BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Robert McCann (University of Toronto\, Canada) DTSTART:20250226T150000Z DTEND:20250226T160000Z DTSTAMP:20260423T053017Z UID:SIAM-PDE/49 DESCRIPTION:Title: The monopolist's free boundary problem in the plane: an excursion into t he economic value of private information\nby Robert McCann (University of Toronto\, Canada) as part of Seminar In the Analysis and Methods of PD E (SIAM PDE)\n\n\nAbstract\nThe principal-agent problem is an important pa radigm in economic theory for studying the value of private information: t he nonlinear pricing problem faced by a monopolist is one example\; others include optimal taxation and auction design. For multidimensional spaces of consumers (i.e. agents) and products\, Rochet and Chone (1998) reformul ated this problem as a concave maximization over the set of convex functio ns\, by assuming agent preferences are bilinear in the product and agent p arameters. This optimization corresponds mathematically to a convexity-con strained obstacle problem. The solution is divided into multiple regions\, according to the rank of the Hessian of the optimizer.\n\nApart from four possible pathologies\, if the monopolist’s costs grow quadratically wi th the product type we show that a smooth free boundary delineates the reg ion where it becomes efficient to customize products for individual buyers . We give the first complete solution of the problem on square domains\, and discover new transitions from unbunched to targeted and from targeted to blunt bunching as market conditions become more and more favorable to t he seller.\n\nBased on work with Cale Rankin (Monash University) and Kelv in Shuangjian Zhang (Fudan University) https://arxiv.org/abs/2412.15505.\n \nChair: Marcelo Disconzi\, marcelo.disconzi@vanderbilt.edu\n LOCATION:https://researchseminars.org/talk/SIAM-PDE/49/ END:VEVENT END:VCALENDAR