I contacted James Nicoll, of the rather wonderful science fiction LiveJournal blog More Words Deeper Hole with three half-remembered concepts from it, and literally four minutes later he wrote back to let me know it was Michael G Coney's The True Worth of Ruth Villiers, from New Writings in SF in 1970. (It was a relatively obscure British magazine.)
It is, amazingly, online. Mr. Coney's utopia is a little more strict than my own modest proposal. In mine, if you have no money you are not treated to healthcare. In True Worth, if you have no money, you are not treated to health care or any other services, and it would be an unfair advantage to allow relatives or friends to give or lend you that money. Never fear though. In the story, the establishment recognizes you can incur some costs before you earn enough to pay, so it gives each individual a certain amount to be going on with - specifically a "Birthright" of 600 credits.
Here is an excerpt:
Suppose someone is in the hospital, awaiting an expensive operation. The obvious question poses itself: is the patient worth treating, bearing in mind his value to the community? So the hospital sends me a claim based on the estimated cost.
Then I call the National Bank and find that the patient has accumulated savings totaling (say) Cr. 2,000 to date.
And I consult my own punch-card index and find that he has a Social Value Cred Rating of (say) Cr. 1,500.
That person, therefore, is worth Cr. 3,500 to the community. Nothing more; nothing less.
So if the operation costs up to Cr. 3,500, the scalpels will flash and he will be healed, presumably.
But if the operation (including pre- and post-operational care and treatment) is estimated at Cr. 3,501, his flesh will remain uncarved. He can, however, receive lesser treatment and drugs to the value of Cr. 3,500, at which point he will be discharged from the hospital. What he does then is up to him; but assuming he is able to start work again he must repay the loan of Cr. 1,500 on his Social Value Cred Rating before he can start to accumulate any personal savings again. In repaying this amount, he will be allowed the bare minimum of his wages for living expenses. In fact, he will probably be fed and lodged by his friends, provided they are not caught doing it.The story gives an example of how well this works in practice. The eponymous Ruth is trapped after a mineshaft collapse. Her social worth is not enough to pay the rescuers to dig her out, though it does pay for an airshaft to be drilled. And yet, months later, Ruth is rescued, proving that the system works and wishy-washy liberal "compassion" and "social responsibility" is not needed.
How can this be? You can learn the answer here.
(It's a very quick read.)