This misses the point entirely, I think. The problem isn't income inequality so much as low income in general in that region. There is very little opportunity. But low opportunity is coupled with generally high education and literacy rates and a massive population boom. A young population, unemployed intellectuals, and authoritarian government has
always led to revolution. Always. It's human nature. It's happened at points in European history, and it's happened in China and Japan and elsewhere.
As a musician, I play some middle eastern music and own several instruments from the region. I have a doumbek (cast aluminum goblet drum) from the well-known GEF in Egypt, and another from Syria. The difference in construction quality is shocking. When showing the Syrian drum to people, I sometimes say "You've heard about the precision industrial powerhouses of Syrian manufacturing, right? No? Here's why." But what's even more shocking is the difference in the quality of the "good" Egyptian drum versus pretty much any instrument made in China or Indonesia these days - CNC-milled parts, quality finishes, and tight construction rule in even the cheapest Asian manufacturing.
Manufacturing in the Arab world, such as it is, is mostly trapped in the 19th century, unable to escape craftsman roots. This is terribly inefficient and unproductive. The Arab world is technologically incapable of manufacturing complex devices like cars and surface-mount electronics. And it's not for lack of educated people or a desire to do better. Other forces are at play here.
Revenue from raw resource extraction (oil) is just exploitation, and it's time-locked. Sooner or later, oil fields run dry, and they'll be back where they started, basically just agricultural communities. It's a shame, because the region and cultures there have provided some of the most important advances in history (like the number zero and algebra), and I'm sure it could rise to that effectiveness again, given the right conditions.
But oil exploitation is good for both the local authoritarian regimes, and for the western powers that run their economies on cheap Arab oil. That leads to a massive militarization and government-level resistance to modernization and advancement. It sucks. In a way, oil is the worst thing to happen to the middle east.
And who has an answer? Clearly, the world of desert kingdoms and post-fascist Baathist regimes is ripe for revolution. But the answers seem to be either go forward, into the scary world of modern relatively peaceful democracy and freedom, or backwards into the glory days of centuries ago. And the Islamic fundamentalists who want to go backwards are strengthened by the general lack of interest in the west for real democratization, and the preference for petty regimes we can control from afar.
Sigh.