Working Papers

A mechanism-design approach to property rights (with P. Dworczak)
We propose a framework for studying the optimal design of rights relating to the control of an economic resource — which we broadly refer to as property rights. An agent makes an investment decision, affecting her valuation for the resource, and then participates in a trading mechanism chosen by a principal in a sequentially rational fashion, leading to a hold-up problem. A designer — who would like to incentivize efficient investment and whose preferences may differ from those of the principal — can endow the agent with a menu of rights that determine the agent’s set of outside options in the interaction with the principal. We characterize the optimal rights as a function of the designer’s and the principal’s objectives, and the investment technology. We find that optimal rights typically differ from a classical property right giving the agent full control over the resource. In particular, we show that the optimal menu requires at most two types of rights, including an option-to-own, which grants the agent control over the resource upon paying a pre-specified price.

Optimal Hotelling Auctions (with S. Loertscher)
We derive the optimal mechanism for a designer with products at each end of the Hotelling line for sale. Buyers have linear transportation costs and private information about their locations. These are independent draws from a commonly known distribution. Two independent auctions are optimal if and only if two independent auctions are efficient. Otherwise, the problem exhibits countervailing incentives and worst-off types that are endogenous to the allocation rule. Combining a saddle point property with an appropriate ironing procedure allows us to characterize the optimal selling mechanism as a function of a single parameter and to derive associated comparative statics. The optimal mechanism is always ex inefficient; it involves entering a set of types into a lottery with positive probability. This set and the associated ex post lotteries vary non-trivially with the problem parameters. A two-stage clock auction involving coarse bidding implements the optimal selling mechanism in dominant strategies.

Optimal labor procurement under minimum wages and monopsony power (with S. Loertscher)
We derive the optimal procurement mechanism for a monopsony under a minimum wage constraint. For a setting where a continuum of workers have private information about their opportunity cost of working, we show that under cost-minimizing procurement at most two wages are paid. Cost-minimizing procurement involves two wages and involuntary unemployment if and only if the procurement cost under optimal uniform wage-setting lies above its convexification at the optimal employment level. Setting the minimum wage equal to the highest wage offered under laissez-faire increases total employment and workers’ pay, and decreases (and possibly eliminates) involuntary unemployment. Binding minimum wages can make a two-wage mechanism and involuntary unemployment optimal even if a uniform wage is optimal under laissez-faire. If a minimum wage does not induce involuntary unemployment or induces both involuntary unemployment and wage dispersion, then a marginal increase in the minimum wage generically increases employment and decreases involuntary unemployment.

Contracting and vertical control by a dominant platform (with Z.Y. Kang)
Accepted for presentation at EC’22; taught as part of a tutorial at EC’23
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.

The matching benefits of market thickness (with S. Loertscher)
We use an independent private values model to analyze the social benefits and costs of monopoly market makers. Calling products niche (mass) if the fraction of agents who trade in a Walrasian market is small (large), we show that for sufficiently niche products a thick market monopoly generates more consumer (producer) surplus per buyer (seller) than ex post efficient bilateral trade. Moreover, relative to bilateral trade, the matching benefits of thick markets grow unboundedly for increasingly niche products. If bilateral trade offers an outside option to trading with a thick market monopoly, mass products better mitigate the monopoly’s market power, suggesting a role for regulatory scrutiny in markets for niche products.

Publications

Monopoly pricing, optimal randomization and resale (with S. Loertscher), Journal of Political Economy, 130(3):566–635, 2022

Optimal market thickness (with S. Loertscher and P. Taylor), Journal of Economic Theory, 200, 2022

Road to recovery: Managing an epidemic (with S. Loertscher), Journal of Mathematical Economics [Special Issue on the economics of epidemics and emerging diseases], 93, 2021

A general noncentral hypergeometric distribution (with S. Loertscher and P. Taylor), Communications in Statistics – Theory and Methods, 46(9):4579–4598, 2017

Approximating the equilibrium quantity traded and welfare in large markets (with K. Borovkov), Stochastic Models, 33(3):411–429, 2017

Commentary

The economics of COVID-19 (with S. Loertscher), Pursuit, 22 July 2020