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We present a framework for studying the relation between the distributions of income and house prices that is based on an assignment model where households are heterogeneous by incomes and houses by quality. Each household owns one house and wishes to live in one house; thus everyone is potentially both a buyer and a seller. In equilibrium, the distribution of prices depends on both distributions in a tractable but nontrivial manner. We show how the impact of increased income inequality on house prices depends on the shapes of the distributions, and can be inferred from data. In our empirical application we find that increased income inequality between 1998 and 2007 had a negative impact on average house prices in six US metropolitan areas.