Free boundary regularity for the monopolist's problem: an excursion into the economic value of private information

To be held at ESB 2012 and on Zoom: https://ubc.zoom.us/j/68285564037?pwd=R2ZpLy9uc2pUYldHT3laK3orakg0dz09
Meeting ID: 682 8556 4037
Passcode: 636252

Reception and refreshments at 14:30 in the PIMS lounge, ESB 4th floor.

The principal-agent problem is an important paradigm in economic theory for studying the value of private information; the 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) reformulated this problem as a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a (quasi)linear sensitivity to prices. This optimization corresponds mathematically to a convexity-constrained obstacle problem. The solution is divided into multiple regions, according to the rank of the Hessian of the optimizer.