Price Levels and the Exchange
Rate in the Long Run
Chapter 16
International Economics
Udayan Roy
Overview
• Long-run analysis
– Real variables
– Nominal variables
• Flexible exchange rates
– We will study fixed exchange rates in Chapter 18
The Real Exchange Rate
• We discussed exchange rates in Chapter 14
– Example: €1 = $1.50
• Those exchange rates are nominal exchange
rates
• Now we’ll discuss real exchange rates
The Real Exchange Rate
• Let us consider the price of an iPhone in US
and Europe:
– In US, it is PUS = $200
– In Europe, it is PE = €150
– The value of the euro is E = 2 dollars per euro
– So, Europe’s price in dollars is E × PE = $300
– So, each iPhone in Europe costs as much as 1.5
iPhones in US
– E × PE / PUS = 1.5
– This is the real dollar/euro Exchange Rate for
iPhones
The Real Exchange Rate
• In general, the real exchange
rate is a broad summary
measure of the prices of one
country’s goods and services
relative to another’s.
– The real dollar/euro exchange
rate is the number of US
reference commodity
baskets—not just iPhones—
that one European reference
commodity basket is worth
– Equation (16-6) in KOM9e
q $ / 
E $ /  PE
PUS
E$/€ is the nominal exchange rate, the
price of one euro in dollars
PE is the overall price level in Europe, such
as the consumer price index
PUS is the overall price level in the United
States
Depreciation and Appreciation
Euro
Dollar
Europe’s exports
America’s exports
q$/€↑ Real
Real
More expensive
Appreciation Depreciation
Less expensive
q$/€↓ Real
Real
Less expensive
Depreciation Appreciation
More expensive
The Real Exchange Rate
• Example: If the European reference
commodity basket costs €100, the U.S. basket
costs $120, and the nominal exchange rate is
$1.20 per euro, then the real dollar/euro
exchange rate (q$/€) is 1 U.S. basket per
European basket.
Real Depreciation and Appreciation
• Real depreciation of the dollar against the euro
– A rise in the real dollar/euro exchange rate (q$/€↑)
• is a fall in the purchasing power of a dollar within Europe’s borders
relative to its purchasing power within the United States
• Or alternatively, a fall in the purchasing power of America’s
products in general over Europe’s.
• Real appreciation of the dollar against the euro is
the opposite of a real depreciation: a fall in q$/€.
Absolute PPP
• A very simple theory of the real exchange rate
is called Absolute Purchasing Power Parity
• It says that:
q=1
• Why?
Law of One Price
• Going back for a second to the iPhone
example, one can argue that PUS, the dollar
price in the US, ought to be equal to E × PE,
the dollar price in Europe. That is,
• E × PE = PUS.
• In general, E$/€ x PE = PUS.
• Therefore, q$/€ = (E$/€ x PE)/PUS = 1.
• This is the Law of One Price or Absolute
Purchasing Power Parity.
Absolute and Relative PPP
• Chapter 16 of the textbook (KOM9e) uses
Absolute PPP in the first part of the chapter
and Relative PPP in the second part
– Absolute PPP: q = 1
– Relative PPP: q = a constant, not necessarily 1
• Although the results in the following slides
have been proved for APPP, they are also true
under RPPP
Prices and the Exchange Rate
• Absolute PPP says: 𝑞 =
• Therefore, 𝐸 =
𝑃
𝑃∗
𝐸∙𝑃∗
𝑃
=1
• Therefore, the faster domestic prices (P) grow,
the faster the foreign currency’s exchange
value (E) will grow
• And, the faster foreign prices (P*) grow, the
slower the foreign currency’s exchange value
(E) will grow
Prices and the Exchange Rate
• In general, 𝐸𝑔 = 𝜋 − 𝜋
∗
Equation (16-2) of the
textbook, KOM9e
– where Eg is the growth rate of E. This is the
appreciation rate of the foreign currency
– π* is the foreign inflation rate, and
– π is the domestic inflation rate
• Example: If US inflation is 3% a year and
Canadian inflation is 1% a year, then the
exchange value of the Canadian dollar,
measured in US dollars, will increase 2% a year
The Interest Rate
• We have seen in Chapter 15 that the interest
parity equation is 𝑅 = 𝑅∗ +
𝐸 𝑒 −𝐸
𝐸
• The second term on the right-hand side is the
expected appreciation rate of the foreign
currency
• Assumption: The expected appreciation rate is
assumed to be equal to the actual
appreciation rate (Eg), in the long run
The Interest Rate
• Therefore, 𝑅 = 𝑅
∗
𝐸 𝑒 −𝐸
+
𝐸
= 𝑅∗ + 𝐸𝑔
• We saw two slides earlier that 𝐸𝑔 = 𝜋 − 𝜋 ∗
• Therefore, 𝑅 = 𝑅∗ + 𝜋 − 𝜋 ∗
Equation (16-5) of the
textbook, KOM9e
• Assumption: The foreign interest rate (R*) and
the foreign inflation rate (π*) will be assumed
to be exogenous constants
The Interest Rate: Fisher Effect
• 𝑅 = 𝑅∗ + 𝜋 − 𝜋 ∗
• As the foreign interest rate (R*) and the
foreign inflation rate (π*) are assumed to be
exogenous constants, any change in the
domestic inflation rate will cause an equal
change (both in magnitude and direction) in
the domestic nominal interest rate
• This is called the Fisher Effect
The Interest Rate
• 𝑅 = 𝑅 ∗ + 𝜋 − 𝜋 ∗ implies 𝑅 − 𝜋 = 𝑅 ∗ − 𝜋 ∗
• R is the nominal interest rate.
– It tells you how fast the dollar value of your wealth is
increasing
• R – π is the real (or, inflation-adjusted) interest
rate.
– It tells you how fast the purchasing power of your
wealth is increasing
• We now see that in the long run equilibrium, real
interest rates must be equal in all countries
The Interest Rate
• Assumption: The domestic inflation rate (π) is
constant in the long run equilibrium
• Then 𝑅 = 𝑅 ∗ + 𝜋 − 𝜋 ∗ must also be constant
in the long run equilibrium
– We will now use this constancy of R to get a
theory of long run inflation
Output
• The real GNP produced when all resources are
fully utilized is known by various names:
– Long-run GNP
– Natural GNP
– Full-employment GNP
– Potential GNP(Yp)
• Assumption: In the long run, the economy
makes full use of all its resources
• Therefore, in long-run equilibrium, Y = Yp.
Inflation
• We have seen in Chapter 15 that equilibrium
in the money market implies 𝑀 𝑠 = 𝑀𝑑
• Moreover, 𝑀𝑑 = 𝑃 ∙ 𝐿(𝑅, 𝑌)
𝑑
• Simplifying a bit, 𝑀 =
𝑃∙𝐿0 ∙𝑌
𝑅
𝑠
• Therefore, in equilibrium, 𝑀 =
• Therefore, 𝑃 =
𝑀𝑠 ∙𝑅
𝐿0 ∙𝑌
𝑃∙𝐿0 ∙𝑌
𝑅
Inflation
• Therefore, in the long-run, 𝑃 =
𝑀𝑠 ∙𝑅
𝐿0 ∙𝑌
=
𝑀𝑠 ∙𝑅
𝐿0 ∙𝑌 𝑝
• We saw three slides back that R is constant in
the long run equilibrium. Moreover, L0 is an
exogenous constant
• Therefore, the faster the money supply (Ms)
grows, the faster the price level (P) will grow
• And, the faster potential GDP (Yp) grows, the
slower the price level (P) will grow
Inflation
• In general, 𝜋 = 𝑀 𝑠𝑔 − 𝑌 𝑝𝑔
• For example, if the Federal Reserve expands
US money supply at the rate of 5% a year and
if the US economy’s potential GDP increases at
the rate of 3% a year, then, in the long run,
the US inflation rate will be 2% a year.
The Interest Rate, again
• So far, we have 𝑅 = 𝑅∗ + 𝜋 − 𝜋 ∗ and 𝜋 =
𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔
• Therefore, the domestic nominal interest rate
in the long run is 𝑅 = 𝑅 ∗ + 𝑀 𝑠𝑔 − 𝑌 𝑝𝑔 − 𝜋 ∗ ,
a constant
The Price Level
• A few slides back, we saw that in the long run
the domestic price level is 𝑃 =
𝑀𝑠 ∙𝑅
𝐿0 ∙𝑌 𝑝
∗
• Moreover, we just saw that 𝑅 = 𝑅 + 𝑀 𝑠𝑔 −
𝑌 𝑝𝑔 − 𝜋 ∗
• Therefore, in the long run, the domestic price
level is 𝑃 =
𝑀𝑠 ∙ 𝑅 ∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
𝐿0 ∙𝑌 𝑝
Appreciation Rate of the Foreign
Currency
• We saw earlier that the foreign currency
appreciates at the rate 𝐸𝑔 = 𝜋 − 𝜋 ∗
• As the inflation rate is 𝜋 = 𝑀 𝑠𝑔 − 𝑌 𝑝𝑔 , we
can now write 𝐸𝑔 = 𝑀 𝑠𝑔 − 𝑌 𝑝𝑔 − 𝜋 ∗
The Exchange Rate: APPP version
• Recall that under absolute purchasing power
parity, we have 𝑞 =
𝐸=
𝑞∙𝑃
𝑃∗
=
𝑃
𝑃∗
𝐸∙𝑃∗
𝑃
= 1, which implies
• We have also seen two slides back that 𝑃 =
𝑀𝑠 ∙ 𝑅∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
𝐿0 ∙𝑌 𝑝
• Therefore, 𝐸 =
𝑀𝑠 ∙ 𝑅 ∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
𝐿0 ∙𝑌 𝑝 ∙𝑃∗
Summary: Long-Run, Flexible Exchange
Rates
• q = 1, absolute PPP
• Y = Yp
• 𝜋 = 𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔
• 𝑅 = 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔 − 𝜋 ∗
• 𝑃=
𝑀𝑠 ∙ 𝑅 ∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
• 𝐸𝑔 =
• 𝐸=
𝐿0 ∙𝑌 𝑝
𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔
− 𝜋∗
𝑀𝑠 ∙ 𝑅 ∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
𝐿0 ∙𝑌 𝑝 ∙𝑃∗
The crucial point to note about
these expressions is that the
variables on the right-hand
sides of these equations are all
exogenous. As exogenous
variables are ‘mystery variables’
about which our theory has
nothing to say, the equations on
this slide say all that our theory
can say about the endogenous
variables on the left-hand sides
of these equations.
Summary: Long-Run, Flexible Exchange
Rates
• q = 1, absolute PPP
• Y = Yp
• 𝜋 = 𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔
• 𝑅 = 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔 − 𝜋 ∗
• 𝑃=
𝑀𝑠 ∙ 𝑅 ∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
• 𝐸𝑔 =
• 𝐸=
𝐿0 ∙𝑌 𝑝
𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔
− 𝜋∗
𝑀𝑠 ∙ 𝑅 ∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
𝐿0 ∙𝑌 𝑝 ∙𝑃∗
Keep in mind that we are
talking about the long run here.
So, these equations show us the
long run effects of permanent
changes in the exogenous
variables on the equations’
right-hand sides.
Summary: Long-Run, Flexible Exchange
Rates
• q = 1, absolute PPP
• Y = Yp
• 𝜋 = 𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔
•
•
•
The first two variables are real
variables: they can be measured even
in barter (or, non-monetary)
economies. The remaining variables
nominal variables: they make
𝑅 = 𝑅∗ + 𝑀 𝑠𝑔 − 𝑌 𝑝𝑔 − 𝜋 ∗ are
sense only on monetary economies.
𝑀𝑠 ∙ 𝑅 ∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
s) has
𝑃=
Note
that
the
money
supply
(M
𝐿0 ∙𝑌 𝑝
no effect on real variables. This is an
instance of monetary neutrality in the
𝐸𝑔 = 𝑀 𝑠𝑔 − 𝑌 𝑝𝑔 − 𝜋 ∗
long run.
𝑠
∗
𝑠
𝑝
∗
𝑀 ∙ 𝑅 +𝑀 𝑔 −𝑌 𝑔 −𝜋
• 𝐸=
𝐿0 ∙𝑌 𝑝 ∙𝑃∗
Summary: Long-Run, Flexible Exchange
Rates
• q = 1, absolute PPP
• Y = Yp
• 𝜋 = 𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔
• 𝑅=
• 𝑃=
“A change in the supply of money has
effect on the long-run values of the
𝑅∗ + 𝑀 𝑠𝑔 − 𝑌 𝑝𝑔 − 𝜋 ∗ no
interest rate or real output.” (p. 369)
𝑀𝑠 ∙ 𝑅 ∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
• 𝐸𝑔 =
• 𝐸=
Flashback to Ch. 15 of the textbook
(KOM9e):
𝐿0 ∙𝑌 𝑝
𝑀 𝑠 𝑔 − 𝑌 𝑝𝑔
− 𝜋∗
𝑀𝑠 ∙ 𝑅 ∗ +𝑀𝑠 𝑔 −𝑌 𝑝 𝑔 −𝜋∗
𝐿0 ∙𝑌 𝑝 ∙𝑃∗
“A permanent increase in the money
supply causes a proportional increase
in the price level’s long-run value. In
particular, if the economy is initially at
full employment, a permanent increase
in the money supply eventually will be
followed by a proportional increase in
the price level.” (p. 370)
Absolute PPP: logical but not factual
• Despite the logical appeal of Absolute
Purchasing Power Parity, available data
suggests that it is not true
• We need to look for another theory of the real
exchange rate, q.
Law of One Price for Hamburgers?
We will return to this after
discussing Chapter 17
The balance on a country’s current account (CA) is roughly its net exports
What does CA depend on in the long run?
BONUS TOPIC: THE CURRENT
ACCOUNT
The Current Account
• Recall the goods market equilibrium equation:
𝑌 = 𝐶 𝑌 − 𝑇 + 𝐼 + 𝐺 + 𝐶𝐴
• Therefore, 𝐶𝐴 = 𝑌 − 𝐶 𝑌 − 𝑇 − 𝐼 − 𝐺
• Recall that 𝑌 = 𝑌 𝑝 in the long run
• Therefore, 𝐶𝐴 = 𝑌 𝑝 − 𝐶 𝑌 𝑝 − 𝑇 − 𝐼 − 𝐺
The Current Account
• 𝐶𝐴 = 𝑌 𝑝 − 𝐶 𝑌 𝑝 − 𝑇 − 𝐼 − 𝐺
• If Yp increases by, say, $100, then, in the long
run, income (Y) will increase by $100 and
consumption (C) will increase, but by less than
$100
• Therefore, CA will increase
• Therefore, in the long run, Yp and CA move in
the same direction
The Current Account
𝑝
𝑝
• 𝐶𝐴 = 𝑌 − 𝐶 𝑌 − 𝑇 − 𝐼 − 𝐺
• It is also straightforward to check that
Y
CA
Yp
+
+
T
0
+
I, G
0
−
– When taxes (T) change, CA moves in the same
direction, and
– When I and G change, CA moves in the opposite
direction
• Fiscal austerity (T↑ or G↓) is a way to raise CA
• A fall in consumer wealth—caused by, say, a real
estate crash or a stock market crash—has the
same effect as a tax increase. So, CA will increase!
The Long Run
• The macroeconomic analysis of the long
run is characterized by the concept of
monetary neutrality
• That is, monetary arrangements and
monetary policy have no effect on the
behavior of real variables
• Therefore, the predictions summarized by
the table on this and the previous slide are
true for both the flexible exchange rate
system of this chapter and the fixed
exchange rate system of Chapter 18
Y
CA
Yp
+
+
T
0
+
I, G
0
−