>The restriction of new housing increases rent on the remaining lots. NIMBYism, architectural codes, zoning, etc., serve to restrict what can be built, so that the rent on what can be built increases.

If reductions in supply raise the price, you are saying that it is elastic. I basically agree with you on this, it seems. Supply restrictions raise prices.

If price were elastic, the demand would change as prices increased.

Demand largely does not. Instead, as supply is constrained, the price increases because demand remains constant.

https://budgeting.thenest.com/price-elasticity-affect-housin...

This is the whole idea behind a land value tax. Where a tax is made on the unimproved value of land, surplus value is taken by the taxing authority (and presumably returned as public expenditures). The landlord cannot increase rent to compensate (supply hasn't changed, price has), and the result, if other conditions permit, should be increased supply in the sense that idle property is now rented, and low-density / low-value uses are replaced by higher-density / higher-value uses.

The tax applies to the unimproved value so that property investments which increase utility and utilisation are not discouraged. Idle land is penalised.

Real-world validation of the theory ... varies, though seems generally to bear it out. A considerable problem is in getting the LVT in place to begin with, and in dealing with other barriers to enhancement, including zoning and building codes.

In the alternative, increasing asset valuation allows property owners to benefit from constrained supply. Part of their gains come through rent, but a large share is simply in the asset inflation of their property. This can be exercised as collateral on loans for other spending or investment.

I think your facts are plausible but your terminology is wrong. The market can be elastic if either the supply or the demand is elastic, or both. You are saying that the price is not elastic but then contradicting yourself by correctly saying that supply changes change the price.

That's a paper talking about agricultural land use...

It details how and why land is price inelastic, and how elasticity is defined.

Economically, ag and urban land behave similarly. To wit: they're not making it any more. The supply is price-inelastic.

Your understanding is incorrect.

Tenants in cities don't rent land, they rent housing. You can vary the amount of housing on a plot by making investments.