Square Root Day

Last week's question: Why is comparative advantage defined between people and countries, but not between units such as counties, states, or continents?

The question is actually slightly deceptive. I asked it to get at another point, because simple answer is easy: there are more people looking at production of countries and people than the production of counties or continents.

I also noticed that last week's post was incorrectly titled; I was originally thinking about production possibility frontiers, but then sliped into comparative advantage and forgot to change the post name.

By to the topic at hand, I am troubled by the idea of comparative advantage. There seems to be a problem of scale which needs to be addressed. Let's say, for example, that Iowa and Wisconsin both produce cheese and corn. Even if one state is better at doing both, the theory of comparative advantage says they should specialize and trade instead, because that will increase the total yield of corn and cheese combined.

But now, let's switch to a country level view. US and China may both produce corn and cheese, and again the theory says they should specialize and trade to maximize output, regardless of how much they can produce.

So what happened to the state level loss? If the US specializes in corn, in Wisconsin in particular there will be a lost of opportunity cost. Similarly, if the US specializes in cheese, Iowa will incur an opportunity cost. That is, all else being equal, the total production would be higher if the level of production was measured at a smaller unit. If Iowa could trade with a province in China for cheese, and that province can produce cheese cheaper than Wisconsin can (assuming similar quality), then the specialization makes sense.

The smaller the unit, the higher the total production. This argument leads to a human level comparative advantage. You might be an excellent painter and sculpture, but if your painting is better, you should paint rather than sculpt, and buy other people's sculptures. Logically, then, comparative advantage argues that everyone only do what they do cheapest comparative to other people. In addition, direct people to people trading generates the largest total production.

I guess my question (privately, not the question of the week) is, why are we analyzing economics through countries? It would make more sense to analyze by industry - all the corn growers vs. all the cheese makers and how much they trade.

I know, I know, people care more about countries than industries. But it makes more sense to do it.

This week's question: 2009-03-03 was called "square root day" by many, presumably because 3*3 = 9. How often does square root day occur? What about higher order roots?