arXiv subjects

Mitchell Watt

Publications and source records attributed to Mitchell Watt.

3 recordsLinked to original sources

arXiv2026

Topping Up and Optimal Redistribution

This paper studies how topping up -- allowing recipients of in-kind transfers to supplement subsidized consumption in a private market -- affects optimal redistribution. Consumers can access a competitive private market, while a social planner offers an alternative nonlinear price schedule. We show that the effect of topping up depends on the correlation between redistributive priority and demand. When the correlation is positive, topping up does not affect the optimal mechanism. When the correlation is negative, topping up weakens screening and reduces redistribution. At the extensive margin, topping up reduces the set of environments in which intervention is optimal. At the intensive margin, topping up weakly reduces both the scope of a free public option and the mass of consumers served, and shifts redistribution away from the consumers with the highest redistributive priority. We characterize the optimal mechanisms and show how topping up changes the comparative statics of optimal redistribution with respect to redistributive priorities.

econ.GN↗

arXiv2024

Optimal In-Kind Redistribution

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.

econ.GN↗

arXiv2021

Concavity and Convexity of Order Statistics in Sample Size

We show that the expectation of the $k^{\mathrm{th}}$-order statistic of an i.i.d. sample of size $n$ from a monotone reverse hazard rate (MRHR) distribution is convex in $n$ and that the expectation of the $(n-k+1)^{\mathrm{th}}$-order statistic from a monotone hazard rate (MHR) distribution is concave in $n$ for $n\ge k$. We apply this result to the analysis of independent private value auctions in which the auctioneer faces a convex cost of attracting bidders. In this setting, MHR valuation distributions lead to concavity of the auctioneer's objective. We extend this analysis to auctions with reserve values, in which concavity is assured for sufficiently small reserves or for a sufficiently large number of bidders.

econ.TH↗