> No one will build affordable housing when they can build expensive housing instead.

This problem is due to restrictions on supply. Consider the statement, "No one will build affordable cars when they can build expensive cars instead"

Cars can be moved and occupy shared spaces. Dwellings are anchored to the earth and exclude other dwellings from the same location.

Yup, that's one restriction on supply. Other restrictions include:

1. Limits on the height of new buildings

2. Limits on the ability to demolish or extend existing buildings

3. Limits on the minimum size of new apartments

4. Limits on the number of people who can live in an apartment

How does this affect the validity of the original statement?

Affordable cars get built because the market for cars is saturated. Where the supply of some key component of cars a limiting factor on the production capability of car manufacturers, expensive cars would be the only ones produced.

> The market has demonstrated that hotels and similar will be built until supply mostly meets the demand.

Actually I think what we're seeing is precisely that this is not happening. If that were the case, hotel rooms in NYC would not cost 2-3x what they do in the suburbs. The price is high because short term rentals are scarce.

So your answer to an under supplied market is to try to control what is supplied?

One could argue that "affordable" long-term housing is a market who's supply should take precedence on the temporary housing market. Since the two must, by nature, compete with each other for the same real estate.

> No one will build affordable housing when they can build expensive housing instead.

Its the same problem SF has. I completely agree.