But you can't say it is inflation because purchasing power didn't decrease. Theoretically the value of the old coin will be (Y-1)/Y so everybodies wealth increa

But you can't say it is inflation because purchasing power didn't decrease. Theoretically the value of the old coin will be (Y-1)/Y so everybodies wealth increased by 1. If it's greater than 1 good! You can even call it deflation, let's hope it's stable. If it's less than 1 something went very very wrong with multiple possible reasons: let's hope killing one restores the balance.