<p>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.</p>

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

<p>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>

<p>P.S. Americans receive positive utility from bombs and British receive positive utility from airplanes.</p>

CC BY-SA 3.0
2018-03-26T14:21:03.783Z
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.
123
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2018-03-26T14:40:47.620Z
"What you describe is not necessarily PO" Why?
KarmaPeasant
CC BY-SA 3.0
2018-03-26T19:01:58.623Z
Suppose Americans receive no utility from bombs. Only airplanes. This meets your conditions. Transfering all bombs to Brits is a Pareto improvement.
123
CC BY-SA 3.0
2018-03-26T20:04:29.630Z
Oh, I see. The devil is in details.
KarmaPeasant
CC BY-SA 3.0
2018-03-26T22:26:12.803Z
Indeed. Edge cases like that are easy to gloss over so don't worry ... they get us all.
123
<general-equilibrium><pareto-efficiency><welfare-economics><competitive-equilibrium><welfare>
Do I understand the second welfare theorem correctly?
KarmaPeasant
# Do I understand the second welfare theorem correctly?

(Asked by: username_0 on 2018-03-26)

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.

**Tags:** general-equilibrium, pareto-efficiency, welfare-economics, competitive-equilibrium, welfare

> **Comments:**
> **username_1**: 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.  
> **username_0**: "What you describe is not necessarily PO" Why?  
> **username_1**: Suppose Americans receive no utility from bombs. Only airplanes. This meets your conditions. Transfering all bombs to Brits is a Pareto improvement.  
> **username_0**: Oh, I see. The devil is in details.  
> **username_1**: Indeed. Edge cases like that are easy to gloss over so don't worry ... they get us all.  

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## 0 answers

