Central places in a square

Revisiting Hotelling and Central Place Theory in a bounded square surface seems to still be quite insightful and productive. In this short note, it is shown that agglomeration at the center occurs under market conditions involving duopolistic competition, as expected. In an optimum framework, a hierarchy of centers emerges in a number of ways qualitatively different from the classical Central Place Theory structure. Superimposed on this hierarchy of central places an optimum road system takes shape with certain interesting features in it.