Tuesday, April 26, 2022

One of the Oddest Posts I've Ever Written (Not Required)

SE was in one of my principles sessions during Fall 2020. It was on Zoom. A lot of you were in those Zoom classes: TB, EC, BH, AH, TH, IP, BU, AW, CY (and probably others I can't recall).

He asked a question on 11/24/20 through chat rather than audio. I saw it, but thought it took some extra consideration, and told him I'd answer it later on.

So I took a screen capture, and promptly lost the image somewhere on my hard drive.

And would you believe I've felt bad about that ever since? I can even remember telling him as that semester wound down that I'd answer that question, while covering up for the fact that I couldn't find it, and hoping that I would.

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There's a wicked search tool you should all have on your PC's. It's called Everything, it's made by VoidTools, and it's freeware. (Ninite also has it, if you use that service).

While searching for something with the word emblem in it on Saturday, I got halfway through the word, and up in my search results popped an image with SE's last name.

I opened it up, and there was his missing question from 17 months ago.

***

Now I feel obligated to answer it. We were doing comparative advantage examples, and he asked:

I'm not sure I quite understand the question anymore. But here goes.

First, in the real world that whole "whoever can produce more" goes right out. Small countries do get comparative advantages, and they do specialize in them successfully. But big countries are so much bigger (see Chapter VI in the Handbook) that a source of comparative advantage for them is sometimes that the global market is so big that a bunch of it gets filled by the big players even if they don't have comparative advantage. This is why a place like the U.S. has someone somewhere making pretty much everything.

But I think SE was asking about textbook examples, so let's work that out.

Consider the two region two good case: Iowa and Nebraska producing corn and wheat. So you need 2 pair of numbers (one for each good) to work out a comparative advantage problem. There are 4 possibilities for those numbers.

The numbers in both pairs are ties.


Corn Wheat
Iowa 2 3
Nebraska 2 3

In the above case, no one has a comparative advantage, so the example is irrelevant to the question.

The second case is that number in one pair is tied. But in the other pair, one of the regions, say Iowa, has a higher number: so Iowa has an absolute advantage at wheat.


Corn Wheat
Iowa 2 4
Nebraska 2 3

If you work out this table, then Nebraska has the comparative advantage in corn (and Iowa in wheat). Now I'm not sure what to write. The question says "Unless one country has an absolute advantage ...", but Iowa does, so I'm not sure if that means the question  doesn't apply here. But the second part is right: the comparative advantage does go to the one with the bigger number.

The third case is that neither pair is tied, but the higher value in one pair is for Iowa, and the higher value is for Nebraska in the other pair.


Corn Wheat
Iowa 2 4
Nebraska 3
3

You can actually prove that this third table is a special case of the second one, and the pattern of trade is the same. I have the same problem with the question though, since now we have two absolute advantages.

The last case is that neither pair is tied, and one region, say Iowa, always has a bigger number, and, the proportions in the rows are not the same.


Corn Wheat
Iowa 3
4
Nebraska 2 3

In this one, there's two possibilities. With the numbers above, Iowa has the comparative advantage in corn. But if we slowly increase that 4, eventually the pattern will shift so that Iowa has the comparative advantage in wheat (and the same sort of thing could happen if we changed the other numbers too). So in this one, the comparative advantage does not always go to the bigger number.

I think the lesson here is just to always work out comparative advantage because it's just not that easy to eyeball the numbers and get it right.

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