Question

# According to the textbook, it says that "If the U.S. price level rises by 10 percent...

According to the textbook, it says that
"If the U.S. price level rises by 10 percent over a year while Europe’s rises by only 5 percent, for example, relative PPP predicts a 5 percent depreciation of the dollar against the euro. The dollar’s 5 percent depreciation against the euro just cancels the 5 percent by which U.S. inflation exceeds European inflation, leaving the relative domestic and foreign purchasing powers of both currencies unchanged."
I now understand why relative PPP predicts a 5 percent depreciation of the dollar against the euro but I do not understand why the dollar’s 5 percent depreciation against the euro just cancels the 5 percent by which U.S. inflation exceeds European inflation, leaving the relative domestic and foreign purchasing powers of both currencies unchanged.
I know that the depreciation of the dollar would lead to the increase in price level of dollar which is another increase in inflation level thus this would not offset the 5 percent by which U.S. inflation exceeds European inflation since it would mean that 5 percent increase in price level would be added to the current price level this leading 10 percent?
Thank you!

No it is not like that

As usa prices rise by 10-5=5% more than Europe's, usa exports fall because they are now more expensive and usa imports from Europe rise since they are now relatively less costly. Thus there is more demand for euros and less demand for dollars. This depreciates dollars. Now usa prices are greater by 5%. On the other hand in terms of euros the prices of dollars fall by 5% due to depreciation of dollars. So for European customers 5-5=0.so in this sense relative purchasing power remains same.

Note depreciation means dollars can now buy less and in terms of euros they are now cheaper. Exchange rate means no. Of dollars required to buy a euro and depreciation here means this no. rises. It will not increase price level of dollar. Dollars price is euros which falls.