no work for the parents and no education for the children. The lack of options for the children when they grow up is presented starkly at the end of the paragraph. Since there is no honest work for them to do in Ireland, they must either become thieves or go to another country to seek their fortune, perhaps as mercenaries in a foreign army or as indentured servants, little better than slaves, in the West Indies.

This gloomy picture at the beginning of the essay lends point to the satire that follows. Although the "modest proposal" is even worse than the problem it purports to solve, it is only by going to the greatest extremes imaginable that this effect can be achieved. Anything less might actually seem like a possible answer to such an appalling situation. The desperation of the Irish people's plight is therefore accentuated by the drastic nature of the proposal. Placing this paragraph at the beginning of the essay prevents it from being merely a grisly fantasy and makes it closer to an expression of despair that no humane solution to this atrocious waste of human life appears to be possible.

In a nutshell, the problem in Dublin circa 1700 (and the problem Jonathan Swift wrote about in A Modest Proposal) was extreme poverty. The narrator of the compact Proposal specifically highlights the plight of poor families with many children, and also the generally low rate of employment in Ireland at the time of the essay's composition. This poverty led to many social problems, and the narrator points out that lack of gainful employment has forced many Irish citizens into the army or slavery. As one might expect, Ireland's poverty is also accompanied by extreme hunger.

Swift's satirical proposal (the cannibal consumption of Ireland's young) is meant to combat both this extreme poverty and hunger, as eating children will simultaneously reduce the cost of raising a family while also providing a reliable food source. This suggestion is, of course, appalling, but it's also brilliant as a literary device, as it symbolically represents the fact that Great Britain, a primary cause influencing Ireland's poverty, was figuratively devouring Ireland's impoverished population.  

"A Modest Proposal" is a satirical essay written by Jonathan Swift, the purpose of which is to call out the extremely deplorable living conditions that existed in Ireland during a time when the English government showed no care or intention to resolve it.

Famine was just one of the consequences of the unequal political status of the Irish. Swift is clear that the Irish are suffering not just from famine, but also from everything related to extreme poverty:

It is very well known, that they are every day dying, and rotting, by cold and famine, and filth, and vermin, as fast as can be reasonably expected.

This shows that the Irish lived in deplorable conditions trying to survive in a land of famine, while also fighting the consequences of squalid living where contamination, rats, and disease were the norm.

Swift also calls out the political and social obstacles that prevent even able-bodied Irish people from attempting to make a living:

Young labourers ... cannot get work, and ... pine away from want of nourishment ... that if at any time they are accidentally hired to common labour, they have not strength to perform it ... The country and themselves are happily delivered from the evils to come.

The serious tone employed by Swift in this writing is one of the elements of satire. He proposes a crude, cruel, cannibalistic, and extremely unethical proposal, which he sarcastically describes as "modest" solution to what the English upper classes see as an Irish problem.

Clearly, he does this to cause a stir and wake the minds of those who obliviously look into what is happening in Ireland and continue on without a degree of empathy, care, or concern.

The 'scarce years' during Swift's lifetime do not refer to the Great Potato Famine in Ireland per se - that had happened about a century beforehand. More specifically, Swift points a finger at Britain's exploitation of Ireland, leaving the rural population in quasi-starvation:

In 1729, Swift attacked with A Modest Proposal for Preventing the Children of Poor People of Ireland from Being a Burden to Their Parents (1729), which suggested that since Britain had consumed all the wealth of Ireland, only one source of profit was left: the children, doomed to starvation, whom the writer, a supposedly concerned and informed citizen, suggested might well be turned into a new and delicate food for those who had profited from Ireland’s political tragedy.

Swift imitates a "Selah,selah" attitude in his essay "A Modest Proposal," whose nonchalant and detached stance is in striking contradiction with the grotesque "solution" he has found to Ireland's problems.

Insomuch, Swift aptly uses parody (a form of satire), hyperbole (exaggeration in content) and understatement (banalization in tone) to make the point that the ruling state was altogether unabashed at its brutal exploitation of Ireland's resources.  Understood was the fact that his suggestions were barbaric, not 'modest,' and that his 'proposal' was as absurd as the government's oversimplification of its abusive policy (depletion of Ireland's resources) to the point of denial.

Note that the same "unfair trade" policy towards the American colonies led to their revolt (and ultimately, their independance) some fifty years later....

Conditions in Ireland in 1729 are incredibly bad for the Irish.  For many years, wealthy English had been purchasing land in Ireland so that, by the time "A Modest Proposal" is published, 90% of the land in Ireland is owned by the English.  These landowners raised rents in order to make more money, rendering it nearly impossible for the Irish tenant farmers to pay their rents and feed and clothe their families (which were typically large).  This meant that some people had to abandon the land their families had worked for generations and others had to choose whether to pay rent or feed their children.  The number of beggars in the streets increased.  Crime went up.  It seemed that, as the English got fatter and fatter on their wealth, the Irish got thinner and thinner while they starved; one group seemed to be "eating up" the other, and so Swift capitalizes on this figurative idea, making it literal in his satire.