Solution: Tax everything and pay the poor
In fact, pay everybody.
Everyone registers and gets paid a flat fee to live. Then all purchases get taxed to earn money to pay that flat fee. Providing you can weed-out the false ID's the system will work. All wages and income gets captured at the point of purchase. All savings stay to build national prosperity and retirement income for individuals.
You probably need death duties to stop the lucky bankrolling their heirs in perpetuity. Everyone needs to earn their own money to some extent, not inherit it all.