### Pop Quiz

Commenting on this essay by former Intel chief Andy Grove, Tyler Cowen writes that “Only he who first shows he understands comparative advantage has license to partially reject it.”

Hear hear. When someone says “I understand comparative advantage, but in this case it doesn’t apply”, or “I understand comparative advantage but in this case it is overridden by other considerations”, my experience tells me that you can be nearly sure you’re talking to someone who does not in fact understand comparative advantage.

If I were permitted to write a licensing exam for economic commentators, I would surely incorporate a standard textbook exercise or two on this subject. Being lazy, I’d probably lift them from an existing textbook. For example:

Suppose that an acre of land in Iowa can yield either 50 bushels of wheat or 100 bushels of corn, while an acre of land in Oklahoma can yield either 20 bushels of wheat or 30 bushels of corn.

Which state has the comparative advantage in growing wheat? Which state has the comparative advantage in growing corn?

Suppose the residents of each state consume 200 bushels of wheat and 360 bushels of corn. If, instead of pursuing policies of self-sufficiency, each state specializes in its area of comparative advantage, how many acres of Iowa and Oklahoma farmland are freed up for other uses?

Anybody? Bueller? Grove?

#### 48 Responses to “Pop Quiz”

1. 1 1 Bennett Haselton

Well I think the way it’s phrased here might leave some people scratching their heads :) because you asked “how many acres of Iowa and Oklahoma farmland are freed up for other uses”? But “freed up” relative to what situation? (OK, it says “instead of pursuing policies of self-sufficiency”, but it may not be clear that the question is asking for a comparison between these two situations.)

The version of the question in the textbook (which I have) is more clear: First, calculate how many acres each state would have to devote to agriculture, IF they both had to be self-sufficient. Then, allow each state to specialize in their area of comparative advantage, and ask how much farmland is freed up as a result, compared to the original scenario of self-sufficiency.

2. 2 2 EricK

The reason the wheat/corn example works is that presumably a corn farmer can switch to becoming a wheat farmer and vice versa. When the two goods are, say, designing innovative products and working in the factory which makes those products, we are in a different situation. If one country has a comparative advantage in design and the other has a comparative advantage in manufacture, what happens to the people in the former country who are good at manufacture but terrible at design? Presumably they should all emigrate to the latter, with a similar wave of migration of good designers/bad manufacturers in the other direction.

3. 3 3 Peter

If an existing textbook costs \$180, while David Friedman’s is free online, then where do you have a competitive advantage?

My tentative answer: Iowa would need 7,2 acres of land to supply corn for both states (freeing up 0,8 acres in the process); while Oklahoma would need 20 acres to supply wheat for both (freeing up 2 acres).

5. 5 5 Harold

I get 29.6 and 27.2, but I haven’t checked my results.

I am not convinced by Groves “Figure A”, supposedly showing that the cost per job has risen from a few thousand to a hundred thousand today. The trend does not look all that clear, there are few data points at “recent” times, they are of very diverse industries,it ignores jobs created in other companies (such as Foxconn), and trends could easily be introduced by converting everything to todays dollars.

However, his main point is that scale-up and manufacturing provide more value to a country than simply the value of goods provided. there is a “knowledge premium”, which may not go to the original company, so they will have no incentive to invest in it.

Obviously, if this added value does not go to America, it will go to somewhere else, say China, so it is not lost. But lets say we are more concerned with American welfare than Chinese welfare (perhaps not Steve, but just for the sake of argument). Lets also suppose that America will benefit most if this added value were to stay in America.

If we say USA is Oklahoma and China is Iowa. Manufacturing is Corn and starting-up companies is Wheat. Overall, it is more efficient if USA does Wheat (start-ups), and China does corn. America gets an extra 2 acres to do something else with. However, lets say that the knowledge gained by growing corn provides an extra value above growing wheat. In 10 years time, this knowledge would be worth the equivalent of 30 acres of land. It would be worthwhile for Oklahoma (USA) to use some of its land for growing corn (manufacturing), so it can get a share of the added value. If you can demonstrate that the added value is greater than that of the land used for corn, then does it not make sense for the Govt. to susidise companies to grow corn?

It may not be realistic that the added value would be this much, but if it were, would this not justify Grove’s thesis?

6. 6 6 Stephan

@Harold
Me too.

Iowa: Opportunity costs for 1 bushel wheat 2 bushel corn. For 1 bushel corn 1/2 bushel wheat. Oklahoma: Opportunity costs for 1 bushel wheat 3/2 bushel corn. For 1 bushel corn 2/3 bushel wheat.

Thus Iowa specialises in corn and Oklahoma in wheat. The rest follows.

7. 7 7 Al

Oklahoma has the comparative advantage growing wheat.
Iowa has the comparative advantage growing corn.

Pursuing policies of self-sufficiency Iowa needs to dedicate 4 acres to growing wheat and 3.6 acres to growing corn for 7.6 acres total farmland; Oklahoma needs to grow 10 acres of wheat and 12 acres of corn for 22 acres total farmland.

They can both do better by dedicating themselves to the appropriate crop (Oklahoma to wheat and Iowa to corn) and trading. If they pursue such a policy of specialisation Iowa will dedicate 7.2 acres to growing solely corn (freeing up 0.4 acres) and Oklahoma 20 acres to growing solely wheat (freeing up 2 acres).

8. 8 8 Harold

Of course, you can free up a total of 14 acres if Iowa grows all the corn AND wheat.

9. 9 9 Mike

I got 29.6 for the isolated production in each state and then 26.6. No acreage is gained in Iowa and 3 acres are gained in OK. If we specialize to the point that Iowa ONLY produces corn and Oklahoma only wheat then the 27.2 number that Harold got is correct.

10. 10 10 Dave

Harold I get 14.4 saving if Iowa does both.

That annoys me….didn’t think of that.

Does that somehow negate some of the so defined benefits of trade under comparitive advantage?

ie it would seem for the most efficient outcome, Iowa would have to be altruistic and grow all the required crops for everyone and donate the excess to Oklahoma?

11. 11 11 Dave

My above comment assumes that Oklahoma produces nothing to trade with Iowa under this model. Iowa could of course lend Oklahoma the money required to buy the crops which in turn “creates” jobs for Iowans and in the Keynesian world, everyone wins. Oklahomans could stupidly declare that Iowa needs Oklahoma more than Oklahoma needs Iowa because Oklahoma is doubling the employment of Iowa.

12. 12 12 Dave

Mike – how do you get 26.6?

13. 13 13 Harold

I presume that Oklahoma would use the freed up land to produce something to trade with the Iowans. If they could not do this, then presumably the Oklahomans would all move to Iowa to work on the farms there.

14. 14 14 Dave

Thanks Harold – does that mean that in a world of complete free migration, comparitive advantage becomes irrelevant and people just move to where there is an absolute advantage?

15. 15 15 Douglas Bennett

Dave-

Since Iowa is now using more of its land for farming in that scenario, Oklahoma could rent some of its newly freed up land to the Iowas for apartments, casions, and waterparks. Or it could build factories and produce farming equipment to sell to Iowans, or any number of other things (pick any 2 other economic activities and again one will have a comparative advantage over the other. Even if one state is, in absolute terms, better than the other at everything, the Oklahomans’ land will still get used for something more productive than in the self-sufficiency case, and likewise for the Iowan land). The key is that if Iowa does all the farming, Oklahoma is the one with all the extra land, which it can now use for some other productive activity, the proceeds of which will presumably be traded to Iowa for food.

16. 16 16 Douglas Bennett

Iowans, casinos… I apologize for my spelling!

17. 17 17 Harold

I suppose that there would be nothing grown in Oklahoma until Iowa can no longer supply enough to meet total demand. This assumes free migration and no transport costs. So I suppose the camparitive advantage is only significant if total demand is greater than can be supplied by the place with the absolute advantage. That is, if there are so many people in Iowa and Oklahoma that you cannot feed them from Iowa alone, then you are better off to stick to growing only wheat in Oklahoma.

18. 18 18 Dave

Apologies for the multiple posts on this but this has gripped me.

Douglas – thanks for your response. I get what you are saying but in the simplified model, there is nothing left to produce or consume. In the complex model, everything is produced in Iowa. Maybe replace “Iowa” with “Earth” and Oklahoma with “The Sun”. Makes sense for the inhabitants of Earth to produce everything and if there are no immigration laws, any of the Sun’s inhabitants should move to Earth to produce there?

19. 19 19 Harold

This is basically why there are very few people living in deserts.

20. 20 20 Dave

Which brings me back to my question: in a world of complete free migration, does comparitive advantage become irrelevant? Or maybe I’m not getting the definition of “comapritive advantage” enough (it’s been 10 years since I studied this at uiniversity).

21. 21 21 Ken B

He with the lower opportunity cost to produce more of X has the comparative advantage in X.
Opportiunity cost is what you must forego; in this case it is the other crop you
do not grow.
So let’s see. Wheat first.
What is the opportunity cost of an extra bushel 50 B of wheat?
In Iowa you move 1 acre from corn to wheat; cost 100 B corn.
In OK it takes 2.5 acres moved, cost 75 B corn.
The relative cost is lower for OK so OK has the comparative advantage in wheat.
So logiaclly we now we know Iowa must have the comparative advantage in wheat but I
will do the calculation explicitly.
What is the opportunity cost of an extra 100 B of corn?
In Iowa it means 1 acre moved from wheat, cost 50 B wheat.
In OK it takes 3.33 acres moved from wheat, cost 66.67 B wheat.
Iowa has the lower opportunity cost so has the comparative advantage in corn.

Note that Iowa corn/wheat = 2 and OK corn/wheat = 1.5. You can get the answer more directly from this

SL’s other question is ill-posed. 200 total or per capita? These lead to very different answers.

22. 22 22 Scott F

@ Harold/Dave/Douglas Bennett story
Let me get this straight…
So we make Iowa make all the crops… Oklahoma either produces farming equipment or is abandoned for Iowa… at which point I take the crops to a windowless “factory” on the west coast that has a special machine which turns the crops into say… Toyota’s. It also happens to have ships constantly going back and forth to Japan but we can assume that’s irrelevant. Now, we can study the comparative advantages of Iowa, Oklahoma, and Japan. And then attempt to explain it to an ex-employee of GM as he cries his sob story to a journalist through the window of his new dirt-cheap Corolla.
Dr. Landsburg, I would love to hear a blogged retelling of the wheat to cars story… with any relevant twists and applications to modern policy woes that you can conjure. Please.

23. 23 23 Al

@ Ken B

You’ve made a typo, where you say
“So logiaclly we now we know Iowa must have the comparative advantage in wheat but I will do the calculation explicitly.”

You mean:

“So logically we now we know Iowa must have the comparative advantage in CORN but I will do the calculation explicitly.”

24. 24 24 Mike

I got 26.6 by Iowa producing all of the corn (which is most efficient) using 7.2 acres to do so. Iowa then has another .4 acres available (because if it was self-sufficient previously it was using 7.6 acres total). I use that .4 acres tp produce 20B of Wheat. I then only need to produce 380B of Wheat, which takes 19 acres in Oklahoma.

25. 25 25 Dave

KenB – thanks! Realised I didn’t even remember how to spell “comparative”.

I’m still stuck on the point though that if there is no free migration, there are benefits to trade. But if there is free migration, then the benefits to move should outweight any benefits to trade (in an oversimplified world).

26. 26 26 Ken B

@Al,
Yes you are right, a ‘typo’ to be kind. ‘Temporary brain death’ is anothe term I like.

27. 27 27 Seth

I agree with other answers. OK has the comparative advantage in wheat, IA in corn. 0.2 acres would be freed up in IA and 2 acres in OK.

“Of course, you can free up a total of 14 acres if Iowa grows all the corn AND wheat.” Harold

Not in IA. Iowa would use 7.6 more acres to meet demand for both states. But, how would we see to it that Iowa would provide OK what it demands when the people of OK have nothing to offer in return?

Not sure I buy your free migration argument. Why wouldn’t someone stay in OK if they can get what they need there simply by growing and trading. In fact, the results illustrate just that. It’s mutually beneficial for them to do so.

28. 28 28 Dave

Seth:

“Not sure I buy your free migration argument. Why wouldn’t someone stay in OK if they can get what they need there simply by growing and trading. In fact, the results illustrate just that. It’s mutually beneficial for them to do so.”

because they can spend a day in OK and yield 20 bushels of wheat, or move to IA and spend a day yielding 50 bushels of wheat.

It’s why Mexicans try to move to USA (for now).

29. 29 29 Seth

Dave – I don’t buy this sentence of his specifically:

“If they could not do this, then presumably the Oklahomans would all move to Iowa to work on the farms there.”

I think (not sure) this is an example of what Landsburg describes in his second paragraph. This sentence ignores that OK does have a comparative advantage in wheat. Because of this it’s not necessary for “all” to move to IA to satisfy their demand.

30. 30 30 Dave

All else being equal, if I can yield more in a day of work in IA than OK, I move to IA. I wouldn’t even flinch.

31. 31 31 Seth

Dave – Go ahead. Move to IA. Soon you will learn you’ll be better off producing corn there (opportunity cost) and you’ll switch to that. You will be able to produce plenty of it to trade some with your old pal Seth in OK for some of my wheat.

32. 32 32 Dave

What am I missing? You’re making it sound like if we were both Mexican goat herders and I shifted to NY, decided to switch careers and became a hedge fund manager using some pittance of my bonus to buy some cheese off you, I’d realise I had moade some sort of mistake?

33. 33 33 DividedLine

Like Harold, if my math is right, I also get 29.6 acres if both states pursue self sufficiency. I get 27.2 acres if OK produces all the required wheat for both states, and IA all the corn. Actual mileage will vary depending on other factors…

But, whether you like what the Intel CEO has to say or not, having worked in one of the companies he mentions, he makes some excellent points which seem to be simplified out of the wheat corn model. When manufacturing is moved far away from design, over time feedback loops are lost and designs become much less efficient and eventually obselete. Or to put it another way, on paper a design can be brilliant, but if the engineer can’t (or doesn’t) walk over to the factory on a regular basis to see how it impacts the actual making of the product, designs become less good. Sort of like if all you do is grow corn on an acre of land year after year, the soil will become depleted faster than if you rotate crops (or so I’ve read).

Also, if I remember my Econ 101 right (probably not), full employment of the production factors in both states must be in place before the principle of comparative advantage can be applied. Something neither IA or OK seems to have right now. Lot’s of the other considerations have already been mentioned (many of which float on cheap energy to grow and move wheat and corn).

34. 34 34 Seth

I believe you may be missing the proper valuation of opportunity cost.

Producing wheat in IA means you give up the value of the corn you could produce in IA and and wheat in OK (and don’t forget to add the cost of moving to that).

You changed the problem. If you moved to NY to become a goat herder (your originally move from OK to IA to do the same thing you were doing in OK) you would soon realize that you made a mistake because you’re giving up that hedge fund manager bonus (opportunity cost), so you’d become a hedge manager.

So, are you a hedge fund manager?

35. 35 35 Dave

I am….send me all your money and I’ll triple it. Hard to get in touch online so if you just post your bank account details here, I’ll make sure one of my leggy executive assistants withdraws the required funds.

OK let me change it up a bit. Goat herder in Mexico earning \$4 a day versus goat herder in California earning \$40 a day. I’d move – forget the moving costs.

36. 36 36 Bob

Hear hear. When someone says “I understand comparative advantage, but in this case it doesn’t apply”, or “I understand comparative advantage but in this case it is overridden by other considerations”, my experience tells me that you can be nearly sure you’re talking to someone who does not in fact understand comparative advantage.

They like big buts and they cannot lie…

Regarding your exercise, here is my answer, keeping in mind the Iowa caucuses: I reject the false choice being offered. The farmers of this great state should continue in their glorious tradition of growing both wheat and corn, and I intend to support them in their efforts. God bless this great state, and God bless America. Good night.

37. 37 37 Harold

The gap between Iowa and OK yields are unrealistic (I think). If we replace OK with Mojave, we might be a bit close to these differences. The absolute advantage is so great that all the potential farmers in the Mojave have located themselves in Iowa instead.

The model only works if Iowa is already farmed to capacity, as Mike assumed in his calculation. OK folk cannot re-locate to Iowa because there is nowhere for them to go. More realistically, the good land in Iowa is used up, and the marginal land left has the same productivity as OK land. This is where using this as a model for manufacturing has weakness. There is no absolute capacity in manufacturing, as there is in land. Unless limiting resources are fully utilised, does it not make sense for those with the absolute advantage to do everything? I guess this could mean that I don’t understand comparative advantage. All those freed up from manufacturing must be re-deployed to something useful, or you have not gained anything. If they can be re-deployed, then you have gained.

38. 38 38 mobile

Are we assuming that Oklahoma and Iowa have the same number of residents? If Oklahoma has a lot more people and they start importing corn from Iowa, then more land would be used up in Iowa and more land would be freed for other uses in Oklahoma.

The result I get is that in Iowa, specialization saves 4 acres of land for each resident of Iowa and costs 3.6 acres for every resident of Oklahoma. Oklahoma saves 12 acres for every resident of Oklahoma and uses an additional 10 acres for every resident of Iowa.

39. 39 39 Josh

I think I remember solving this problem in college, on a test. I believe I set up a pair of equations with the same variables and solved for the variables. We used this textbook, but it was many years ago (2001)… the book was white then.

40. 40 40 Colin

Dave:

Of course you would, if there were no moving costs. But you would soon realize that you’re better off spending your time being a movie star for \$40,000 a day, and trading the entertainment that you produce with a mexican for all your goat herding needs. And I, trying to make it as a movie star in Mexico, earning \$3 a day, realizing that I am missing out on \$4 a day goat herding, would switch to goat herding. And I would sell you my goat herding services for \$4 a day, and we would both be better off than we would have without specialization and trade.

41. 41 41 Colin

Actually, the movie star/goat-herder analogy is too absurd to be useful.

You’re a mexican goat-herder/winemaker and I am a californian goat-herder/winemaker. All we care about or need is wine and cheese. We are each trying to determine how much herding and winemaking we each should do. You can make the following combinations in a day:

Wine (bottles) Cheese (blocks)
0 and 5 or
1 and 4 or
2 and 3 or
3 and 2 or
4 and 1 or
5 and 0

I can make the following combinations:

Wine (bottles) Cheese (blocks)
15 and 0 or
12 and 2 or
9 and 4 or
6 and 6 or
3 and 8 or
0 and 10

Obviously I can make more of either one than you. No matter what I do, I’m better off than you are. However, I can do even BETTER than that by specializing in the good in which I have comparative advantage, and trading for the good in which you have comparative advantage. Obviously from looking at the table, for every 3 bottles of wine I make, I give up 2 blocks of cheese. For every 1 bottle of wine you make, you give up 1 block of cheese. My opportunity cost for wine is lower than yours.

If I ONLY make wine and you ONLY make cheese, more production occurs in the world. We can divvy up the production however we want, but overall there is more of everything for everyone.

Comparative advantage has nothing to do with whether you would move to California or not. You probably would, or at least should. But that’s beside the point. The point is that we are better off through specialization and trade.

42. 42 42 EricK

Colin, this example shows that everyobdy should specialise into whatever field they have a comparative advantage in. That is very different from showing that large groups of people (eg states or countries) shoud specialise into whatever field they have an aggregate comparative advantage in. Different people have different skills, and when an industry abandons one country altogether, then individuals whow would have had a comparative advantage in that industry are not able to profit from it unless they too migrate along with the industry.

43. 43 43 Colin

If “an industry abandons a country” then no one in that country has comparative advantage in that industry anymore.

44. 44 44 EricK

Let me put it another way. The wheat/corn exmaple assumes that everyone is equally skilled in producing wheat or corn, the only difference is in the quality of the land. But suppose it were the case that an acre of land in Iowa could produce 50 bushels of wheat when farmed by a skilled wheat farmer or 100 bushels of corn when farmed by a skilled corn farmer (and 20 and 30 bushels respectively in Oklahama), but that a wheat farmer trying to farm corn or a corn farmer trying to farm wheat would produce only 1 bushel or less of the crop wherever they were. Also assume that each farmer can only farm a fixed acreage of land. Now the comparative advantage that Iowa has in corn can only be realised if the corn farmers move to Iowa and the wheat farmers move to Oklahama. Where mass migration is possible, it may be that the states/countries should specialise; where it isn’t possible, then it is not at all clear that they should.

45. 45 45 David Grayson

Here’s my solution to the original problem:

Oklahoma has a comparative advantage of for growing wheat, because a bushel of wheat only costs 30/20 = 1.5 bushels of corn in Oklahoma, but it costs 100/50 = 2 bushels of corn in Iowa.

Iowa has the comparative advantage for growing corn.

If Iowa is to be self-sufficient, it needs 200/50 = 4 acres of wheat farms and 360/100 = 3.6 acres of corn farms (7.6 acres total).

If Oklahoma is to be self-sufficient, it needs 200/20 = 10 acres of wheat farms and 360/30 = 12 acres of corn farms (22 acres total).

If each state specializes in its area of comparative advantage, then Iowa needs to have 2*360/100 = 7.2 acres of corn farms and Oklahoma needs to have 2*200/20 = 20 acres of wheat farms. This frees up 2 acres of farmland in Oklahoma and 0.4 acres of farmland in Iowa, freeing up a total of 2.4 acres.