If you own 1/1000 of property the tax is low.

@embolism: Apartment costs more than a house in the same spot?

If 1000 people share ownership of multistorey building also the land the building stands on, also the land tax, also roof, walls, infrastructure, it's bound to be far cheaper than 5 houses with 20 people at most occupying same space.

The price of an apartment is determined by supply and demand for housing units, not by dividing the price of a house occupying similar land area by the number of units.

Taxes are typically levied on the value of each housing unit.

Don't you at least agree that if you'd replace a block of flats for thousand people with houses for 10 you'd seriously reduce supply of housing in this spot without affecting the demand much and so you'd increase the value and tax on each housing unit in this spot?

I'm no sure how land tax works in the US but in my country it is calculated by multiplying tax rate for given region by area of the plot and then divided between people who own the plot. Share is usually proportional to the area of the buildings or parts of them they own on this plot.

No - an apartment usually costs more per sq metre than a house.