Optimal private housing supply under various schemes of public housing provision

Allocating land for public housing is an essential step in providing affordable housing for lowincome citizens, as practiced in Hong Kong and Singapore. Locating public housing projects in suburban areas causes a spatial mismatch between public housing tenants and job opportunities, while placing public units in urban areas exacerbates the shortage of urban land, which may result in a more compact urban development that worsens the living conditions of urban private flats. We extend the stochastic bid-rent framework to derive the optimal supply decisions of profit-seeking developers under various schemes of public housing provision. The residence and travel choices of heterogeneous households are simulated under the optimal supply decisions. We find that placing a certain number of public flats in urban areas will lead to a higher profit for developers. With more public housing in urban areas, developers condense the urban development and provide more urban micro flats to capture the privilege of accessibility, which lowers the quality of private urban flats. On the other hand, compact development accommodates more residents in urban areas, thereby alleviating congestion in suburban areas. This improvement in accessibility, however, results in rent increases for suburban private flat residents, who will suffer a loss of consumer surplus. Similarly, policy measures that aim to improve living standards or shorten the commuting time for residents (e.g., imposing restrictions on minimum flat size or upgrading suburban transport facilities) may affect the welfare of other stakeholders adversely. Thus, it is unlikely that a land allocation that improves the welfare of all stakeholders can be found, rendering the importance of considering this trade-off judiciously.