If land price is still capitalized rent, then rent must be known before price can be. And rent does not depend upon who owns the land.
Much more land is available for sale or new use than just the fringe.
Most cities have at least a quarter of area vacant or underutilized. Askk any assessor. Owners of underutilized sites would be motivated to put their land to better use or sell to someone else who will - which increases supply, not decreases it.