This paper provides a theoretical analysis of three alternative auto ownership rationing schemes, including lottery, auction and the hybrid scheme. The city's residents are differentiated by their income level, which is assumed to follow a uniform distribution. Expected social cost minimization models are proposed for determining the optimal auto quota for these schemes and the optimal proportion allocated to the lottery and auction in the hybrid scheme. The solution properties of the proposed models are analytically explored, and a comparison of these schemes is made. The results show that the auction scheme is most efficient and the lottery scheme is most inefficient in terms of the expected social cost. The optimal auto quota increases with degraded transit services, but decreases with increased auto travel time/cost. Increasing the proportion of allocation to the lottery in the hybrid scheme may lead to an increased or a decreased optimal auto quota, depending on the road service level. Residents' income gap can significantly affect the optimal quota solution: widening the income gap via raising the income of the rich pushes the government to increase the quota to be provided. However, narrowing the income gap via raising the minimum salary standard may require an increased or a decreased quota provision. The efficiencies of the lottery and auction schemes are very close in terms of the expected social cost, which justifies the use of the lottery scheme in practice.