One way a city can reduce the incentive to "upgrade" housing is to charge an excise tax on home purchase transactions in gentrifying neighborhoods. The buyer of the home pays a tax based on the percent change in income between the original owner and new owner. In addition, a higher flat tax should also applied to homes being sold to investors. Should property be transferred from a low-income homeowner to an investor or a higher income household, the low-income seller can benefit from the property sale and the tax generated from the sale could be used to benefit housing for low-income people.
A taxes of this kind have multiple benefits. In the first place, it makes buying out low-income residents somewhat less attractive. Since it applies only to homes, it encourages brownfield redevelopment and infill. Secondly, the tax extracts value from the many transactions that may be occurring in high-growth areas, without preventing development that may benefit all residents. A city can use the revenue captured to deliver renter assistance or build more affordable housing.