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This paper studies the optimal sharing of value added between consumers, producers, and labor. We first define a constrained optimum. We then compare it with the decentralized allocation. They coincide when the price maximizes the expected marginal revenue of the firm in the goods market, an outcome of the competitive search equilibrium, and when the wage exactly offsets the congestion externality of firm entry in the labor market, which is the traditional Hosios condition. Under price and wage bargaining, this allocation is achieved under a double Hosios condition combining the logic of competitive search and Hosios efficiency. The consumer receives a share of the goodsmarket trading surplus equal to the amount of externality occasioned by its search activity and the worker receives a share of the labor match surplus to offset the externality of firm entry in the matching process. A calibration of the model to the US economy indicates that the labor market is near efficient, and free-entry of consumers leads to excess excess consumer market power in setting prices. Restoring efficiency leads to a modest change in welfare.

When Hosios Meets Phillips: Connecting Efficiency and Stability to Demand Shocks