Input approach to determining comparative advantage | AP Macroeconomics | Khan Academy

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. Then we use 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 going to start with input.

So right over here, we have a table that shows us the worker hours per item per country. 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 of 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 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 produce a belt.

What we're going to do next is convert this into the world that you might be more familiar with of thinking in an output world. To do that, we'll just assume that there are eight working hours per day in either country.

So from this, can we construct an output table? Let me put this right over here. Output table, where once again we're going to think about the output in country A; we're going to 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 going to have toy cars in this row, and we're going to have belts in this row. Let me just draw some lines so it's clear that we're dealing with a table here. There we go, and then one more column.

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.

All right, 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. Then we could think about in which country 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 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 that 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 the belt, 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.

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 going to be able to make eight-thirds belts per worker per day.

This is the same thing as two and two-thirds belts per worker per day. So as you can see, we can easily translate between the input world and the output world. 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, 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? 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. If I start with this original equation and just divide both sides by eight, I would solve for the energy for a belt.

So that would be four over eight is one-half. The energy to make a car is equal to the energy to make a belt. Thus, the opportunity cost of a belt is one-half a car, one-half a car. Like always, this and this are reciprocals of each other.

We could do the 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.

All right, in country B, the same energy to make two toy cars—with that same energy, I could make eight-thirds belts, eight-thirds 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 four-thirds of a belt.

So I'll just write this as one and one-third of a belt. Then if I start right over here and I multiply both sides by three-eighths—actually, let me do that over here.

So I have three-eighths times two c is equal to eight-thirds b times three-eighths. These cancel out, and over here I'm going to have six-eighths c. Six-eighths c is the same thing as three-fourths c is equal to b.

So instead of making one belt, I could take that same energy and make three-fourths of a toy car, three-fourths of a toy car. So given everything that we've just done, which country has a comparative advantage in toy cars?

Well, to figure that out, we just look at the opportunity costs for toy cars and we compare them. In country A, the opportunity cost is two belts; in country B, it's only one and one-third belts. So country B has the comparative advantage right over here: comparative advantage in toy cars.

Then in belts, one-half of a car is less than three-fourths 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. Instead of thinking about it 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.