A Walrasian Mechanism with Markups for Nonconvex Markets

Abstract We introduce markup equilibrium—an extension of Walrasian equilibrium in which consumers pay a fixed percentage markup over producer prices. In quasilinear markets, markup equilibria exist despite nonconvexities. They are resource-feasible and envy-free, incur no budget deficit, and require little more communication and computation than ordinary Walrasian equilibrium. The associated markup mechanism is asymptotically incentive-compatible. We also introduce a Bound-Form First Welfare Theorem, which states that for any feasible allocation, the welfare loss compared to the first-best is bounded, using any price vector, by the sum of the resulting (i) budget surplus and (ii) rationing losses suffered by the participants. Using producer prices, this bound implies that any markup equilibrium with a small markup and few unallocated goods is nearly efficient.