ECON 102: International Finance Formulas
In this document, we present the most important formulas used in Module 9.
Nominal Exchange Rate
To illustrate the different formulas, we define the following variables: • E1: The CAD/USD nominal exchange rate.
• E2: The CAD/EUR nominal exchange rate.
Changing the Units of Exchange Rates
The USD/CAD and EUR/CAD exchange rates are respectively 1 and 1
E1 E2 How to Convert a Price in Another Currency
If P is the price of a good in CAD, its price in USD and EUR are respectively: P and P
E1 E2 IfP isthepriceofagoodinUSD,itspriceinCADis:
P × E1 IfP isthepriceofagoodinEUR,itspriceinCADis:
P × E2
Appreciation Versus Depreciation
The rule is: If a nominal exchange rate increases, the currency in the numerator depreciates and the currency in the denominator appreciates. Therefore:
• E1 increases: The CAD depreciates against the USD and the USD appreciates against the CAD. • E2 increases: The CAD depreciates against the EUR and the EUR appreciates against the CAD. • E1 decreases: The CAD appreciates against the USD and the USD depreciates against the CAD. • E2 decreases: The CAD appreciates against the EUR and the EUR depreciates against the CAD.
Econ 102 Module 9: Formulas Page 1 of 3
How to Obtain a Third Exchange Rate
The USD/EUR exchange rate is
The EUR/USD exchange rate is
Real Exchange Rate
E2 E1
E1 E2
In this section we need the following additional variables: • PCA: Price level in Canada.
• PUS: Price level in the United States. • PEU : Price level in Europe.
• ε1: the CAD/USD real exchange rate. • ε2: the CAD/EUR real exchange rate. • ε3: the USD/EUR real exchange rate.
The CAD/USD real exchange rate is:
The USD/CAN real exchange rate is:
The CAD/EUR real exchange rate is:
The EUR/CAD real exchange rate is:
The USD/EUR real exchange rate is:
The EUR/CAN real exchange rate is:
ε =E PUS 1 1 PCA
1 = 1 × PCA ε1 E1 PUS
ε =E PEU 2 2 PCA
1 = 1 PCA ε2 E2 PEU
ε3 = E2 × PEU E1 PUS
1 = E1 × PUS ε3 E2 PEU
Econ 102
Module 9: Formulas
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Appreciation Versus Depreciation
The rule is the same as for the nominal exchange rate.
• ε1 increases: in real term.
• ε2 increases: in real term.
• ε1 decreases: in real term.
• ε2 decreases: in real term.
The CAD depreciates against the USD and the USD appreciates against the CAD The CAD depreciates against the EUR and the EUR appreciates against the CAD The CAD appreciates against the USD and the USD depreciates against the CAD The CAD appreciates against the EUR and the EUR depreciates against the CAD
Interpretation of Real Exchange Rates
• ε > 1 implies that the cost of goods in the country using the currency in the numerator is relatively lower than the cost of goods in the country using the currency in the denominator, and vice versa if ε < 1
• ε1 > 1: It is relatively less costly to buy goods in Canada than in the US.
• ε1 < 1: It is relatively more costly to buy goods in Canada than in the US.
• ε2 > 1: It is relatively less costly to buy goods in Canada than in Europe.
• ε1 < 1: It is relatively more costly to buy goods in Canada than in Europe.
• ε3 > 1 It is relatively less costly to buy goods in the US than in Europe.
• ε3 < 1 It is relatively more costly to buy goods in the US than in Europe.
Purchasing Power Parity (PPP)
According to the theory, the cost of goods should be the same in all countries. In other words, we should have:
ε1 =ε2 =ε3 =1
Using the growth rate approximations, it implies the following for Canada and US:
∆%E1 ≈ πCA − πUS
where ∆%E1 is the growth rate of the CAN/USD nominal exchange rate, πCA is the inflation rate in Canada and πUS is the inflation rate in the US. For example, if inflation is 1 percentage point higher in Canada, the CAD should depreciate by 1% (E1 will increase by 1%).
Econ 102 Module 9: Formulas Page 3 of 3