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...

In general equilibrium theory for private good economies, possible discontinuities in budget correspondences create obstacles to decentralizing Pareto efficient allocations, as well as to existence of Walrasian equilibrium with gains from trade. Then McKenzie's (1957) notion of compensated...