Where does irony exist in Swift's essay, "A Modest Proposal"?

Swift's opening epigraph is the first instance of irony
and lays the foundation for all irony that is
upcoming:

For
preventing the children of poor people in Ireland, from being a burden ..., and for
making them beneficial to the
publick.

Children are
generally not thought of in terms of benefit to society. They are, instead, usually
thought of in terms of how they may themselves be benefited (e.g., education, health
care) or, in less fortunate cases, how they may add to the benefit of their families.
Hence, Swift starts his political pamphlet with the biting irony that will occur,
indeed, with heightening effect, throughout the
essay.

Aside from the generally ironical tone ("would
deserve so well of the publick, as to have his statue set up for a preserver of the
nation"), the first sign of explicit irony is when he speaks of Irish children as
one-year-olds. While up to the age of one, babies may exist on mother's milk, or be
supplemented with "other nourishment: at most not above the value of two shillings,"
Swift ironically suggests that at one year old, babies may perform a public function,
for "they shall, ... contribute to the feeding, and partly to the cloathing of many
thousands" of other people.

After this obscure
pronouncement, Swift carries on through an artfully placed ironic digression from his
point while he ironically discusses the "expence" of abortion and statistics relevant to
the age at which children may become thieves. Swift then makes his first
significant--and ironic--point, casting dispersion on Americans while doing so, that
babies might be sold at one year of age as an additional dietary
source:

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 boiled; and I make no doubt that it will
equally serve in a fricasie, or a
ragoust.

There are many
instances of irony, either subtle (like the statue) or significant (like the nutritional
value of babies). To find more, as a detailed examination is not possible in this
format, look for "incongruity between what might be expected and what actually" is
suggested by Swift (American Heritage Dictionary).