David R. Henderson  

Freakonomics Discovers Alchian's and Allen's "Oranges Principle"

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Never reason from an inflation... Robert Bradley on Enron...

UPDATE BELOW:

Anyway, there were a few houses I worked on where we got J-grade lumber, which is lumber that is destined for Japan. It is a grade above A-grade that you can't even buy at a lumber yard. You have to know someone at the sawmill and buy it directly from there. The J-grade lumber is perfect. You don't have to check for anything because it is all straight and knot-free. You could make beautiful furniture with it if you were inclined. We were making houses that were designed to last at least 100 years at least. It's unfortunate then, that all the best lumber is going into houses that will be demolished in 38 years.

I think the argument was that the cost of shipping the lumber was at least the cost of the lumber itself, so it made sense to buy the best lumber possible considering the high transport costs. Maybe it has something to do with currency differences as well or maybe it takes less lumber to build the smaller houses. Regardless, the best lumber in Canada (and likely the U.S. northwest) goes to Japan so they can throw it away in 38 years. Thank you, capitalism.


This is from a blog post by Stephen J. Dubner, over at Freakonomics. Dubner is quoting a commenter named Kevin. The post is titled, "Why Use the Best Lumber in a House That Won't Last?"

This fact would not have surprised the late Armen Alchian or co-author William Allen. Introductory textbooks in which the authors lay out new theoretical insights that have not already appeared in academic journals are rare. University Economics, by Alchian and Allen, first published in 1964, was rare. They gave no name to their insight and so we graduate students at UCLA, where Alchian and Allen taught, called it the "oranges principle." The idea is that the cost of shipping low-quality oranges is the same as the cost of shipping high-quality oranges. Say the price of a high-quality orange in Florida is PH and the cost of a low-quality orange in Florida is PL. Obviously, PH > PL. But let the cost of shipping to Minnesota be X. Then the price of a high-quality orange in Minnesota is PH + X. The price of a low-quality orange in Minnesota is PL + X. PH/PL > (PH +X)/(PL + X). Therefore the relative price of a high-quality orange in Minnesota, relative, that is, to the price of the low-qualty orange in Minnesota, is lower than the relative price of a high-quality orange in Florida relative to the price of a low-quality orange in Florida. That's why a disproportionately high percentage of oranges tend to be shipped out.

The same goes for lumber. Notice that Kevin, although probably not an economist, almost gets there by talking about the shipping cost.

UPDATE WITH NUMBERS
A reader on Facebook pointed out that I can make the point clearer with numbers. Imagine high-quality oranges sell for $2 a pound and low-quality oranges sell for $1 a pound, all in Florida. Transportation cost to Minnesota is $0.50 per pound. The relative price of high-quality to low-quality oranges in Florida: 2/1. High-quality oranges are twice as expensive. The relative price of high-quality to low-quality oranges in Minnesota: 2.5/1.5, or 5/3. High-quality oranges are only 67% more expensive.


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CATEGORIES: Microeconomics



COMMENTS (31 to date)
Greg Heslop writes:

Beautiful! I did not know the theorem was called the "Oranges Principle" at UCLA. I thought the alternative name was the "Ship-the-good-apples-out" Theorem, but the Oranges Principle is neat, too.

In my 1983 edition of 'University Economics' (then called 'Exchange and Production'), the Theorem can be found on pp. 36-37 for anyone curious. Incidentally, this is one of my favourite results in economics.

This is a well-timed post, because on Saturday (12th April), Armen Alchian would have been 100 years old.

nl7 writes:

Not everyone has to value a product the same way. Imagine product W is beautiful, durable, safe, and long-lasting.

Person J cares primarily that W is beautiful, appreciates that it is durable, and cares only that it is at least minimally safe, but does not need the product to be long-lasting.

Person A cares primarily that W is long-lasting, but also appreciates its beauty, safety, and durability. In the aggregate, Person A emotionally cares more about all four positive characteristics of W, relative to Person J.

Person J will pay the retailer X BTC for a unit of W products. Person A will pay the retailer only 0.8X BTC for a unit of W products.

Why should the retailer accept that person A's emotional satisfaction of W should compensate for the loss of revenue? If the emotional satisfaction was not able to motivate A to pay more for W, then why should the retailer have any extra regard for A's deprioritized emotions?

Moreover, there may be tons of products that are even more long-lasting than W (as there are with home construction materials) but no other products as beautiful as W (which may be the case for a wood-emphasizing Japanese design). So Person A's preference could have better alternatives than W, but Person J does not have better alternatives. The fact that J may be wasting some portion of product W's potential is not going to make it a bad deal for the retailer, for J, or for A.

Rolf Penner writes:

We find the same with the agricultural commodities that we ship to Japan. They get the best canola, wheat and hogs we produce and always pay a premium for it.

On the other hand China seems to buy more of the lower quality stuff, which now seems odd based on the principle you just cited.

I don't know if China buys more lower quality stuff than Canadians though.

When I see the numbers and the data its always in terms of exports. We hardly ever talk about the domestic market. Probably because something like 80% (rough number, don't quote me on it) of what we produce goes for export.

David R. Henderson writes:

@Rolf Penner,
Thanks.
It’s quite possible that the Chinese data fit also. One wouldn’t expect them to import the same percentage of high-quality items (as a % of the total) that Japanese people import because the Chinese are much poorer.
Also, even if the Chinese buy a lower % of high quality than the Canadians buy, this is not necessarily inconsistent. Alchian and Allen’s theorem holds ceteris paribus. Here, what’s not held equal is per capita income and per capita wealth.

Steve S writes:

I'm not sure if shipping cost is the driver, but this appears to be happening in the coffee market as well.

When I was in Costa Rica, our guide apologized for the coffee he served us, saying that we were used to drinking the best stuff, where the coffee that the locals drink is C-grade at best (I don't know the actual grading system...)

Is this a shipping thing? Or is it just demand? Why not sell your highest quality goods instead of consuming them? Think of the quinoa farmers in Peru/Bolivia as well. Same story.

David R. Henderson writes:

@Steve S,
Good point. People in Costa Rica are much poorer than here. That alone would drive the good coffee out, even if shipping costs were zero.
That’s why I like, and probably why Alchian and Allen liked, the oranges example. There’s not a huge difference in per capita income between Minnesota and Florida.

Steve S writes:

@David

That makes sense. The China/Costa Rica/Peru examples are clouded by the differences in income.

I think it was on Cafe Hayek some time ago where it was pointed out that some of the crab in Maryland was actually "imported" from Louisiana. I'm sure they get the highest quality crab out of Louisiana, if not because people demand high quality crab while in Maryland, then because the restaurants have a reputation to uphold.

foobarista writes:

We're going through a remodel, and since labor costs are about 90% of the cost of the remodel, we've gone ahead and gotten high-end stuff for the materials, as getting cheap junk would only save a few percent of the price - and still be cheap junk.

David R. Henderson writes:

@foobarista,
NICE application of the principle.

magilson writes:

It'd be great if someone could study this via Amazon. It would be interesting if their "Prime" product will shift people back toward the cheaper product because they can effectively forget their membership fee as an adder to every product they buy.

If a consumer sees a shipping cost that's fixed because that cost doesn't change necessarily with the product's quality then do they more often opt for the higher or lower quality product? What if the shipping is free?

And what about odd items where higher quality lowers weight and so perhaps shipping costs? Like high-end carbon fiber bicycles? Or does that not change cost because size and shape ( where shape doesn't really change with quality) are factored into shipping and handling?

MingoV writes:

Half of Japanese homes are demolished within 38 years. To know that, they had to look back further than 38 years. I would bet that the housing situation has changed greatly over the decades.

What is the difference between houses that were axed versus houses that remained? Perhaps the difference was mediocre construction with mediocre materials. Perhaps the use of top grade lumber today is to help currently built houses last a century or longer.

Andrew_FL writes:

This, also known as the 3rd law of demand, is also, interestingly enough, the reason drugs become more potent as a consequence of drug prohibition.

Taras writes:

Great post David. It is unfortunate that people complain about the distribution of goods and services without understanding the fundamentals of what is going on.

One small nitpick at the bottom: You say 2.50/1.50 reduces to 3/2. It should be 5/3.

Hazel Meade writes:

Why do houses only last 38 years in Japan?

Is that a regulation, or does wood rot faster there?

BC writes:

I understand that this oranges principle may describe actual behavior, but is this behavior rational? In the numerical example, for consumers in both FL and MN, the opportunity cost of consuming one pound of high-quality oranges instead of low-quality oranges is $1 --- that is the amount of other consumption that they must give up. The price *difference*, not the ratio, determines the opportunity cost. The difference in ratios, of course, arises when combining the cost of the oranges with the cost of shipping. But, that seems like an example of so-called mental accounting.

Suppose, you lived in FL and chose low-quality oranges over high-quality due to the lower price. Now, suppose you moved to MN and your preferences/tastes didn't change. Why would you now pay $1/lb more for high-quality oranges when you wouldn't do so in FL? If shipping has any effect, it might be an income effect: needing to pay for shipping could make you poorer, leaving you less money for oranges. But, that effect should make you even less likely to choose the more expensive oranges!

Again, I'm not doubting that consumers behave this way. I'm just asking whether utility-maximizing consumers would behave this way? I think a similar effect may occur when people add expensive options to houses and cars that they would not purchase in isolation because the options add only a small percentage to the cost of the house or car. That's a pure framing or mental accounting effect.

David R. Henderson writes:

@Taras,
Oops. Thanks. Correction made.

Kurt Schuler writes:

As much as I respect Alchian and Allen, Alfred Marshall published the insight associated with their name about 40 years before they did in Money, Credit and Commerce, and in fact Marshall uses lumber as one of his examples.

BC writes:

Just to provide an example of my point, suppose that in addition to HQ and LQ oranges, gum costs $1 in both FL and MN. In FL, for $2 one can buy either 1 lb of HQ oranges or 1-lb LQ oranges + gum. Suppose one prefers the LQ oranges + gum, so that one's utility function has the property U(LQ+gum) > U(HQ). Now, in MN, for $2.50 one can also buy either 1 lb of HQ oranges or 1-lb LQ oranges + gum. So, if one's preferences in MN are the same as in FL, then one should still prefer the 1 lb of LQ oranges and the gum over just the 1 lb of HQ oranges. The 0.50 shipping cost shouldn't matter. While it's true that the relative price of HQ oranges to LQ oranges is lower in MN than in FL, so is the relative price of gum.

Now, it's possible that consumer tastes in MN are different from those in FL and those in Japan are different from those in Canada. Also, maybe due to high shipping costs, only wealthier Minnesotans and Japanese can afford oranges and houses and those wealthy people place a higher value on the premium oranges and wood. But, that is a difference of utility functions and is different from an "oranges principle" that arises from a framing or mental accounting effect.

AbsoluteZero writes:

@Hazel,

It has nothing to do with the houses not lasting. Many houses are much older. If a house continues to be occupied by the same family, it will likely not be torn down.

This is usually what people do: they buy a piece of land (that's how they think about it, they're buying the land, not the house), tear down the existing house, and hire an architect to design and a contractor to build a new one exactly the way they want it. If a family can afford to buy a piece of land, they will almost always build a new house instead of living in the existing one.

The kind of suburbs you find in North America, with rows of mostly identical houses, are exceedingly rare in Japan. The thing is, if most houses are custom, chances are a new family won't like what the previous family designed, so they build a new one, and the cycle repeats when they sell the land.

This is also one reason the number of architects per capita is so high. Many architects specialize exclusively in designing single family homes.

Sometimes you get a family with successive generations living in the same house, and that's usually why a house is older. These also tend to be larger families with larger houses.

David Friedman writes:

The problem with the argument is that it depends on an implicit assumption about utility--that X good apples substitute for Y poor apples, X less than Y, hence that it is the ratio of prices that determines which kind of apple is preferred.

There is no good reason to expect that to be true in general. Suppose you assume, instead, that one good apple substitutes for one bad apple plus one dollar—as would be the case (going beyond apples) if bad could be converted into good at some fixed expenditure (washed vs unwashed spinach, say). Now the theorem vanishes.

I am struck, David, that the oranges principle as you describe it relies upon an assumption not stated. BC is onto the same thing. I know because I am a tightwad. I can grump about an added dollar that does not buy me anything I want -- even after I've spent a hundred.

I am not sure, but perhaps there is an assumption about the price elasticity of demand: being the same in Florida (around the price of oranges without the added cost of shipping) and in Minnesota (around the price of oranges with the added cost of shipping).

ChrisA writes:

I am with BC, there is an apparent paradox here. After all, even though the shipping costs are higher, cheaper oranges should still be cheaper. So why doesn't a competitor start selling the cheaper oranges and undercut the more expensive seller? The example of the Japanese bound wood may be actually caused by another factor, such as the fact that in Japanese homes the wood is usually visible, whereas in US houses the wood is usually hidden behind dry wall or carpet. Japanese homes are more like actual furniture than houses in some respects.

Hazel Meade writes:

@AbsoluteZero:

That seems incredibly wasteful. It has to be extremely costly to tear down and rebuild a house. And there must be many families who cannot afford to do that. Certainly in America, I'm sure lots of families would do just that, but most cannot afford the cost of tearing a house down and rebuilding it.

I have to wonder what the homeownership rates in Japan are. My guess is it is low and that the vast majority of the cost of the home is in the land, rather than in the house itself. So basically a rich family that can afford the land may as well tear down and rebuild, since the cost of doing that is small compared to just buying the lot.

David R. Henderson writes:

@David Friedman,
Suppose you assume, instead, that one good apple substitutes for one bad apple plus one dollar—as would be the case (going beyond apples) if bad could be converted into good at some fixed expenditure (washed vs unwashed spinach, say). Now the theorem vanishes.
True. That’s part of a more general point that if you change the starting assumptions, many theorems vanish. I know, however, of no good way of converting bad apples into good apples. If the technology arose to do that, which may not be impossible, then the theorem would vanish. Meanwhile, I think Alchian and Allen had a brilliant explanation of a widespread phenomenon, whether or not we call it a theorem.

David R. Henderson writes:

@Kurt Schuler,
As much as I respect Alchian and Allen, Alfred Marshall published the insight associated with their name about 40 years before they did in Money, Credit and Commerce, and in fact Marshall uses lumber as one of his examples.
Interesting. Thanks. If the quote you quoted at your link is the whole quote, though, then Marshall didn’t lay it out as completely as Alchian and Allen did. It’s quite possible, though, that Marshall didn’t think he needed to because he might have thought the conclusion was obvious once he stated what he did.

AbsoluteZero writes:

@Hazel,
Withuot getting too off-topic:
- Home ownership rate in Japan is lower than that of many countries, but it's not that low. The issue is correctly interpreting the numbers. In North America, most people who own their own homes live in houses or condos. People who live in apartments are mostly renters. In Japan (and other places in East Asia), many people own apartments. If you buy an apartment, you pay only a small fraction of the price of the land. If you want a detached house, you need to buy the land. With land scarce, one obvious solution is high-rise apartment buildings, but there are laws in Japan that limit them, such as total floor area to land area ratio (limited to below 2 in some areas). So many places can only have detached houses, and they're expensive. Then there's the more general issue of how the construction industry works, which brings us to the Yakuza, and politics, and that's truly off-topic. Suffice it to say, it's complicated.
- Yes, it is very wasteful. Japan is a rather wasteful society in general. In fact, Japan is probably considerably more wasteful and less efficient than most in the West realize.

Bob Murphy writes:

David,

To some extent I am mirroring some of the doubts expressed by others above, but hopefully I can put the matter in a way so you see our concern:

The assumption here is that when someone is trying to decide whether to buy higher versus lower quality oranges, the thing he cares about is their relative prices. But why do we think that?

E.g. if very few people in Florida are willing to pay $1 more per pound for the tasty oranges, then why are so many people in Alaska willing to do so--especially since they are (other things equal) poorer than the people in Florida?

Does this phenomenon apply to cars? Do people in Alaska tend to drive luxury models with all of the extras (DVD players in the back seat, power windows, etc.) compared to people in the 48 states?

I'm not saying A&A are wrong, just that your exposition didn't seem as self-evident to me as I think you intended it.

awp writes:

(what follows is quick and dirty but I hope everyone gets the point)

I think the problem is an or/and distinction. People don't decide between high quality and low quality, they decide on a ratio of high quality to low quality consumption.

I think the problem might be something that might be called something like price elasticity of quality.

Suppose H/(H+L) = (QH/QL)/(PH/PL)

H-quantity of high quality
L-quantity of low quality
(QH/QL)-quality ratio
(PH/PL)-price ratio

with quick and dirty assumptions that place the appropriate limits on the left had side, or whatever else it needs, you can see that

the percentage of high quality good bought varies positively (+) with the quality of the high quality good and the price of the low quality good

and negatively(-) with the quality of the low quality good and the price of the high quality good.

We would expect to see something like this if the people valued both the total quantity and quality in consumption of some type of good.

I don't think anything like this is unreasonable. Most people
cook for themselves and go out to eat
watch t.v. at home and go to the movies
eat steak and hamburgers.

and would do the high quality version more if the relative prices changed. I know if the average restaurant meal cost $2.....

Another example of the phenomenon I have heard of (but not fact checked) is Singapore having an over representation of fancy cars due to a large surcharge on the importation of all cars.

awp writes:

should have put it in these terms

the percentage of high quality good bought varies negatively(-) with the ratio PH/PL.

which exactly translates to
"That's why a disproportionately high percentage of oranges tend to be shipped out."

David R. Henderson writes:

@Bob Murphy,
The assumption here is that when someone is trying to decide whether to buy higher versus lower quality oranges, the thing he cares about is their relative prices.
Good point. That is the driver. And if the income effect of the higher price is big enough, the Alchian/Allen result will not hold. That’s why I hesitated to go along with David Friedman in calling it a theorem. There was a University of Washington professor in the 1970s or 1980s who got a Journal of Political Economy article out of pointing this out. I can’t remember his name although I can picture him. It was an unusual name.

ChrisA writes:

David, it seems like you are suggesting the answer to this paradox is due to something similar to the money illusion, i.e. the percentage increase to buy higher quality oranges is less in areas where the logistic costs are higher, so the consumer ignores the fact that the absolute price difference is the same in dollars and cents. Maybe this is correct, although as others point out, it could easily go the other way, with people looking for bargains because of increased costs.
May I suggest an alternative explanation for the phenomenon that high logistic costs mean that quality rises? Let posit that the buyer pool contains people who have one of only two concerns, cost and quality i.e. that some people only care about cost and some people only care about quality. In a low logistics cost environment, the buyer pool contains many buyers who care about cost, since they are able to buy oranges at the price level they want. In a high logistic cost case the buyers who have cost as their driver drop out of the buying pool and so you are left with only the buyers who favour quality. So the average quality rises but the overall volume sold falls.

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