About seven months ago I offered this answer on a similar topic which might interest you.

Do we know if real estate prices were a significant driver in urban expansion? I don't know, I can only answer "Possibly."

What I do know is that beyond the strictly practical desire to enclose a larger area (possibly including some agricultural spaces) in a defensible perimeter, one thing commonly driving the expansion of a city wall was taxes.

Medieval taxes were difficult to collect, and urban walls made the task simpler since gatehouses are convenient points where everything moving through could be taxed. If suburban settlements outside the walls grew such that significant numbers of goods from the hinterland were being taken there (be they raw materials for artisans' workshops, or even mere foodstuffs to sustain the community) the city authority would be missing out on potential tax revenue.

This is why even cities with imposing walls could be surrounded by an additional larger ring which, while sometimes made of stone, might alternatively be as simple as a palisade atop a ditch (or earthworks) which served little purpose apart from tax collection and stopping livestock from wandering too far, and also why walls (whatever the intent behind their initial construction) might survive well past the age in which they might be of any use (as occurred in, just as an example, the French city of Paris). Indeed, sometimes only serious military crises might spurn a given city authority to take serious action in order to convert wooden palisades into stone fortifications capable of withstanding any sort of military siege, as for example occurred in the twelfth century in Italian cities like Milan and Bologna.