Core Equivalence for Residential Land Use Models

I demonstrate that in the monocentric city model, an allocation is in the core if and only if it is an equilibrium allocation, as long as households are endowed with strictly positive quantities of a composite consumption good, enjoy any net trade bundle at least as much as they enjoy one on the boundary of their choice set, have monotonic preferences, have preferences and endowments that are not too different, and as long as there is land at every location. I also show that equilibria exist in these circumstances, so the core is not empty