## Working papers

### Optimal redistribution through public provision of private goods | [PDF]

August 2021

Accepted for presentation at EC'21

How does a private market influence the optimal design of a public program? In this paper, I study a
designer who has preferences over how a public option and a private good are allocated. However, she
can design only the public option. Her design affects the distribution of consumers who purchase the
private good—and hence equilibrium outcomes. I characterize the optimal mechanism and show how it can be
computed explicitly. I derive comparative statics on the value of the public option and show that the
optimal mechanism generally rations the public option. Finally, I examine implications on the optimal
design when the designer can intervene in the private market or introduce an individual mandate.

### Markets for goods with externalities | [PDF]

April 2020

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]

September 2019

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.