# Pareto optimality with Lagrange

I understand that you find the interior solutions for the pareto efficient set with Lagrange (Maximizing the utility with the endowment constraints and holding the other player's utility fixed) How do I proceed with finding corner solutions with this method? Or in general how do I find corner solutions mathematically (without looking at the graph)?

• Could you elaborate more about the specific model you're working with? – Theoretical Economist Dec 19 '16 at 11:19
• Let's take for example the utility functions of two players u1=2x+y and u2=x+2y. How can I derive the set of pareto optimal allocations from there? If I graph them I see it should be the east and south border of the edgeworth box. I am asking myself how should I derive it mathematically – Maria Dec 19 '16 at 12:03
• you solve for optimal bundles given the prevailing rate of linear transformation between goods 1,2. That is, you characterize optimal bundles for each agent in such a way that you provide a solution that partitions possible prices. – 123 Dec 20 '16 at 22:03