Who should not share? The merits of withholding unused vehicles

People repeatedly demand travel, using available vehicles scattered around space. What can justify vehicle withholding (i.e. preventing others from using it, for own future use) from the social welfare perspective? This paper investigates heterogeneity in the potential cost of search for alternative vehicles as such justification. It is shown that travellers whose search cost is substantially higher than that of others (e.g. limited-mobility people) can optimally withhold a vehicle. The heterogeneity of search costs should be sufficiently strong, e.g. a uniform distribution is not variable enough to justify withholding by anyone. In an example calibrated for car use in London, it is shown that at most 39% of car users should withhold their vehicles under the most extreme modelling assumptions, while all others should share. An extension of the model rules out some other justifications for withholding, such as short duration of stay and aversion of risk of having to search for another vehicle.