The Left doesn't care if there are poor people -- they just want everyone to be at the same level.
The Rigth doesn't care if some people have more success than others -- they just want a viable path out of poverty.
It is not an either/or question.
If you have income equality, then everyone will be poor. Where is the incentive to improve yourself?
Poverty is not a fixed state. People enter and exit poverty all the time. Or I should say, before the great society created a new form of poverty, people for various reasons find themselves in poverty (look at the 1930s and the dust bowls). Without a safety net the population moved to where jobs could be found. Almost all those that were in poverty managed to re-enter middle class later.
It is a trick question because both sides of your choices lead to the same point, but there are other options.
You want to get rid of poverty, do away with welfare, minimum wage, reduce regulation to the minimum, lower taxes, allow freer competition.
...and in general get government out of the way(when possible, I understand the need for some regulation, but truth is we are buried under laws, restrictions and regulation).
For there to be a path from poverty, there still must be poverty. As for the initial post, removing either means exactly the same thing; those who wish to do nothing will have exactly the same as those who do everything. It is exactly as others have said, a trick question.
The real problem, everywhere in the 'civilized' world, is that while the situation for those in 'utter poverty' are constantly having their standard of living raised, those who have crawled out of poverty hit the wall of high taxation and costs and are unable to breach further. And the only way to reinspire innovation and creativity is to stop stealing so many resources to simply hand to those who will do nothing.
Give the man a fish, feed him for a day. Teach a man to fish, feed him for a lifetime.. until you take all but one fish to feed to those who won't bother.
Your post #7 is excellent!