Revisiting the Pigouvian tax in urban roads: Housing supply restrictions, leaking profits and spatial inequality

I examine road taxes in a polycentric city where congestion coexists with housing supply restrictions. Despite the quantity distortion that housing supply constraints cause, I show that the socially optimal tax for using a road is still its marginal external cost. However, the artificial housing scarcity generates potential profits, which are either accrued by the construction sector or absorbed by raising land prices. If land rents and developer profits are not fully recycled within the urban area, the Pigouvian road tax ceases to maximize the welfare of that area. To maximize local welfare, road tolls should then lie below (above) their Pigouvian level insofar as they increase (decrease) housing demand in areas where supply cannot be adjusted upwards. I derive analytical formulas for the impact of other spatially relevant aspects on the optimal road tax. Property taxes and spatially invariant lump-sum transfers can both render the Pigouvian rule for taxing road externalities suboptimal.