“Derivation of Some Social-Demographic Regularities from the Theory of Time-Minimization”, 1979-03 (; backlinks; similar):
Earlier work on the size-density hypothesis [political unit size vs density scales by negative 2⁄3rds] led to a theory of time-minimization from which the size-density relation could be derived. Subsequently, time-minimization theory was employed to derive expected relations between population and area for cities and urbanized areas, expectations which were empirically confirmed.
The present paper derives 3 well-known and empirically supported relationships from the time-minimization assumption:
the gravity model of interaction,
the intra-urban density function, and the
rank-size rule for cities.