<p>After more thought and research, I am fairly confident in saying the basic analysis holds, ie this is a &quot;counter-example&quot; in the sense that trade yields Pareto-inferior results.
The result relies on the existence of some market distortion; trade can reduce aggregate welfare when it makes the distortion worse. The distortion can take various forms:</p>
<ul>
<li>If there is a minimum wage, trade can force more people to be unemployed who would prefer to work for sub-minimum wage.</li>
<li>If there is any kind of externality or  &quot;congestion effect&quot;, trade can exacerbate this; for example, it's easy to convert the scenario to one where the materials cost of housing for engineers or factory workers rises with density, and again trade lowers aggregate welfare</li>
<li>In the presence of finite credit markets, free trade could redirect investment in a way that reduces aggregate welfare (this could be observed as an &quot;infant industry&quot; effect).</li>
<li>In the dynamic counterexample of <a href="http://willmann.com/%7Egerald/counterexample.pdf" rel="nofollow noreferrer">Willmann (2003)</a>, the distortion is underinvestment aimed at affecting redistribution</li>
<li>In <a href="https://ideas.repec.org/a/eee/inecon/v11y1981i4p531-551.html" rel="nofollow noreferrer">Markusen (1980)</a> (<a href="https://core.ac.uk/download/pdf/61658423.pdf" rel="nofollow noreferrer">PDF</a>), in the presence of increasing returns to scale, monopoly can be exacerbated by trade, though not in a stable equilibrium</li>
<li>In <a href="https://mitpress.mit.edu/books/market-structure-and-foreign-trade" rel="nofollow noreferrer">Helpman and Krugman (1985)</a>, as cited by <a href="https://www.semanticscholar.org/paper/Advanced-international-trade-%3A-theory-and-evidence-Feenstra/fa9012e6dd54af9681e428d4dcc3d1be3fbcedab" rel="nofollow noreferrer">Feenstra (2004)</a>, we have a fairly general set of conditions for trade to increase aggregate welfare in the presence of some distortions, including the provision that &quot;world output of
each differentiated goods industry does not contract.&quot; To me this condition appears to somewhat beg the question, and I see no inherent reason to assume it would be fulfilled more than about half the time in the presence of arbitrary distortions.</li>
<li>Partial trade reform, including regional trade agreements, can be more complicated (see ch 9 of Feenstra (2004), though I haven't studied it all yet)</li>
</ul>
<p>Furthermore, even when trade does result in Pareto-superior results / gains in aggregate welfare, the redistribution that would be required to actually make everyone better off is not only potentially difficult politically, but often actually impossible to implement, eg requiring perfect knowledge of unrevealed preferences (<a href="http://willmann.com/%7Egerald/gft.pdf" rel="nofollow noreferrer">Facchini &amp; Willman (2001)</a>).</p>
<p>Personally, this seems to tell a very different story than the popular conception of the economics profession's view on trade, and the narrative I got from my undergraduate International Trade course (at a prestigious US research university), which focused on distortion-free static models like the basic Heckscher-Ohlin and suggested that while there were losers from trade, by and large it was expected to yield aggregate gains. It seems to me that in practice, distortions like the above are rather the norm, and so reflexive advocacy of trade liberalization should perhaps consider the potential for exacerbating distortions in any particular case.</p>

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2022-08-01T16:16:48.647Z
Hi! This does not answer your question, which is about whether your very specific example results in PO allocation, not about free trade in general.
Giskard
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2022-08-01T16:17:22.993Z
But I am happy that you dropped Brass!
Giskard
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2022-08-01T17:21:51.507Z
@Giskard The first sentence is meant to answer the question in the affirmative, with a caveat. That is, in the presence of some distortion (in the latest version of the question, minimum wage), the example does show that trade results in Pareto-inferior allocation. I then attempt to answer the more general questions about this phenomenon.
ozb
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2022-08-01T17:33:08.307Z
I actually do still think that Braess (and more generally, network flow analysis) is relevant. In particular, my takeaway is that in an economic production/trade network with market distortions (which I would argue is a good description of the real world), alleviating some distortions (or equivalently, adding new production technologies or trade opportunities) can counter-intuitively exacerbate the overall impact of distortions and ultimately result in aggregate welfare losses; and this phenomenon is [likely](https://pubsonline.informs.org/doi/10.1287/trsc.17.3.301) to be prevalent.
ozb
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2022-08-01T17:47:58.180Z
Perhaps most interesting, the reformulation of the welfare-gains question in terms of network flows could allow us to use the extensive literature on network flow optimization ([eg](https://www.sciencedirect.com/science/article/pii/S0191261517303211)) to make sure we are actually tackling the right distortions to avoid these phenomena.
ozb
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2022-08-01T18:59:10.493Z
The first sentence is an assertion, not a proof. You do not explain how any of this violates the first welfare theorem, which guarantees PO outcomes.
Giskard
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2022-08-01T19:00:25.470Z
You are free to think this network analogies; I too find the concept intriguing! I don't think they were relevant to this particular example though.
Giskard
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2022-08-01T19:32:48.673Z
@Giskard I believe the question as it stands is enough of a proof, with the answer as (weak) confirmation that I looked it over a couple more times and am more confident. The First Welfare Theorem does not apply in the presence of distortions; my claim is that not only does it not formally apply, but also that it is not always a good approximation or heuristic, ie trying to approach perfectly competitive markets without distortions does not necessarily get us closer to Pareto optimality.
ozb
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2022-08-02T06:03:17.833Z
"*I believe the question as it stands is enough of a proof, with the answer as (weak) confirmation that I looked it over a couple more times and am more confident.*" Here and in academia it is customary to lay out your proofs & findings to make it easier for others to learn the same lessons. Sometimes it also helps one order their thoughts and doublecheck their own work. But if you don't want to do that I certainly won't make you! Have a nice day!
Giskard
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2022-08-02T15:19:34.993Z
What is missing in terms of proof? I've laid out a detailed example with mathematical reasoning and come out with a welfare loss. My analysis may well be wrong (indeed, it did originally have some gaps that required additional assumptions as you helped me see more than once), but I'm genuinely not sure what more I can do to make the case. To be explicit, I'm open to hearing what's missing and adding it as needed.
ozb
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2022-08-02T18:10:21.223Z
Not sure what to say that I have not said before; I laid out several arguments to show that your reasoning is faulty: 1. not all resources are accounted for in your comparison 2. the first welfare theorem guarantees PO outcomes, and I don't see why your example would violate any of its conditions.
Giskard
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2022-08-02T18:11:35.833Z
Look, I get it, you are satisfied with your arguments, which I perhaps simply do not get. That is fine, I will agree to disagree. Cheers!
Giskard
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2022-08-01T14:48:59.440Z
2022-08-01T15:44:01.260Z
2022-08-01T15:44:01.260Z
ozb
<p>The usual <a href="https://ideas.repec.org/a/mul/jb33yl/doi10.1428-2005y2001i2p207-216.html" rel="nofollow noreferrer">assumption</a> is that free trade always increases aggregate gains. This has in fact been proven for various models of trade between countries, though there are <a href="https://www.sciencedirect.com/science/article/abs/pii/S0165176503003598" rel="nofollow noreferrer">counterexamples</a> if one makes different assumptions.</p>
<p>I believe the following is a rather simple counterexample that relies on even fewer assumptions, and in particular uses <a href="https://en.m.wikipedia.org/wiki/Braess%27s_paradox" rel="nofollow noreferrer">Braess's paradox</a> rather than dynamic expectations:</p>
<p>Suppose we have two countries, hypothetically named US and China (any resemblance to actual countries is purely coincidental). Each independently produces a single type of good called &quot;phones&quot;. Production of phones is a two-step process: first, the phone is designed by engineers, then it is built by factory workers.</p>
<p>In the initial scenario, there is no trade: each country produces 1400 phones on its own.</p>
<p>In the US, engineers are efficient and factory workers are scarce; to produce one phone costs \$100 of engineering time for the design and $200 to be built by factory workers.</p>
<p>In China, engineers are less efficient and factory workers are available in abundance; to produce one phone costs \$200 of engineering time for the design and $100 to be built by factory workers.</p>
<p>Now, suppose trade opens up between the US and China. So now, 2800 phones are designed in the US and built in China.</p>
<p>However, let's assume the supply curves for each type of labor slope upward (as is usually the case). In particular, in order to attract enough US engineers to design 2800 phones, US engineering wages go up to \$175/phone. Likewise, in order to attract enough Chinese factory workers to build 2800 phones, factory wages in China rise to $175/phone. At the same time, US factory wages fall to \$185/phone, and China engineering wages fall to \$185/phone.</p>
<p>So far, we are still Pareto-efficient, since the increased wages allow US Engineers and Chinese factory workers to buy the same 2800 phones that were bought before; equivalently, a government with full knowledge of preferences could redistribute money (or phones) to make everyone as well off as they were before trade.</p>
<p>But now, assume that cross-Pacific collaboration incurs an additional \$5/phone cost, eg for undersea cables. Phones now cost \$355, but aggregate income is only \$350*2800=\$980,000, ie not enough for 2800 phones. I believe that only distortionary taxation/subsidies can bring everyone back to their previous welfare, eg taxing US Engineers enough to make trade unprofitable.</p>
<p>Is my analysis correct, ie is this a genuine theoretical counter-example? Is there a particular reason to expect this type of situation would be rare? Consider that Braess's paradox has been <a href="https://pubsonline.informs.org/doi/10.1287/trsc.17.3.301" rel="nofollow noreferrer">found</a> to occur in 50% of networks, under certain simple assumptions.</p>
<p>Assuming my analysis is correct, is this phenomenon well-known? Can you point me to relevant literature on similar ideas?</p>
<p>Before trade:</p>
<p><img src="https://www.plantuml.com/plantuml/png/YrQ8LT2rKuWE3LPmIItEJCyhZbMmKW3oNFFIC_DIKukA5JHK30qCDBcGb42q16JavwN2bBib9fVa5rKgbESNPKCq6O4qmOntpiZCIqIs0Im0jmIX7YAEQGz24wfL2FUXEb1Fpqu1YxKbHOafgGhv1GNvHIMbUPabbG00" alt="production network before trade" /></p>
<p>With trade:</p>
<p><img src="https://www.plantuml.com/plantuml/png/YrQ8LT2rKuWE3LPmIItEJCyhZbMmKW3oNFFIC_DIKukA5JHK3CrDDRcGb42q16JavwN2bBib9fVa5rKgbESNPKCrMG0rmOntpiZCIqIs0Im0jmIX7YAEQGz24wfL2FUXE51Fpqu1YwqbHOafgK0Dffe0" alt="production network with trade" /></p>
<p>(apologies for my limited diagramming skills)</p>
<p>EDIT: here's what happens in terms of actual resources:</p>
<p>In the US, assume you have 100 &quot;engineer&quot; workers who are each able to use US technology to design 14 phones; and you have 200 &quot;factory&quot; workers who are each able to build 7 phones.
In China, you have 200 engineers who can each design 7 phones, and 100 factory workers who can each build 14 phones.</p>
<p>US Engineers cannot build, and Chinese factory workers cannot design.</p>
<p>175 of the US factory workers can also design, though only 8 phones each</p>
<p>175 of the Chinese engineers can also build, but only 8 phones each</p>
<p>So, under autarky we produce 2800 phones (1400 in each country).</p>
<p>Under free trade we still produce 2800 phones (designed in the US and built in China), though we leave 25 US factory workers and 25 Chinese engineers unemployed.</p>
<p>But now, assume that transmitting designs for up to 560 phones from the US to China (and training overseas workers) requires one US engineer and one Chinese factory worker.
Furthermore, assume that there is a minimum wage in both countries, so the unemployed workers cannot be profitably employed, nor benefit from their unemployment.</p>
<p>We can now only produce 2730 phones, and no lump-sum redistribution can recover previous welfare levels.</p>

CC BY-SA 4.0
2022-07-27T20:43:52.607Z
@1muflon1 Can you provide some examples of models where it yields non-Pareto optimal outcomes? I have found one source indicating that this is less common (as of 2000), and one source with a counterexample in the dynamic case (both cited in the question); can you provide other sources which show that in most models trade does not lead to Pareto optimal outcomes?
ozb
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2022-07-27T20:44:41.823Z
In most cases that I'm aware of, feasibility of redistribution is challenged rather than Pareto optimality
ozb
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2022-07-27T22:17:22.993Z
@ozb HO model for some parameter values leads to non-Pareto optimal outcomes for example. You can have look at any textbook for example feenstra advanced international trade
1muflon1
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2022-07-28T05:46:39.207Z
@1muflon1 "*HO model for some parameter values*" Can you please be more precise, as I also do not get the reference. I thought HO model under free trade satisfies Arrow-Debreu conditions and thus first welfare theorem applies?
Giskard
CC BY-SA 4.0
2022-07-28T05:49:24.697Z
@ozb "*3. There is an isomorphism between this example and the network of roads in Braess's paper. Both are modeled by the same graph structure.*" Not sure why you feel it  is important to include Braess, the question works without it. Note that you do not write about networks while discussing the trade model at all. Also note that for any two sets of three elements an isomorphism can be defined... Again, the question works without Braess, no need to die on this hill.
Giskard
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2022-07-28T10:09:27.393Z
@Giskard in basic static HO model yes in dynamic HO model with non-homothetic preferences you get multiple equilibria not all of them are Pareto optimal
1muflon1
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2022-07-28T14:32:49.707Z
@1muflon1 Ah yes, a dynamic case is covered in my "counterexample" link. What makes this example potentially more interesting is that it's static and makes few assumptions about preferences.
ozb
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2022-07-28T14:41:53.323Z
@Giskard The isomorphism is not just between sets of 3 elements but the graphs of  4 nodes and 4 edges (in the trade example, edges are transformation from one good to another rather than roads) turning to 5 (A->C, A->D, C->B, D->B; and later adding C->D); the same weight conditions that result in the Braess paradox result in a higher price of phones, and the same transformation could turn any road network into a graph of production/trade. I think referencing Braess gives a bit more intuition about when, why, and how often such phenomena might occur.
ozb
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2022-07-28T15:02:09.597Z
@Giskard compare the diagrams I added to the diagram at https://en.wikipedia.org/wiki/Braess's_paradox#Example
ozb
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2022-07-29T13:22:10.483Z
Not all resources are accounted for in your examples.

In the no trade scenario (NTS), some time of US engineers, US workers, PRC engineers and PRC workers is used to produce 2000 phones. 

In free trade scenario (FTS), **more** time of US engineers and PRC workers is used to produce phones. The number of phones produced is less than 2000, because some resources/time/money goes towards international collaboration costs.

It is not clear what US workers and PRC engineers are doing in the FTS.
Because of this it is unclear if one situation Pareto-dominates the other.
Giskard
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2022-07-29T17:59:55.083Z
@Giskard does the latest edit answer your question?
ozb
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2022-07-29T22:21:14.590Z
Wait, that doesn't quite work, need to add some actual resources to be spent rather than hours; eg 1kg coffee for design and 1kg silicon for building rather than $100 or 1/14 engineer
ozb
CC BY-SA 4.0
2022-07-31T08:20:09.217Z
@ozb You assume a labor supply curve, since wages change when more workers are employed, so clearly work hours have some other possible use/value. Yet this is not outlined in the model.
Giskard
CC BY-SA 4.0
2022-07-31T08:20:59.503Z
@ozb Are you familiar with the first welfare theorem? Do you see any particular reason why your model would violate its conditions and result in a non Pareto-optimal equilibrium?
Giskard
CC BY-SA 4.0
2022-07-31T08:25:43.270Z
On a side note: I like this [juvenile SMBC comic](https://www.smbc-comics.com/comic/2012-03-21) about experts discovering a field outside their expertise and finding it trivial.
Giskard
CC BY-SA 4.0
2022-08-01T14:52:08.880Z
@Giskard see my answer below
ozb
<international-trade><networks>
Under what circumstances does trade yield Pareto-inferior results?
ozb
# Under what circumstances does trade yield Pareto-inferior results?

(Asked by: username_0 on 2022-07-27)

The usual [assumption](https://ideas.repec.org/a/mul/jb33yl/doi10.1428-2005y2001i2p207-216.html) is that free trade always increases aggregate gains. This has in fact been proven for various models of trade between countries, though there are [counterexamples](https://www.sciencedirect.com/science/article/abs/pii/S0165176503003598) if one makes different assumptions.

I believe the following is a rather simple counterexample that relies on even fewer assumptions, and in particular uses [Braess's paradox](https://en.m.wikipedia.org/wiki/Braess%27s_paradox) rather than dynamic expectations:

Suppose we have two countries, hypothetically named US and China (any resemblance to actual countries is purely coincidental). Each independently produces a single type of good called "phones". Production of phones is a two-step process: first, the phone is designed by engineers, then it is built by factory workers.

In the initial scenario, there is no trade: each country produces 1400 phones on its own.

In the US, engineers are efficient and factory workers are scarce; to produce one phone costs \$100 of engineering time for the design and $200 to be built by factory workers.

In China, engineers are less efficient and factory workers are available in abundance; to produce one phone costs \$200 of engineering time for the design and $100 to be built by factory workers.

Now, suppose trade opens up between the US and China. So now, 2800 phones are designed in the US and built in China.

However, let's assume the supply curves for each type of labor slope upward (as is usually the case). In particular, in order to attract enough US engineers to design 2800 phones, US engineering wages go up to \$175/phone. Likewise, in order to attract enough Chinese factory workers to build 2800 phones, factory wages in China rise to $175/phone. At the same time, US factory wages fall to \$185/phone, and China engineering wages fall to \$185/phone.

So far, we are still Pareto-efficient, since the increased wages allow US Engineers and Chinese factory workers to buy the same 2800 phones that were bought before; equivalently, a government with full knowledge of preferences could redistribute money (or phones) to make everyone as well off as they were before trade.

But now, assume that cross-Pacific collaboration incurs an additional \$5/phone cost, eg for undersea cables. Phones now cost \$355, but aggregate income is only \$350\*2800=\$980,000, ie not enough for 2800 phones. I believe that only distortionary taxation/subsidies can bring everyone back to their previous welfare, eg taxing US Engineers enough to make trade unprofitable.

Is my analysis correct, ie is this a genuine theoretical counter-example? Is there a particular reason to expect this type of situation would be rare? Consider that Braess's paradox has been [found](https://pubsonline.informs.org/doi/10.1287/trsc.17.3.301) to occur in 50% of networks, under certain simple assumptions.

Assuming my analysis is correct, is this phenomenon well-known? Can you point me to relevant literature on similar ideas?

Before trade:

![production network before trade](https://www.plantuml.com/plantuml/png/YrQ8LT2rKuWE3LPmIItEJCyhZbMmKW3oNFFIC_DIKukA5JHK30qCDBcGb42q16JavwN2bBib9fVa5rKgbESNPKCq6O4qmOntpiZCIqIs0Im0jmIX7YAEQGz24wfL2FUXEb1Fpqu1YxKbHOafgGhv1GNvHIMbUPabbG00)

With trade:

![production network with trade](https://www.plantuml.com/plantuml/png/YrQ8LT2rKuWE3LPmIItEJCyhZbMmKW3oNFFIC_DIKukA5JHK3CrDDRcGb42q16JavwN2bBib9fVa5rKgbESNPKCrMG0rmOntpiZCIqIs0Im0jmIX7YAEQGz24wfL2FUXE51Fpqu1YwqbHOafgK0Dffe0)

(apologies for my limited diagramming skills)

EDIT: here's what happens in terms of actual resources:

In the US, assume you have 100 "engineer" workers who are each able to use US technology to design 14 phones; and you have 200 "factory" workers who are each able to build 7 phones.
In China, you have 200 engineers who can each design 7 phones, and 100 factory workers who can each build 14 phones.

US Engineers cannot build, and Chinese factory workers cannot design.

175 of the US factory workers can also design, though only 8 phones each

175 of the Chinese engineers can also build, but only 8 phones each

So, under autarky we produce 2800 phones (1400 in each country).

Under free trade we still produce 2800 phones (designed in the US and built in China), though we leave 25 US factory workers and 25 Chinese engineers unemployed.

But now, assume that transmitting designs for up to 560 phones from the US to China (and training overseas workers) requires one US engineer and one Chinese factory worker.
Furthermore, assume that there is a minimum wage in both countries, so the unemployed workers cannot be profitably employed, nor benefit from their unemployment.

We can now only produce 2730 phones, and no lump-sum redistribution can recover previous welfare levels.

**Tags:** international-trade, networks

> **Comments:**
> **username_0**: @username_1 Can you provide some examples of models where it yields non-Pareto optimal outcomes? I have found one source indicating that this is less common (as of 2000), and one source with a counterexample in the dynamic case (both cited in the question); can you provide other sources which show that in most models trade does not lead to Pareto optimal outcomes?  
> **username_0**: In most cases that I'm aware of, feasibility of redistribution is challenged rather than Pareto optimality  
> **username_1**: @username_0 HO model for some parameter values leads to non-Pareto optimal outcomes for example. You can have look at any textbook for example feenstra advanced international trade  
> **username_2**: @username_1 "*HO model for some parameter values*" Can you please be more precise, as I also do not get the reference. I thought HO model under free trade satisfies Arrow-Debreu conditions and thus first welfare theorem applies?  
> **username_2**: @username_0 "*3. There is an isomorphism between this example and the network of roads in Braess's paper. Both are modeled by the same graph structure.*" Not sure why you feel it  is important to include Braess, the question works without it. Note that you do not write about networks while discussing the trade model at all. Also note that for any two sets of three elements an isomorphism can be defined... Again, the question works without Braess, no need to die on this hill.  
> **username_1**: @username_2 in basic static HO model yes in dynamic HO model with non-homothetic preferences you get multiple equilibria not all of them are Pareto optimal  
> **username_0**: @username_1 Ah yes, a dynamic case is covered in my "counterexample" link. What makes this example potentially more interesting is that it's static and makes few assumptions about preferences.  
> **username_0**: @username_2 The isomorphism is not just between sets of 3 elements but the graphs of  4 nodes and 4 edges (in the trade example, edges are transformation from one good to another rather than roads) turning to 5 (A->C, A->D, C->B, D->B; and later adding C->D); the same weight conditions that result in the Braess paradox result in a higher price of phones, and the same transformation could turn any road network into a graph of production/trade. I think referencing Braess gives a bit more intuition about when, why, and how often such phenomena might occur.  
> **username_0**: @username_2 compare the diagrams I added to the diagram at https://en.wikipedia.org/wiki/Braess's_paradox#Example  
> **username_2**: Not all resources are accounted for in your examples.  In the no trade scenario (NTS), some time of US engineers, US workers, PRC engineers and PRC workers is used to produce 2000 phones.   In free trade scenario (FTS), **more** time of US engineers and PRC workers is used to produce phones. The number of phones produced is less than 2000, because some resources/time/money goes towards international collaboration costs.  It is not clear what US workers and PRC engineers are doing in the FTS. Because of this it is unclear if one situation Pareto-dominates the other.  
> **username_0**: @username_2 does the latest edit answer your question?  
> **username_0**: Wait, that doesn't quite work, need to add some actual resources to be spent rather than hours; eg 1kg coffee for design and 1kg silicon for building rather than $100 or 1/14 engineer  
> **username_2**: @username_0 You assume a labor supply curve, since wages change when more workers are employed, so clearly work hours have some other possible use/value. Yet this is not outlined in the model.  
> **username_2**: @username_0 Are you familiar with the first welfare theorem? Do you see any particular reason why your model would violate its conditions and result in a non Pareto-optimal equilibrium?  
> **username_2**: On a side note: I like this [juvenile SMBC comic](https://www.smbc-comics.com/comic/2012-03-21) about experts discovering a field outside their expertise and finding it trivial.  
> **username_0**: @username_2 see my answer below  

---

## 1 answers

### Answer by username_0 on 2022-08-01. Score: 1 | Accepted answer

After more thought and research, I am fairly confident in saying the basic analysis holds, ie this is a "counter-example" in the sense that trade yields Pareto-inferior results.
The result relies on the existence of some market distortion; trade can reduce aggregate welfare when it makes the distortion worse. The distortion can take various forms:

* If there is a minimum wage, trade can force more people to be unemployed who would prefer to work for sub-minimum wage.
* If there is any kind of externality or "congestion effect", trade can exacerbate this; for example, it's easy to convert the scenario to one where the materials cost of housing for engineers or factory workers rises with density, and again trade lowers aggregate welfare
* In the presence of finite credit markets, free trade could redirect investment in a way that reduces aggregate welfare (this could be observed as an "infant industry" effect).
* In the dynamic counterexample of [Willmann (2003)](http://willmann.com/%7Egerald/counterexample.pdf), the distortion is underinvestment aimed at affecting redistribution
* In [Markusen (1980)](https://ideas.repec.org/a/eee/inecon/v11y1981i4p531-551.html) ([PDF](https://core.ac.uk/download/pdf/61658423.pdf)), in the presence of increasing returns to scale, monopoly can be exacerbated by trade, though not in a stable equilibrium
* In [Helpman and Krugman (1985)](https://mitpress.mit.edu/books/market-structure-and-foreign-trade), as cited by [Feenstra (2004)](https://www.semanticscholar.org/paper/Advanced-international-trade-%3A-theory-and-evidence-Feenstra/fa9012e6dd54af9681e428d4dcc3d1be3fbcedab), we have a fairly general set of conditions for trade to increase aggregate welfare in the presence of some distortions, including the provision that "world output of
  each differentiated goods industry does not contract." To me this condition appears to somewhat beg the question, and I see no inherent reason to assume it would be fulfilled more than about half the time in the presence of arbitrary distortions.
* Partial trade reform, including regional trade agreements, can be more complicated (see ch 9 of Feenstra (2004), though I haven't studied it all yet)

Furthermore, even when trade does result in Pareto-superior results / gains in aggregate welfare, the redistribution that would be required to actually make everyone better off is not only potentially difficult politically, but often actually impossible to implement, eg requiring perfect knowledge of unrevealed preferences ([Facchini & Willman (2001)](http://willmann.com/%7Egerald/gft.pdf)).

Personally, this seems to tell a very different story than the popular conception of the economics profession's view on trade, and the narrative I got from my undergraduate International Trade course (at a prestigious US research university), which focused on distortion-free static models like the basic Heckscher-Ohlin and suggested that while there were losers from trade, by and large it was expected to yield aggregate gains. It seems to me that in practice, distortions like the above are rather the norm, and so reflexive advocacy of trade liberalization should perhaps consider the potential for exacerbating distortions in any particular case.

> **Comments:**
> **username_2**: Hi! This does not answer your question, which is about whether your very specific example results in PO allocation, not about free trade in general.  
> **username_2**: But I am happy that you dropped Brass!  
> **username_0**: @username_2 The first sentence is meant to answer the question in the affirmative, with a caveat. That is, in the presence of some distortion (in the latest version of the question, minimum wage), the example does show that trade results in Pareto-inferior allocation. I then attempt to answer the more general questions about this phenomenon.  
> **username_0**: I actually do still think that Braess (and more generally, network flow analysis) is relevant. In particular, my takeaway is that in an economic production/trade network with market distortions (which I would argue is a good description of the real world), alleviating some distortions (or equivalently, adding new production technologies or trade opportunities) can counter-intuitively exacerbate the overall impact of distortions and ultimately result in aggregate welfare losses; and this phenomenon is [likely](https://pubsonline.informs.org/doi/10.1287/trsc.17.3.301) to be prevalent.  
> **username_0**: Perhaps most interesting, the reformulation of the welfare-gains question in terms of network flows could allow us to use the extensive literature on network flow optimization ([eg](https://www.sciencedirect.com/science/article/pii/S0191261517303211)) to make sure we are actually tackling the right distortions to avoid these phenomena.  
> **username_2**: The first sentence is an assertion, not a proof. You do not explain how any of this violates the first welfare theorem, which guarantees PO outcomes.  
> **username_2**: You are free to think this network analogies; I too find the concept intriguing! I don't think they were relevant to this particular example though.  
> **username_0**: @username_2 I believe the question as it stands is enough of a proof, with the answer as (weak) confirmation that I looked it over a couple more times and am more confident. The First Welfare Theorem does not apply in the presence of distortions; my claim is that not only does it not formally apply, but also that it is not always a good approximation or heuristic, ie trying to approach perfectly competitive markets without distortions does not necessarily get us closer to Pareto optimality.  
> **username_2**: "*I believe the question as it stands is enough of a proof, with the answer as (weak) confirmation that I looked it over a couple more times and am more confident.*" Here and in academia it is customary to lay out your proofs & findings to make it easier for others to learn the same lessons. Sometimes it also helps one order their thoughts and doublecheck their own work. But if you don't want to do that I certainly won't make you! Have a nice day!  
> **username_0**: What is missing in terms of proof? I've laid out a detailed example with mathematical reasoning and come out with a welfare loss. My analysis may well be wrong (indeed, it did originally have some gaps that required additional assumptions as you helped me see more than once), but I'm genuinely not sure what more I can do to make the case. To be explicit, I'm open to hearing what's missing and adding it as needed.  
> **username_2**: Not sure what to say that I have not said before; I laid out several arguments to show that your reasoning is faulty: 1. not all resources are accounted for in your comparison 2. the first welfare theorem guarantees PO outcomes, and I don't see why your example would violate any of its conditions.  
> **username_2**: Look, I get it, you are satisfied with your arguments, which I perhaps simply do not get. That is fine, I will agree to disagree. Cheers!  

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