The two things that I am aware of that seem to be tied to a high income inequality are an increase in crime and a reduction in meritocracy.
High crime rates are probably not terribly germane to this discussion.
The way that the high income inequality affects meritocracy is that, in general, people are naturally nepotistic. If you are wealthy, you want your children to go to the best schools, you’re willing to hire them into your business at an unreasonable starting point or use your contacts to get them hired. Poor schools end up getting the worst teachers, the worst property, and their students can only get accepted into the lowest wrungs of the economy. Since corporate hierarchies are pyramid shaped, there aren’t very many spots at the top, so it’s very easy - even if you’re a small part of the economy - to crowd out the top of the pyramid and prevent others from entering it from below, by inserting people higher up into the hierarchy.
This creates two problems.
Firstly, you instantly take a toll by preventing the best candidates from filling the positions that are available in the economy. The people in those positions are there because of connections not because of competence. And, often, that requires extra layers (and cost) to create mechanisms for these offices to continue to function around the incompetent jackass that’s been put in the position. It’s a big economic waste with no gain.
Secondly, this system strongly encourages corruption. The top layers of the economy are full of people getting by based on connections and gifts from the powerful to others, to get their children into positions of power. That instills a general sense among those lower in the hierarchy that this method of dealing with one another - through gifts and bribery - is all-okay. But also, because people know that there’s no chance to rise any higher in the hierarchy, they know that there’s no way to improve their lot in life by working hard and doing a good job. Competence and honesty are not rewarded. Taking kickbacks is the only way to increase your take-home over time.
Corruption really slows down the economy, because you have to apply graft at every single layer of everything that is involved in a project. Giving someone a bribe when you get a bus is one thing, it’s a one-and-done deal. But if you’re trying to build new infrastructure, where you’re dealing with several construction companies, several government agencies, issues of eminent domain, etc. and everyone is more interested in getting their cut than they are in seeing the project through the completion, then they’re all aiming to bleed you very every cent that they think you can afford. You have to bribe the top honcho of every group you deal with. You have to bribe the middle men. You have to bribe the workers on the ground. You have to bribe the guys who bring in the concrete. You have to bribe the inspectors.
It adds a massive cost and time spent negotiating with each group at each level.
In the case of Timbuktu, this might not matter much to the global economy. But China has such a huge population that it does matter.
There’s also the problem that the greater the income inequality, the harder it becomes to fight, since the people at the top have so much free money, then can spend it - like Harvey Weinstein - on harassing people, lobbying people, taking things to court, etc. There’s a certain cutoff point at which it becomes a self-propelling mass towards national implosion.