The Simple Economics of the Impossibility of Efficient Trade
Abstract: We introduce a variant of a two-sided market with continuous quantities and show that efficient trade cannot be achieved using both classical economic and duality theory methods. This framework enables a direct comparison between the dominant strategy equilibrium induced by the Vickrey-Clarke-Groves (VCG) mechanism and the competitive equilibrium. We find that under the VCG equilibrium, buyers pay less and sellers receive more than what they would in a competitive equilibrium by an amount known as the Harberger triangle. Consequently, the deficit faced by the market maker can be decomposed into the sum of individual Harberger triangles, the size of which depends on agents' market power. Furthermore, we uncover a novel link between Shapley's inequality and Harberger triangles, suggesting that horizontal mergers may have negative effects, and demonstrate that as market thickness approaches infinity, VCG payments approach competitive payments while the deficit stabilizes at a constant value.