How should a policymaker allocate a good to consumers via a public option when they are also able to purchase the good from a competitive private market? I consider a designer who has preferences over the outcomes of both the public option and the private market, but can design only the public option. However, her design affects the distribution of consumers who purchase in the private market—and hence equilibrium outcomes. I find that the optimal design involves rationing the public option with a small number of tiers, where the probability of allocation is constant in each tier. I derive first-order conditions that characterize how each tier should be set in the optimal design. Finally, I show that tiered rationing remains optimal under a variety of different assumptions.
I consider the welfare and profit maximization problems in markets with externalities. I show that when externalities depend generally on allocation, a Pigouvian tax is often suboptimal. Instead, the optimal mechanism has a simple form: a finite menu of rationing options with corresponding prices. I derive sufficient conditions for a single price to be optimal. I show that a monopolist may ration less relative to a social planner when externalities are present, in contrast to the standard intuition that non-competitive pricing is indicative of market power. My characterization of optimal mechanisms uses a new methodological tool—the constrained maximum principle—which leverages the combined mathematical theorems of Bauer (1958) and Szapiel (1975). This tool generalizes the concavification technique of Aumann and Maschler (1995) and Kamenica and Gentzkow (2011), and has broad applications in economics.
Fixed-price approximations to optimal efficiency in bilateral trade (with Jan Vondrák) | [PDF]
This paper studies fixed-price mechanisms in bilateral trade with ex ante symmetric agents. We show that the optimal price is particularly simple: it is exactly equal to the mean of the agents’ distribution. The optimal price guarantees a worst-case performance of at least 1/2 of the first-best gains from trade, regardless of the agents’ distribution. We also show that the worst-case performance improves as the number of agents increases, and is robust to various extensions. Our results offer an explanation for the widespread use of fixed-price mechanisms for size discovery, such as in workup mechanisms and dark pools.