Between 1970 and 1990 the share of elderly widows living alone grew by 23.2% in the U.S. (from 52.1% to 64.2%), the share living with their children decreased in a similar magnitude, while the other types of living arrangements remained stationary. In the same period there was a moderate increase in national incomes and a big increase in the income of widows. We pose a variety of models of the determination of living arrangements between widows and their children where living together provides consumption gains due to economies of scale, and it may also provide utility directly. We estimate those models using 1970’s data and for some of them we obtain an excellent fit despite the fact that the data display a very nonlinear relation between living arrangements and income. We use the models to measure the contribution of income changes on changes in living arrangements. Our findings are very sharp. The simplest version of the model performs very good and it predicts that changes in the incomes of both the widow and her off-spring generates three quarters of the increase in the number of elderly widows that live alone. An extension of the basic model that takes into account the marital status of children provides slightly better estimates and imputes one half of the observed changes in living arrangements to changes in the incomes and in the marital status of the children.