The social problem in Ireland Swift addresses in "A Modest Proposal" is
poverty.
After describing his city that is full of beggars, Swift proposes that the children that are starving and ragged should be sold to rich people, so they would be feed and then they could be eaten by knives, landowners and their families.
With this proposal, he was sure that the kids would survive after being feed because no butcher would have the guts to kill any child.