The Mortensen Rule and Efficient Coordination Unemployment

We study the implementation of constrained-efficient allocations in labour markets where a basic coordination problem leads to an equilibrium matching function. We argue that these allocations can be achieved in equilibrium if wages are determined by ex post bidding. This holds true even in finite sized markets where the equilibrium matching function has decreasing returns to scale where the Hosios rule does not apply to both with and without heterogeneity. This wage determination mechanism is similar to the one proposed by Mortensen (1982) in a different setting.