Jonathan Swift's satirical essay "A Modest Proposal" is rife with hyperbole. The entire proposal itself is hyperbolic. A hyperbole is an extreme exaggeration that is used to emphasize an author's point. In the case of satires, like "A Modest Proposal," hyperboles are often used to create humor and draw the reader's attention to the ridiculous nature of an idea or situation.
In making his proposal, the speaker uses many statistics and numbers to make his argument sound convincing and well-researched. The numbers themselves are a bit absurd, though, and the way he reasons through them adds humor to the piece. For example, when the speaker is first setting the groundwork for his proposal and establishing the contextual "facts" that he feels should be recognized before making his suggestion, he reasons,
The number of Souls in this Kingdom being usually reckoned one Million and a half, Of these I calculate there may be about two hundred thousand Couple whose Wives are breeders, from which number I Subtract thirty Thousand Couples, who are able to maintain their own Children, although I apprehend there cannot be so many, under the present distresses of the Kingdom, but this being granted, there will remain an hundred and seventy thousand Breeders. I again Subtract fifty Thousand for those Women who miscarry, or whose Children dye by accident, or disease within the Year. There only remain an hundred and twenty thousand Children of poor Parents annually born: (paragraph 6)
This math is hyperbolic in the sense that the numbers are inflated and make the speaker seem a bit over-the-top even though he is trying to sound learned and logical. Further, the speaker is treating human lives like simple statistics, which emphasizes the inhumanity of his proposal.
The speaker's exaggerated diction continues as he inches closer to his actual proposal. He writes,
I have been assured by a very knowing American of my acquaintance in London, that a young healthy Child well Nursed is at a year Old, a most delicious, nourishing, and wholesome Food, whether Stewed, Roasted, Baked, or Boyled, and I make no doubt that it will equally serve in a Fricasie, or Ragoust. I do therefore humbly offer it to public consideration, that of the hundred and twenty thousand Children, already computed, twenty thousand may be reserved for Breed, whereof only one fourth part to be Males, which is more than we allow to Sheep, black Cattle, or Swine, and my reason is, that these Children are seldom the Fruits of Marriage, a Circumstance not much regarded by our Savages, therefore, one Male will be sufficient to serve four Females. That the remaining hundred thousand may at a year Old be offered in Sale to the persons of Quality, and Fortune, through the Kingdom, always advising the Mother to let them Suck plentifully in the last Month, so as to render them Plump, and Fat for a good Table (9-10).
The speaker introduces the idea of selling children as food. He again includes figures that seem to indicate a well-researched plan, but the plan is so ridiculous that it makes the reader laugh (or feel horrified). The exaggerated yet casual way that the speaker talks about the styles in which the children could be cooked is quite humorous. Then, we have again the hyperbolic calculations of how many children can be sold for these purposes. He next goes on to say that a child could be eaten for two meals, so that's a great value.
The speaker makes another clever comment about why his proposal will be reasonable in pararaph 12:
I grant this food will be somewhat dear, and therefore very proper for Landlords, who, as they have already devoured most of the Parents, seem to have the best Title to the Children.
The choice of the word "devoured" here is an example of hyperbole and is obviously figurative but has a double meaning when we consider the speaker's proposal. The speaker means that the landlords have taken such advantage of their tenants as to basically have eaten them or sucked them dry. This word is an exaggeration of the reality, but it figuratively captures how disadvantaged the poor were at the hands of higher classes.
The proposal to raise and sell babies as food immediately strikes the reader as exaggerated and ridiculous. Within that larger frame, Swift also uses hyperbole to poke fun at the speaker's self-assured and seemingly reasonable ideas.