Yesterday’s pop quiz posed this question:

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?

Quite a few people got this right in comments. In Iowa, the opportunity cost of a bushel of wheat is 2 bushels of corn. In Oklahoma, the opportunity cost of a bushel of wheat is 3/2 bushels of corn. Becauses 3/2 is less than 2, Oklahoma is the low-cost wheat producer, which is the same thing as saying that Oklahoma has the comparative advantage in wheat.

For a bushel of corn, the opportunity cost is 1/2 bushel of wheat in Iowa or 2/3 bushels of wheat in Oklahoma. Because 1/2 is less than 2/3, Iowa is the low-cost corn producer, which is the same thing as saying that Iowa has the comparative advantage in corn.

Knowing the comparative advantages tells us, without any further computation, that everyone can be richer if Oklahoma exports wheat and Iowa exports corn. But if we choose to do the extra computation, we see that with self-sufficiency, Iowa needs 7.6 acres to feed its people and Oklahoma needs 22 acres. whereas if Iowa grows enough corn for both states and Oklahoma grows enough wheat for both states, then Iowa needs only 7.2 acres and Oklahoma needs only 20 acres. The remaining acres are available to feed even more people, or to build NASCAR tracks.

(Edited to add: It was pointed out in comments that in the first couple paragraphs of this answer, I said “corn” when I meant wheat and vice versa. This is, I think, fixed now. Very sorry for not proofreading better.)

This example is ultra-simplistic in several ways of which here are two:

• It assumes that the yield in either state is a simple multiple of the number of acres under cultivation—in other words, we (unrealistically) assumed away diminishing returns.
• It assumes that food consumption in each state is fixed, as opposed to varying with price.

Econonerds might recognize that these assumptions are tantamount to assuming that all supply curves are horizontal and all demand curves are vertical.

But do not make the mistake of dismissing the example because of its simplicity. As I tell my students, you can’t understand the hard stuff till you’ve mastered the easy stuff. And as those students progress to more difficult and realistic exercises, they come to realize that the underlying logic remains pretty much inescapable—compute the comparative advantages, and you will discover an opportunity for everyone to gain from trade.

#### 23 Responses to “Pop Answers”

1. 1 1 Lawrence Kesteloot

You have your states backwards for most of that. It’s Iowa that has a comparative advantage in corn and Oklahoma that has it in wheat. You get it right at the end.

2. 2 2 Al

Agreed with Lawrence, you’re answer is a bit jumbled up, you go from:

“…Oklahoma has the comparative advantage in corn.” “…Iowa has the comparative advantage in wheat.” and “everyone can be richer if Oklahoma exports corn and Iowa exports wheat”

to

“…if Iowa grows enough corn for both states and Oklahoma grows enough wheat for both states, then [everyone is better off.]”

You get it right at the end, but you’ve got the states the wrong way around for the first 2 1/2 paragraphs. This has the potential to confuse anyone already struggling to understand comparative advantage.

It’s reassuring to know that even an economics professor can get a little confused with such problems from time to time.

3. 3 3 noobee

figured you must’ve been trying to mess with laymen. good thing i came to the site to check the comments.

4. 4 4 Harold

Thanks Steve for the illustration. It is important to learn the right thing. This is very informative, and is good to illustrate comparative advantage. It allows this concept to be incorporated into discussion and contemplation of international trade etc. However, it must be recognised that there are other factors, and it does not necessarily mean that countries should only do what they have an apparent comparative advantage in. It does require that if you wish to do otherwise, you must have some extra justification for doing so.

In the Grove article, I think that China has a comparative advantage in manufacturing. This means that the opportunity cost for Americans employed in manufacturing is greater than for Chinese workers. It therefore makes sense for the Chinese to do the manufacturing, and the Americans to do something else. However, I think that Grove is identifying an extra opportunity cost for Americans – that of lost experience in manufacturing, which would promote new developments. If this opportunity cost is sufficiently large, then the comparative advantage could swing back the other way.

But the opportunity cost would be the same for the Chinese, wouldn’t it? So this brings it back to where we started. Thinking some more, Groves argument works if there is diminishing returns on manufacturing experience. It provides a very large benefit to have a certain level of manufacturing, but once you have this amount the benefits drop off. This means that the comparative advantage may be for America to do enough manufacturing to maintain the experience level, then let the Chinese do the rest. I think Groves point is that this state of affairs will not occur by itself,since it is the benefit of the country as a whole, and the cost to individual companies.

5. 5 5 Dave

Steven, I’m really curious on how you would respond to Harold’s answer:

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

Seems right to me but I suspect you would mark that as incorrect if one of your students put that down in an exam?

6. 6 6 Steve Landsburg

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

You are adding Iowa acres and Oklahoma acres, which is like adding apples and oranges. The goal is not to free up acres, it is to free up productive capacity.

7. 7 7 michael webster

Has anyone done any experiments in this simple world set-up to see if participants learn how to obtain this result over time? Something similar to the early Vernon Smith experiments on simple auctions.

8. 8 8 AJSoaks

Steve’s comment says “The goal is not to free up acres, it is to free up productive capacity”
Steve’s question says “how many acres … are freed up for other uses?”
So the phrasing of the original question implies an intent to optimize for free acres, while the true intent is to optimize for productive capacity.
Just goes to prove the point that you get different answers based on the questions you ask.

9. 9 9 Steve Landsburg

AJSoaks: The original question asks how many acres of Iowa farmland are freed up and how many of Oklahoma farmland are freed up. Those *are* questions about productive capacity, because the productive capacity of each sort of land has been specified. It still makes no sense to add one kind of acre to the other.

10. 10 10 Mike

I’m not sure I understand how my 26.6 answer was wrong. If we’re looking to maximize efficiency then Iowa has a relative advantage in both and only needs 7.2 acres to produce all of the corn for both states, why wouldn’t Iowa use it’s remaining .4 acres to some of the wheat needed?

11. 11 11 Steve Landsburg

Mike: First, you are using language in non-standard ways. Iowa is the efficient the corn producer and Oklahoma is the efficient wheat producer. The phrase “relative advantage” has no standard meaning. Iowa has the comparative advantage in corn and Oklahoma has the comparatie advantage in wheat. Iowa has the absolute advantage in both crops.

As to why Iowa would not use additional acreage to produce wheat, the answer is that Iowans can get more wheat by growing corn on that additional acreage and then trading than they can get by growing additional wheat themselves.

12. 12 12 Dave

Bang – Steve your sentence: “As to why Iowa would not use additional acreage to produce wheat, the answer is that Iowans can get more wheat by growing corn on that additional acreage and then trading than they can get by growing additional wheat themselves” just made all the pieces fall into place in my head!

Danke

13. 13 13 Seth

Dave – Which is why when you move to IA from OK, you will soon decide to grow corn and trade some of it with your pal Seth in OK.

14. 14 14 Dave

Aha! Got it. see you at the market.

15. 15 15 cory

Steve- It is very realistic not to assume diminishing marginal returns. Modern agricultural practices would allow for a constant or increasing marginal returns due to access to better technology (bigger more efficient machinery) and scale economies.

16. 16 16 Steve Landsburg

Cory: But don’t forget, I’ve implicity fixed the labor supply in this problem, so my assumptions allow you to double the cultivated land without any increase in labor and *still* get an increase in output.

17. 17 17 AJSoaks

Steve: I do understand the point behind the quiz. I’m (indirectly) suggesting that you could choose to lead people to the answer by phrasing the question in more direct terms. I imagine that a question optimized to discriminate grades for people who have taken your class might benefit from the indirection, but perhaps the audience for your blog is a little different.

18. 18 18 NathanS

An interesting complication might be to say that we must consume 10% of the resources being traded (assuming wheat or corn = gas in a roundabout sense) in transport.

Is there a stable way to solve this sort of problem?

19. 19 19 Justin P

AJ – Steve’s example is very easy to understand the exact way he phrased it. Just because it was hard for you, don’t assume it’s hard for everyone else.

20. 20 20 Dan Rosenberry

Thinking this through, there’s a way to save even more land within the constraints of the problem. Dave and Harold have hinted at it. Oklahoma has a comparative advantage in land. Iowa has a comparative advantage in both corn and wheat. Having Iowa produce both corn and wheat and Oklahoma producing land is more efficient.

It takes 15.2 acres in Iowa to produce all the corn and wheat needed by both states. So long as Oklahoma cedes at least 8 and no more than 20 acres to Iowa, Iowa and Oklahoma are both at least as well off under the standard solution. (If this is a one time deal, have the land revert afterwards)

This does assume that an acre is an acre is an acre. Maybe acres that used to be in Oklahoma aren’t as valuable outside of corn/wheat production as those that have been in Iowa from the start.

21. 21 21 Harold

Putting a couple of the comments together, particularly Mikes point about growing wheat on the freed up Iowan acres. None of this invalidates the initial post, which asks specific questions to illustrate the point of comparitive advantage. However, just playing around with the scenario. We assume:

All land in both states is the same.
Iowa’s land is all used up in the initial situation, or Oklahomans are prevented from occupying it. Otherwise all the produce would be grown in Iowa.
Iowa and Oklahoma are closed systems in corn and wheat – no trading outside the two states.

Thus when the states specialise, some land is freed up in Iowa. As this has the absolute and comparative advantage in growing corn, we might assume it will put this land to the best use, and grow corn on it. The excess will be traded for wheat, as Steve says. However, this will mean that there is now 760 bushels of corn produced, which is more than the 720 needed in both states. Therefore Iowa will not be able to trade the extra corn (remember demand is fixed). So what will it do instead? Well, as far as we know, the only things it can do is grow wheat or corn, so it will grow wheat instead. This makes Mike’s answer correct. Steves answer is correct in the terms of the question – each state specialises in its area of comparative advantage, this does not allow Iowa to grow wheat.

22. 22 22 BobR

me to clarify the issue of comparative advantage. I could
Iowa growing everything. You may not be able to add Iowa
and Oklahoma acres, but to make this a well-posed optimization
problem, you have to relate them in some way. For example
the solution you give to illustrate the benefits of trade
has IA saving 0.4 acres and OK saving 2, a ratio of 5.
But it is not clear that the residents of the two states
would agree to trade at this ratio. Iowa might not think
that’s such a good deal.

You can specify any ratio of acres saved and solve
the linear optimization problem (although this turned
out to be harder than I had expected). The limiting cases are
those when one state gets all the land savings and
the other gets no benefit (or harm). Anything in
between would represent a Pareto improvement (if I
understand that term correctly) over the case of no trade.

The best case for Iowa is saving 1 acre while OK saves none.
This results when IA grows 3.6 acres of corn for its own use
and exports 3, while OK grows 2 acres of corn and 10 acres of
wheat for itself and exports 10 acres of wheat.

The best case for Oklahoma is saving 3 acres while IA saves none.
Here again IA uses 3.6 acres of its own corn, exports 3.6, but
grows 0.4 acres of its own wheat. OK consumes 10 acres worth
of its own wheat and exports the wheat from 9 acres.

The only thing special about the ratio of 5 is that OK doesn’t
grow any of its own corn and IA doesn’t grow any of its own
wheat, but these are not general features of the optimum solutions.

23. 23 23 Steve Landsburg

BobR:

The only thing special about the ratio of 5 is that OK doesn’t
grow any of its own corn and IA doesn’t grow any of its own
wheat, but these are not general features of the optimum solutions.

This is exactly right.

This example, though, is extreme because of the assumed linearity of the production functions. Under the standard assumptions (which this example violates), there is a unique competitive equilibrium, i.e. a unique price ratio at which the amount of wheat Oklahomans want to sell is equal to the amount of wheat Iowans want to buy. (It is then necessarily the case that the amount of corn Oklahomans want to buy is equal to the amount of corn Iowans want to sell.) But even then, although the competitive equilibrium is unique, there are many other (non-equilibrium) outcomes that would be better than self-sufficiency for both states.