Tenho certeza que este é o "The Vitanuls" de John Brunner.
Tem uma pílula de semi-imortalidade (não perfeita e apenas lançada):
"I think I follow you," the matron said at length. "I take it the anti-death pill is a success?" ... "You in the rich countries like America and Russia have been trying for years to find a broad-spectrum specific against aging, and I think--knowing your countries by hearsay--that there must have been a loud angry argument over who should benefit first."
Ele ocorre na Índia, o que lhes dá a configuração para trazer a reencarnação como uma arma de Chekov:
The matron gave him a chill stare. "I think that is uncivil of you. The teaching of Hinduism is that the soul is born again, throughout an eternal cycle, until it achieves one-ness with the All."
Eu não posso fornecer cotações de página direta para o final (eu estava citando o Google Livros e eles omitem as próximas páginas), mas
E tem essa linha:
"No, that's absurd. You can't mean to maintain that we've run short of human souls, as though they were stored in a cosmic warehouse and issued off the shelf every time a child is born!"