Apart from being unjust, that approach would completely break the market and put people out on the street. You buy a house for $200k; its value increases to $400k; you sell it, and the city takes $200k, leaving you with $200k. You now cannot afford any of the houses currently for sale for $400k, even though the additional $200k you don't have would just go to the city, and the seller just gets the $200k you actually have.
Typical price controls affect both sides of the transaction, so the house value can't increase, or doesn't increase faster than a certain limit. That at least doesn't directly prevent people from selling one house and buying another comparable house.
To answer your original question, though: to what extent do the areas in most dire need of housing have any undeveloped land? Those areas don't have much undeveloped land; they have underdeveloped land. If you had price controls on undeveloped land but not on developed land, at some point you'd end up with a price inversion where a given property with a house on it has less value than the same property without the house. At which point someone wanting to extract the increased value could demolish the house and then sell the land at market value.
Why would the houses continue to be for sale for $400k? I can't see why people would bother to charge any more than the price they bought the house for, once they realized that the government would pocket any profit. If selling for either $400k or $200k gives you either way $200k, it's in your interest as a seller to sell for the lesser amount, because you get more buyers more quickly that way.
> At which point someone wanting to extract the increased value could demolish the house and then sell the land at market value.
That was actually partly the point! It incentivizes property-management companies to try to lobby to remove the NIMBY barriers in the way of tearing down old buildings.
That sounds like a plausible (but not certain) outcome, assuming a 100% tax with no way around it. I wouldn't underestimate creative (legal) solutions, though. A structure like this creates major incentives for under-the-table sales, fees, or anything that doesn't qualify as "part of the sale price". For instance, it would create an incentive for "buyer pays" transactions, where the buyer directly pays for all associated services involved with a sale without paying the seller directly, including those costs typically paid by the seller or split between the two.
> That was actually partly the point! It incentivizes property-management companies to try to lobby to remove the NIMBY barriers in the way of tearing down old buildings.
Interesting notion. What stops them from tearing down those old buildings today, though? It seems like the bigger problem is that they can't build new buildings that aren't just as sparse and under-developed as the old.
https://en.wikipedia.org/wiki/Price_controls
Let's say we implement full controls tomorrow in SF, where all real estate appreciation is capped at, say, inflation.
As demand for housing continues to grow, you'll find that the government-mandated capped price will rapidly diverge from what the free market price is, e.g. someone is willing to pay $1mm for a house but it can only be sold for $600,000.
Since the seller is essentially being forced to take a bath, property owners will simply not sell. The market becomes extremely illiquid and everyone loses.
The key to understanding the seller's behavior, by the way, is because under price controls the market becomes extremely asymmetric. An excess of demand means that every potential seller has MANY potential buyers who are all willing to pay the asking price, so buying becomes a huge lottery. So if you own a property and you sell, there's very little chance you can change your mind later on and buy a different property, whereas in a normal market you just pay the normal transaction fees.
(In other words: a roundabout mechanism to do to "land under your mattress" what inflation does to "cash under your mattress.")
Since the growth is exponential, if the pain becomes too great after N years, then everyone is forced to sell after N years. Looks suspiciously like a fixed-term lease, no?
So instead of price controls on real estate, now we've gotten rid of real estate altogether and just have price controls on rental rates.
This is one reason why mixing a command economy with markets is tricky, btw. Once you start down the rabbit hole of using coercion instead of price signals to get people to do things, you'll find you need to use more and more coercion (whether strange taxes or more draconian measures) to make things work.
The interesting thing here, to me, is that the government wouldn't want to control allocation as in a command economy; instead, they merely want to punish people for making the market inefficient. They want the market to clear, so that they don't have to figure out how to centrally allocate anything. We already have a lot of government regulations with this explicit goal. I'd be shocked if we couldn't work one out for real estate.
The SF real estate market right now is quite efficient; houses and condos sell quickly at the going market rate, but you might find the effect on the allocation of housing to be very unfair in that some people have much easier access to housing than others.
Price controls favor fairness over efficiency; e.g. selling bread below market price means everyone waits in line, which is by definition inefficient. It is fair, however, in that both rich and poor wait equally.
> They want the market to clear
That's what I mean by compulsion begetting compulsion -- the market clears just fine right now, but price and/or rent controls will probably make it not clear, at which point you need to add other taxes to force it to clear again.
This is why a real land-value tax wouldn't simply grow, but would rather reflect the current market value of the land.
It's called the Land Transfer Tax: http://www.fin.gov.on.ca/en/tax/ltt/