> Landlord costs affect supply in the long term, so you will see changes, just not necessarily immediately over a one year period, but definitely over a 5-10 year period.

In fact - although that logic is usually correct - in the case of a land value tax it isn't useful because landlords do not supply land. Someone is still going to own the land and it is still going to be used for something. There is no incentive to leave it unused. There aren't any less resources in the overall system and resources haven't been diverted from a productive use to an unproductive use (quite the reverse, they're being redirected away from someone who was doing nothing to earn them). That is the theoretical advantage of taxing the land.

If it were anything else (eg, taxing the houses on the land) then the argument would be useful because the tax was on transforming less valuable resources into more valuable and there would be less productive economic activity and losses leading to less supply of something that the economy was signalling a need for.

There might be a reallocation from housing to some other purpose if an LVT is bought in, who knows. But it is a context-dependent change and not possible to reason about as a general outcome. It might be that the economy produces exactly the same amount of housing before and after. Less resources overall will be allocated to landlords, obviously, but not in a fashion that penalises building houses. Maybe that means house prices drop and more people own their houses outright. Maybe there is even more housing because resources move from landlords to housebuilders.

> If it is just a land tax, however, you can game it by building as much as possible...

I've never heard an entirely satisfactory process for valuing the land either. Although to some extent all tax systems have questionable underpinnings and compliance.