<p>(My answer is based on what I learned from the answer and comments of user 1muflon1. This answer wouldn't be possible without their patient attempts to put some knowledge under my thick skull. Here I will pretend to be another person and address Past-Me as "You"). </p>

<p>At first, let's start with intuition for why increased consumption implies increased PPF. Then we will give more rigorous explanation if you won't be satisfied with said intuition.</p>

<p>The intuition: </p>

<p>Suppose we have a choice. We can either produce X of wine or produce Y of cheese and then trade Y of cheese for X of wine or produce Y of cheese and then use an alchemist to magically transform Y of cheese into X of wine. In all cases resulted wealth in terms of wine will be equal to X of wine. In the first case it's because 1 wine = 1 wine, in the second case it's because the exchange rate for Y cheese is equal to X of wine, in the third case because the transformation rate for Y cheese is equal to X of wine. Please note that even if we produce Y of cheese and then refuse to exchange/transform it the resulted wealth (i.e. Y of cheese) will still be worth X of wine. Just ability to perform exchange/transformation is enough for it to be X of wine. Consequently, if exchange/transformation rate will change, then so will worth of our wealth in terms of wine. </p>

<p>Now suppose we can hire a more experienced alchemist (who knows more advanced and nuanced alchemy) to replace our current alchemist. This new alchemist can transform Y of cheese in Z of wine, where Z>X. What will happen if we hire them? It would mean that transformation rate for our cheese production improved, meaning that by producing Y of cheese we now produce more in terms of wine, that now we have better alchemist technology. As a consequence, it would mean that our our PPF increased.</p>

<p>Now suppose that we have our not very good old achemist, but we have a possibility to improve our exchange rate for Y of cheese. Suppose our current exchange rate is based on our internal (i.e. national) market and we are an autarky. But in the external world there is a country that can give us a better bargain for our cheese, let's call it Winetopia. If trade negotiations with Winetopia will be successfull then it will agree to exchange Y of our cheese for Z of its wine, where Z>X. Thus after we negotiate terms of trade with Winetopia value of our Y of cheese in terms in wine will increase. We still produce only Y of cheese, but now Y of cheese represents more wealth in terms of wine thanks for better exchange rate. As we saw in the example above, we could have the same increase in wealth if we hired a better alchemist. In the example with a better alchemist we concluded that use of a better alchemist leads to increased PPF. This example with Winetopia has no significant difference with the above alchemical example, thus by analogy we can make similiar conclusion, namely that improved exchange rate leads to increased PPF.</p>

<p>If you don't like this explanation, then we can take the alternative approach:</p>

<p>GDP measures production, if real GDP (nominal GDP isn't enough because its changes can be attributed to deflation/inflation) increased after trade (assuming that before trade stared we already were on PPF, rather than below it) with Winetopia then our PPF increased too. </p>

<p>For this we first have to put some numbers on the problem to be able to draw PPFs and consumption curves. Lets assume that Cheestopia can produce 1 cheese at 1 labor, and 1 wine at 2 labor and Winetopia 1 cheese at 2 labor and 1 wine at 1 labor, and both countries have 100 labor avaiable for production, this gives us the following PPFs for both countries in autarky(the chart was created by 1muflon1):</p>

<p><a href="https://i.sstatic.net/Dvhvv.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Dvhvv.png" alt="enter image description here"></a></p>

<p>Production and consumption curves are equal here (for now) because everything produced domestically is consumed domestically and everything consumed domestically was produced domestically. Cheesetopia has the comparative advantage at producing cheese, while Winetopia has the comparative advantage at producing wine. For this particular example let's suppose that Cheesetopia doesn't value cheese at all, but values wine, while Winetopia doesn't value wine at all, but values cheese. Thus Cheesetopia spends all its labor to produce 50 wine, while Winetopia spends all its labor to produce 50 cheese. From given information we will be able to deduce/calculate following table:</p>

<p><a href="https://i.sstatic.net/GUALj.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/GUALj.png" alt="enter image description here"></a></p>

<p>Numbers in yellow cells (except of price of 1 cheese in terms of cheese, which is obviously always 1 cheese under any circumstances) were calculated based on numbers in white cells. Theoretically it's possible to calculate price of 1 wine in terms of cheese from data that we already have, but here I will just take word of user 1muflon1 that said prices are correct and omit calculations. Calculations for the table themselves are based on what was described in comments by 1muflon1 here(It starts with words "repeating itself"):<a href="https://economics.stackexchange.com/questions/33431/do-i-make-correct-conclusions-about-international-trade-and-ways-to-increase-gd">Do I make correct conclusions about international trade (and ways to increase GDP) from the expedenture approach formula for GDP?</a>  As for nominal GDP of Cheesetopia (we don't count GDP for Winetopia because it's excessive for our purposes), it's GDP=100 before trade(C=100, everything else equals zero) and GDP=100+50-50 (C=100, X=50, M=50) after trade. In all cases GDP is shown in terms of cheese. Thus we see why both nominal GDP for Cheseetopia before trade (i.e. "Cheesetopia Old") and nominal GDP for Cheesetopia after trade (i.e."Cheesetopia New") are equal to 100. The table shows real GDP of Cheesetopia increased after trade, thus we can conclude that its PPF increased after trade. Its PPF now ends in point (0ch,100w) instead of old point (0ch,50w).</p>

<p>One more thing. A sceptic could try to provide the alternative explanation: "Post-trade production in terms of cheese increased NOT due to trade, but because Cheesetopia now spends all its labor on producing the good of its comparative advantage, namely cheese". But they would be wrong.Production in terms of cheese will <strong>never</strong> increase just due to specialization. Because no matter if we specialize or not, we are still on the same PPF, thus real GDP will be the same anyway. </p>

CC BY-SA 4.0
2020-01-10T17:53:54.877Z
2020-01-10T18:15:37.470Z
2020-01-10T18:15:37.470Z
KarmaPeasant
<p>For this you first have to put some numbers on the problem to be able to draw PPF and consumption. Lets assume that Cheestopia can produce 1 cheese at 1 labor, and 1 wine at 2 labor and Winetopia 1 cheese at 2 labor and 1 wine at 1 labor, and both country has 100L avaiable for production, this gives you the following PPFs for both countries in autarky (the chart was created by 1muflon1):</p>

<p><a href="https://i.sstatic.net/Dvhvv.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Dvhvv.png" alt="enter image description here"></a> </p>

<p>Now, I wont post full solution for a Ricardian model because it is not part of your question but in this case valid solution would be that the trade prices will be 1 cheese for 1 wine (if you want to know why maybe post it as a separate question about solving Ricardian model). Now under this trade scenario both cheestopia and Winetopia can produce only the good in which they have comparative advantage (i.e. only cheese in Cheesetopia and only wine in Winetopia) and at the trade 1ch for 1 w they can now access all the following points in consumption (note the points for two countries overlap but I ploted them next to each other so you see that second country does not disapear):</p>

<p><a href="https://i.sstatic.net/5RdTB.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/5RdTB.png" alt="enter image description here"></a></p>

<p>Now, whether anyone agrees that this increases a PPF it is indisputable that it increases the consumption possibilities of two countries. Thats plain from the picture. So now a question is following. Can we call this expansion of consumption possibilities increase in PPF? I think yes and also many textbooks call it like that for the following reasons:</p>

<ol>
<li><p>From economic point of view there is no difference between producing, say, X of wine and between producing Y of cheese and then trading Y of cheese for X of wine. Just imagine that there a wizard/machine that converts Y of cheese in X of wine. From an economic perspective trade is like having access to production technology of the other country. Also macroeconomically consumption must be in long run equal to income and income in the long run must be equal to production.</p></li>
<li><p>By standard measures of production (such as GDP) this increases the production at any other point than the vertex (100ch, 0w) which overlaps with autarky PPF and PPF is by definition all possible combination of production. To show that this is the case lets consider one point on the new consumption line and lets use one standard output/production measure - GDP.</p></li>
</ol>

<p>Lets select Cheesetopia and lets select point of consumption (0c,100w) which is a point of consumption only accessible by trade. Now if you claim that this point does not represent new PPF, at this point the production then a consumption point (0c,100w) should not show up on aggregates as GDP which measures the production as that would imply that production is outside PPF which by definition must include all production possibilities of a country. To calculate GDP we have to choose some good as numeraire (money) it does not matter which one we choose lets do cheese. So at the consumption point 0 cheese and 100 wine the components of GDP will be C= 100ch (here ch is the currency cheese they actually consume wine), X = 100ch (they export cheese) and M = 100ch (they import 100 wine and again cheese is the currency here). So GDP in this case is GDP = 100 + 100-100 = 100. So here we have a contradiction and there is only two ways how to resolve this contradiction:</p>

<ol>
<li><p>You will say that GDP does not measure production. Which I dont think even the biggest critics of GDP would say.</p></li>
<li><p>PPF must be at consumption point (0ch,100w) at least 100 because by definition PPF is the combination of <strong>all</strong> production possibilities of the country, so if GDP measures production it must be within PPF it cannot be outside.</p></li>
</ol>

<p>Now you can pick your 'poison' from the above option. Economically, the second makes sense. Intuition is that there is no meaningful difference between producing cheese at home and via trade transform this production of cheese into production wine and between actually being able to produce wine at home at the terms of trade. Or another way how you could express that intuitively is that in the new PPF any combination of goods can be produced by producing just cheese which is the highest point on the pre-trade PPF and which is also the single point where pre and post trade PPF will be exactly same.</p>

<p>Furthermore, to see that this is the same lets consider this scenario. 1 Winetopia gets destroyed by a tsunami so only Cheesetopia is left in the world. Now imagine that Cheesetopia will send some scubadivers to recover the Winetopia's wine production technology hence now Cheesetopia can produce both wine and cheese at 1 labor. Now the PPF is exactly the same as with the trade (meaning there is no meaningful economic distinction between trading.)</p>

<p><a href="https://i.sstatic.net/ImY19.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ImY19.png" alt="enter image description here"></a></p>

CC BY-SA 4.0
2020-01-07T10:13:52.640Z
"lets select point 0 cheese and 100 wine", wait, point of what? PPF of Cheestopia? But there is no such point, even with trade. Cheesetopia can't produce 100 wine. Neither it can consume 100 wine while producing 0 cheese.
KarmaPeasant
CC BY-SA 4.0
2020-01-07T10:21:48.687Z
@user161005 but it can consume 100wine thanks to trade that’s what I meant by selecting the point. It’s a complete valid point at terms of trade 1ch=1w. The point is that under trade cheesetopia can “produce” wine by producing cheese in Ricardian model there is 0 distinction between trade and having wizard at cheese factory who by magic changes one cheese to 1 wine. Trade allows you to make a projection of 100 production of cheese on any combination of cheese and wine in this 2D cheese-wine space. Economically it does not matter that this is “indirect” wine production through trade
1muflon1
CC BY-SA 4.0
2020-01-07T10:24:47.393Z
Also, yes point 100ch is available also for autarky but the point is that under autarky this point cannot be projected. So the PPF expands at all points except this one so it’s not strict expansion meaning PPF(trade) is not > PPF(autarky) but it’s PPF(T)=>PPF(A) because they share one point but thanks to projection of the cheese production on any other combination of wine and cheese production in trade any other point on PPF(T) will be higher.
1muflon1
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2020-01-07T10:27:30.507Z
However, if we would include utility function we could say that PPF(T) > PPF(A) because under standard preferences the corner production points in autarky case will never be on equilibrium path (but this is just side note in above explanation I on purpose did not assume any utility or anything since you said in your question you are not interested in that here)
1muflon1
CC BY-SA 4.0
2020-01-07T10:35:09.603Z
"but it can consume 100wine thanks to trade" No, it can't. Otherwise it would mean that there is no internal consumption of wine in Winetopia (You already established that Winetopia can produce 100 at most).
KarmaPeasant
CC BY-SA 4.0
2020-01-07T10:35:19.927Z
Also maybe this will clear it out. Under autarky 100ch 0w is valid point, 50ch25w is valid point, and 0ch,50w is valid point. In trade production will always be 100ch never anything else in this simple model but 100ch can be projected not only into 100ch 0w but also on 50ch 50w and also on 0ch 100w. Economically there is no meaningful distinction between this projection and physical production the same way as there is no meaningful distinction between income and output (even though names are different) or consumption and income etc.
1muflon1
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2020-01-07T10:39:07.827Z
@user161005 here you did not wanted to include any utility function. So consumption 0w in winotopia is valid. Winotopia will consume 100cheese because it exchanges 1ch for 1w.
1muflon1
CC BY-SA 4.0
2020-01-07T12:13:32.003Z
1.I see, it's possible if both countries hunger for their disadvantaged good, while wanting zero of their comparative advantage good. Trade also makes sense with such utility functions. 2." should not show up on aggregates as GDP " What do you mean by "aggregates"? Aggregates of production of country? What do you mean by "show up"? To increase or to just contribute? 3."So here we have a contradiction" Contradiction of GDP=100 with what?
KarmaPeasant
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2020-01-07T12:39:04.380Z
By the way, what is the price of wine in terms of cheese BEFORE trade?
KarmaPeasant
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2020-01-07T15:53:46.180Z
@user161005 2. by that I mean that any possible production should should be inside PPF as by definition PPF is a collection of any possible production. So any measure of production (like rGDP) cannot be by definition outside PPF if it’s outside then either it does not measures production or actually thinking it was outside PPF was wrong. The pre trade prices were: cheesetopia 1cheese = 2 wine and in winetopia 2chese =1 wine so if we select cheese (ch) as numeraire the prices were 1cheese= 1ch and 1 wine = 2ch in cheesetopia and 1cheese =1 cheese and 1 wine =0.5 cheese in winotopia...
1muflon1
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2020-01-07T15:54:32.757Z
But remember if comparing pre and post trade GDP you have to calculate real GDP so you need to control first for the price levels.
1muflon1
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2020-01-07T17:17:19.763Z
Is following correct: Price level for Cheesetopia is (2+1)/(1+1)=1.5, while price level for Winetopia is (1+0.5)/(1+1)=0.75 Thus GDP deflator for Cheesetopia=0.(6), while for Winetopia GDP deflator=1.(3) [It's assumed that we talk about new GDP of either country]
KarmaPeasant
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2020-01-07T17:43:00.977Z
@user161005 yes that seems pretty much right assuming your base is the pre trade price level.
1muflon1
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2020-01-07T18:02:09.037Z
Is following correct: old nominal GDP for Cheesetopia 100, while old nominal GDP for Winetopia is 75
KarmaPeasant
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2020-01-07T18:18:28.027Z
@user161005 well GDP at what production/consumption? But assuming it’s on the frontier it’s correct
1muflon1
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2020-01-07T18:21:33.453Z
1.Yes, consumption where Cheesetopia consumes only wine and Winetopia consumes only cheese. 2.Is following correct: New real GDP of Cheesetopia 150, while new real GDP of Winetopia is 75
KarmaPeasant
CC BY-SA 4.0
2020-01-07T18:25:50.967Z
There is link to spreadsheet where I calculated everything: https://drive.google.com/file/d/1kv6BsRqx8XZQ2Gp7yDrHwlv-MWR7d30s/view?usp=sharing        It seems that Winetopia decreased its GDP due to free trade.
KarmaPeasant
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2020-01-07T18:28:54.133Z
@that is correct also preciously there was actually a mistake the old GDP was supposed to be 50 in winotopia because the price of wine was 0.5 so if you say it was all wine production it’s 100units of wine times price 0.5
1muflon1
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2020-01-07T18:36:44.963Z
I agree, I see now that old GDP for Winetopia=50. I corrected my spreadsheet, so here is new link: https://drive.google.com/file/d/1XYIK59aNpeHyHO2JOGbP_ayP1mInJngv/view?usp=sharing     Now GDP of Winetopia increased due to free trade
KarmaPeasant
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2020-01-07T18:37:38.917Z
Yea in the spreadsheet the nominal GDP should be 50, as I mentioned in my last comment you say it only produces wine so GDP measures at current prices is just C=100*0.5ch so 50ch (also sorry it was my bad that I previously said it was correct I did not noticed the mistake right away). Also 75 vs 75 is not decrease that would be remained constant but it’s actually 50 vs 75
1muflon1
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2020-01-07T18:39:17.583Z
How did you get old real GDP in winotopia 66.66? In a base year real and nominal GDP are always the same here the base “year” is the pre trade scenario real GDP can’t be 66.66 as for a base year deflator must be 1. In pre trade the deflator is 0.75/0.75 post trade it is 1/0,75.
1muflon1
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2020-01-07T18:46:28.027Z
Thanks for correcting. The answer is simple, I messed up deflator for old GDP of Winetopia. Now it's 1 and consequently its old real GDP for Winetopia is now 50, while new real GDP is 75. "Also 75 vs 75 is not decrease that would be remained constant" What do you mean?
KarmaPeasant
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2020-01-07T18:49:06.540Z
@user161005 well a decrease would be for example old GDP 75 and new 50 if both old and new rGDP are 75 then we will say “GDP remained constant” that is its a constant function of time in these two periods GDP(t)=75, GDP(t+1)=75...
1muflon1
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2020-01-08T15:05:25.297Z
1."From economic perspective there is no meaningful distinction between producing 2 goods within a border of country or producing 1 good and trading for the other." Did you mean trading 1 good for 2 goods? 2. "income is by definition production" Did you mean "equal to production"? 3." So GDP in this case is GDP = 100 + 100-100 = 100" Your answer lacks comparison. Please add old  real GDP
KarmaPeasant
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2020-01-08T15:06:49.450Z
@user161005 I meant trading the first good for the second. They are both equal and equivalent. Within a economy if you produce let’s say 1 theater play then that’s your income. Money is just measuring the value of that play and then to get consumption you exchange that play (using money to solve double coincidence of wants) for some goods and services. Hence income and production are equivalent and in long run income and production will exactly equal consumption (the equality with consumption requires assumption of increasing utility in consumption but that’s totally reasonable)
1muflon1
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2020-01-08T15:15:16.253Z
"They are both equal and equivalent" Okay, but what you wrote tells a different story. Producing 2 goods isn't equal to producing 1 good and then trading it for another 1 good, at the least if goods are equal. I think you miswrote there?
KarmaPeasant
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2020-01-08T15:17:38.237Z
@user161005 maybe, this is what I meant by that. From economic perspective if prices are such that 1cheese =1wine there is no meaningful difference between producing 100chese and ‘producing’ 50chese and 50wine where the 50wine was obtained not by directly producing the cheese by your own hands but by exchanging it... it might make difference from legal or literary point of view but from economic point of view they are the same as for example from economic point of view social contributions are just taxes, no matter that government tries to hide that by giving them nice sounding name
1muflon1
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2020-01-08T15:21:20.350Z
Also, I wonder why you didn't include old real GDP (and its formation)  in your answer? Hmm... Is it irrelevant that real GDP increased thanks to trade?
KarmaPeasant
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2020-01-08T15:26:56.900Z
@user161005 because your question was about if we can say that PPF increased and talking about old and new GDP is not necessarily required to show that. For showing the PPF increases it’s sufficient to show that there is one new point that is outside the old PPF. Also my answer was already really long. Furthermore, I worried that someone who did not read our previous discussions would not understand why I do all the old and new real GDP calculations and the answers here should be not directed just at people asking it but also to new readers who might have similar question
1muflon1
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2020-01-08T15:43:06.397Z
I don't understand, how is it sufficient? To show that new point is outside of the old PPF we need to show this old PPF, or its part, somehow. Old real GDP shows us exactly that, it shows our previous point on the old PPF. But without old real GDP how can we know that new point is really outside of the old PPF? P.S. Besides, new point is in nominal GDP, instead of real GDP, which doesn't make much sense for me.
KarmaPeasant
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2020-01-08T15:44:05.813Z
@user161005 this can be shown this way: forget about old GDP, let’s focus on PPF there was no dispute that old PPF had vertexes at (100,0) and second vertex at (0,50), now on new picture the consumption possibilities have vertexes at (100,0) and (0,100). Now a question is do these consumption possibilities represent production? If yes they must be measurable by something like GDP which measures production so the question now is can the vertex (0,100) -  which is outside old PPF - measured by GDP? If yes then either it’s production for practical purposes or GDP is wrong measure of production
1muflon1
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2020-01-08T16:21:46.367Z
Also, in a base period you select the nominal and real GDP will always be same. So it’s always valid to say that second GDP is real and the first is nominal that has to be adjusted (as mentioned also before), but again as my previous comment explained none of this is necessary for this answer about PPF - this being said calculating real GDP pre and post trade would also be valid way of showing it but less direct given the question emphasized PPF. If you think that would make the answer more clear I can include that as well later.
1muflon1
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2020-01-08T16:31:16.887Z
"If yes they must be measurable by something like GDP". Let's suppose that they are **not**. In this case what result would we get if we tried to calculate GDP?
KarmaPeasant
CC BY-SA 4.0
2020-01-08T16:42:15.033Z
@user161005 if the vertex (0,100) would only be consumption but could not be thought of as expansion of PPF then PPF should be still at its original area where on wine axis the vertex was at (0,50) so the GDP should be maximum 50 (in that case for example there would be have to be some other channel like for example some dissaving so while C=100 I=-50 and X = M=100 so for example so GDP would be GDP=100-50+100-100. But in this case this would not be possible because there were no saving so all consumption must have come from production.
1muflon1
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2020-01-08T17:15:12.563Z
"so the GDP should be maximum 50". But why? How did you arrive to 50? We measure GDP in cheese, but in (0,50) 50 isn't 50 cheese, it's 50 wine. And before trade 1 wine <>1 cheese.
KarmaPeasant
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2020-01-08T17:18:49.397Z
@user161005 because we are talking about post trade scenario here. There is no debate about what PPF is in pre trade case the question is if post trade it expanded. So with this GDP calculation we are in a post trade state with post trade prices so since now prices are 1 the post trade GDP **if PPF did not** expand at a consumption vertex (0,100) the production should not be larger than 50 because if PPF did not expand then post trade it should still have vertex at (0,50)
1muflon1
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2020-01-08T17:36:58.200Z
Wait, why do we apply prices of post-trade world to pre-trade production arrangement? If we are in post-trade world then it means that we specialize in producing 100 cheese, we don't produce 50 wine anymore.
KarmaPeasant
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2020-01-08T17:43:10.637Z
@user161005 because we exchange that 100ch for 100w and then the question is if this wine consumption counts as production. So we have to compare the actual result 100w with counterfactual where we assume that no we cannot say that this represents production it’s only consumption. In this counterfactual we assume that PPF is unchanged. This is where the intuition comes from since after trade always 100chese is produced and wine is always got by trade the PPF rotates around the vertex (100,0) outwards and hence its larger since any cheese production can be projected on wine at rare 1ch=1w
1muflon1
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2020-01-08T18:03:04.867Z
" In this counterfactual we assume that PPF is unchanged". Right, but what level of production is unchanged? From my understanding it would neccessarily be 100 cheese because our production has value of 100 cheese due to specialization. Why would we lie to ourselves and pretend like we produce production in terms of 50 cheese while we produce in terms of 100 cheese?
KarmaPeasant
CC BY-SA 4.0
2020-01-08T18:09:52.683Z
@user161005 because both pre and post trade PPF share the vertex 100,0 we have to compare them at any other point. Most points would require some calculation, so it’s convenient to choose other vertex (0,100) for this comparison. Then if you compare two claims that are mutually exclusive it’s a valid logical technique to suppose that claim 1 which you want to disprove (in this case PPF remains unchanged) is true and then find a contradiction. In fact in logic it’s called proof by contradiction. If you find contradiction claim 1 cannot be true. And in this case claim 2 is true if claim 1 isn’t
1muflon1
CC BY-SA 4.0
2020-01-09T15:31:20.503Z
So, you decided to compare before-trade production (0,50w) with post-trade consumption (0,100w).
You have shown that post-trade production (in terms of cheese) increased. But a sceptic can always provide the alternative explanation: "Post-trade production in terms of cheese increased not because consumption increased, but because Cheesetopia now spends all its labor on producing the good of its comparative advantage, namely cheese"
KarmaPeasant
CC BY-SA 4.0
2020-01-09T16:22:23.667Z
@user161005 yes but that’s the whole point. Before trade if country wanted to have mixed consumption it had to produce some cheese and some wine. After trade it never has to produce wine directly it indirectly ‘produces’ it through trade, and using that whole proof by contradiction I simply established that from economic perspective this trade is the same as being able to produce wine at 1 labor instead of at 2 labor. Hence the Production **Possibilities** Frontier expands at all other points except the point where under autarky country would still choose 100cheese but that’s only one shared..
1muflon1
CC BY-SA 4.0
2020-01-09T16:27:01.237Z
Point whereas PPF is collection of all possible points so it’s completely valid to say PPF expands even if you show there is at least one new point that’s outside the old PPF. In this case actually any point except for that one vertex expands but I only showed that rigorously for 1 point (the vertex 0,100) because showing it for all would require more serious math, but you could check that by the point by point comparison of real GDP if you have enough patience.
1muflon1
CC BY-SA 4.0
2020-01-09T18:08:17.163Z
(1/2)I'm afraid that your answer doesn't make it clear how to refute the sceptic. But it's OK because I've had an insight of my own:Production in terms of cheese will never increase just due to specialization. Because no matter if we specialize or not, we are still on the same PPF, thus real GDP will be the same anyway.
KarmaPeasant
CC BY-SA 4.0
2020-01-09T18:08:28.147Z
(2/2)Also it implies that it doesn't matter if there was specialization under autarky if we compare our post-trade consumption point to a point of pre-trade PPF.
Also now trade is the only explanation that we have for increased real GDPs of Cheesetopia and Winetopia. Real GDP shows overall production in economy, thus its increase means PPF increased and it increased due to trade.
KarmaPeasant
CC BY-SA 4.0
2020-01-09T19:51:59.817Z
@user161005 your comment 2/2 is correct but I don’t understand the 1/2. It’s precisely due to the fact that trade allows for full specialization no matter what preferences you have that we can think of it as an expansion of PPF. But we are already starting to discuss this in circles. The point is even if you are complete skeptic you can’t deny that in all but one specific point the real GDP increases. Now as long as we agree that GDP measures production it must also increase the PPF since GDP cannot be outside PPF as by definition PPF is any production possibility and GDP is national product
1muflon1
CC BY-SA 4.0
2020-01-10T17:56:17.350Z
I made answer-compilation/adaptation based on your answer and comment. Does it look good enough from your point of view? Or do you see things that must be imporved?
KarmaPeasant
CC BY-SA 4.0
2020-01-10T18:12:56.627Z
@user161005 I think it’s fine some parts are more clear than in my original answer, but then there are some other parts like the last paragraph that I honestly have no idea what what are you trying to say. Also if you are taking other peoples graph you should make separate attribution for the graph- it’s not that I care about attribution itself but I don’t want other people thinking I plagiarized you - In any case it seems you already got the gist of it so there is no need to discuss it further in comments if you are still interested in discussing something let’s put it in chat.
1muflon1
CC BY-SA 4.0
2020-01-11T15:35:23.690Z
You said that if I want to know how exact prices for international trade are formed I can ask separate question. I would, but I have doubts if it will make practical sense for me. I want to know, but I'm afraid that you will give me answer that I will able to understand only if I literally have PhD (as the book with full Ricardian model that you referenced in your other answer). Would you answer be accessible to bachelor students, especially not the most bright ones?
KarmaPeasant
CC BY-SA 4.0
2020-01-11T23:22:27.253Z
@user161005 well on your other question I gave you the Bsc level but not rigorous answer which is that for one industry not to die off, in autarky, you need the prices be equal to their marginal productivity, and under trade they must be in range between the relevant productivities of the two countries this is what you would find in Bsc textbook. However, if you start asking additional heavy question how come we can do this without demand then you need to go to PhD lvl model. Because your question is basically why is Ric. model so simple (ie no demand) but then answer is it’s a student version
1muflon1
CC BY-SA 4.0
2020-01-07T09:45:32.423Z
2020-01-10T18:18:16.763Z
2020-01-10T18:18:16.763Z
1muflon1
<p>PPF shows us different combinations of goods that we would be able to produce if we employed existing resources of our country in the most efficient way. </p>

<p>One thing to notice about PPF: It's completely independent from our agregate utility function. For an example, if we have only two types of goods, wine and cheese, then maximum production of only cheese (like 100;0) will be on our PPF, even if we would want to have some wine too or if we don't need so much cheese. </p>

<p>Now suppose we (Cheesetopia) trade with another country (Winetopia) and specialize in our comparative advantage (cheese). We will be able to consume, for an example, 50 cheese and 50 wine at the same time, a feat impossible for us under autarky. We would be consuming outside our production capabilities, outside of our PPF. But our current production would be on our good old PPF. </p>

<p>Thus I fail to see how free trades causes any shift in PPF or causes a country to produce outside its PPF. At the least for the Ricardian model.</p>

CC BY-SA 4.0
2020-01-07T11:23:49.430Z
What has prompted this question?  Have you read somewhere that trade and specialisation can shift a country's PPF outwards?  If so a link or reference would be useful.
Adam Bailey
<macroeconomics><international-trade><comparative-advantage>
Why do we say that trade and specialization according to comparative advantage lead to one-time increase in PPF of given country?
KarmaPeasant
# Why do we say that trade and specialization according to comparative advantage lead to one-time increase in PPF of given country?

(Asked by: username_0 on 2020-01-07)

PPF shows us different combinations of goods that we would be able to produce if we employed existing resources of our country in the most efficient way.

One thing to notice about PPF: It's completely independent from our agregate utility function. For an example, if we have only two types of goods, wine and cheese, then maximum production of only cheese (like 100;0) will be on our PPF, even if we would want to have some wine too or if we don't need so much cheese.

Now suppose we (Cheesetopia) trade with another country (Winetopia) and specialize in our comparative advantage (cheese). We will be able to consume, for an example, 50 cheese and 50 wine at the same time, a feat impossible for us under autarky. We would be consuming outside our production capabilities, outside of our PPF. But our current production would be on our good old PPF.

Thus I fail to see how free trades causes any shift in PPF or causes a country to produce outside its PPF. At the least for the Ricardian model.

**Tags:** macroeconomics, international-trade, comparative-advantage

> **Comments:**
> **username_1**: What has prompted this question?  Have you read somewhere that trade and specialisation can shift a country's PPF outwards?  If so a link or reference would be useful.  

---

## 2 answers

### Answer by username_0 on 2020-01-10. Score: 0 | Accepted answer

(My answer is based on what I learned from the answer and comments of user username_2. This answer wouldn't be possible without their patient attempts to put some knowledge under my thick skull. Here I will pretend to be another person and address Past-Me as "You").

At first, let's start with intuition for why increased consumption implies increased PPF. Then we will give more rigorous explanation if you won't be satisfied with said intuition.

The intuition:

Suppose we have a choice. We can either produce X of wine or produce Y of cheese and then trade Y of cheese for X of wine or produce Y of cheese and then use an alchemist to magically transform Y of cheese into X of wine. In all cases resulted wealth in terms of wine will be equal to X of wine. In the first case it's because 1 wine = 1 wine, in the second case it's because the exchange rate for Y cheese is equal to X of wine, in the third case because the transformation rate for Y cheese is equal to X of wine. Please note that even if we produce Y of cheese and then refuse to exchange/transform it the resulted wealth (i.e. Y of cheese) will still be worth X of wine. Just ability to perform exchange/transformation is enough for it to be X of wine. Consequently, if exchange/transformation rate will change, then so will worth of our wealth in terms of wine.

Now suppose we can hire a more experienced alchemist (who knows more advanced and nuanced alchemy) to replace our current alchemist. This new alchemist can transform Y of cheese in Z of wine, where Z>X. What will happen if we hire them? It would mean that transformation rate for our cheese production improved, meaning that by producing Y of cheese we now produce more in terms of wine, that now we have better alchemist technology. As a consequence, it would mean that our our PPF increased.

Now suppose that we have our not very good old achemist, but we have a possibility to improve our exchange rate for Y of cheese. Suppose our current exchange rate is based on our internal (i.e. national) market and we are an autarky. But in the external world there is a country that can give us a better bargain for our cheese, let's call it Winetopia. If trade negotiations with Winetopia will be successfull then it will agree to exchange Y of our cheese for Z of its wine, where Z>X. Thus after we negotiate terms of trade with Winetopia value of our Y of cheese in terms in wine will increase. We still produce only Y of cheese, but now Y of cheese represents more wealth in terms of wine thanks for better exchange rate. As we saw in the example above, we could have the same increase in wealth if we hired a better alchemist. In the example with a better alchemist we concluded that use of a better alchemist leads to increased PPF. This example with Winetopia has no significant difference with the above alchemical example, thus by analogy we can make similiar conclusion, namely that improved exchange rate leads to increased PPF.

If you don't like this explanation, then we can take the alternative approach:

GDP measures production, if real GDP (nominal GDP isn't enough because its changes can be attributed to deflation/inflation) increased after trade (assuming that before trade stared we already were on PPF, rather than below it) with Winetopia then our PPF increased too.

For this we first have to put some numbers on the problem to be able to draw PPFs and consumption curves. Lets assume that Cheestopia can produce 1 cheese at 1 labor, and 1 wine at 2 labor and Winetopia 1 cheese at 2 labor and 1 wine at 1 labor, and both countries have 100 labor avaiable for production, this gives us the following PPFs for both countries in autarky(the chart was created by username_2):

[![enter image description here](https://i.sstatic.net/Dvhvv.png)](https://i.sstatic.net/Dvhvv.png)

Production and consumption curves are equal here (for now) because everything produced domestically is consumed domestically and everything consumed domestically was produced domestically. Cheesetopia has the comparative advantage at producing cheese, while Winetopia has the comparative advantage at producing wine. For this particular example let's suppose that Cheesetopia doesn't value cheese at all, but values wine, while Winetopia doesn't value wine at all, but values cheese. Thus Cheesetopia spends all its labor to produce 50 wine, while Winetopia spends all its labor to produce 50 cheese. From given information we will be able to deduce/calculate following table:

[![enter image description here](https://i.sstatic.net/GUALj.png)](https://i.sstatic.net/GUALj.png)

Numbers in yellow cells (except of price of 1 cheese in terms of cheese, which is obviously always 1 cheese under any circumstances) were calculated based on numbers in white cells. Theoretically it's possible to calculate price of 1 wine in terms of cheese from data that we already have, but here I will just take word of user username_2 that said prices are correct and omit calculations. Calculations for the table themselves are based on what was described in comments by username_2 here(It starts with words "repeating itself"):[Do I make correct conclusions about international trade (and ways to increase GDP) from the expedenture approach formula for GDP?](https://economics.stackexchange.com/questions/33431/do-i-make-correct-conclusions-about-international-trade-and-ways-to-increase-gd) As for nominal GDP of Cheesetopia (we don't count GDP for Winetopia because it's excessive for our purposes), it's GDP=100 before trade(C=100, everything else equals zero) and GDP=100+50-50 (C=100, X=50, M=50) after trade. In all cases GDP is shown in terms of cheese. Thus we see why both nominal GDP for Cheseetopia before trade (i.e. "Cheesetopia Old") and nominal GDP for Cheesetopia after trade (i.e."Cheesetopia New") are equal to 100. The table shows real GDP of Cheesetopia increased after trade, thus we can conclude that its PPF increased after trade. Its PPF now ends in point (0ch,100w) instead of old point (0ch,50w).

One more thing. A sceptic could try to provide the alternative explanation: "Post-trade production in terms of cheese increased NOT due to trade, but because Cheesetopia now spends all its labor on producing the good of its comparative advantage, namely cheese". But they would be wrong.Production in terms of cheese will **never** increase just due to specialization. Because no matter if we specialize or not, we are still on the same PPF, thus real GDP will be the same anyway.


---

### Answer by username_2 on 2020-01-07. Score: 0

For this you first have to put some numbers on the problem to be able to draw PPF and consumption. Lets assume that Cheestopia can produce 1 cheese at 1 labor, and 1 wine at 2 labor and Winetopia 1 cheese at 2 labor and 1 wine at 1 labor, and both country has 100L avaiable for production, this gives you the following PPFs for both countries in autarky (the chart was created by username_2):

[![enter image description here](https://i.sstatic.net/Dvhvv.png)](https://i.sstatic.net/Dvhvv.png)

Now, I wont post full solution for a Ricardian model because it is not part of your question but in this case valid solution would be that the trade prices will be 1 cheese for 1 wine (if you want to know why maybe post it as a separate question about solving Ricardian model). Now under this trade scenario both cheestopia and Winetopia can produce only the good in which they have comparative advantage (i.e. only cheese in Cheesetopia and only wine in Winetopia) and at the trade 1ch for 1 w they can now access all the following points in consumption (note the points for two countries overlap but I ploted them next to each other so you see that second country does not disapear):

[![enter image description here](https://i.sstatic.net/5RdTB.png)](https://i.sstatic.net/5RdTB.png)

Now, whether anyone agrees that this increases a PPF it is indisputable that it increases the consumption possibilities of two countries. Thats plain from the picture. So now a question is following. Can we call this expansion of consumption possibilities increase in PPF? I think yes and also many textbooks call it like that for the following reasons:

1. From economic point of view there is no difference between producing, say, X of wine and between producing Y of cheese and then trading Y of cheese for X of wine. Just imagine that there a wizard/machine that converts Y of cheese in X of wine. From an economic perspective trade is like having access to production technology of the other country. Also macroeconomically consumption must be in long run equal to income and income in the long run must be equal to production.
2. By standard measures of production (such as GDP) this increases the production at any other point than the vertex (100ch, 0w) which overlaps with autarky PPF and PPF is by definition all possible combination of production. To show that this is the case lets consider one point on the new consumption line and lets use one standard output/production measure - GDP.

Lets select Cheesetopia and lets select point of consumption (0c,100w) which is a point of consumption only accessible by trade. Now if you claim that this point does not represent new PPF, at this point the production then a consumption point (0c,100w) should not show up on aggregates as GDP which measures the production as that would imply that production is outside PPF which by definition must include all production possibilities of a country. To calculate GDP we have to choose some good as numeraire (money) it does not matter which one we choose lets do cheese. So at the consumption point 0 cheese and 100 wine the components of GDP will be C= 100ch (here ch is the currency cheese they actually consume wine), X = 100ch (they export cheese) and M = 100ch (they import 100 wine and again cheese is the currency here). So GDP in this case is GDP = 100 + 100-100 = 100. So here we have a contradiction and there is only two ways how to resolve this contradiction:

1. You will say that GDP does not measure production. Which I dont think even the biggest critics of GDP would say.
2. PPF must be at consumption point (0ch,100w) at least 100 because by definition PPF is the combination of **all** production possibilities of the country, so if GDP measures production it must be within PPF it cannot be outside.

Now you can pick your 'poison' from the above option. Economically, the second makes sense. Intuition is that there is no meaningful difference between producing cheese at home and via trade transform this production of cheese into production wine and between actually being able to produce wine at home at the terms of trade. Or another way how you could express that intuitively is that in the new PPF any combination of goods can be produced by producing just cheese which is the highest point on the pre-trade PPF and which is also the single point where pre and post trade PPF will be exactly same.

Furthermore, to see that this is the same lets consider this scenario. 1 Winetopia gets destroyed by a tsunami so only Cheesetopia is left in the world. Now imagine that Cheesetopia will send some scubadivers to recover the Winetopia's wine production technology hence now Cheesetopia can produce both wine and cheese at 1 labor. Now the PPF is exactly the same as with the trade (meaning there is no meaningful economic distinction between trading.)

[![enter image description here](https://i.sstatic.net/ImY19.png)](https://i.sstatic.net/ImY19.png)

> **Comments:**
> **username_0**: "lets select point 0 cheese and 100 wine", wait, point of what? PPF of Cheestopia? But there is no such point, even with trade. Cheesetopia can't produce 100 wine. Neither it can consume 100 wine while producing 0 cheese.  
> **username_2**: @user161005 but it can consume 100wine thanks to trade that’s what I meant by selecting the point. It’s a complete valid point at terms of trade 1ch=1w. The point is that under trade cheesetopia can “produce” wine by producing cheese in Ricardian model there is 0 distinction between trade and having wizard at cheese factory who by magic changes one cheese to 1 wine. Trade allows you to make a projection of 100 production of cheese on any combination of cheese and wine in this 2D cheese-wine space. Economically it does not matter that this is “indirect” wine production through trade  
> **username_2**: Also, yes point 100ch is available also for autarky but the point is that under autarky this point cannot be projected. So the PPF expands at all points except this one so it’s not strict expansion meaning PPF(trade) is not > PPF(autarky) but it’s PPF(T)=>PPF(A) because they share one point but thanks to projection of the cheese production on any other combination of wine and cheese production in trade any other point on PPF(T) will be higher.  
> **username_2**: However, if we would include utility function we could say that PPF(T) > PPF(A) because under standard preferences the corner production points in autarky case will never be on equilibrium path (but this is just side note in above explanation I on purpose did not assume any utility or anything since you said in your question you are not interested in that here)  
> **username_0**: "but it can consume 100wine thanks to trade" No, it can't. Otherwise it would mean that there is no internal consumption of wine in Winetopia (You already established that Winetopia can produce 100 at most).  
> **username_2**: Also maybe this will clear it out. Under autarky 100ch 0w is valid point, 50ch25w is valid point, and 0ch,50w is valid point. In trade production will always be 100ch never anything else in this simple model but 100ch can be projected not only into 100ch 0w but also on 50ch 50w and also on 0ch 100w. Economically there is no meaningful distinction between this projection and physical production the same way as there is no meaningful distinction between income and output (even though names are different) or consumption and income etc.  
> **username_2**: @user161005 here you did not wanted to include any utility function. So consumption 0w in winotopia is valid. Winotopia will consume 100cheese because it exchanges 1ch for 1w.  
> **username_0**: 1.I see, it's possible if both countries hunger for their disadvantaged good, while wanting zero of their comparative advantage good. Trade also makes sense with such utility functions. 2." should not show up on aggregates as GDP " What do you mean by "aggregates"? Aggregates of production of country? What do you mean by "show up"? To increase or to just contribute? 3."So here we have a contradiction" Contradiction of GDP=100 with what?  
> **username_0**: By the way, what is the price of wine in terms of cheese BEFORE trade?  
> **username_2**: @user161005 2. by that I mean that any possible production should should be inside PPF as by definition PPF is a collection of any possible production. So any measure of production (like rGDP) cannot be by definition outside PPF if it’s outside then either it does not measures production or actually thinking it was outside PPF was wrong. The pre trade prices were: cheesetopia 1cheese = 2 wine and in winetopia 2chese =1 wine so if we select cheese (ch) as numeraire the prices were 1cheese= 1ch and 1 wine = 2ch in cheesetopia and 1cheese =1 cheese and 1 wine =0.5 cheese in winotopia...  
> **username_2**: But remember if comparing pre and post trade GDP you have to calculate real GDP so you need to control first for the price levels.  
> **username_0**: Is following correct: Price level for Cheesetopia is (2+1)/(1+1)=1.5, while price level for Winetopia is (1+0.5)/(1+1)=0.75 Thus GDP deflator for Cheesetopia=0.(6), while for Winetopia GDP deflator=1.(3) [It's assumed that we talk about new GDP of either country]  
> **username_2**: @user161005 yes that seems pretty much right assuming your base is the pre trade price level.  
> **username_0**: Is following correct: old nominal GDP for Cheesetopia 100, while old nominal GDP for Winetopia is 75  
> **username_2**: @user161005 well GDP at what production/consumption? But assuming it’s on the frontier it’s correct  
> **username_0**: 1.Yes, consumption where Cheesetopia consumes only wine and Winetopia consumes only cheese. 2.Is following correct: New real GDP of Cheesetopia 150, while new real GDP of Winetopia is 75  
> **username_0**: There is link to spreadsheet where I calculated everything: https://drive.google.com/file/d/1kv6BsRqx8XZQ2Gp7yDrHwlv-MWR7d30s/view?usp=sharing        It seems that Winetopia decreased its GDP due to free trade.  
> **username_2**: @that is correct also preciously there was actually a mistake the old GDP was supposed to be 50 in winotopia because the price of wine was 0.5 so if you say it was all wine production it’s 100units of wine times price 0.5  
> **username_0**: I agree, I see now that old GDP for Winetopia=50. I corrected my spreadsheet, so here is new link: https://drive.google.com/file/d/1XYIK59aNpeHyHO2JOGbP_ayP1mInJngv/view?usp=sharing     Now GDP of Winetopia increased due to free trade  
> **username_2**: Yea in the spreadsheet the nominal GDP should be 50, as I mentioned in my last comment you say it only produces wine so GDP measures at current prices is just C=100*0.5ch so 50ch (also sorry it was my bad that I previously said it was correct I did not noticed the mistake right away). Also 75 vs 75 is not decrease that would be remained constant but it’s actually 50 vs 75  
> **username_2**: How did you get old real GDP in winotopia 66.66? In a base year real and nominal GDP are always the same here the base “year” is the pre trade scenario real GDP can’t be 66.66 as for a base year deflator must be 1. In pre trade the deflator is 0.75/0.75 post trade it is 1/0,75.  
> **username_0**: Thanks for correcting. The answer is simple, I messed up deflator for old GDP of Winetopia. Now it's 1 and consequently its old real GDP for Winetopia is now 50, while new real GDP is 75. "Also 75 vs 75 is not decrease that would be remained constant" What do you mean?  
> **username_2**: @user161005 well a decrease would be for example old GDP 75 and new 50 if both old and new rGDP are 75 then we will say “GDP remained constant” that is its a constant function of time in these two periods GDP(t)=75, GDP(t+1)=75...  
> **username_0**: 1."From economic perspective there is no meaningful distinction between producing 2 goods within a border of country or producing 1 good and trading for the other." Did you mean trading 1 good for 2 goods? 2. "income is by definition production" Did you mean "equal to production"? 3." So GDP in this case is GDP = 100 + 100-100 = 100" Your answer lacks comparison. Please add old  real GDP  
> **username_2**: @user161005 I meant trading the first good for the second. They are both equal and equivalent. Within a economy if you produce let’s say 1 theater play then that’s your income. Money is just measuring the value of that play and then to get consumption you exchange that play (using money to solve double coincidence of wants) for some goods and services. Hence income and production are equivalent and in long run income and production will exactly equal consumption (the equality with consumption requires assumption of increasing utility in consumption but that’s totally reasonable)  
> **username_0**: "They are both equal and equivalent" Okay, but what you wrote tells a different story. Producing 2 goods isn't equal to producing 1 good and then trading it for another 1 good, at the least if goods are equal. I think you miswrote there?  
> **username_2**: @user161005 maybe, this is what I meant by that. From economic perspective if prices are such that 1cheese =1wine there is no meaningful difference between producing 100chese and ‘producing’ 50chese and 50wine where the 50wine was obtained not by directly producing the cheese by your own hands but by exchanging it... it might make difference from legal or literary point of view but from economic point of view they are the same as for example from economic point of view social contributions are just taxes, no matter that government tries to hide that by giving them nice sounding name  
> **username_0**: Also, I wonder why you didn't include old real GDP (and its formation)  in your answer? Hmm... Is it irrelevant that real GDP increased thanks to trade?  
> **username_2**: @user161005 because your question was about if we can say that PPF increased and talking about old and new GDP is not necessarily required to show that. For showing the PPF increases it’s sufficient to show that there is one new point that is outside the old PPF. Also my answer was already really long. Furthermore, I worried that someone who did not read our previous discussions would not understand why I do all the old and new real GDP calculations and the answers here should be not directed just at people asking it but also to new readers who might have similar question  
> **username_0**: I don't understand, how is it sufficient? To show that new point is outside of the old PPF we need to show this old PPF, or its part, somehow. Old real GDP shows us exactly that, it shows our previous point on the old PPF. But without old real GDP how can we know that new point is really outside of the old PPF? P.S. Besides, new point is in nominal GDP, instead of real GDP, which doesn't make much sense for me.  
> **username_2**: @user161005 this can be shown this way: forget about old GDP, let’s focus on PPF there was no dispute that old PPF had vertexes at (100,0) and second vertex at (0,50), now on new picture the consumption possibilities have vertexes at (100,0) and (0,100). Now a question is do these consumption possibilities represent production? If yes they must be measurable by something like GDP which measures production so the question now is can the vertex (0,100) -  which is outside old PPF - measured by GDP? If yes then either it’s production for practical purposes or GDP is wrong measure of production  
> **username_2**: Also, in a base period you select the nominal and real GDP will always be same. So it’s always valid to say that second GDP is real and the first is nominal that has to be adjusted (as mentioned also before), but again as my previous comment explained none of this is necessary for this answer about PPF - this being said calculating real GDP pre and post trade would also be valid way of showing it but less direct given the question emphasized PPF. If you think that would make the answer more clear I can include that as well later.  
> **username_0**: "If yes they must be measurable by something like GDP". Let's suppose that they are **not**. In this case what result would we get if we tried to calculate GDP?  
> **username_2**: @user161005 if the vertex (0,100) would only be consumption but could not be thought of as expansion of PPF then PPF should be still at its original area where on wine axis the vertex was at (0,50) so the GDP should be maximum 50 (in that case for example there would be have to be some other channel like for example some dissaving so while C=100 I=-50 and X = M=100 so for example so GDP would be GDP=100-50+100-100. But in this case this would not be possible because there were no saving so all consumption must have come from production.  
> **username_0**: "so the GDP should be maximum 50". But why? How did you arrive to 50? We measure GDP in cheese, but in (0,50) 50 isn't 50 cheese, it's 50 wine. And before trade 1 wine <>1 cheese.  
> **username_2**: @user161005 because we are talking about post trade scenario here. There is no debate about what PPF is in pre trade case the question is if post trade it expanded. So with this GDP calculation we are in a post trade state with post trade prices so since now prices are 1 the post trade GDP **if PPF did not** expand at a consumption vertex (0,100) the production should not be larger than 50 because if PPF did not expand then post trade it should still have vertex at (0,50)  
> **username_0**: Wait, why do we apply prices of post-trade world to pre-trade production arrangement? If we are in post-trade world then it means that we specialize in producing 100 cheese, we don't produce 50 wine anymore.  
> **username_2**: @user161005 because we exchange that 100ch for 100w and then the question is if this wine consumption counts as production. So we have to compare the actual result 100w with counterfactual where we assume that no we cannot say that this represents production it’s only consumption. In this counterfactual we assume that PPF is unchanged. This is where the intuition comes from since after trade always 100chese is produced and wine is always got by trade the PPF rotates around the vertex (100,0) outwards and hence its larger since any cheese production can be projected on wine at rare 1ch=1w  
> **username_0**: " In this counterfactual we assume that PPF is unchanged". Right, but what level of production is unchanged? From my understanding it would neccessarily be 100 cheese because our production has value of 100 cheese due to specialization. Why would we lie to ourselves and pretend like we produce production in terms of 50 cheese while we produce in terms of 100 cheese?  
> **username_2**: @user161005 because both pre and post trade PPF share the vertex 100,0 we have to compare them at any other point. Most points would require some calculation, so it’s convenient to choose other vertex (0,100) for this comparison. Then if you compare two claims that are mutually exclusive it’s a valid logical technique to suppose that claim 1 which you want to disprove (in this case PPF remains unchanged) is true and then find a contradiction. In fact in logic it’s called proof by contradiction. If you find contradiction claim 1 cannot be true. And in this case claim 2 is true if claim 1 isn’t  
> **username_0**: So, you decided to compare before-trade production (0,50w) with post-trade consumption (0,100w). You have shown that post-trade production (in terms of cheese) increased. But a sceptic can always provide the alternative explanation: "Post-trade production in terms of cheese increased not because consumption increased, but because Cheesetopia now spends all its labor on producing the good of its comparative advantage, namely cheese"  
> **username_2**: @user161005 yes but that’s the whole point. Before trade if country wanted to have mixed consumption it had to produce some cheese and some wine. After trade it never has to produce wine directly it indirectly ‘produces’ it through trade, and using that whole proof by contradiction I simply established that from economic perspective this trade is the same as being able to produce wine at 1 labor instead of at 2 labor. Hence the Production **Possibilities** Frontier expands at all other points except the point where under autarky country would still choose 100cheese but that’s only one shared..  
> **username_2**: Point whereas PPF is collection of all possible points so it’s completely valid to say PPF expands even if you show there is at least one new point that’s outside the old PPF. In this case actually any point except for that one vertex expands but I only showed that rigorously for 1 point (the vertex 0,100) because showing it for all would require more serious math, but you could check that by the point by point comparison of real GDP if you have enough patience.  
> **username_0**: (1/2)I'm afraid that your answer doesn't make it clear how to refute the sceptic. But it's OK because I've had an insight of my own:Production in terms of cheese will never increase just due to specialization. Because no matter if we specialize or not, we are still on the same PPF, thus real GDP will be the same anyway.  
> **username_0**: (2/2)Also it implies that it doesn't matter if there was specialization under autarky if we compare our post-trade consumption point to a point of pre-trade PPF. Also now trade is the only explanation that we have for increased real GDPs of Cheesetopia and Winetopia. Real GDP shows overall production in economy, thus its increase means PPF increased and it increased due to trade.  
> **username_2**: @user161005 your comment 2/2 is correct but I don’t understand the 1/2. It’s precisely due to the fact that trade allows for full specialization no matter what preferences you have that we can think of it as an expansion of PPF. But we are already starting to discuss this in circles. The point is even if you are complete skeptic you can’t deny that in all but one specific point the real GDP increases. Now as long as we agree that GDP measures production it must also increase the PPF since GDP cannot be outside PPF as by definition PPF is any production possibility and GDP is national product  
> **username_0**: I made answer-compilation/adaptation based on your answer and comment. Does it look good enough from your point of view? Or do you see things that must be imporved?  
> **username_2**: @user161005 I think it’s fine some parts are more clear than in my original answer, but then there are some other parts like the last paragraph that I honestly have no idea what what are you trying to say. Also if you are taking other peoples graph you should make separate attribution for the graph- it’s not that I care about attribution itself but I don’t want other people thinking I plagiarized you - In any case it seems you already got the gist of it so there is no need to discuss it further in comments if you are still interested in discussing something let’s put it in chat.  
> **username_0**: You said that if I want to know how exact prices for international trade are formed I can ask separate question. I would, but I have doubts if it will make practical sense for me. I want to know, but I'm afraid that you will give me answer that I will able to understand only if I literally have PhD (as the book with full Ricardian model that you referenced in your other answer). Would you answer be accessible to bachelor students, especially not the most bright ones?  
> **username_2**: @user161005 well on your other question I gave you the Bsc level but not rigorous answer which is that for one industry not to die off, in autarky, you need the prices be equal to their marginal productivity, and under trade they must be in range between the relevant productivities of the two countries this is what you would find in Bsc textbook. However, if you start asking additional heavy question how come we can do this without demand then you need to go to PhD lvl model. Because your question is basically why is Ric. model so simple (ie no demand) but then answer is it’s a student version  

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