Individuals can then purchase separate private insurance for optional health procedures and for faster elective care.

Australia's healthcare system works on a similar model. Everyone gets basic free cover, but waiting lists for elective surgery can range from weeks to months.

If you optionally pay for private health insurance then you can get better, faster treatment, including for elective surgeries.

In your hypothetical 2090, the sick impoverished child gets their basic needs taken care of by the basic cover, and the elderly bureaucrat gets his life extending tech and augmentation paid for by the private insurance he's been paying in to his entire working life.

Once the sick, impoverished child recovers, they can return to school, graduate, get a good job and pay in to private insurance so that by the time they are elderly they can also afford life extending tech and augmentation.