This paper considers the problem of pet overpopulation. It develops a tractable dynamic model whose positive predictions square well with key features of the current U.S. market for pets. The model is used to understand, from a welfare economic perspective, the sense in which there is overpopulation of pets and the underlying causes of the problem. The paper also employs the model to consider what policies might be implemented to deal with the problem. A calibrated example is developed to illustrate these corrective policies and quantify the welfare gains they produce.