> It becomes unprofitable to increase the housing stock, so housing becomes more expensive

There's no way that this occurs with actual property taxes at the levels they are in the US. Sure, an improvement may result in higher property taxes which go into effect before the value of the improvement begins being realized, but overall effective property tax rates in the US range between 0.37% and 2.22% per year; this plausibly could make uses where the value would be realized entirely in direct-use by the owner unviable, but there is no way it makes any use where the value is realized through commercial exploitation (whether productive or rent) unviable, even with something of a delay in realization. Including things like densifying housing for rent or sale.

Yes, abstractly it might be a problem with property taxes, if you had a system where property taxes were the principal tax in society. Of course, the only people who even propose real estate taxes as the primary tax are…Georgists arguing for a heavy LVT replacing other taxes.

> It’s not that they encourage it so much as that they stop discouraging it

No, especially if they are heavy (as LVT proponents often propose), they don’t merely “stop discouraging” improvements, they make them necessary, because land uses that don’t provide a substantial fraction of the income potential of the land become unviable. In fact, land ownership by people who don’t have capital for both improvements and to stay afloat until those improvements bear fruit becomes unviable; a heavy LVT is an efficient way to assure acceleration of the concentration of land ownership.

> Sure, an improvement may result in higher property taxes which go into effect before the value of the improvement begins being realized, but overall effective property tax rates in the US range between 0.37% and 2.22% per year; this plausibly could make uses where the value would be realized entirely in direct-use by the owner unviable, but there is no way it makes any use where the value is realized through commercial exploitation (whether productive or rent) unviable, even with something of a delay in realization.

Why not?

Suppose you could invest $100,000 to create housing in an area where that would have a 5.5% ROI, compared to a 5% ROI for some non-housing alternative investment with equivalent risk. Then you're going to build housing. Add a 1% property tax and you're going to invest the money in the other thing instead until local rents increase to raise the housing ROI.

> No, especially if they are heavy (as LVT proponents often propose), they don’t merely “stop discouraging” improvements, they make them necessary, because land uses that don’t provide a substantial fraction of the income potential of the land become unviable.

That doesn't actually change the math.

Suppose you could spend $100,000 to construct more housing on your property and then, in the local housing market, the additional housing would have a net present value of $90,000, e.g. because local rents are already low. Then you're not going to do it, because you'd just lose $10,000.

If you suddenly owe a lot of land value tax, you're still not going to do it, because losing $10,000 more doesn't help you pay the extra tax.

Whereas if you could spend $100,000 to produce something with a net present value of $200,000, you were going to do that either way.

The weirdest thing about LVT is that if you got rid of the disincentive to build from property tax (and, of course, restrictive zoning) then the "land value" would crash because if rents were higher than construction costs then construction would happen until they weren't. At which point housing scarcity would be low and collectable rents would be predominantly attributable to construction costs, and only higher in cities to the extent that higher density structures have a higher construction cost per unit area.

But the same thing happens just by getting rid of property tax and restrictive zoning, doesn't it?

Yeah it is likely with heavy LVT there would be huge funds that would purchase land and let it out for a small profit (“ground rent”).

Encourages in the sense that leaving land empty while it gains value is easy and free. Once you are paying for that land you have to do something with it otherwise it costs more than the inflation of the value.