The wealthiest people in the world are able to exploit the tendency, no necessity, of fiat monetary bases to expand at parabolic rates. The ability to leverage dollars before their inflationary effects are felt in the economy is the key that gives the wealthiest people in today's society the ability to expand their wealth at accelerating rates versus every body else. I am making no value judgements, this is simply the way it is. While there is evidence to support this conclusion, my assertions thusfar are extrapolated from the framework Mises laid out in Human Action.
Admittedly I am rather new to the praxeological method so I may be cutting a few corners, but at any rate I'm here to learn, so my premises are as follows:
1. Inflation hurts the wealthy less than the Average Joe because the wealthy can and do invest their capital productively, thereby protecting their wealth by growing it at a higher rate than inflation.
2. Those who are able to spend "new" dollars in the economy first benefit more as the inflationary effects of new money entering the system haven't yet debased their value.
3. New money enters the system through debt, it is leveraged into existance. Compounding interest dictates that the rate of credit expansion must eventually outstrip the real growth rate of an economy lest more debt is payed off than is issued and deflation sets in.
4. 1 and 2 are not possible under sound money. A gold monetary aggregate (gold monetary base, gold-backed fiduciary media) cannot expand exponentially as fiat must.
Therefore, under a gold standard, the wealthy are not able to exploit exponential credit expansion at the expense of the average Joe's purchasing power. As per premise 4, under a gold standard there would be perpetual deflation, upon which you cannot leverage like you can on fiat today, removing the "cash cow" that has thusfar been the primary culprit in widening the economic inequality gap. The mechanics of a gold standard preclude the possibility of the equality gap ever being as large as it is today because growth would be real, more linear, and more equally apportioned across sectors while at the same time not permitting the pyramiding of leverage atop large principles that allows the wealthy of today to acquire real resources with paper money loaned on a whim into existence.