Terms of Trade and the Gains from Trade | AP Macroeconomics | Khan Academy

Let's imagine a very simple world, as we tend to do in economics, that has two countries that are each capable of producing either pants or shirts, or some combination.

So, what we have here are the production possibility curves for each of those countries, and this is in per worker per day. For example, in country A, per worker per day, they could, if they put all of their energy into pants, produce 20. If they put all their energy into shirts, they could produce 10, or there could be some combination that would sit on this line.

Now, to help us digest the production possibility curves for these two countries, let me construct an output table. This will be this column for the output for country A, this column for the output for country B, and we're going to think about the maximum number of pants, the maximum pants, the maximum output of pants per worker per day. The input is the worker per day, and then let's think about the maximum number of shirts.

Pause this video and see if you can fill this out. What are the max pants and shirts in country A and country B? One country I already talked about is that the maximum pants is 20, 20 pants, and then the maximum shirts if they didn't make any pants are 10. In country B, the maximum pants are 30, and the maximum shirts, it looks like that is about 45.

Now, from either these production possibility curves or from this output table, because we have a constant opportunity cost, these production possibility curves are straight lines with a fixed slope. We can calculate the opportunity cost, so let's do that next.

So this is country A, and then this is country B. Let me calculate the opportunity cost of pants, and let's calculate the opportunity cost of shirts. So pause this video and see if you can figure that out. What are the opportunity costs of pants and shirts in countries A and B? Fill out this table.

Well, one way to think about it in country A, I could put all of my energy into pants and produce 20 pants, or I could put all of my energy into shirts and produce 10 shirts, 10 shirts (s for shirts, p for pants). If I want the cost of pants, I could just divide both sides by 20, and I would get pants.

The amount of energy per pant is equal to, well, 10 divided by 20 is one half a shirt. So the energy for a pant is one half for is the same as the energy for half a shirt. We could say the opportunity cost of producing a pant is half a shirt. If we want the opportunity cost for shirts, we could take the reciprocal of this number. We could say it's going to be 2 over 1 pants, or we could start with this equation right over here and instead of solving for p, we could solve for s.

How much energy in terms of pants does it take for us to produce one shirt? If you divide both sides of this equation by 10, you would get 2p is equal to s. Another way of thinking about it, the energy to create one shirt is equal to the energy to create two pants. So the opportunity cost of producing a shirt is two pants.

Now let's also fill it out for country B, and if you haven't done so already, try to use the same method to fill this in, the opportunity cost for pants and shirts for country B. Well, in country B, I could put all of my energy into pants and produce 30 pants, or all of my energy into shirts and produce 45 shirts.

So the opportunity cost per pant, if I divide both sides by 30, it would be 45 over 30, which would be equal to— they're both divisible by 15—three halves of a shirt. The energy for one pair of pants is the same as the energy for one and a half shirts, I guess I could say.

So let me write it that way. The opportunity cost of pants is, for each pair, I'm giving up one and a half shirts. Then, in the opportunity cost for shirts, well, I could just solve for s here. If I divide both sides by 45, I get the same energy for one shirt would be thirty forty-fifths of a pair of pants, which is the same thing as two-thirds of a pair of pants.

So I could write that as two-thirds of a pair of pants, or if I wanted, let me just write it that way, two-thirds of a pair of pants. So, given the opportunity costs, what should each of these countries focus on? Pause this video and try to figure that out.

Well, let's first compare their opportunity costs in pants. It is clear that country A has a lower opportunity cost for producing a pair of pants; it's only giving up half a shirt, while country B is giving up one and a half shirts. So, country A has the comparative advantage right over here, so comparative advantage right over here in pants, and so it should focus all of its energy, according to the theory of comparative advantage, on pants.

Likewise, if we look at shirts right over here, if we look at their opportunity costs, country B is only giving up two-thirds of a pair of pants, while country A would be giving up two pairs of pants. So country B has the lower opportunity cost or the comparative advantage in shirts. Therefore, country B should put all of their focus here on shirts.

Now, I know what you might be thinking: people can't just walk around wearing only shirts. That might make people cold below their waist, or people don't want to only wear pants; they might get cold above their waist. So how can people in these countries get the other type of garment?

Well, the obvious answer is if they focus in this way, they can trade. What would be an acceptable trading price? Let's say for pants, let's focus on pants for a second. If we're thinking about the market for pants, what would you be willing to sell pants for, in terms of shirts?

Well, a good price, so to speak, would be something higher than your opportunity cost. So you're willing to sell pants at a price—I'll put that in quotes because we're really thinking of price in terms of another good—at a price greater than their opportunity cost, greater than one-half of a shirt. You could think of this as willing to trade or sell.

Likewise, what about country B? Well, B is willing to buy pants; they need pants. Otherwise, they would just be walking around with only shirts on. They're willing to buy pants at a price less than their opportunity cost for pants, and so that would be less than one and a half of a shirt.

So what would be a price that is greater than half a shirt and less than one and a half shirts? Really, any price in between these two values would work. A nice round number is that they could trade at one pair of pants for one shirt.

Now, let's appreciate the gains from trade that they would both have here. Let's imagine this world where country A is producing 20 pants per worker per day, but let's say they decide that they want, instead of those 20 pants, to trade 15 of them away for shirts.

They would get, at this price, 15 shirts. So they're going to give up 15 pants. They'll only have five pants right over here, but they're going to get 15 shirts. So they're going to get 15 shirts, and they're going to end up right over here. This is where country A is going to end up.

What's cool about this is we've gone beyond the production possibilities curve. You see very clearly the gain from trade. Country A could not have gotten to this point on its own; this is above the production possibilities curve. Likewise, country B was over here with 45 shirts. It gave up 15 of those shirts; it now has 30 shirts but now has 15 pants. At least some of the people in the country are going to be able to wear pants now, so it now has 15 pants.

Once again, it too is in a point beyond its production possibilities curve; it would not have been able to get here without the trade. So they are both better off.

The key takeaway from this video is that we now appreciate why comparative advantage is valuable. Once again, making all the assumptions for these simplified economic models, we can calculate our opportunity costs from that comparative advantage and then think about what's a good price that they'd be willing to trade at. We can see that when they trade, they both are able to get beyond their production possibilities curve.