This paper studies the regulation of a good that generates different amounts of an externality on consumption, but direct taxation of the externality is infeasible. Under certain conditions, I show that the deadweight loss due to any (possibly nonlinear) tax on the good is equal to the Bregman divergence between the allocation that the tax induces and the first-best allocation. This yields a regression-based method to derive the tax that minimizes deadweight loss in any family of taxes. I use this method to characterize the second-best nonlinear tax and show that quantity restrictions, such as bans and mandates, can be optimal. I quantify the welfare gains of using a nonlinear tax over a linear tax. Finally, I illustrate policy implications by applying my results to the taxation of vehicle miles traveled to regulate automobile externalities.

This paper examines how the equilibrium effects of a public option on the private market impact its optimal design. I develop a model in which a policymaker can choose the quality and allocation of the public option, which affect the prices of private goods (and vice versa) in equilibrium. I demonstrate how these equilibrium effects change both the optimal quality and optimal allocation: they create new incentives to distort quality in either direction depending on the policymaker's redistributive objective and provide a new justification for rationing the public option rather than using market-clearing prices. Finally, I show how my results can accommodate additional frictions in the private market and additional policy instruments.

May 2022, revision requested at the American Economic Review

Economists routinely make functional form assumptions about consumer demand to obtain welfare estimates. How sensitive are welfare estimates to these assumptions? We answer this question by providing bounds on welfare that hold for families of demand curves commonly considered in different literatures. We show that commonly chosen functional forms, such as linear, exponential, and CES demand, are extremal in different families: they yield either the highest or lowest welfare estimate among all demand curves in those families. To illustrate our approach, we apply our results to the welfare analysis of energy subsidies, trade tariffs, pensions, and income taxation.

We study a platform that sells productive inputs (such as e-commerce and distribution services) to a fringe of producers in an upstream market, while also selling its own output in the corresponding downstream market. The platform faces a tradeoff: any output that it sells downstream increases competition with the fringe of producers and lowers the downstream price, which in turn reduces demand for the platform’s productive inputs and decreases upstream revenue. Adopting a mechanism design approach, we characterize the optimal menu of contracts the platform offers in the upstream market. These contracts involve price discrimination in the form of nonlinear pricing and quantity discounts. If the platform is a monopoly in the upstream market, then we show that the tradeoff always resolves in favor of consumers and at the expense of producers. However, if the platform faces competition in the upstream market, then it has an incentive to undermine this competition by engaging in activities, such as “killer” acquisitions and exclusive dealing, that harm both consumers and producers.

August 2021, in Proceedings of the 2022 Annual ACM–SIAM Symposium on Discrete Algorithms (SODA '22), pp. 2964–2985.

We consider the bilateral trade problem, in which two agents trade a single indivisible item. It is known that the only dominant-strategy truthful mechanism is the fixed-price mechanism: given commonly known distributions of the buyer's value $B$ and the seller's value $S$, a price $p$ is offered to both agents and trade occurs if $S \leq p \leq B$. The objective is to maximize either expected welfare, $\mathbb{E}\!\left[S + (B-S) \mathbf{1}_{S \leq p \leq B}\right]$, or expected gains from trade, $\mathbb{E}\!\left[(B-S) \mathbf{1}_{S \leq p \leq B}\right]$.

We improve the approximation ratios for several welfare maximization variants of this problem. When the agents' distributions are identical, we show that the optimal approximation ratio for welfare is $(2+\sqrt{2})/4$. With just one prior sample from the common distribution, we show that a $3/4$-approximation to welfare is achievable. When agents' distributions are not required to be identical, we show that a previously best-known $(1-1/e)$-approximation can be strictly improved, but $1-1/e$ is optimal if only the seller's distribution is known.

September 2019, partially superseded by "Fixed-Price Approximations in Bilateral Trade" (with Francisco Pernice and Jan Vondrák).

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.