There isn't really agreement on whether or not income inequality is a problem, but there is wide agreement on what causes it (other than government corruption, that is), and if we look at cause-and-effect relationships, we can start to look at viable social strategies that take care of those at the bottom of the income spectrum, without sacrificing the incentives to produce.
This article looks at the way productivity, and incomes, follow a pareto diagram, and discusses the ramifications and options society has for handling this fact.
The link sends you to a gun control article
Sorry. I’ve corrected the link.