What is the problem the speaker wants to solve?
The speaker in "A Modest Proposal" is desirous to solve the problems associated with the poor Irish: families become so big -- even when the parents are poor -- that the children cannot be supported, and they end up begging in the streets instead of becoming productive members of society. For this reason, he proposes that parents sell their year-old babies as a food source for the rich English Protestants, and this will decrease the size of their families, making them easier to support, as well as provide them with an additional source of income. (It will also lessen the number of Catholics in the world, which would please the English Protestants as well.)
However, this is not the same problem that the writer means to address. The narrator is not Jonathan Swift, and Swift is attempting to draw attention to the plight of the poor Irish; wealthy English landowners have purchased around 90% of the land in Ireland by the time he penned this pamphlet, and many raised rents so high that the Irish tenant farmers could no longer afford to pay rent and feed their often large families. He reasons, ironically (not sincerely), that if the English are willing to figuratively devour the Irish, then why not go one step further and actually devour them?