Unless there is another cataclysm like WW I, Depression, WW II to level society within countries and to cause great inequality between countries, all nations will evolve towards the long-term stable social model of India or Brazil.
In 1950, the US emerged from the previous Half Century with a society that had grown rich from exploiting our natural resources to be the provider of arms and supplies to the winning side of global wars. The rich had been taxed to pay for the effort, the depression had impoverished others, and income inequality was at a low. On the other hand income inequality was at a maximum between nations, with the US by far the richest with its intact industrial empire.
So inequality globally was at a maximum in 1950, with universally rich Americans and other countries ranking downwards to destitute third world countries.
Since then, the evolution has been towards greater equality between countries, as first Europe and Japan recovered, as the Asian tigers became industrialized, and as the BRICs began their upwards progress.
Since there really is a zero sum game with respect to raw materials, energy, etc, it is impossible for global progress to result in a world where all the people enjoy the wealth of the average American. You would have to quadruple the output of the oil industry for one thing.
Therefore, the evolution is towards greater inequality in each nation, but within each nation, the wealthy enjoy a high level of income similar to the American middle class, but the rest of the population are much poorer.
Because of competitive trade and finance globally, the US is unable to provide a middle class income for everyone, and its middle class has to shrink as well. Thus, it will come to more closely resemble other large countries like China, Brazil, Indonesia, India, etc.
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