Differentiable strategy-proof mechanisms for private and public goods in domains that are not necessarily large or quasi-linear

In this paper, we develop a differentiable approach to deal with incentives in a, possibly small, subset of a general domain of preferences in economies with one public and one private good. We show that, for two agents, there is no mechanism which is efficient, strategy-proof and where consumption of both goods is positive for all agents. For the case of two or more agents the same result occurs when nondictatorship is replaced by Individual Rationality. We are very grateful to Atila Abdulkadiroglu, Carmen Beviá, Xavier Calsamiglia, Marco Celentani, Bernardo Moreno, Antonio Romero-Medina, William Thomson, Walter Trockel, an associate editor, three anonymous referees and participants at seminars at Universities of Alicante, Autónoma de Barcelona and Rochester and the Spanish Economic Association meeting in Sevilla for very helpful comments and suggestions.