Exchange rates can be quoted as foreign currency per unit of
domestic currency or domestic currency per unit of foreign
currency. Unless otherwise stated, we adopt the convention that is
given in your textbook, that is, we define exchange rates as
domestic currency per unit of foreign currency. Using the dollar
and euro as a currency pair, the bilateral exchange rate is E$/€,
expressed as dollars per euro.
a. Suppose that the initial exchange rate is given as $1/€1, i.e., E$/€ = 1. Now, it has changed to $0.85/€1, i.e., E$/€ = 0.85. What does the fall in E$/€ mean in terms of the
value of the dollar (domestic currency) and the euro (foreign currency)?
b. Now, suppose instead that the initial exchange rate is $1/€1.30. Write down the value for E$/€. What is the value of E$/€ when the exchange rate changes to $1/€1? Has E$/€ increased or decreased? Has the domestic currency (dollar) appreciated or depreciated? What about the foreign currency (euro)?
The fall in E$/€ means that, while earlier 1 euro could buy 1 dollar, after the change 1 euro can buy 0.85 dollars. It means that dollar has become more valuable, so dollar has appreciated. Euro has become less valuable, so euro has depreciated.
When exchange rate is $1/€1.30, it means that E$/€ = 1/1.30 = 0.7692
When exchange rate is $1/€1, it means that E$/€ = 1/1 = 1
Therefore, E$/€ has increased (from 0.7692 to 1).
It means that, while earlier 1 euro could buy 0.7692 dollar, after the change 1 euro can buy 1 dollar. It means that dollar has become less valuable, so dollar has depreciated. Euro has become more valuable, so euro has appreciated.
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