| Summary: | In this paper, I am going to assume that the economy is large, or, more precisely, there is a non-atomic measure space of agents. For a private economy, it then becomes easy to characterize the entire class of incentive compatible mechanisms, as will be done in Theorem 2 of Section 3. It is also possible to make rigorous the idea that lump-sum transfers cannot be imposed to achieve a full welfare optimum, because they depend on information which agents will want to hide. In a broad class of economies, in which utilities and demands are continuously differentiable functions of agents' characteristics, the competitive mechanism without lump-sum transfers is the only mechanism which is both incentive compatible and Pareto efficient.
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