Most paths I see for your world involve collapse. There's many paths it could take, depending on details you'd have to work out yourself.
The first and most obvious would be the development of massive loopholes. A fundamental problem people in your world would have to solve is that any money earned above the limit is basically useless to them. If the cap is \$100,000, and I'm earning \$100,000, there's no incentive for me to take on a job that would earn me \$1,000,000 every year, because \$900,000 of that is unspendable useless paper completely devoid of value because I can't spend it. Or can I? What if I am permitted to "donate" that money to the poor? What if I can "donate" \$20,000 to a poor person, in exchange for him "donating" me a \$10,000 car I couldn't purchase on my own because I'd hit my limit. Such loopholes would lead the rich to view the poor as tools, valued by how much of their limit they aren't using and how well they can be manipulated to provide goods and services to the rich.
So let's say we plug those loopholes. We've never been able to plug the loopholes in any major economic system, so I won't say how its done, but let's just handwave it away. So now any paycheck I get above my \$100,000 limit is worthless, right? Well, I did gloss over one use for this extra cash: vacations! I may earn \$1,000,000 one year, then retire for the next 9 years bleeding off those reserves! Now you have income equality, but the "rich" have more leisure time. Most certainly those rich who like their position in life will busy putting that time to lobbying for the jobs they want, locking the poor into a perpetual grind.
Of course, society could always just rebel against your system. Bartering would almost certainly become a solution immediately, so you'd have to put your foot down and demand that all barters be documented and counted at "fair market rates." But what's a fair market rate? What if nobody buys these things with cash? What would quickly happen is a massive deflation of your currency. A car that once cost \$10,000 might suddenly cost \$2,000, and wages would drop by 1/5 to support that. Now that the prices are devalued, the rich that were making \$500,000 are now only making \$100,000, which was the limit, so they can spend all of their money. All of this because you had to document bartering to prevent it from being a loophole.
Of course, you can also become a despot and fix the market rates for goods. In every documented case of price fixing ever, a black market springs up. You set the price of a coffee cup at \$10? No problem, someone begins selling a "topology teaching device: donuts" for \$5. It's purpose is to teach youngsters about topology. In topology, a donuts and a coffee cup are treated as the same shape, because they have the same number of holes in them. But you don't have a fixed price on tools for teaching higher order mathematics to children, do you?
In the end, things don't go the way you want. It's very hard to apply gross changes to a system as complicated as economics without massive issues. Changes have to be smooth and subtle.