As far as I understand, the second welfare theorem says that all Pareto-optimal allocations can be reached by market equilibrium on free competitive markets.

Yet it seems that this understanding is not without problems. I will provide you with an example:

There are two sides, Americans and British. Americans prefer airplanes over bombs and British prefer bombs over airplanes. There are no money, only barter between them. Let's suppose that initially Americans have 100 airplanes and 100 bombs, while British can suggest nothing in return because they have neither airplanes nor bombs. This is Pareto-optimal situation, yet it's unclear for me how we can end up here due to market equilibrium.

P.S. Americans receive positive utility from bombs and British receive positive utility from airplanes.

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    $\begingroup$ What you describe is not necessarily PO. Let us suppose you fix your example so that it is necessarily PO. Well, then all you've done is described an endowment economy in which the initial allocation is PO and in equilibrium. That is, you describe a trivial problem. $\endgroup$ – 123 Mar 26 '18 at 14:21
  • $\begingroup$ "What you describe is not necessarily PO" Why? $\endgroup$ – user161005 Mar 26 '18 at 14:40
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    $\begingroup$ Suppose Americans receive no utility from bombs. Only airplanes. This meets your conditions. Transfering all bombs to Brits is a Pareto improvement. $\endgroup$ – 123 Mar 26 '18 at 19:01
  • $\begingroup$ Oh, I see. The devil is in details. $\endgroup$ – user161005 Mar 26 '18 at 20:04
  • $\begingroup$ Indeed. Edge cases like that are easy to gloss over so don't worry ... they get us all. $\endgroup$ – 123 Mar 26 '18 at 22:26

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