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I know that the First Welfare theorem holds for pure exchange economies for strict monotonicity of preferences, and logically it should also hold for local nonsatiation, but does anyone have a simple proof for this?

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    $\begingroup$ I don't know what you mean by "logically it should also hold for local nonsatiation", but the standard proof works under local nonsatiation. $\endgroup$ – Michael Greinecker Nov 14 '17 at 7:45
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    $\begingroup$ @MichaelGreinecker can you explain how ? $\endgroup$ – Lola1984 Nov 14 '17 at 17:57
  • $\begingroup$ I have no idea what proof you know for the case of monotone preferences or what your background is. You can certainly find the standard proof in the textbook by Mas-Colell, Whinston, and Green. $\endgroup$ – Michael Greinecker Nov 14 '17 at 21:45
  • $\begingroup$ Is this just straight up asking for a proof of the first welfare theorem? Surely if you are exposed to the assumptions needed and the theorem itself you should be able to find many proofs of it online. Is there a specific aspect of the proof you are struggling with? I recommend trying to narrow down what you are having trouble with, otherwise it is hard to know what sort of proof will be "simple" enough for your purposes. $\endgroup$ – Kitsune Cavalry Nov 15 '17 at 18:48

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