Warning: this is a fairly philosophical post!

I very much embrace the mustachian lifestyle, and live well below my means and try to invest my savings in index funds, which I hope continue to increase in value. But, as a mathematically minded person I have a hard time believing the long-time validity of our assumption that you should expect about 5% real value increase in invested money, or even any positive long-time average fixed real return. Hopefully someone can explain this to me.

My confusion can be summarized in the following simple argument/estimate:

Basic googling indicates that about a tenth of the total assets and money in the world are owned by about 0.1% of the people on the planet. Supposing that these people do not spend much of their wealth each year and have it invested, then we would expect their real return to be about 5% per year. By real return, I mean above inflation, which I will assume to be equivalent to their fraction of the total wealth in the world. In fifty years, their fraction of the total world wealth would therefore be expected to increase by about a factor of 11.5 = (1.05)^50. But this is clearly not possible, since they cannot have more than all of the assets in the world. Therefore we conclude that a 5% average real return cannot hold long term as it leads to a contradiction.

To try to pick holes in my own argument, we could say that we should not expect 5% of real return, but something less - but then it will just take a little longer before the richest 0.1% own everything, and the contradiction will still arise. Or maybe we could say some of the wealthiest 0.1% will actually squander lots of their money instead of investing it, but again, we could just focus on a subset of the group who do invest most of their wealth and eventually their share of the worlds assets, growing at some fixed positive rate, will reach the point that they own everything.

The only way I can think of to counter my argument is that I should not take the real value of an individuals wealth to be equivalent to their fraction of the total wealth in the world. Clearly over the past hundred years, the world population has increased a lot, and we have also increased the average standard of living by destroying the planet, such that the real value of an individuals wealth has not been tied to their fraction of the total wealth. But if we expect that in our lifetimes, the earth's population will plateaux and we will begin to run out of extra resources we can extract from the finite planet that we live on, then I would expect that the real value of an individuals wealth will indeed become tied to their fraction of the total wealth.

If someone can point me toward another thread or a good book which could help me understand these issues a little better, I would be very grateful!