> The sale value won't stay flat unless you tax land (or use leasehold like Singapore), because typically incomes rise, and in most places the rate of building new housing has an equilibrium lower than the rate of demand, because profit is needed for private developments to go ahead.

Developments can be profitable without the price per unit significantly increasing.

Suppose that an existing unit is $50,000 and it costs $150,000 in construction costs including profit to replace one unit with four. Then you have a stable equilibrium; a construction company could buy one unit for $50,000, convert it into four, sell them for $50,000 each and net $150,000 which covers their costs and profit. They'll stop doing this if the price per unit falls to $45,000. They'll start doing it again if the price per unit rises to $60,000 and keep doing it until it gets back down below $50,000. Therefore, the price per unit remains stable at ~$50,000, even if demand increases, because that just triggers more construction as the price temporarily gets slightly above the breakeven point.

This is why zoning restrictions cause housing costs to increase. If you declare that 95% of the land is zoned exclusively for single-family homes, you can't replace one unit with four or even two in any of those areas. Then the remaining 5% of the land already has a 20-unit complex on it and in order to add units, you have to replace it with a 30-unit complex. Taller buildings require more expensive materials, you've had to demolish 20 units instead of one and only increased the number of units by 50% instead of 300% and land on which you can even do this at all is now more scarce so you're paying even more per unit for the ones you're going to demolish. Now the breakeven price for new construction is $500,000/unit and if growth continues it has to rise to the level that can cover the cost of demolishing a 30-unit building to build a 40-unit one, even though 95% of the local land is still single family homes.