<p>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)?</p>

CC BY-SA 3.0
2016-12-19T11:19:42.053Z
Could you elaborate more about the specific model you're working with?
Theoretical Economist
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2016-12-19T12:03:01.253Z
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
CC BY-SA 3.0
2016-12-20T22:03:36.827Z
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.
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<pareto-efficiency>
Pareto optimality with Lagrange
Maria
# Pareto optimality with Lagrange

(Asked by: username_0 on 2016-12-19)

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)?

**Tags:** pareto-efficiency

> **Comments:**
> **username_1**: Could you elaborate more about the specific model you're working with?  
> **username_0**: 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  
> **username_2**: 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.  

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