How can eu countries have different inflation rates when they all use euros? Do euro have different value in each country?

Question

Edit: Thank you all for the answers.

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Answer 1

Let’s say you live next to a tomato farm and want to buy a pound of tomatoes. It costs 10 money units, because the farmer can just hand it to you. Now let’s say you live at the top of a small mountain with a difficult path. The farmer needs to pay for a cart and horse and make a tremendous effort to get up the mountain to sell you a pound of tomatoes, he of course wants additional compensation for his trouble so charges you 20 money units for the same tomatoes someone bought for only 10 who lives close by.

Now let’s say a landslide made the path up the mountain much more dangerous. The farmer doesn’t want to cross it for only 20 moneys but the people in the mountain town really need tomatoes so are willing to pay 40 moneys for their pound of tomatoes. The farmer is now willing to make the trip and charge 40.

Person who lives at the bottom has seen no inflation. Town on the mountain has seen 100% inflation. Its the same currency its just where you are effects your purchasing power