"Almost" subsidy-free spatial pricing in a multi-dimensional setting

Consider a population of citizens uniformly spread over the entire plane, that faces a problem of locating public facilities to be used by its members. The cost of every facility is financed by its users, who also face an idiosyncratic private access cost to the facility. We assume that the facilities’ cost is independent of location and access costs are linear with respect to the Euclidean distance. We show that an external intervention that covers a tiny portion of the facility cost is sufficient to guarantee secession-proofness or no cross-subsidization, where no group of individuals is charged more than its stand alone cost incurred if it had acted on its own. Moreover, we demonstrate that in this case the Rawlsian access pricing is the only secession-proof allocation.