Whether house prices rise faster or slower than average incomes affects the level of home ownership and the riskiness of different means of financing house purchase. This study develops a model of the housing market with the property that the major determinant of house price rises relative to incomes is the evolution of population density. The model implies that if population density is on an upward trajectory, rises in population and in incomes increasingly generate price responses and diminishing rises in the stock of housing. Rises in population density make high and rising levels of house prices likely; this makes alternatives to standard debt financing of home ownership become more desirable. The impact this has on the structure of risk-sharing contracts between providers of outside equity and homeowners is analysed.