What did Gatsby’s parents do for a living?

Gatsby's parents were farmers.

His parents were shiftless and unsuccessful farm people—his imagination had never really accepted them as his parents at all. The truth was that Jay Gatsby of West Egg, Long Island, sprang from his Platonic conception of himself. He was a son of God – a phrase which, if it means anything, means just that – and he must be about His Father's business, the service of a vast, vulgar, and meretricious beauty. So he invented just the sort of Jay Gatsby that a seventeen-year-old boy would be likely to invent, and to this conception he was faithful to the end.