The Home Selling Problem: Theory and Evidence†

This paper formulates and solves the problem of a homeowner who wants to sell their house for the maximum possible price net of transactions costs (including real estate commissions). The optimal selling strategy consists of an initial list price with subsequent weekly decisions on how much to adjust the list price until the home is sold or withdrawn from the market. The solution also yields a sequence of reservation prices that determine whether the homeowner should accept bids from potential buyers who arrive stochastically over time with an expected arrival rate that is a decreasing function of the list price. This model was developed to provide a theoretical explanation for list price dynamics and bargaining behavior observed for a sample of homeowners in England in a new data set introduced by Merlo and Ortalo-Magné (2004). One of the puzzling features that emerged from their analysis (but which other evidence suggests holds in general, not just England) is that list prices are sticky: By and large homeowners appear to be reluctant to change their list price, and are observed to do so only after a significant amount of time has elapsed if they have not received any offers. This finding presents a challenge, since the conventional wisdom is that traditional rational economic theories are unable to explain this extreme price stickiness. Recent research has focused on “behavioral” explanations such as loss aversion in attempt to explain a homeowner’s unwillingness to reduce their list price. We are able to explain the price stickiness and most of the other key features observed in the data using a model of rational, forward-looking, risk-neutral sellers who seek to maximize the expected proceeds from selling their home net of transactions costs. The model relies on a very small fixed “menu cost” of changing the list price, amounting to less than 6 thousandths of 1% of the estimated house value, or approximately £12 for a home worth £200,000.