What if, instead, we were talking about bread? Assuming that rich people are fairly rare, then raising the price of bread high enough to be expensive but not so high that people cannot pull enough cash out of their pocket to pay for it, then the effect seems to me like it should be an approximation of a ration.
Clearly if Donald Trump gets to the store first and buys all the bread then nobody else would have any, but he could do that no matter the price. So long as the price is painful but feasible for anyone to afford, everything should work out more or less okay.
If the price is so high that nobody but Donald Trump can afford the bare minimum necessary, then there is certainly an issue, but I suspect raising prices that high would not be very effective.