What would it take for inflation to be inconsequential?

For inflation to be inconsequential and not cause a loss of well-being: All incomes (wages, self-employed income, welfare benefits, pensions, etc.) would have to be perfectly indexed; There would have to be no money or nominal bonds and only inflation-indexed financial assets; The exchange rate would have to follow purchasing power parity. This is impossible: even if all incomes were re-indexed and the exchange rate followed purchasing power parity, the existence of money and nominal bonds would result in the presence of an inflation tax, levied above all on low-income households.