Just as one example: housing prices often rise in response to a process frequently referred to as "gentrification" (often with a somewhat disparaging tone, to put it mildly). But that process tends to start when people with very little income to spend on housing move into low cost of living neighborhoods and subtly shift their demographics and nature. So is gentrification a process driven by the "poor" (the initial influx of new tenants) or by the "rich" (developers who can carry out significant remodelling and/or new construction) ? The answer is clearly both, yet even that doesn't really cover the whole mechanism. For a start, for gentrification to become significant in driving up housing costs, existing owners need to sell. These are often neither the newcomers nor the developers. Gentrification also requires a modest but distinct influx of businesses into an area, which in turn requires businesses to either start or expand.
I'm citing this as just one single example of where bullshit simplifications drawn from "basic" economics fail to describe the real world. There are so, so many more.
Why does it gentrify in the first place? Because the initial group of "gentrifiers" took the time and money to develop the area to make it more appealing, thus increasing demand.
Economics says you can't fix it no matter how much regulation you impose because at some point all the surrounding businesses, etc. will be gentrified too and force out poor people. Even if you freeze rent, ban new businesses from coming in, etc. the existing business owners will start to cater to their new clientele simply because the demand from those customers is much higher. The only thing you _can_ do is ban people from moving to the neighborhood, at which point you've turned into the worst parts of the Soviet Union.
Wildly simplistic. The first stage of gentrification involves almost no money and almost no development. It doesn't even really involve much time. It's the result of a demographic shift (and often not a very big one at at that) between the existing residents and newcomers who are willing to trade currently less-than-ideal living conditions for lower costs.