Input approach to determining comparative advantage

- [Instructor] In other videos we have already looked at production possibility curves and output tables in order to calculate opportunity costs of producing a certain product in a certain country. And then we used that to think about comparative advantage. We're going to do something very similar in this video, but instead of thinking about, or instead of starting with output, we're gonna start with input. So right over here we have a table that shows us the worker hours per item per country. So, instead of this being an output table where we say in a given country, how much of, say, toy cars can a worker in country A produce per day? Here we're saying, how many hours does a worker in country A take to produce A toy car? In country A it is two hours. That labor, that two hours of labor, this is the input. So we're not counting the number of cars per day here. We're saying how many hours per car, A, we need to put in to produce it. Similarly, we have the input required in country A to produce a belt. One hour of worker time. In country B, four hours of worker time produces a toy car. And in country B, three hours of worker time produces a belt. So what we're gonna do next is convert this into the world that you might be more familiar with, of thinking in an output world. And to do that, we'll just assume that there are eight working hours per day in either country. And so from this, can we construct an output table? Let me put this right over here. Output table, where once again we're gonna think about the output in country A. We're gonna think about the output in country B. And this is going to be in how many units of that product can a worker produce per day in each of those countries? So once again, we're gonna have toy cars in this row, and we're going to have belts in this row. And let me just draw some lines so it's clear that we're dealing with a table here. So there we go. Then one more column. And so, see if you can fill these in. So how many toy cars per worker per day can we produce in country A? Then think about it for belts. Then think about both of them for country B. Pause the video and try to figure that out. Alright, now let's think about how many toy cars per worker per day. Let me make it very clear. We're thinking per worker per day here. Because if we can fill out this output table from this, I guess you could call this an input table, then we can think about opportunity cost in the traditional way. And then we could think about in which country do we have a comparative advantage? So, let's see. Toy cars in country A. If it takes two hours to produce one toy car in country A, and if you're working, if the average, or if the worker is working eight hours per day, well then, a worker can produce four cars. Four cars times two hours is eight hours. So, an average worker per day in country A can produce four toy cars. Let me write than in that red color. Four toy cars. I just took eight hours and I divided by the number of hours it takes to produce a toy car. Similarly for belts, if I have eight hours and it takes an hour for a worker to make one belt, then per worker per day, eight divided by one, I could produce eight belts. And we could do the same thing for country B, and I encourage you to pause the video if you haven't done so already and try to fill this column out. Well, in country B, if it takes four hours to produce a toy car per worker, that means you take eight hours divided by four hours that you could produce two toy cars in a day per worker. If it takes three hours to produce a belt, well then you take your eight hours, divide it by three hours per belt, and you're gonna be able to make 8/3 belts per worker per day. This is the same thing as 2 2/3 belts per worker per day. So as you can see, we can easily translate between the input world and the output world. And then we could use this to calculate opportunity cost. So let's do that. Let me write opportunity cost. And I'll make another table here. So country A, country B, and then I have the toy cars, and then I have the belts. Let me do the belts in that orange color. I have the belts, and then let me set up my table. We're almost there. At any point in time, pause this video and see if you can figure out the opportunity cost given the information that we already have. We took this table to figure out this table, and now we could take this table to figure out this one. Well, let's do this together now. So, toy cars. What's the opportunity cost in country A? Well, one way to think about it is in country A, the same energy to produce four toy cars, I'll call it four c, c for cars. We could also use that to produce eight belts. So, if I were to divide both sides by four, the energy to create one car is equal to the energy to create two belts. So my opportunity cost of a car is two belts. And if I start with this original equation and just divide both sides by eight, I would solve for the energy for a belt. And so that would be four over eight is 1/2 of the energy to make a car is equal to the energy to make a belt. And so the opportunity cost of a belt is 1/2 a car. 1/2 a car. And like always, this and this are reciprocals of each other. And we could do this same exercise for country B. And once again, I keep emphasizing, try to pause the video. If you do this on your own as opposed to just watching me do it, it'll stick a lot better in your brain. Alright, in country B, the same energy to make two cars, toy cars, with that same energy I could make 8/3 belts. 8/3 belts right over here. So the energy to make a car, divide both sides by two, is equal to, instead of one car I can make 4/3 of a belt. And so I'll just write this as 1 1/3 of a belt. And then if I start right over here and I multiply both sides by 3/8, actually, let me do that over here. So I have 3/8 times two c is equal to 8/3 b times 3/8. These cancel out. And over here I'm gonna have 6/8 c. 6/8 c is the same thing as 3/4 c is equal to b. So, instead of making one belt, I could take that same energy and make 3/4 of a toy car. 3/4 of a toy car. So given everything that we've just done, which country has the comparative advantage in toy cars? Well, to figure that out, we just look at the opportunity cost for toy cars and we compare them. In country A, the opportunity cost is two belts while in country B it's only 1 1/3 belts. So country B has the comparative advantage right over here. Comparative advantage in toy cars. And then in belts, 1/2 of a car is less than 3/4 of a car. In belts, we see that country A has the comparative advantage. And now what's always interesting about thinking about this is notice, country B has the comparative advantage in toy cars. It has less of an opportunity cost in toy cars. Even though country A has the absolute advantage, its workers are more efficient at producing toy cars. A worker can produce four cars in country A versus two in country B. But despite that, because of the opportunity cost, it would actually make sense for country B to focus on cars and for country A to focus on the belts. But the big picture here is we're thinking about comparative advantage. And instead of thinking about with an output lens from the beginning, we started with an input lens, converted that to an output lens, calculated opportunity cost, and then was able to figure out which countries had a comparative advantage in which products.