Comparative advantage and usefulness of models

Since I still haven’t set up LaTeX, this time we’ll do some economics. Let’s consider two countries, which we will call England and Portugal (any coincidences are accidental). England produces 1 unit of wine per worker per day, Portugal produces 2 units of clothes per worker per day. We can represent this in a table:

England Portugal
Wine 1
Clothes 2

It makes sense that given this setting England will sell wine to Portugal and Portugal will sell clothes to England. Both countries benefit from this. We may also try to draw some simple conclusions from this. For example, one may suggest that the price of a unit of wine would be approximately twice the price of clothes.

It is easy to see this. Let’s assume that the price of a unit of wine is $50, but the price of a unit of clothes is $20. It means that one worker in Portugal makes $40 a day, but one worker in England makes $50 a day. There is an incentive to move from Portugal to England to make $10 more, so if this move is easy enough, quite soon not many people would produce clothes, so the price for clothes will go up. We can make a similar argument if the price of wine would be less than twice the price of clothes.

The reality is more complex than this model. We have to take into account not what one particular worker can produce, but what a whole factory can produce. We also have to consider the cost of production, taxes, salaries and many other factors. All of these doesn’t change the theoretical output of the model much: substitute “a worker moved” to “company moved its business” and you will get exactly the same argument about price balance as above. I’ll keep talking about the productivity of separate workers below just to make an explanation a little bit more accessible, but all of what I am going to say can be made more precise.

Let’s make our model more complex. Now both countries produce wine and clothes (here and below we assume the equal quality of products), but the productivity is not equal:

England Portugal
Wine 1 3
Clothes 3 2

I think this is obvious that in this case England would sell wine to Portugal and Portugal would sell wine to England. At this point, prices will be considerably more complicated, but we are not interested in it. The only important point here is that both countries would trade for the mutual advantage.

Let’s consider this situation:

England Portugal
Wine 1 5
Clothes 3 4

Now Portugal is much better at producing both goods. There is no way for England to export products since both wine and clothes are more expensive to produce in England than in Portugal. At the same time, Portugal could sell its products to England, but England wouldn’t be able to afford to pay for these products. If you want to buy something, you first have to sell something, and as we understood, England is not selling anything. It seems that England is in a dreadful position where either all of the business would move to Portugal or the trade between these countries will be banned and England would just have higher prices and lower quality of life.

In 1817 David Ricardo rightfully challenged the argument which I proposed above with the following example (he used England and Portugal as well). Let’s say that one worker in Portugal switches from producing clothes to producing wine. Portugal’s market will have 4 units of clothes less, but 5 units of wine more. Then two workers in England switch from producing wine to producing clothes. After this England has 6 additional units of clothes and 2 units of wine less.

Now, these two countries can actually trade. If Portugal sends 3 units of wine to England, while England sends 5 units of clothes to Portugal, both countries benefit from this trade. See in a table:

England Portugal
2 workers switch: 1 worker switch:
-2 wine, +6clothes +5 wine, -4 clothes
Sell 5 clothes to Portugal: Sell 3 wine to England:
+1 wine, +1 clothes +2 wine, +1 clothes

It is surprising, isn’t it? We’ve made an additional 3 units of wine and 2 units of clothes for these two countries to share by using trade in a situation where any trade seemed impossible.

Here is what’s going on. It is true that Portugal has an advantage in each of the industries,  but the relative productivity of producing clothes is still higher in England than in Portugal. England is 3 times more efficient in producing clothes than wine, but Portugal is just 1.25 times more effective in producing wine, so switching from producing wine to cloth in England is more efficient than switching from cloth to wine in Portugal. This difference in productivity actually makes it feasible for these countries to trade for a mutual benefit.

This argument was widely used as a ground for international trade. I hope that I was able to convince you that this is actually beneficial. Now let’s look at the slightly more realistic example:

Somalia Switzerland
Computers 1 5
Potatoes 3 4

Now it should be clear that comparative advantage would make the poor country focus on agriculture, while the developed country will focus on hi-tech. This way the poor country has no chances of getting out of poverty, while the rich country is only getting richer. The trade deal which looked perfect in the case of England and Portugal above became a disaster when applied to poor and rich countries.

What does the Ricardian model teach us? Is it good to trade or is it bad? Does the model of Ricardo even work? In most situations it doesn’t give any concrete answers (although it still can be used by politicians, those folks can use any kind of tricks anyway) as well as it doesn’t model well real-life situations. It has too many implicit assumptions which make it difficult to apply. First of all, the model considers only two countries and two products. It doesn’t take into account the demand for these products, cost of transportation, competition on the local market and dozens of other factors. There were many attempts to make this model more realistic, but I am not sure if any of these attempts could be called successful.

Should we throw this model away? Not exactly. Even though it doesn’t work quite well, this model is non-obvious and no one before Ricardo was able to think about the trade from this point of view. Even though this model doesn’t give us many answers, it motivates us to ask many interesting questions, which weren’t asked before this model was proposed. This model fueled follow-up research for centuries. It still can be applied in some very limited context, since this model is still logically sound. And some people think that the model still can be refined to the point when it can be applied directly.

Here’s an important lesson: the good model is not necessarily the one which reflects reality well. Other not so easily measured qualities of a model such as the ability to raise new questions may be even more important than the correctness of the model itself.

This applies not only to mathematical models. Newtonian mechanics is incorrect and works only under very specific conditions of ridiculously low velocities of Earth life and only within measurement error. This doesn’t make Newtonian mechanics bad–it has actually proved to be quite useful for almost all of the engineering so far.

Another example is Godel’s proof of god’s existence. The proof was based on so shaky foundations that Godel himself didn’t even try to publish it during his lifetime. And even though the foundation of this work appeared to be incorrect, this proof inspired serious development in mathematical logic and even affected research of Artificial Intelligence.

The most recent example of this kind which actually motivated this post is Theodore Hill’s  “Evolutionary Theory for Variability Hypothesis”. In short, the model explains mathematically that there are more idiots as well as geniuses among males than among females. The work is based on extremely shaky foundations and the model is incorrect for sure at least in case of the human population, but it doesn’t make the model bad! Actually, quite opposite: the model is still logically sound, the shaky assumptions can be potentially refined in the future and even if it appears that the model cannot be fixed at all, it can potentially raise questions which weren’t asked before.

Unfortunately, in this particular case, the refinements wouldn’t be made and questions wouldn’t be asked because the paper was effectively banned. What is so wrong with the model that it has to be banned? All the arguments are purely political: this result can be used by right-wing propaganda, the result can discourage women from going into tech, after all, it doesn’t match with the idea that men and women are equal. No purely scientific arguments against this paper were presented, but the political ones were enough for the ban. Unfortunately, this is not the first time when scientific results got banned based on political grounds. This is harsh to say, but I cannot resist comparing this situation to the suppressed research of genetics, informatics and other fields in the Soviet Union and with Aryan Physics in Nazi Germany. I would really like to provide other examples instead of these two, but it seems that in the modern world other examples of banning science just doesn’t exist. The case of Hill’s model is just the third such case in modern history. I hope this situation wouldn’t go so far, but the direction which the western academy has taken is worrying.

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