"If both the rich individual and the poor individual are competing over the same scarce source material (eg Petrol, Rice, Real Estate) then the market will elevate the price of that material to the highest level that the rich will bear."
This is actually not always the case. Food prices are a prime example. It turns out that the rich often pay less for food than the poor.
Take a look at some of the conclusions of this study:
"Do the Poor Pay More for Food? An Analysis of Grocery Store Availability and Food Price Disparities."
The researchers conclude that the poor do indeed pay more in the Twin
Cities grocery market... In part, the poor pay more for grocery
products because the stores that charge the lowest prices are not
located in their neighborhoods.
The study has overviews of a lot of other research that supports these findings. For example,
In 1991, for example, New York's Consumer Affairs Department compiled
a report on grocery store price-fixing in several neighborhoods
(Freedman 1991). The report showed the poor paid more for groceries in
inner-city neighborhoods, yet they received poorer quality foods and
services. The report consisted of price surveys in sixty stores and
140 interviews in various New York neighborhoods.
Real estate, on the other hand seems like a classic example of a case where the concentration of wealth really can make poor people poorer, by crowding them out of more and more of the real estate market through gentrification.
Of course, this depends on there being an actual scarcity of land. In areas where new land can easily be developed, it's much less of an issue.
There might be plenty of land, but I think there will always be more desirable land. Either it is more central - better transport, trade, jobs. Or it is near a natural resource, for instance water - which provides fresh air, views, transport.
The poor benefit as much (or more) than the rich do by having access to this better land.
This is actually not always the case. Food prices are a prime example. It turns out that the rich often pay less for food than the poor.
Take a look at some of the conclusions of this study:
"Do the Poor Pay More for Food? An Analysis of Grocery Store Availability and Food Price Disparities."
http://www.thefreelibrary.com/Do+the+Poor+Pay+More+for+Food%...
The study has overviews of a lot of other research that supports these findings. For example,