 Look, please. Yeah, thanks, Paul and Sam. So the question I have is, so imagine we are in part of the world called Europe. Sam kind of lumped it all together, treating it as one country with sort of different individuals, different products. But what if we think of sort of the individuals in your models as the different member states, some of high productivity, some of low productivity? Actually, I'm even thinking that EU may be a better sort of test case than the US, because I think I agree with Sam there. I think more about the degree of labor mobility being very important. So in Europe, you have very high, I would say, higher than in the US version to inequality. You have more progressive tech systems. And then you have this large differential labor productivity across member states. So what would your model imply for Europe where we move to basically an internal market, so complete free trade? Sam, so a couple of questions? Sure, yeah. I mean, the background here is that there is sort of a different kind of political backlash that is more, I would say, more regional across the different member states between high and low productivity workers in different countries. Yeah. So I want to, there was a beautiful picture on the economies of a couple of months ago, I think, of showing consensus to globalization in several countries with showing, documenting a huge divide between the Asian countries and the Western countries. And consensus to globalization was astonishingly high in the Asian countries. In Vietnam, it was 97% of the population was supportive of globalization. And in the US, not even a majority was supportive of globalization. I suppose that a model of this sort should talk to the people's support to globalization. And I was wondering whether you can sort of do a back of the envelope calculation to see whether you can, using the same parameters, that is clearly sort of heroic assumption, perhaps adjusted for difference in the progressivity of the tax system, to back up a back of the envelope calculation of the welfare gains from openness. And then see how you fit the economist correlation with and without the adjustment for inequality. I have two more questions. There's a rapidly growing literature in monetary economics that looks at the implications of heterogeneity and inequality for monetary policy. Now, the focus of this literature is not so much the effects of monetary policy interventions on income inequality or welfare, which is also and some interest in that, but on the consequences that this redistribution implied by monetary policy has on the aggregate effects of monetary policy itself. And I was wondering whether in the kind of model that you showed or the models you have in trade, would there be a force at work along these lines as well? OK, three more questions. One in the back and then two on the left here and then we wrap it up. Yeah, just a quick question concerning inequality aversion. What is it in the model? You treat it like risk aversion, at least you sort of the same kind of standard utility function in that respect. Risk aversion is a purely egotistic concept. Inequality aversion is an altruistic concept. And we know that these two measures when measured at the individual level in the laboratory or so on are quite different. So what do you actually mean with inequality aversion when calibrating the model? So the question is to Professor Antras, but using what was said during the discussion. So during the discussion, the discussions said that the model works as if there were six different goods. Does it mean that the model would mostly apply in cases where the quality of the good produced in one country is very different from the quality of the good produced in another country so that they can be considered as two different goods? Here are France for the question. From what I understood was that the numbers that you showed were mostly in the end positive welfare gains in the end, even after correcting for tax distortions and other things. So I wonder, is there a plausible parameterization that gives you negative welfare losses? And the other thing I was wondering is the symmetric calibration seems plausible for countries that are similar, like the US and nearby countries. But I wonder, how do you think about comparing the US, let's say, with China, trade with China? Great. Thanks for all the questions and comments. This is awesome. I don't have much time, I guess, to respond to everything, but I'm going to try to quickly address the main thing. So thank you, Sam. This was a very generous discussion. I appreciate all the efforts that went on preparing this, and I look forward to chatting more about the example. I think when I started to listen to your discussion, I thought you were going to go through trying to see whether the sufficient statistic approach that you mentioned that Donaldson has used, other people have used, whether one could resuscitate it here. I'm not super hopeful in the sense that the fact that we have a labor supply decision probably messes things out. It'd be cool if we could do that, because as you're saying, there's W till there's not something we would typically observe. But it's something that would be worth thinking about. Then the other thing that you mentioned, that it's also something that I meant to say during the presentation, is you pointed out this fact that the amount of inequality that comes out of the model, the trade-induced inequality is actually rather small. Yet the adjustment is non-trivial. Why? Well, because the size of the gains from trade is small. Now, we know now how to beef up the gains from trade. If you put input output linkages, you put multiple sectors, things that are not in the framework that one could put in. It's not easy to put that in, because the tax data we have, the income distribution data, the IRS data we have, doesn't tell us who's working where. So we couldn't do that there. But I would imagine that the same way that the gains would raise, presumably, the inequality implications of the model might actually be amplificated as well. So this ratio we're getting, this corrections, I mean, I'm not quite sure whether they're going to be too different in those environments. But it's important to mention that there's a lot more inequality that could be coming out of trade that is not captured by the model. Now, in terms of, and we can talk about the other things maybe later, in terms of the excellent questions that came up, Eastern Europe, the first two questions actually, I mean, I'm going to think more about the precise sort of things you suggest. But it sort of leads me to kind of briefly mention something that I didn't mention either. I think that has to do with the Asian perceptions of globalization that might have implications for euro integration, which is the fact that, in the same way that we're saying that, within a country, if there's changes in inequality coming from trade and there's no full compensation and there's variation in marginal utility across individuals of different income levels, this has also implications for thinking about the overall gains from trade and how that may vary across countries. Maybe, if we're saying that by increasing inequality, we should reduce the implied wealth for implications from trade, when we think about the aggregate world level gains from trade, maybe we want to take into account that trade liberalization has lifted very poor countries out of poverty. And in those countries, the marginal utility of consumption is presumably orders of magnitude larger than the marginal utility of consumption in rich countries. So, it's natural that individuals in Asian countries are super happy about this, individuals in rich countries are not, and how do I aggregate all these things is really not trivial. And I'd love to kind of play around and think a bit more about that. So that's, we can talk about the other details. Yes, I know a bit about that literature. These models don't have borrowing constraints, they don't have that type of frictions that would generate variation in the marginal propensity to consume. So, I don't think we're quite there in trade models in sort of having a feedback from inequality to aggregate demand based on sort of variation in marginal propensity to consume, but we might get there at some point, we can talk more about that. Inequality, risk aversion, yeah, they're the same here. I understand, these are different concepts. We play around with different values of row. They don't seem to matter too much, that ties it back to Monica's question, which is a very good one. Could we get negative gains from trade, of course. I mean, in principle, any model that would generate some losers, if you go to the high enough degree of inequality aversion, you go to the Rawlsian criterion that's gonna generate negative gains from trade. We don't have that here because of a very peculiar feature of the model that I think is tied to your other question, which is the symmetry versus a symmetry, which is despite the fact that low-able individuals are facing higher import competition from foreign countries, in the model, those guys are actually not worse off. So the model is not generating losers, which I think is a limitation of the framework, and that basically tells you that as you start jacking out the degree of inequality aversion, there's only so much you're gonna get in terms of an attenuation again from trade. Now, I don't think that's a general feature. I think that a symmetry is, trade with China would be a way to kind of undo this, and that's certainly something that we would wanna play around with. And I think I'll stop here. Thank you very much. You're welcome. Two thoughts on the questions. One is, on the one about the figure and the economist, one kind of first-order thing to, even without thinking about inequality, is just the fact that small countries in this setting gain a lot more from trade than large countries, and that's true in Pulse model as well as a lot of other models, and you can kind of see it in that gains-from-trade formula that a big country is gonna be already buying mostly from itself. It'll already be getting most of the gains-from-trade by trading with other people within the country, but maybe Vietnam is gaining a huge amount by trading with the rest of the world, so that could be one of the things explaining. And then on the first question, this is kind of fun to answer as a trade economist, because, or maybe in honor of Ricardo is, he'd say, well, that doesn't make any difference at all. I mean, that's just productivity, that's just absolute advantage differences, and that just leads, there'll be no trade generated by that, and so you really gotta get it something beyond just one country's productive and another country's not, or else it just, the wages equate that product, or balance out that productivity difference, and then they don't trade, and so then you've gotta get to the next layer of why are they trading to really get the answer to that? I mean, of course, with some stickiness and so on, that may not be the answer, but it's kind of the clean theoretical answer, I think. Well, thank you very much for all the participation in the nice morning session, so I think we can have a 20-minute coffee break and then resume at 10.30.