We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely...

We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme...

The main result in Daskalakis, Deckelbaum, and Tzamos (2017) establishes strong duality in the monopoly problem with an argument based on transportation theory. We provide a short, alternative proof using linear programming.