Supply is fairly inelastic, so if a helicopter drop (or gold rush) were to suddenly create large amounts of wealth in the low wealth city, those who did not receive this new wealth would rapidly find themselves crowded out of such markets, and materially worse off in terms of their ability to consume/purchase real estate (despite having participated in a weak Pareto improvement).
In such situations, one cannot dismiss the relative effect of wealth on demand and supply, and cannot assume that these are static (see also General equilibrium).
However, according to David Backus the wealth effect is not observable in economic data, at least in regard to increases or decreases in home or stock equity.
[2] Economist Dean Baker disagrees and says that “housing wealth effect” is well-known and is a standard part of economic theory and modeling, and that economists expect households to consume based on their wealth.
He cites approvingly research done by Carroll and Zhou that estimates that households increase their annual consumption by 6 cents for every additional dollar of home equity.