I read this short story at least 30 years ago. I suppose it was in a collection, since I rarely read magazines. I don't remember if I read it in English or in French, but it might have been a translation from any language.
All of Earth's food production is just enough to feed the human population, which is strictly regulated : no baby may be conceived unless someone dies. But there is a last legal zoo, and the food to support the few animals there perforce keeps the human population down by a few units. So a very high psychological pressure is put on the owners, even though they are legally allowed to keep their animals. But after hearing for years that they are preventing a few more humans to be born, they finally give up and euthanise their last animals.
The last line of the story is something like "and finally the human population on Earth was allowed to reach its absolute maximum".