GP was incorrect that it doesn't increase supply, but correct on pricing. Besides, if I can't afford $3000/mo rent, it doesn't matter to me how many rental units are available at $4000/mo. With massive pricing collusion having been the standard for the last few years (RealPage) and the demand for housing always being extremely inelastic, the supply/demand curve is extremely complex.
But paper often neglects reality. A reality where it can be more profitable to simply hold the land rather than lease out the home on it. Where a constructive loss can improve tax savings. Where the intent is to have it vacant for some other perceived use or gain - like a vacation home, AirBnB rental, Pied-a-terre, or just letting the structure languish until it can be condemned and bypass red tape around teardowns/rebuilds.
Current incentives and structures do not mandate that homes are made available when someone buys another domicile. That’s one of the myriad of issues affecting the housing crisis.
All that means is, that building one unit of housing and selling it means that the pool of available housing is increased by less than one unit. It does not mean that the available housing supply did not change, or decreased.
So if building one unit of housing increases the housing supply by 0.7 units on average or whatever, then the same logic applies, just overbuild by 30%.