> There would be an equilibrium. If the need is an average of 1.2 stories, why would developers build until there is 2.5 stories?

Because LVT doesn't scale with buildings.

Suppose you already have enough housing. More than enough, even. There is a 25% vacancy rate. Units are renting for $2000/month, half what they were before LVT. Of that, $1000 is the amortized construction cost and other upkeep. For a 1-story building, there is also another $1000/unit/month in LVT. They're already losing money because 25% of their units are vacant and they'd need a 0% vacancy rate just to break even. But they also lose money by renting for any less than $2000/month, so they're resistant to lowering rents below that because a large proportion of the units are the existing single-story housing stock.

But the same LVT is only $200/unit/month for a 5-story building and $100 for a 10-story building. The landlord with a 10-story building is still turning a decent profit even with 25% of the units empty. So landlords with a 1-story building start putting up 10-story buildings even though there is already oversupply because they go from losing money to making some, and the vacancy rate increases even more.

There will be an equilibrium where they stop, but by then the vacancy rate could be arbitrarily high depending on how high the LVT is relative to construction costs.

> The way I understand it, the LVT is 'automatically' set by the land values, hence the LVT name. Of course the government can play with what percentage of the land value the tax is set to, but presumably it would be very unproductive to set it higher than the rate of return of that land in the first place. So even a 'maximal' LVT would be capped (assuming basic economic saneness on the behalf of the government).

This is the issue. Land values become quite meager without artificial scarcity in housing, and then the government doesn't receive much revenue from the tax. Since the government wants tax revenue, they now have a perverse incentive to bring about artificial scarcity in housing. Which is the same incentive they have now with property tax, but the premise of LVT is that they're not going to act on it.

> So if somebody builds a 50-story building, then there is suddenly an oversupply of housing, and as result land values drop, and thus the LVT a land owner needs to pay drops as well.

For which the endgame is that land values fall to be level with the ground, and the government either charges more than the land value in tax, or enacts policies to bring about artificial scarcity to increase the land value, or has negligible tax revenue.

> And likely the developer of the 50-story building will then make a huge loss, because building such an extremely tall building is very expensive, and tends to make sense only where land prices and demand are huge, not in a place where the requirement is an average 1.2 stories.

Very tall buildings are very expensive (but also contain a very large number of units to rent out). Medium buildings aren't all that expensive per unit. If you only need 1.2 stories on average and then fill half the city with 5-story buildings, you'd have no scarcity of housing without anybody ever building a 50-story building.

If you're in a place like NYC the developer of the 50-story building is making a lot more money than the developer of a 10-story building notwithstanding the higher construction costs because they're paying five times less LVT.

> Well, that's the crux isn't it: What is 'some other way'? (Almost) all taxes cause economic inefficiency in some way.

In general a broad-based tax so that the rate can be lower and minimize the distortionary effect, e.g. VAT.

> LVT, proponents claim, is almost unique in not causing any deadweight loss because the supply of land is fixed. So from an economic efficiency point of view, it seems LVT is the (or at least, among the) least bad tax.

A head tax also has no deadweight loss but that's not the only criteria. Moreover, if LVT causes land values to go down and then generates negligible revenue, this is a problem unless you find it convenient for the government to have negligible revenue.