Separating Hyperplanes & Second Welfare Theorem by Seha Karabacak ’24

Separating Hyperplanes & Second Welfare Theorem by Seha Karabacak ’24, Wednesday April 3, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Colloquium

Abstract: In this talk, we will delve into convexity and compactness, and we will see how they matter for optimization. First, we will prove an important result for disjoint convex sets, Hyperplane Separation Theorem. Second, we will use this result to prove the Second Welfare Theorem—the esoteric “converse” of the First Welfare Theorem—which states ​that we can use “the market” to reach an “efficient distribution” of our choosing.