Matching Models and Housing Markets: the Role of the Zero-Profit Condition

The recent and growing literature which has extended the use of search and matching models even to the housing market does not use the free entry or zero-profit assumption as a key condition for solving the equilibrium of the model. This is because a straightforward adaptation of the basic matching model to the housing market seems impossible. However, this short paper shows that the zero-profit condition can be easily reformulated to take the distinctive features of the housing market into account. Indeed, the zero-profit condition considers the possibility that a buyer can become a seller and vice versa, since it is used to find the equilibrium of the model where the transition process from seller (buyer) to buyer (seller) comes to an end.