According to the proposal, what is the worst problem of the moment?

The satire is intended to draw attention to the worst problem of the moment which is the exploitation of Ireland at the hands of England.  The English stripped Ireland of all her resources, so much so that there was a famine in the country. While the English enjoyed the crops grown in Ireland, the Irish were starving and struggling to feed their children.

"A Modest Proposal is considered one of the finest examples of satire in world literature. Written in the persona of a well-intentioned economist and published in the form of a popular pamphlet, the tract argues that the problem of poverty in Ireland can best be remedied by selling the children of the poor as food for the wealthy."

So Swift suggests tongue in cheek that the problem of feeding the ravenous English and the taking care of Irish children could be a part of the same solution.

"I think it is agreed by all parties that this prodigious number of children in the arms, or on the backs, or at the heels of their mothers, and frequently of their fathers, is in the present deplorable state of the kingdom a very great additional grievance; and, therefore, whoever could find out a fair, cheap, and easy method of making these children sound, useful members of the commonwealth, would deserve so well of the public as to have his statue set up for a preserver of the nation." (Swift)

Swift writes this satire to expand on the notion of England's exploitation of the Irish to the degree that the Irish children could well become the next English delicacy.  Why not take advantage of this resource, since England has taken Ireland's bounty away from the Irish people, they could benefit financially from the many children that they have and cannot raise properly.

And in doing this, Swift suggests both problems would be solved, the need to feed the English and solve the problem of hunger and poverty in Ireland by getting rid of a good number of the children that the Irish were having a difficult time taking care of under the current economic conditions.