lengthy justification for the idea only gives them more time to be aware of the ironic tone of the essay.

A reader would definitely understand that Swift is satirizing people who are good at understanding things via facts but don't understand actual human logic and emotions. Someone reading it when it was published would probably recognize political and social connections to events taking place. This would help a reader to even more clearly see that his ludicrous suggestion is satire and not meant to be seriously considered.

In his essay “A Modest Proposal,” Jonathan Swift suggests a way to alleviate poverty and human suffering in Ireland. He begins by writing the first three paragraphs in a formal tone and straightforward manner with specific and somber details (large broods of children, beggars, helpless infants, etc.). Images of offspring climbing all over the unemployed bodies of their mothers and fathers evokes the reader’s sympathy in Swift’s call to arms to help the poor.

By the end of the fourth paragraph, however, the reader wonders what solution Swift has planned: he gives the puzzling suggestion that infants be cared for until the age of one year, when they will “contribute to the feeding, and partly to the clothing of many thousands.” How would this work? In the fifth paragraph, Swift uses the word “scheme” to hint to the reader that his plan might not really be serious, realistic, or ethical. Paragraphs six and seven contain satirical economic calculations of the population (how many kids are born to poor parents, how many will live, etc.) and a cost-benefit analysis of raising a child. Swift points out that they can’t work or even steal until they are six years old; he heard from merchants that kids younger than age twelve don't even command prices that recoup the amount expended feeding and clothing them up to that point.

Having argued the need for a plan, in the eighth paragraph, Swift preps the reader for his proposal with an ironic tone: “I shall now therefore humbly propose my own thoughts, which I hope will not be liable to the least objection.” Obviously, what follows is neither humble nor unobjectionable.

Paragraph nine is exactly where the reader can be certain that Swift is being ironic: he proposes using the children as food! This proposal alleviates poverty in two ways; it eliminates food shortage and cuts down the overwhelming number of hungry mouths to feed. He claims that children are tasty and nutritious, “whether stewed, roasted, baked, or boiled; and I make no doubt that it will equally serve in a fricasee, or a ragoust.”

Swift continues to detail his absurd, gruesome, and immoral plan by strategizing that of one hundred and twenty thousand children, twenty thousand be saved and set aside for breeding. The other one hundred and twenty thousand children should be sold as food. He suggests fattening up the children like cattle before killing them.

The rest of his essay argues for the benefits of his proposal… only now, the reader knows that Swift is being ironic.

In this paragraph, the speaker mentions another proposal that he heard from a person he holds in high esteem as both a patriotic and virtuous individual. This man suggests that the shortage of venison in the country might be alleviated by selling the bodies of poor children between the ages of 12 and 14 as a substitute form of "venison." He argues that these children are often starving to death anyway, and this sale would both raise money and save the parents or relatives the problem of having to dispose of the children's corpses after they starve. However, the speaker rejects this idea, not out of compassion, but because he believes the meat of the boys will be too tough to be tasty, and he believes the girls are so close to puberty and childbearing that they would be better put to use birthing babies to be sold a gourmet delicacies.

After dispensing with the idea on the basis of its impracticality, the speaker then comments:

Besides, it is not improbable that some scrupulous people might be apt to censure such a practice, (although indeed very unjustly) as a little bordering upon cruelty, which, I confess, hath always been with me the strongest objection against any project, how well soever intended.

Swift's essay means to show what happens to a person's moral compass when he begins to look at a certain class of people, such as the "poor," as a problem rather than as fully human beings. Once a group becomes an economic problem to be solved, it is easy to dehumanize them. Swift uses the rhetorical strategy of introducing ever more absurd levels of hyperbole or exaggeration to illustrate this. It is exaggeratedly inhumane to think of using pre-adolescent children for food, and absurd, having proposed cannibalism, to protest that "cruelty" is his "strongest objection" to any project. Swift uses hyperbole so the reader will easily grasp the gap between what the speaker proposes and any normal concept of kindness or compassion. In a bigger picture sense, Swift wants the reader to abandon the idea of having to economically justify aid to the poor rather than simply giving them the help they need.

In this paragraph, Swift outlines a satirically logical argument. Obtaining this idea from a friend, Swift notes that it is possible to replace the overtaxed venison demand with the bodies of children ages 12-14. After all, these children are starving anyway, so this would put their bodies to good purpose. However, he notes that this isn't the most practical age to obtain children for food purposes; the male bodies, he has been told by an American, are simply too lean due to exercise, and fattening them up doesn't change the lean muscle mass. And females of this age, he reasons, don't make an excellent choice for consumption, either; they will soon be of age to become (food) breeders themselves, so it is wasteful to eat them just a few years before they can become of consistent service to the upper classes.

The primary rhetorical strategy Swift uses in this paragraph (and elsewhere in his satirical essay) is logos. He approaches the subject from a place of (false) logic, showing how it just makes practical sense for the upper classes to physically consume the poor since they have been metaphorically consuming them for years. Swift's detached and systematic approach to the advantages of eating the children of the poor shocked readers of his time—which was exactly his intent. Trying to reason with the upper classes on the need for reform in other ways hadn't garnered the attention Swift desired, so he used a logic-filled essay to bring needed attention to the plight of Ireland's poor.

The speaker begins the paragraph by assuring us of the "virtues" of his friend who has offered a "refinement upon [his] scheme." He believes that he can enhance the credibility of his friend by assuring readers that he is "a true lover of his country" and of his expertise on the subjects of meat and children. This virtuous and knowledgeable friend suggests that a lack of venison can be remedied by consuming children between the ages of twelve and fourteen, children who would otherwise starve from lack of work. This friend, apparently, has "frequent experience" consuming this kind of child, and, from speaking with the narrator, the narrator believes that meat from boys is too tough and lean, and it would be inadvisable to eat girls because they will soon become "breeders" who can produce more babies. The narrator also declares that this practice, of eating older children, strikes him as cruel, and this "hath always been with [him] the strongest objection against any project," he claims.

In this way, the narrator hopes to increase his own credibility and enhance our view of the justness of his proposal: this wonderful, intelligent man has proposed something that even the narrator finds somewhat cruel. This argument seems designed by him to elevate him in our estimation by relying on ethos. We see where he draws the line, and he attempts to convince us of the justice of this line, as it makes him appear to be more reasonable. The more reasonable and just and ethical he appears, the more apt we are to agree with his original proposal.

The narrator of this essay develops his plan to single-handedly solve the Irish famine problem through advancing a solution to the shortage of venison. He mentions how an American acquaintance he had assured him that this lack of venison could be solved if teenage children were to be eaten:

He said, that many gentlemen of this kingdom, having of late destroyed their deer, he conceived that the want of venison might be well supply'd by the bodies of young lads and maidens, not exceeding fourteen years of age, nor under twelve; so great a number of both sexes in every country being now ready to starve for want of work and service...

Note the justification he provides for this suggestion: there are so many young boys and girls of this age who are willing to "starve for want of work and service" that this would be a good solution to the lack of venison, as it would take these spare bodies and convert them into a form that would mean they no longer needed to starve and needed to be provided for, because they would be eaten. Rhetorically, Swift uses a monstrous argument conveyed in a serious and sincere tone to point out the monstrous attitude of the British towards the Irish famine. It is this that makes this essay such an effective persuasive document, as it condemns the British through their own indifference to the situation. Swift risks being labelled monstrous in order to point out the monstrosity of his audience.

Let's first define irony and see if there is dramatic irony in this particular writing. 

Irony is what is known as a "figure of speech," which means that words are said, but you cannot take their meaning at face value. This means also that the intended meaning of the word is not the same as its actual meaning; rather, it potentially means the opposite.

Irony occurs in everyday life. In any given situation, irony occurs when the result is completely different from what people thought it was going to be.

In literature, we have a few types of irony:

Verbal is the type of irony explained previously, where words mean something totally different than what their original meaning entails.

If this is the type of irony you are looking for, then Jonathan Swift is your answer. "A Modest Proposal" is neither modest nor should it exist as a proposal. At the same time, it is not intended to be one; it is a macabre, long satire written by Swift in a way that we can equate with the likes of Jon Stewart, Stephen Colbert ,and all the other sarcastic comedians who say things when they really mean the opposite. In fact, the entire piece is ironic in nature.

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.

Imagine if he were serious about this!

Situational irony is what we also described previously, where something happens that nobody expected to happen because they thought that the exact opposite would result. For example, suppose that a villain is plotting the end of a superhero, only to have the entire plan fall upon him, making him his own victim. This is irony in a situation. 

Now, let's return to your question on dramatic irony. In dramatic irony, something will happen to a character that you, as the audience, are aware of, but the character is not. Think about a play where you already know that the ending will be tragic, but the characters are oblivious to it. 

Like the title says, "A Modest Proposal" is an essay that supposedly attempts to provide a solution to the "Irish problem" and the issues of poverty taking place at the time. It is a satirical speech, which does not include a plot, nor characters. For this reason, there is no dramatic irony in this work, and there could not be unless Swift had told us a tale of someone to which something happens that everyone else expected, except that very person. This being said, the type of irony in "A Modest Proposal" is mainly verbal, and not dramatic. 

Readers who don't catch the sarcasm in Swift's A Modest Proposal would think him a cruel and barbaric man, indeed. This type of sarcasm which is used to criticize others' ideas is actually called satire. Swift's target audience included the rich landowners in Ireland who seemed either ignorant to or insensitive to the poverty all around them. Instead of writing with a serious tone and carefully outlining all his main points, Swift uses satire as a different approach in hopes it would sensitize the wealthy to the plight of the poor.

Swift opens by seemingly aligning himself with the wealthy landowners. He notes the many offspring that the poor have and then mentions that they are always begging for money. He notes that all these children contribute to the "deplorable state of the kingdom" and that they should at least find a way to create some use for all these kids who are serving no other purpose.

If the reader pauses here, it is easy to imagine the wealthy nodding their collective heads, ready for a means of lessening the burden of all these poor beggars on their streets. What they likely didn't see at this point is that Swift has drawn them in with satire.

His solution is to have poverty-stricken wives serve as "breeders" and to collect these poor children as a food resource. After all, he notes,

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.

Swift continues with this "plan," noting that skins can be used to make gloves, and he notes that older boys couldn't easily be used because their amount of physical activity would create tough meat.

Shocking, right? And that is just what Swift is hoping for. He hopes the wealthy will see that the poor are suffering and that to ignore them is cruel. Maybe not as cruel as consuming their children, but he creatively uses satire (or sarcasm) to capture their attention and bring light to a relevant issue in his society. Swift wasn't afraid of using the shock value of satire to find solutions for the famine and starvation that he saw plaguing Ireland.

Sarcasm—or, as it is often called, verbal irony—is saying the opposite of what you think. When a person falls down while walking across the room, a sarcastic response is "Graceful!" or "Good job!"

In his essay, Swift creates a seemingly clueless narrator who expresses the opposite of what Swift believes. This narrator suggests that the problems of the poor in Ireland can be solved if the poor sell their one-year-old babies to the rich English landlords as food for their tables. The narrator suggests that babies, served hot on the edge of a knife, would be a sought-after gourmet delicacy.

While the narrator thinks his is a perfectly reasonable and "modest" idea, Swift found the tendency to treat the "poor" purely in economic terms appalling. He wanted to create a character and a proposal that would shock his audience fully. He hoped in this way to motivate people to come up with a humane solution to the problem of Irish poverty. He meant exactly the opposite of what he had his narrator propose.

Let me start off by saying that the answer to your question is going to be different from reader to reader. Certain readers might pick up on the irony very early, while other readers might actually finish the essay and take the entire thing literally. That's happened in several of my English classes before. I've had students outraged that Swift could propose such a thing. That's when I begin the discussion about satire. Satire is defined as follows:

the use of humor, irony, exaggeration, or ridicule to expose and criticize people's stupidity or vices, particularly in the context of contemporary politics and other topical issues

Swift uses irony throughout the piece. Irony is defined this way:

the discrepancy between what is said and what is meant

Swift most definitely is not writing that eating children is a reasonable solution to the problems of overpopulation, starvation, and economic woes. What he is doing is calling attention to the problems that the people of Ireland are experiencing. He wants the ruling English to realize what they are doing and put reforms in place to solve the problems.

I think most readers have their "Wait, what?!" moment when Swift bluntly states his proposal.

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, . . . the remaining hundred thousand may, at a year old, be offered in the 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. A child will make two dishes at an entertainment for friends; and when the family dines alone, the fore or hind quarter will make a reasonable dish, and seasoned with a little pepper or salt will be very good boiled on the fourth day, especially in winter.

Perhaps a reader would be suspicious of Swift in the previous paragraph when he tells readers about his American friend who assured him that children taste delicious, are nourishing, and can be cooked in a variety of ways.

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 fricassee or a ragout.

For other examples of irony that Swift uses, I would check the section of the text where he numbers the advantages of his proposal. My personal favorite is number six. His proposal would encourage healthier marriages and families because mothers would take better care of their children in order to bring a better market price. Fathers would take better care of their wives and never beat them for fear of miscarriage. Swift even says that the men would begin to see their wives as on par with pregnant cows.

Men would become as fond of their wives during the time of their pregnancy as they are now of their mares in foal, their cows in calf, their sows when they are ready to farrow; nor offer to beat or kick them (as is too frequent a practice) for fear of a miscarriage.

Verbal irony is a language technique more commonly referred to as sarcasm. In effect, when a writer uses verbal irony, it means that he or she is saying the opposite of what he or she means. This generally contributes to a sardonic tone and has a comedic effect, as is the case in Swift's famous parody. In the section you have highlighted, Swift first refers to the "dying" and "rotting" of the poor as they succumb to disease, age and illness, and then describes this as a "hopeful . . . condition." Evidently, Swift does not really mean that the condition of these people—or the young laborers he then goes on to discuss—is hopeful. Instead, he is using a word that conveys the exact opposite of what is really meant. Likewise, verbal irony is achieved through the use of the word "accidentally" in reference to these people being hired for labor—his suggestion being that this happens so infrequently that it seems to have occurred by accident rather than by design. Finally, Swift describes the laborers' eventual death as representing both the laborers and the country being "happily delivered from the evils to come." This statement has a dual meaning—the laborers themselves will be dying, although Swift describes that process very euphemistically here; they will certainly not be happy. But will the country be happy to have rid itself of the burden of worrying about these people? The tone of the piece certainly implies that the richer classes will be glad not to have to think about the poor any longer.

The verbal irony in this passage turns on the narrator's misinterpretation of what "persons of a desponding Spirit" mean when they express "concern" about the large numbers of older, diseased and disabled poor people dying in Ireland. What his friends mean, of course, is that they are morally concerned and distressed over the situation and would like the narrator to come up with a plan to end the suffering of the poor by making their lives better. The narrator, however, interprets his friends' "great concern" as wanting to get rid of the poor because they are an economic drain on the system. He interprets their "despond" as the result of the fact that the poor are not dying fast enough.

To the narrator's mind, the people who approach him with this question are unnaturally depressed--ie "desponding Spirits"--because actually there is no problem! As the narrator points out, there's no need for a scheme to rid the country the burden of the poor because they are dying off so fast anyway. The narrator, who defines the "matter" wholly in economic terms, says "I am not in the least pain  upon that matter... [for] they are every Day dying, and rotting, by cold, and famine, and filth, and vermin, as fast as can be reasonably expected." The irony, of course, is that the fact that old, sick and disabled people are dying and rotting in cold, hunger and filth is exactly what should cause pain in the narrator's mind. Likewise, the narrator finds the younger workers in a similarly "hopeful condition:" so starved that if they do happen to get work, they can't do it and die anyway, thus "happily" solving the problem of how to get rid of them.

The verbal irony lies narrator's inability to see the poor in anything but economic terms, so that he misinterprets people's "concern" for them not as compassion for their plight, but as an economic desire for the poor to die faster. Thus, the narrator turns morality itself on its head, describing as "hopeful" and "happy" a morally disgraceful situation in which the poor are dying in cruel, horrible and preventable ways. In doing this, Swift hopes to shock people into treating the poor as human beings deserving of empathy and compassion. 

Concerning Swift's "A Modest Proposal," Swift had previously tried conventional writing methods in attempts to convince the wealthy English, the wealthy Irish, and the English government that oppression of the Irish poor needed to be stopped.  Near the end of this ironic essay, Swift actually lists the solutions he had previously suggested:  they're in italics, to separate them from his ironical proposal and to let the reader know that these are, indeed, serious proposals.  He lists, for instance, the idea that landlords "have at least one degree of mercy toward their tenants."  The italics are Swift's. 

Since his previous efforts showed little results, he wrote "A Modest Proposal" in an attempt to shock his targets into doing something positive to help the Irish poor.  The verbal irony allows him to do this.  He couldn't seriously propose something like this, people would have just dismissed him as a lunatic, and, since he was on the Irish side of the situation, he couldn't honestly have done so, he wouldn't have wanted to.  So, since it would make no sense to do it seriously, he does it ironically. 

The essay is shocking, but once the reader "gets" the irony, it's also hilarious and entertaining. 

Another benefit of verbal irony is that the reader experiences a feeling of discovery and even superiority.  The reader discovers the true meaning behind the essay, and feels superior because he knows something the "targets" apparently do not.

In the end, however, the last bitter irony was at Swift's expense.  Though the essay is still read and admired today, it accomplished nothing to help the Irish poor.            

In general people use irony to emphasize a point.  When we use words in ways where we mean the opposite of the words' literal meanings, it for some reason heightens the effect that the words have.

This is why Swift uses verbal irony in this essay.  He is trying to really drive home to us how bad conditions are in Ireland and, more importantly, how poorly the government has done in trying to fix those conditions.  By using verbal irony, he makes his points more vividly than he would by simply using words whose literal meanings coincide with what he's trying to get across to the reader.