Spatial externalities and land use regulation: an integrated set of multiple density regulations

In a continuous city with three distinct land use zones consisting of business, condominiums and detached houses, we derive the formulae which simultaneously optimize regulations on building size, lot size and the three zonal boundaries under the existence of agglomeration economies and traffic congestion. The formulae show that the optimal regulations require a combination of downward and upward adjustments to the market sizes of buildings within both the business zone and the condominium zone, followed by minimum lot size regulation in the housing zone. The outer boundaries of the condominium and housing zones should be regulated inward whereas the optimal business zone boundary regulation depends on the trade-off between agglomeration economies and traffic congestion costs.