Although I considered it a "problem" my solution wasn't mandate pay rate, but increased education so people could get a better paying job.
Income inequality was an issue in the 1970s with the end of Bretton Woods. It got worse with the Reagan era, becoming "winner-take-all inequality" as scholars Jacob Hacker and Paul Pierson phrase it. That "winner-take-all inequality" is essentially unprecedented in history: the vast majority of the fruits of economic growth have settled into the top 10% rather than the top 20%, and it is in fact even more fractal than that, with the top 1% and the top .1% each taking a massively disproportionate share. The 1990s and 2000s saw those trends being worsened. The 2008 recession just deepened something that had been occurring for decades, and exposed its pathology.
Income inequality has slowed growth. It has increased volatility and capital shocks in the system. It has harmed money velocity. Massive inequality makes it so that people take bigger risks (since they're gambling with money they can easily afford to lose) and lead to a more systemically-risky economy. It's squandered dreams, wasted educations and crushed human capital.