Chapter 15
Price Levels
and the
Exchange Rate
in the Long Run
Slides prepared by Thomas Bishop
Preview
• Law of one price
• Purchasing power parity
• Long run model of exchange rates: monetary
approach
• Relationship between interest rates and inflation:
Fisher effect
• Shortcomings of purchasing power parity
• Long run model of exchange rates: real exchange
rate approach
• Real interest parity
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15-2
4. Empirical Evidence on PPP
and the Law of One Price
• How well does the PPP theory explain exchange
rate determination in real world changes?
• Weak empirical support for PPP and the law of
one price in recent data.

The prices of identical commodity baskets, when
converted to a single currency, differ substantially
across countries.

Relative PPP is sometimes a reasonable
approximation to the data, but overall it also performs
poorly.
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15-3
Shortcomings of PPP (cont.)
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15-4
Shortcomings of PPP (cont.)
Reasons why PPP may not be a good theory
(even in the LR):
1. Trade barriers and non-tradable goods
and services
2. Imperfect competition
3. Differences in price level measures
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15-5
Shortcomings of PPP (cont.)
• Trade barriers and non-tradables

Transport costs and governmental restrictions
make trade expensive and in some cases create
non-tradable goods or services.

Services are often not tradable: services are
generally offered within a limited geographic region
(e.g., haircuts).

The greater the transport costs, the greater the
range over which the exchange rate can deviate
from its PPP value.

One price need not hold in two different markets.
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15-6
Shortcomings of PPP (cont.)
• Imperfect competition may result in price
discrimination: “pricing to market”.


A firm sells the same product for different prices in different
markets to maximize profits
Based on different expectations about how much consumers
are willing to pay across the markets.
• Differences in price level measures

Price levels differ across countries because of the difference
in “representative baskets” of goods and services.
• People of different countries spend their income differently.

Because the purchased goods and services are different,
the measure of their prices need not be the same.
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15-7
Shortcomings of PPP (cont.)
• PPP in the Short Run and Long Run
 Departures
of national price levels from the
PPP (law of one price) may be even greater
in the short- run than in the long run.
• Because many prices are sticky in the short-run.
• Example: An abrupt depreciation of the dollar
causes the price of goods in the U.S. to be
lower than the foreign’s, until markets adjust to
the abrupt exchange rate change.
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15-8
Beyond PPP: A General Model of LR
Exchange Rate: Real exchange rate
approach
• Because of the shortcomings of PPP,
economists have tried to generalize the
monetary approach.

Basic idea of PPP (relating LR exchange rate to
LR national price levels) is a useful starting point.

However, the monetary approach is too simple to
predict the exchange rates in the real world.

Generalize the model.
• Still, this is a LR analysis, ignoring SR complications.
• If PPP holds, the new model loses its significance.
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15-9
The Real Exchange Rate Approach
• The real exchange rate is the rate of
exchange for real goods and services across
countries.
• The real exchange rate q$/€ = (E$/€ x PEU)/PUS,
where E$/€: nominal exchange rate, PEU is the euro price of
a reference commodity basket containing typical weekly
purchase in Europe, and PUS is similarly defined for US
(i.e., different baskets).

Defining this concept is the first step in extending
PPP theory.
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15-10
The Real Exchange Rate Approach
to Exchange Rates (cont.)
• Real exchange rate q $/€ = (E$/€ x PEU)/PUS
• It is the relative price of goods and
services across countries.
• It is the dollar price of a European basket of
goods and services divided by the dollar price
of a American basket of goods and services.

q$/€=2 implies European price level is twice as high
as that of US.

If the EU basket costs €100, the US basket costs
$120 and the nominal exchange rate is $1.20
($2.40) per euro, then the real exchange rate is 1(2)
US basket per 1 EU basket.
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15-11
The Real Exchange Rate Approach
to Exchange Rates (cont.)
• A rise in q $/€ means a fall in a dollar’s
purchasing power for EU products relative to
a dollar’s purchasing power for US products.

A real depreciation of the dollar against the euro

The real depreciation implies that US goods
become cheaper relative to the EU goods
• q $/€ is the relative price of European products in general
in terms of American products.

This may imply that the value of US products
relative to the EU products declines.
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15-12
The Real Exchange Rate Approach
to Exchange Rates (cont.)
• A fall in q $/€ means a real appreciation of the
dollar against the euro.
• A rise in a dollar’s purchasing power of EU products
relative to a dollar’s purchasing power of US products.

This implies that US goods become more expensive relative
to EU goods
• Or the value of US goods relative to value of EU goods rises.
• The real appreciation (depreciation) can take place
through three channels, i.e., change in E$/€, PEU, PUS

Nominal appreciation (depreciation) implies real appreciation
(depreciation), at unchanged output prices.
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15-13
Simple example: real exchange rate
• Suppose the reference basket is identical
between EU and US, composed of only one
good, namely car.

Suppose PEU= €10,000, PUS = $ 12,000, E$/€=1.2 in
2006.
• Then q $/€ =1 in 2006

Suppose PEU = €10,000, PUS = $ 18,000, E$/€=1.5
in 2007.
• Then in 2007, q $/€= (1.5) (10,000/18,000)= 0.833
• Real appreciation of the dollar against the euro
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15-14
Demand, Supply and the LR Real
Exchange Rate
• The LR value of the q $/€ depend on demand
and supply conditions, in a world where PPP
does not hold.

When relative PPP holds, the real exchange
rate never change.
• q$/€= E$/€ x (PEU/PUS), implying that (% change in q$/€) =
(% change in E$/€) + (% change in PEU - % change in PUS)
• The right side will be 0 if the relative PPP holds.
• Two specific cases of interests explaining why
it can change.
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15-15
Demand, Supply and the LR Real
Exchange Rate
• 1. A change in (world) relative demand for US
products

An increase in relative demand for US output causes the
relative price of US products in terms of European goods to
rise (for both tradables and non-tradables).

i.e.: PUS rises relative to E$/€ x PEU

This price change leads to a decline in q $/€ (a real
appreciation of dollar against euro),

A decrease in relative demand for US output leads to a real
depreciation of the dollar against the euro (a rise in q $/€).
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15-16
Demand, Supply and the LR Real
Exchange Rate
• 2. A change in relative supply of US
products

An increase in relative supply for US output (eg.
caused by an increase in US productivity) causes
the relative price of US goods in terms of
European goods to fall.

PUS falls relative to E$/€ x PEU, ,eliminating the
excess supply.

It leads to an increase in q $/€ (a real depreciation
of dollar against euro),

A decrease in relative supply for US output leads
to a real appreciation of dollar (decrease in q$/€).
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15-17
Determining
the Long Run Real
Exchange Rate
In the long run, the supply
of goods and services in
each country depends on
factors of production like
labor, capital and
technology—not prices or
exchange rates.
The demand for US
products relative to the
demand for EU products
depends on the relative
price of these products, or
the real exchange rate.
When the real exchange
rate, qUS/EU =
(E$/€PEU)/PUS
is high, the relative
demand for US products
is high.
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15-18
Determining
the Long Run
Real Exchange
Rate (cont.)
When the relative
supply of US products
matches the relative
demand for US
products, there is no
tendency for the price
of US products
relative to EU
products to change.
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15-19
Demand, Supply and the LR Real
Exchange Rate
• Now, we can analyze the how changes
in world markets affect the real
exchange rate, using the above diagram.
 Examples:
 World
oil price decrease (increase).
• Through its effect on demand of American sport
utility vehicles.
 US
improvement in its health-care system.
• Through its effect on productivity of US workers
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15-20
Nominal and Real Exchange Rates in LR
equilibrium.
• We can see how LR nominal exchange
rates are determined, by pulling together
what we have learned so far.
• Recall that the definition of real
exchange rate is the following.
q $/€ = (E$/€ x PEU)/PUS
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15-21
Nominal and Real Exchange Rates in LR
equilibrium
• According to monetary approach (PPP), exchange
rates are determined by relative price ratios:
E$/€ = PUS/PEU
• According to the general real exchange rate
approach, nominal exchange rates may also be
influenced by the real exchange rate:
E$/€ = q $/€ x PUS/PEU

This approach accounts for possible deviations from PPP
by adding the real exchange rate as an additional
determinant of nominal exchange rate.

Both monetary factors and real factors influence nominal
exchange rates in this approach.
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15-22
Nominal and Real Exchange Rates in LR
equilibrium
• What are the effects on the (LR) nominal exchange rate of
the following changes?
• 1a. changes in monetary levels:
•
All dollar prices, including the dollar price of euro (nominal
exchange rate), rise in proportion to money supply increase.
• 1b. changes in monetary growth rates: leading to
persistent inflation and change in inflation expectation.
•
Dollar interest rate increases thru Fisher effect, leading to jump
in price level and nominal exchange rate, and persistent
increases follow.
• When only monetary factors change and the PPP holds,
we have the same predictions as in monetary approach.

No changes in the real exchange rate.
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15-23
Nominal and Real Exchange Rates in LR
equilibrium
• When factors influencing real output change, the real
exchange rate changes, potentially nominal exchange
rate change, too.
• 2a. changes in relative output demand:


Increase in relative demand for domestic products leads to a
real appreciation.
Nominal appreciation (fall in nominal exchange rate) arises
too, with no change in national price level.
• 2b. changes in relative supply:

Increase in relative supply for domestic products leads to a
real depreciation.

With an increase in relative supply of domestic products, the
situation is more complex for nominal exchange rate.
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15-24
The Real Exchange Rate Approach
to Exchange Rates (cont.)
• With an increase in the relative supply of domestic
products, the real exchange rate adjusts to make the
price of domestic goods depreciate, but also the
relative amount of domestic output increases.

This second effect increases the real money demand in the
domestic economy relative to that in the foreign economy:
PUS = MsUS/L (R$, YUS)

The domestic price level decreases relative to the foreign
price level.

The effect on the nominal exchange rate is ambiguous:
E$/€ = q $/€ x PUS/PEU
?
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15-25
Beyond Purchasing Power Parity: A General
Model of Long-Run Exchange Rates
Table 15-1: Effects of Money Market and Output Market Changes on the
Long-Run Nominal Dollar/Euro Exchange Rate, E$/€
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15-26
Interest Rate Differences
• Under relative PPP combined with interest parity, we had
R$ - R€ = eUS - eEU (Fisher effect)
• A more general equation of differences in nominal interest rates
across countries can be derived from:
(qeUS/EU - qUS/EU)/qUS/EU = [(Ee$/€ - E$/€)/E$/€] – (eUS - eEU)
R$ - R€ = (Ee$/€ - E$/€)/E$/€
R$ - R€ = (qeUS/EU - qUS/EU)/qUS/EU + (eUS - eEU)
• The difference in nominal interest rates across two countries is
now the sum of:
 The expected rate of change (depreciation) in the real
dollar/euro exchange rate
 The expected inflation difference between the domestic
economy and the foreign economy
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15-27
Real Interest Rates
• Real interest rates are inflation-adjusted interest rates:
re = R – πe
• where πe represents expected inflation and R
represents nominal interest rates.
• Real interest rates are measured in terms of real
output: what quantity of real goods and services can
you earn in the future by saving real resources today?
• What should be the differences in real interest rates
across countries?
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15-28
Real Interest Rates (cont.)
• Real interest rate differentials are derived from
reUS – reEU = (R$ - eUS) - (R € - eEU)
R$ - R€ = (qeUS/EU - qUS/EU)/qUS/EU + (eUS - eEU)
reUS – reEU = (qeUS/EU - qUS/EU)/qUS/EU
• The last equation is called real interest parity.

It says that the differences in real interest rates (return on
saving in terms of real resources earned) between countries
is equal to the expected change in real exchange rate (or
expected change in the relative price of goods and services)
between countries.
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15-29
Summary
1. The law of one price says that the same good in
different competitive markets must sell for the same
price, when transportation costs and barriers
between markets are not important.
2. Purchasing power parity applies the law of one price
for all goods and services among all countries.

Absolute PPP says that currencies of two countries have
the same purchasing power.

Relative PPP says that changes in the nominal exchange
rate between two countries equals the difference in the
inflation rates between the two countries.
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15-30
Summary (cont.)
3. The monetary approach to exchange rates uses
PPP, real money supply and real money demand.

Changes in the growth rate of the money supply influence
inflation and exchange rates.

Expectations about inflation influence the exchange rate.

The Fisher effect shows that differences in nominal interest
rates are equal to differences in inflation rates.
4. Empirical support for PPP is weak.

Trade barriers, non-tradable products, imperfect
competition and differences in price measures may all have
effects on the empirical shortcomings of PPP.
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15-31
Summary (cont.)
5. The real exchange rate approach to exchange rates
generalizes the monetary approach.

It defines the real exchange rate as the value/price/cost of
domestic products relative to foreign products.

It allows relative demand and relative supply changes to
influence real and nominal exchange rates.

Interest rate differences are explained by a more general
concept: expected changes in the value of domestic
products relative to the value of foreign products plus the
difference of inflation rates between the domestic and
foreign economies.
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15-32
Summary (cont.)
6. Real interest rates are inflation-adjusted
interest rates.
7. Real interest parity shows that differences in
real interest rates between countries equal
expected changes in the real value of goods
and services between countries.
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15-33
Law of One Price for Hamburgers?
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15-34
Price Levels and Incomes
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15-35
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15-36