Trade: absolute and comparative advantage

Why do we trade at all? To answer this question I'll introduce absolute and comparative advantage.


Absolute advantage
Imagine there are two persons A and B who produce product X and Y. One is faster at producing product X and one is faster at producing product Y. Assume these are their productivities for a day's labor, if they produced either product X or product Y:



If they both spent half their day producing product X and half their day producing product Y, their gains would look like this:



A better way of going about things would be if they each produced what they are faster at, and then traded at the end of the day; person A produces X, and person B produces Y:



Then they trade their properties at a rate of 1 to 1:



If we compare this result with the result of producing only for themselves and not engaging in trade, we can see that they are both better off. Person A has three Y where he otherwise would have had two, and person B has three X where otherwise he would have had two.

This solution was rather straightforward. Can we still benefit from trade if the parties don't have an equal advantage over each other?


Comparative advantage: example 1
In this situation, person A can produce more of product X but also more of product Y:



If they would produce for themselves and split up their day in half:



Now let's say that they again both produce what they are best at. Person A produces X and person B produces Y:



Now person A trades in one X for one Y. Person B is then already better off than he would have been if he produced for himself, and person A still has some X to trade for:



So person A trades with another person C who was in a situation like B:



And person A trades with a third person D again in the same way. Now persons B,C and D are all better off, and person A is also better off than if he wouldn't have traded at all. He now has three Y where he otherwise would have had two:



Can we still benefit from trade if the parties are both best individually at producing the same good?


Comparative advantage: example 2
In this situation, person A can produce more of X than of Y, but person B can also produce more of X than of Y:



To benefit from trade, person A must gain X or Y at a better price than he can make himself.



Let's say person A and B both produce what they are best at, compared to each other. Person A is three times (6 divided by 2) as fast at producing X and four times (4 divided by 1) as fast as producing Y. So person A produces all Y where his comparative advantage is the greatest, and person B produces all X where his comparative disadvantage is the smallest:



Say person A gives up his Y at the same price as it costs him to produce no X, which is at a ratio of 6 X to 4 Y. So he gives up two thirds X for every one Y that he receives:



And he trades at the same price with person C:



And again with person D:



Now persons B,C and D are all better off. They can produce two X for every one Y. But they traded their X for a better price than 2:1, namely 2:1.333 (or 1:0.666). Person A is now the same off as if he would have produced all for himself. But person B can still lower his price so that all can benefit from the trade; as long as the price remains in between their personal rates of production (more than 0.5 Y for every one X and less than 0.666 Y for every one X).


Increasing productivity
As you saw in the example, being highly productive can be rewarding, especially if you can trade. Another way to increase your wealth is to create products of higher quality, or those that are more rare, so that people may be willing to give up more things for it.

The way this happens is as you focus on one specialty, you get more experience and knowledge about the subject. You can avoid overhead time. In the example we used half and half to divide up the time and calculated half the productivity with it. In practice this is not attainable. For example, if your products are fish from the sea and apples from the woods, and you have to walk an hour to the sea and back and an hour to the forest and back, then you cannot attain your maximum hourly productivity. Because if the day was only four hours long, all you could have done is walking, whereas if you had only done one of the tasks, you would have some fish or some apples.

If you save (don't consume all that you produce), then you can use those resources to buy new tools and become more productive. Or you can consume saved resources as you build your own production technology.

All of this overcomes the cost that trading brings with it as well.


The real world
If we look at the real world we see that people's productivity shoots way up as people dedicate their whole career on a specialty or on a focused number of skills.



One person may be a chef and own his own restaurant. He could also use those skills in management alone, but when he combines those skills in cooking his productivity is highest. Another person may specialize in management, and also be reasonable at cooking, and could theoretically teach tennis to children. Roger Federer is very skilled in tennis and has dedicated his whole life to it. He could earn a starter wage at a fast-food restaurant but it really doesn't matter as he has become so good in another valuable skill. Pavarotti may earn more than Federer in one day, but he probably doesn't get to perform as often, so Federer may earn more overall. He may also be a decent cook, but because he does what he does best and does it well he can afford to work less often, if he wishes.

All these people produce almost entirely for the consumption of others. The exercise is to look at the market and predict what people will value, and produce it.