European goods
and services, and consequently they must sell more
dollars, i.e., buy more euros, in order to buy these
goods and services. Therefore the quantity of
dollars supplied by Americans in exchange for euros
increases.
Factors that shift the supply curve of dollars
interest rates in the U.S. and in other countries
the expected future exchange rate.
Interest rates:
The higher the interest rate on U.S. financial assets
(bonds, bank deposits) compared to foreign assets,
the more U.S. assets will be purchased, both by
Americans and by foreigners.
Again, what matters is not the level of U.S. interest
rates by itself, but the U.S. interest rate minus the
foreign interest rate, i.e., the U.S. interest rate
differential.
If the U.S. interest rate differential increases, there will
be a decrease in the supply of dollars. Americans will
be more interested in purchasing their own domestic
assets (and less interested in purchasing foreign
assets) and therefore, at any given exchange rate,
they will be less interested in selling dollars in
exchange for euros. The supply curve of dollars will
shift to the left.
Expected future exchange rate:
The higher the expected future exchange rate, the
greater is the expected profit from holding off on
selling dollars today and waiting for their price to rise
in the future; hence the supply of dollars today will
decrease. If people expect the dollar to be stronger
in the future, they will sell less dollars at any given
current exchange rate and the supply curve of dollars
will shift to the left.
Market clearing equilibrium
At the market clearing equilibrium exchange rate, the
quantity of dollars demanded is equal to the quantity
supplied:
If there is an excess supply of dollars, as there is at
an exchange rate of €0.85, this means that at the
prevailing exchange rate, because the euro is so
cheap and the dollar is so expensive, Americans are
buying more goods from Europeans than Europeans
are buying from Americans.
Therefore, an excess supply of dollars means that the
U.S. has a trade deficit (U.S. imports exceed U.S.
exports) while Europe has a trade surplus (European
exports exceed European imports).
If there is an excess demand for dollars, as there is at
an exchange rate of €0.75, this means that at the
prevailing exchange rate, because the dollar is so
cheap and the euro is so expensive, Europeans are
buying more goods from Americans than Americans
are buying from Europeans.
Therefore, an excess demand for dollars means that
the U.S. has a trade surplus (U.S. exports exceed
U.S. imports) while Europe has a trade deficit
(European imports exceed European exports).
Assuming floating or flexible exchange rates, which
means that exchange rates are free to adjust to
equilibrium, these trade imbalances are eliminated
automatically through competitive market forces.
For example, as the dollar exchange rate weakens
from €0.85 to €0.80, the quantity of European goods
demanded by Americans decreases and the quantity
of American goods demanded by Europeans
increases, thereby eliminating the excess supply of
dollars and also eliminating the U.S. trade deficit and
the European trade surplus.
As the dollar exchange rate strengthens from €0.75 to
€0.80, the quantity of American goods demanded by
Europeans decreases and the quantity of European
goods demanded by Americans increases, thereby
eliminating the excess demand for dollars and also
eliminating the U.S. trade surplus and the European
trade deficit.
Changes in the equilibrium exchange rate
If the demand curve for dollars and/or the supply
curve of dollars shift, the market clearing equilibrium
exchange rate will change.
Both the supply of and demand for dollars are
influenced by the U.S. interest rate differential and by
expected future exchange rates. When these
influences change, both the supply curve and the
demand curve shift, but they shift in opposite
directions.
For example, suppose there is a decrease in the
expected future exchange rate of the dollar.
As we have seen, a decrease in the dollar’s expected
future exchange rate will cause a decrease in the
demand for dollars (a leftward shift of the demand
curve for dollars) and also an increase in the supply
of dollars (a rightward shift of the supply curve of
dollars):
Thus a decrease in the dollar’s expected future
exchange rate causes the market clearing equilibrium
exchange rate of the dollar to depreciate.
As another example, suppose U.S. GDP is increasing
while Europe is in a recession.
U.S. interest rates would rise because, as we have
seen, in a business cycle expansion there is increasing
demand for investment funds due to enhanced profit
expectations on the part of businesses.
European interest rates would fall because in a
recession profit expectations decrease and businesses
demand less funds for investment purposes.
Therefore, the U.S. interest rate differential increases.
As we have see, an increase in the U.S. interest
rate differential causes the demand for dollars to
increases and the supply of dollars to decrease:
Thus an increase in the U.S. interest rate differential
causes the market clearing equilibrium exchange rate
of the dollar to appreciate.
Exchange rate expectations
We have seen that a change in the expected future
exchange rate can cause the market clearing
equilibrium exchange rate to change. But what
causes expectations to change?
One of the major factors driving exchange rate
expectations is the presence or absence of
purchasing power parity (PPP).
PPP means that money buys the same basket of
goods and services in different countries irrespective
of which currency is used.
Thus, for example, if PPP prevails, a dollar buys the
same goods and services in Europe, when converted
into euros, as it would buy at home.
If prices rise in Europe relative to prices in the U.S.,
assuming no change in the exchange rate, then a
dollar, when converted into euros, will buy fewer
goods and services in Europe than it does in the
U.S. and PPP will not hold.
If prices were to rise faster in the U.S. than in
Europe, and again assuming the exchange rate
remains constant, then a dollar will actually buy more
goods and services in Europe than it would at home,
and again the PPP condition would not hold.
Thus PPP depends on the aggregate price level in
one country relative to that of another country. To
determine whether PPP prevails we really need to
look at the price level, i.e., the prices of all goods and
services, in both countries.
However, as a rough approximation, and to illustrate
the meaning of PPP, we will use the The Economist
magazine’s “Big Mac index,” which is based on the
price of a Big Mac in every different country in which
McDonald’s operates.
Suppose the dollar-euro exchange rate is $1 = €0.80.
Also assume that the average price of a Big Mac in
the U.S. is $3.00. In Europe suppose the average
price of a Big Mac is €2.70.
In this case, PPP does not exist: at an exchange rate
of $1 = €0.80, the euro equivalent of $3.00 would be
(3 X 0.80 =) €2.40. But a Big Mac in Europe actually
costs €2.70, which is the equivalent of (2.70/0.80 =)
$3.38.
Thus the dollar has less purchasing power in Europe
than it does in the U.S.: the euro is too expensive,
the dollar is too cheap.
If the euro were cheaper, i.e., if a dollar exchanged
for €0.90 instead of €0.80, then PPP would exist.
At an exchange rate of $1 = €0.90, the euro equivalent
of $3 would be (3 X 0.90 =) €2.70.
Now the price of a Big Mac is identical in both
countries: $3 will buy a Big Mac in both the U.S. and in
Europe.
This example illustrates the point that, if PPP does not
hold, given the price levels in the two countries, then
the exchange rate needs to adjust in order to restore
PPP.
In the Big Mac example, prices are higher in Europe
than in the U.S., therefore the dollar starts out being
too cheap and the euro too expensive. Judged by the
PPP standard, the dollar is undervalued and the euro
is overvalued. The dollar needs to appreciate (the
euro needs to depreciate) in order to bring about
PPP.
If Europe has a higher inflation rate than the U.S., and
the euro exchange rate does not adjust automatically,
then the euro will become overvalued (too expensive)
relative to the dollar and PPP will not exist.
Currency traders would then expect the euro to
depreciate and the dollar to appreciate. Why would
they expect this?
If prices are higher in Europe than in the U.S., there
will be an increase in the demand for dollars, as
Europeans buy more American goods, and a
decrease in the supply of dollars, as Americans offer
less dollars in exchange for euros since they are now
less interested in buying European goods.
The combined effect of an increase in the demand for
dollars and a decrease in the supply of dollars is an
increase in the market clearing equilibrium dollar
exchange rate, i.e., an appreciation of the dollar
(depreciation of the euro).
However, the foreign exchange market is very
efficient. Traders in the market will not sit around
waiting for the euro to depreciate and the dollar to
appreciate. As soon as they realize that PPP does
not hold between the euro and the dollar, they will
expect the euro to depreciate and the dollar to
appreciate.
And as we have seen, an increase in the expected
future value of the dollar will immediately cause an
increase in the demand for dollars and a decrease in
the supply of dollars, so that the dollar will
immediately appreciate in response to these
expectations.
Fixed exchange rates
So far we have assumed that the dollar-euro
exchange rate is floating or flexible, i.e., free to adjust
to equilibrium in response to shifts of supply and
demand.
However, sometimes the monetary authorities in a
country will choose to have a fixed exchange rate.
Under a fixed exchange rate regime, the central
bank announces an official exchange rate, which
need not necessarily coincide with the market
clearing equilibrium exchange rate.
Suppose, hypothetically, that the Fed wanted to fix the
dollar-euro exchange rate at €0.85 per dollar, which is
above the market clearing equilibrium exchange rate
of €0.80 per dollar.
At an exchange rate of $1 = €0.85, the dollar is
overvalued.
Normally, under floating exchange rates, market
forces would bring the exchange rate back to
equilibrium at $1 = €0.80. But the Fed wants to keep
the exchange rate at $1 = €0.85.
To maintain the overvalued exchange rate of $1 =
€0.85, the Fed will need to intervene in the foreign
exchange market by buying dollars, which
decreases the supply of dollars in circulation:
When the Fed enters the foreign exchange market to
buy dollars, the supply of dollars decreases from S0
to S1. The Fed would need to keep buying dollars in
order to maintain the market equilibrium exchange
rate at €0.85 per dollar.
The Fed’s foreign exchange market intervention
affects the domestic monetary base and therefore
the money supply in the U.S.
The dollars that the Fed buys are removed from
circulation, which shrinks the domestic monetary base
and decreases the overall money supply.
The decrease in the money supply is deflationary:
recall from the equation of exchange, M.V = P.Y, that if
velocity, V, is stable and real GDP, Y, is constant at the
full employment level or potential GDP, then any
decrease in the money supply, M, will cause an equal
proportional decrease in the price level, P.
Thus we can conclude that, for a country’s central
bank to keep the currency permanently overvalued, it
must create domestic deflation.
Deflation, by increasing the purchasing power of the
currency, means that the currency would no longer be
overvalued at the higher exchange rate.
Alternatively, suppose that the Fed wanted to fix the
dollar-euro exchange rate at €0.75 per dollar, which is
below the market clearing equilibrium exchange rate
of €0.80 per dollar.
At an exchange rate of $1 = €0.75, the dollar is
undervalued.
Normally, under floating exchange rates, market
forces would bring the exchange rate back to
equilibrium at $1 = €0.80. But the Fed wants to keep
the exchange rate at $1 = €0.75.
To maintain the undervalued exchange rate of $1 =
€0.75, the Fed will need to intervene in the foreign
exchange market by selling dollars, which increases
the supply of dollars in circulation:
When the Fed enters the foreign exchange market to
sell dollars, the supply of dollars increases from S0 to
S1. The Fed would need to keep selling dollars in
order to maintain the market equilibrium exchange
rate at €0.75 per dollar.
The Fed’s foreign exchange market intervention
again affects the domestic monetary base and
therefore the money supply in the U.S.
In order to have enough dollars to sell, the Fed will
need to expand the domestic monetary base and
hence the overall money supply.
The increase in the money supply is inflationary: recall
from the equation of exchange, M.V = P.Y, that if
velocity, V, is stable and real GDP, Y, is constant at the
full employment level or potential GDP, then any
increase in the money supply, M, will cause an equal
proportional increase in the price level, P.
Thus we can conclude that, for a country’s central
bank to keep the currency permanently undervalued,
it must create domestic inflation.
Inflation, by reducing the purchasing power of the
currency, means that the currency would no longer be
undervalued at the lower exchange rate.
Thus, while under a floating exchange rate regime,
the exchange rate itself adjusts to bring about
equilibrium in the foreign exchange market (and
eliminate trade imbalances – deficits and surpluses –
between countries), under fixed exchange rates it is
the domestic price level, and therefore nominal GDP,
that must adjust instead.