Comparative Advantage: Why Both Countries Gain from Trade

Here is a claim that sounds wrong the first time you hear it. Two countries can both come out ahead by trading with each other, even when one of them is worse at making absolutely everything. Not one gains and the other puts up with it. Both gain. So let me build the smallest world I can get away with. Two countries, and I will call them Home and Foreign, and two goods, cloth and wine. Both countries can make both goods, and the only resource either of them has is hours of work. Here is the entire technology of this world, in four numbers. How many hours it takes each country to make one unit of each good. That is all the information there is. Take cloth first. Home turns out a unit of cloth in two hours. Foreign needs six for the same unit. Now wine. Home needs four hours for a unit. Foreign, again, needs six. Read each line across. Two against six on cloth. Four against six on wine. Home wins on the top line, and Home wins on the bottom. There is a name for that, and we will get to it in a minute. But look at what it seems to imply. Home is faster at making everything there is to make in this little world. So what could Foreign possibly sell? And why would Home ever buy anything, when it can make both goods faster itself? It looks as though Home should make everything it needs and keep to itself. That instinct is wrong. Not slightly wrong, and not wrong in some special case. Both of these countries are going to end up with more cloth and more wine than either can get on its own, and neither of them will work a single extra hour to do it. The reason is that we have been counting the wrong thing. Hours are not what an economy really spends. So let me show you what it does spend.

Let us give what we just saw its proper name. When a country can make one unit of a good in fewer hours than the other country can, we say it has an absolute advantage in that good. Home needs two hours for a unit of cloth against Foreign's six, so Home has an absolute advantage in cloth. Home needs four hours for a unit of wine against Foreign's six, so Home has an absolute advantage in wine as well. Home holds both. And if absolute advantage were the thing that decided who trades with whom, we would be finished already. Home would make everything, Foreign would make nothing, and there would be no trade at all. But that is not what happens, in this model or in the world. Foreign does exist, though. Foreign has workers, and those workers are going to spend the week doing something. So the real question was never whether Foreign can beat Home at anything. It is what Foreign should do with the time it has. Here is what the hours are hiding. Nobody in Home is standing idle, waiting for work to arrive. Every hour Home spends on wine is an hour it did not spend on cloth. So take the four hours Home needs for a unit of wine. There they are, from zero to four. Now, what else could Home have done with them? A unit of cloth takes Home two hours. So four hours is not just four hours. Four hours is two whole units of cloth. Look at the picture. On top, those four hours buy Home exactly one unit of wine. Underneath, the very same four hours buy two units of cloth. Same hours, two different baskets, and Home has to pick one. That is the real price of Home's wine. Not four hours. Two units of cloth that never got made. The receipt is written in hours, but the economy pays in cloth. Economists have a name for that too, and it is the one that matters. The opportunity cost of a thing is what you gave up in order to get it. It is measured in goods, not in hours. And it is the number that is actually going to decide who makes what. So let us go back to those four numbers and turn every one of them into an opportunity cost. That is the table that settles the whole question.

Same two countries, same two goods, same four numbers. But this time I am not going to write down hours. I am going to write down what one unit costs, measured in units of the other good. Start with cloth. One unit of cloth takes Home two hours. What else could Home have done with those two hours? Wine costs four hours a unit, so two hours buys half a unit of wine. So one unit of cloth costs Home half a unit of wine. And Foreign? Six hours either way, so a unit of cloth costs Foreign one whole unit of wine. There is the first row of the new table. Now turn it around and price the wine. One unit of wine costs Home four hours, and four hours is two units of cloth. For Foreign it is six against six again, so a unit of wine costs it exactly one unit of cloth. Look down Home's column for a moment. To make a unit of cloth it sacrifices half a unit of wine. To make a unit of wine it sacrifices two units of cloth. Those two numbers are reciprocals of each other, and they always will be. There is the table that matters. And now the important move. Compare across each row, not down the columns. Cloth first. Home gives up half a unit of wine to make a unit of cloth. Foreign gives up a whole unit of wine. So cloth is cheaper in Home. Not faster. Cheaper. Home sacrifices less to get its cloth, and that is what we are going to call having the comparative advantage in cloth. Now wine. Home gives up two units of cloth to make a unit of wine. Foreign gives up one. Wine is cheaper in Foreign, and Foreign is the country that is slower at making wine. Sit with that for a second, because it is the hinge of the whole lecture. Foreign takes six hours to make a unit of wine. Home takes four. Home is genuinely faster at it. But Home's four hours are expensive hours. Home is so good at cloth that every hour it moves to wine throws away a great deal of cloth. Foreign's six hours are cheap hours, because Foreign was never going to make much cloth with them anyway. So here is the definition we actually need. A country has a comparative advantage in a good when making one unit of it costs that country less of the other good than it costs the other country. Home has the comparative advantage in cloth. Foreign has the comparative advantage in wine. And notice the shape of that result. Unless the two countries have identical opportunity costs, each of them has the comparative advantage in exactly one good. You cannot be comparatively better at both. Being cheaper at cloth is the very same statement as being dearer at wine. It is one ratio, read in two directions.

Time to draw this. Wine along the bottom, cloth up the side. Every point in here is a basket: so much wine, so much cloth. Home has two hundred and forty hours of work in a week. Put every one of them into cloth, at two hours a unit, and Home makes a hundred and twenty units of cloth and no wine at all. Put all of them into wine instead, at four hours a unit, and Home makes sixty units of wine and no cloth. That is this corner, down on the wine axis. Every split in between is available too, and all of them lie on the straight line joining those two corners. That line is Home's production possibility frontier. Take a point on it. Thirty units of wine and sixty units of cloth. Sixty cloth is a hundred and twenty hours, thirty wine is another hundred and twenty, and there are the two hundred and forty. It fits exactly. On the frontier every hour is used and nothing is wasted. Inside it Home is idling. Outside it Home simply cannot go, because there are not enough hours in the week. Foreign now. Foreign has three hundred hours, and six hours a unit either way. All cloth is fifty units. All wine is fifty units. Its frontier is this shorter line down here. And there is the paradox, drawn out in full. Home's frontier lies entirely outside Foreign's. Every basket Foreign can produce, Home could produce with hours to spare. Which is exactly what makes the result surprising. If this picture were all you ever saw, you would say Foreign has nothing to offer. The two lines do not even cross. Now suppose there is no trade at all. Each country has to make everything it consumes. Say Home settles on eighty units of cloth and twenty units of wine, right there on its frontier. And Foreign settles on thirty units of cloth and twenty units of wine, right there on its own. Both of them are doing the best they can alone. No wasted hours, nothing left on the table. Add the two together. The world, all in, is producing a hundred and ten units of cloth and forty units of wine. Hold on to those two numbers. Both of those numbers are about to go up. Nobody is going to work an extra hour. Nobody is going to learn anything new. And both of them go up.

Here is the same picture, and the same two no-trade baskets. Home at eighty cloth and twenty wine. Foreign at thirty cloth and twenty wine. Now let us do what the opportunity cost table told us to do. Home gives up less to make cloth, so Home should make cloth. Foreign gives up less to make wine, so Foreign should make wine. Not a bit more of each. All of it. Each country puts every hour it has into the single good it sacrifices least to produce. Which already sounds reckless. Home is better at wine than Foreign is, four hours against six, and I am telling Home to stop making wine entirely. That is precisely the move that feels wrong, and it is the move the whole result depends on. Speed is not the test. Sacrifice is. Home is now all the way up its own frontier, at the cloth corner. A hundred and twenty units of cloth, and not a drop of wine. And Foreign is at the other extreme, down in its wine corner. Fifty units of wine, and not a scrap of cloth. Nothing magic happened there. Nobody worked an extra hour. Nobody invented a better loom. Each country simply stopped doing the thing it was bad at, in the opportunity cost sense, which is the only sense that counts. Now add the world up again. Cloth: a hundred and twenty units, where before there were a hundred and ten. Wine: fifty units, where before there were forty. Ten more units of each good, out of exactly the same labour. And notice where that came from. Not from working harder. It came from moving each hour to the country where spending it throws away the least. That is the first half of the argument, and it is the easier half. There is more stuff in the world. But the world does not eat. Look at where these two countries actually are. Home is sitting on a mountain of cloth with nothing to drink, and Foreign has a lake of wine and nothing to wear. Measured against where they started, both of them are worse off at this exact moment. Specialization on its own is not the gain. It is half a step. So let them trade.

Home is holding a hundred and twenty units of cloth. Foreign is holding fifty units of wine. Now they trade, and the only question left is at what rate. The exchange rate they agree on is called the terms of trade. Any rate strictly between their two opportunity costs is one that both countries will accept. So write down the two bounds first. Foreign gives up one cloth for a unit of wine. Home gives up two cloth for a unit of wine. Below one cloth per unit of wine, Foreign would rather keep its wine and weave its own cloth. Above two, Home would rather keep its cloth and press its own wine. Strictly in between, both say yes. So let us pick a rate in the middle. Three units of cloth for every two units of wine, which is one and a half cloth per wine. Comfortably between one and two. Before we move anything, put the old no-trade baskets back on the picture. Those are the two points to beat, and we will be writing their numbers down in a moment. Home ships thirty-six units of cloth across the water, and gets twenty-four units of wine back. Check the rate: thirty-six over twenty-four is three over two. That is the agreed price. So what does Home end up holding? Start with the line to beat. Without any trade at all, Home consumed eighty cloth and twenty wine. It produced a hundred and twenty cloth, gave thirty-six of them away, and that leaves eighty-four. And it received twenty-four units of wine. Watch where that puts Home. Compare the two lines. Eighty-four beats eighty. Twenty-four beats twenty. Home has more of both goods. And look where that dot is now sitting. It is outside Home's own frontier. There is no way to split two hundred and forty hours that produces that basket. Home cannot make it, but Home can have it. That dashed line is what Home can now consume. Start from the corner where it produces, and trade along it at one and a half cloth per wine. It sits above the frontier everywhere except at the corner itself. Now do the same for Foreign. Without trade it consumed thirty cloth and twenty wine. It produced fifty units of wine, gave away twenty-four, and keeps twenty-six. In return it received thirty-six units of cloth. Thirty-six cloth and twenty-six wine, against thirty and twenty before. Foreign, the country that is slower at cloth and slower at wine, the country that loses on every single line of the hours table, has six more of each. And its dot is outside its frontier too. Both of these dashed lines are consumption possibilities, and both of them lie above what the country can actually produce. So there it is. Both countries ended up with more of both goods. Nobody worked longer. Nobody got better at anything. The only thing that changed is who spent their hours on what. That is comparative advantage, and it is why the claim sounds wrong and is right. Trade is not a race. What a country sells is not its speed. It is the thing it gives up least to make. One last thing, so you know where the argument stops. Suppose the two countries had identical opportunity costs. Suppose a unit of wine cost two units of cloth in both places. Then there is no rate strictly between them. There is no price both would accept, and there is nothing to gain. The gain from trade is made out of the difference in opportunity costs, and out of nothing else.