One year ago (April 9th, 2014) the US dollar price per Euro was $1.40. Read that as it took $1.40 to "buy" 1 Euro dollar. If I wanted to buy something that was priced in Euros, say 100 Euros, I would have had to exchange $140.00US dollars in order to buy it.
Today (April 9th, 2015) the US dollar price per Euro is $1.08. Read that as it takes $1.08 to "buy" 1 Euro--rounded up a bit). If I wanted to buy that same item today and it was still priced at 100 Euros, I would have to exchange $108.00US dollars to make that purchase.
When I exchange my US Dollars to get 100 Euros I give up FEWER US Dollars today than I did one year ago to do so---$32.00 to be exact. The purchasing power of a US Dollar relative to the Euro has INCREASED by 23% ($32.00 divided by $140.00 X 100) in 365 days.
In Macroeconomic terms, we can say the US Dollar has APPRECIATED by 23%.Today I want to look at the same problem but from the standpoint of the Euro.
Currency valuations are simply reciprocals of each other. If you know one, you know the other---with a little math.
The above example read "the US dollar price per Euro was $1.40" one year ago. Expressed as a ratio this would be $1.40/1.00Euro.
If we take the reciprocal of $1.40/1.00Euro we will have 1.00Euro/$1.40. Divide that out and we get "The Euro price of per US Dollar was .71 Euro cents" one year ago.
In other words, last year the holders of Euros had to give up .71 Euro cents in order to "buy" $1.00.
In sum: Holders of dollars had to give up $1.40 to buy 1.00 Euro and conversely the holders of Euros had to give up .71 Euro cents to buy a $1.00.
So, if last year if the holders of Euros wanted to buy something priced at $100.00US they would have had to exchange 71.00 Euros in order to do so (.71 Euro cents X 100).
Move ahead one year.
Yesterday, the US dollar price per Euro was $1.08. If we take the reciprocal of that (1.00 Euro/$1.08) we get the "Euro price per US Dollar was .93 Euro cents.
So, yesterday the holders of Euros would have had to exchange 93 Euros in order to "buy" $100.00. Last year it was 71 Euros. That is a difference of 22 Euros, or in percentage terms, a 31% decrease in value of the Euro relative to the US Dollar (22Euros/71Euros X 100).
In Macroeconomic terms, we can say the Euro has DEPRECIATED by 31%.
Notice while the currencies are reciprocals of each other the percentage changes are not (23% versus 31%). This is because...math. The base numbers are different. One starts at a high base and goes lower and the other a lower base and goes higher. No conspiracy there.
Hopefully you can see from this example that exchange rates matter.
The physical/non-physical properties of the goods or services bought in either the US or Europe are the same (ceterus paribus). The only thing that changes the relative prices of the goods/services is the value of the currencies used to purchase them.