In this paper, we develop a model of redistribution where a social planner, seeking to maximize weighted total surplus, can subsidize consumers who participate in a private market. We identify when subsidies can strictly improve upon the laissez-faire outcome, which depends on the correlation between consumers’ demand and need. We characterize the optimal nonlinear subsidy by quantifying when—and for which units of the good—the social planner uses a full subsidy (i.e., free provision) rather than a partial subsidy or no subsidy. Our findings provide justifications for (i) free provision of a baseline quantity and (ii) subsidizing goods for which demand and need are positively correlated.
This paper develops a model of in-kind redistribution where consumers participate in either a private market or a government-designed program, but not both. We characterize when a social planner, seeking to maximize weighted total surplus, can strictly improve upon the laissez-faire outcome. We show that the optimal mechanism consists of three components: a public option, nonlinear subsidies, and laissez-faire consumption. We quantify the resulting distortions and relate them to the correlation between consumer demand and welfare weights. Our findings reveal that while private market access constrains the social planner's ability to redistribute, it also strengthens the rationale for non-market allocations.
August 2024, revision requested at the American Economic Review
Economists routinely make functional form assumptions on demand curves to derive welfare conclusions. How sensitive are these conclusions to such assumptions? In this paper, we develop robustness measures that quantify the extent to which the true demand curve must deviate from common functional form assumptions in order to overturn a welfare conclusion. We parametrize this variability in terms of the gradient and curvature of the demand curve. By leveraging tools from information design, we show that our measures are easy to compute. Our measures are also flexible and easy to use, as we illustrate through several empirical applications.
This paper studies the regulation of a good that generates different amounts of an externality on consumption. Direct taxation of the externality is assumed to be infeasible; instead, the good itself is taxed to indirectly regulate the externality. I show that the deadweight loss due to any 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 deadweight loss-minimizing tax. I use this method to show that quantity controls, 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.
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.
