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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.

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  • $\begingroup$ 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. $\endgroup$ – Adam Bailey Jan 7 at 11:23
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(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").

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 1muflon1):

enter image description here

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

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"):Do I make correct conclusions about international trade (and ways to increase GDP) from the expedenture approach formula for GDP? 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.

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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):

enter image description here

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

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

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    $\begingroup$ "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. $\endgroup$ – user161005 Jan 7 at 10:13
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    $\begingroup$ @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 $\endgroup$ – 1muflon1 Jan 7 at 10:21
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    $\begingroup$ @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. $\endgroup$ – 1muflon1 Jan 7 at 10:39
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    $\begingroup$ 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] $\endgroup$ – user161005 Jan 7 at 17:17
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    $\begingroup$ 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? $\endgroup$ – user161005 Jan 7 at 18:46

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