Housing Affordabilaty Crises

Standard disclaimer, I'm not particularly knowledgeable about this subject. Rather, this is my attempt to become more knowledgeable about it than I was before I wrote about it.
== What determines housing prices? ==
When I see people arguing about what factors (AKA variables) will cause some number (like prices or wages) to go up or down, I sometimes wonder why I don't see any equations. Especially for something complex (like prices or wages), it seems it should be obvious that there are many factors that can all go into the result. Yet I usually see people propose maybe one variable to focus on, with little explanation to justify this.
Anyways, so with housing I'm seeing a lot of people online proposing simply building more housing, and a lot of other people online saying that won't work due to scalpers. Recently I brought up this objection to someone in the first group, and they replied with the additional variable of "competition".
==== Scalping ====
Some model scalping scenarios: tickets for a stadium, bottled water in a disaster (well, "price gouging"), hand-sanitizer in the pandemic:
* tickets for a stadium
** there are limited number of tickets, demand is high enough that all of them will be sold, so if someone buys some early and holds on to them until all (or nearly all) of the others are sold, they can charge higher prices
* bottled water in a disaster 
** this involves a similar limited supply, but is usually called "price gouging" if they are being sold by a store that already owned them (but if someone else bought them and then tried to sell them for even higher prices, that seems to be "scalping" again), but it seems basically the same
* hand-sanitizer in the pandemic
** once again, limited supply compared tot he demand, someone buys a bunch for the regular price, then tries to sell them for higher.
* were some of the shortages of regular goods [such as toilet paper] mostly due to changes in demand, rather than changes in supply?
==== Supply in in scalping situations ====
We might propose another variable to consider: how much money do the potential scalpers have? How much supply has to exist (and at what price) before scalpers can no longer afford to buy everything?
But I think the stadium example shows that isn't really the only situation that scalping occurs in. They do not buy every ticket in the stadium. They just buy a smaller quantity, and wait until there inevitably is no more supply.
Housing at least seems to be different from stadiums, because stadiums generally can't have seats added to them, yet we can build more houses. Yet, as with the hand-sanitizer situation, the problem isn't just whether supply can be (or is being) increased, the problem is how quickly? A supply rate, relative to a demand rate. Not just quantity, but quantity per unit of time.
==== Competition in scalping situations ====
Situations with limited supply but high demand.
To me it seems that in these situations, you simply have to out-last your competition. You buy some for cheap, and then you wait until the rest of the cheap ones are sold, and then you sell for higher.
==== Price in scalping situations ====
It might be said that the price of stadium tickets and hand sanitizer is perhaps not much affected by scalping. Only the later (re-sell) price is affected. If you buy early, then you get the regular price.
One thing I'm concerned about here is that creating more supply of housing tends to be a much slower drip than the other two model situations. Buildings are just very slow things to build. But, see housing prices below:
==== Housing prices ====
Does housing really have that high of demand? Don't most people already have a home? And aren't most cities with a "housing crisis" in the world already increasing their supply of it? Again, I'd want to see numbers and an equation. (Maybe there is some way to settle the dispute without one, but I don't see it.)
Affordability
[relative to wages etc.]
Speculation
"Demand" seems like it might go up if the item in question is expected to become significantly higher value than the purchase value.