Question

# According to a textbook for relative PPP “It asserts that prices and exchange rates change in...

According to a textbook for relative PPP “It asserts that prices and exchange rates change in a way that preserves the ratio of each currency’s domestic and foreign purchasing powers. 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 understand that the dollar will depreciate due to less demand compared to Euro. What I do not understand is that if dollar depreciates then doesn’t that mean the price level for dollar would go up and appreciation of euro means decrease in price level for euro thus this would lead to increase in the exchange rate rather than completely offsetting the change in relative price levels according to the equation E\$/€=Pus/Pe and making purchasing power more stronger in EU? And also this increase price in dollar would not able to offset the 5 percent by which U.S. inflation exceeds European inflation since the inflation goes up for the dollar?
Thank you and Have a great day!

The relative PPP means that there is a percentage change in the two national currency which is equal to the difference between percentage change in national price levels. Suppose that the price of one country's price level rises(here the US) more than with another country (Europe) price level then the cost of the US goes up more than that of Europe. But the difference here is that the domestic and foreign purchasing power does not change. The relative exchange PPP takes into account the time interval over price level and exchange rate. Generally, the national government cannot make an interest to compute the international standardized commodities. In this case, the relative PPP is useful for calculating the price level. So, it makes sense to calculate the percentage exchange rates and inflation rate.