Armen Alchian passed away in February last year. Had he been alive, today would have been his 100th birthday. On this centennial of his birth, I want to discuss his and William Allen's famous but sometimes misunderstood theorem in price theory, known primarily as the Alchian-Allen Theorem, but also as the "Ship-the-good-apples-out" Theorem, or, I have recently learnt, the "Oranges Principle". I will also provide my favourite application of it. It is a thing of beauty and follows in a straightforward fashion from the First Law of Demand. One of the things that makes it one of my favourite results in economics is the fact that it was first published, not in an academic article, but rather unassumingly in Alchian and Allen's textbook

*University Economics*(later changed to*Exchange and Production*, in which the theorem can be found on pp. 38-39 in the 1983 edition). Here it is:
Imagine some product which varies in quality, such as oranges grown in California. Suppose consumers it costs $1.00/lb to ship oranges from California to New York, regardless of the quality of the oranges. If high-quality oranges sell for $3.00/lb, and low-quality organges sell for $1.50/lb in California. To retain the same profit margin, producers of oranges would have to sell their high-quality produce for $4.00, and their low-quality produce for $2.50, in New York.

A pound of high-quality orange in California costs two pounds of low-quality oranges, but in New York, the same quanitity is obtained at the cost of 1.6 pounds of low-quality oranges.

*Ceteris paribus*, it makes sense for the proportion of high-quality oranges shipped to New York to be greater than the proportion of high-quality oranges that stays in California. This follows from the First Law of Demand, because the cost of high quality relative to low quality declines when transportation costs are added. Hence, the good apples (or oranges, or anything that varies in quality) are shipped out. Adding transportation costs makes New Yorkers act as if they prefer high-quality oranges more strongly. In the illustration below (panel a), the quantity of low-quality goods falls proportionately more than does the quantity of high-quality goods, as the slope of the budget line approaches -1 (click to enlarge).
Now in general, it is not a certainty that the Theorem will be observed, because one could imagine that consumers care not about relative prices but about some constant price difference. If, for instance, consumers are always willing to pay some fixed amount of dollars more for high-quality oranges, the theorem does not apply. In panel b of my simple illustration above, the proportion of high-quality goods which are exported actually goes down when the intersection between indifference curve and budget line moves primarily horizontally and very little vertically.

Nevertheless, although one can easily show that the Theorem needn't always hold, there are very many situations which it neatly helps explain. The Alchian-Allen theorem can be applied even when there are no transportation costs; wherever there are two versions of something and another something working as a cost whose size does not depend on which version was chosen, one can discern the Alchian-Allen Theorem.

I like the Theorem so much because I always think about it when I go for a run. Running a long distance is an expensive run; running a short distance is a cheap one, but one must take a shower afterwards or risk losing all contact with the rest of humanity. I don't dislike showering, but I could easily think of many things I'd rather do. Akin to how transportation costs are the same irrespective of quality, the time lost showering does not vary in length with distance run. And, as the Alchian-Allen Theorem predicts, I do indeed tend to run rather long distances; never less than about 6 miles (10 kilometres) in one go, and frequently much longer distances.

Nevertheless, although one can easily show that the Theorem needn't always hold, there are very many situations which it neatly helps explain. The Alchian-Allen theorem can be applied even when there are no transportation costs; wherever there are two versions of something and another something working as a cost whose size does not depend on which version was chosen, one can discern the Alchian-Allen Theorem.

I like the Theorem so much because I always think about it when I go for a run. Running a long distance is an expensive run; running a short distance is a cheap one, but one must take a shower afterwards or risk losing all contact with the rest of humanity. I don't dislike showering, but I could easily think of many things I'd rather do. Akin to how transportation costs are the same irrespective of quality, the time lost showering does not vary in length with distance run. And, as the Alchian-Allen Theorem predicts, I do indeed tend to run rather long distances; never less than about 6 miles (10 kilometres) in one go, and frequently much longer distances.

People with a greater fondness for showering are predicted to run somewhat shorter distances if everything else is the same. More generally, "transportation costs" may be quite subjective in some applications, so one might think of it as variable, in which case,

Because it is stated in such simple and general terms, it is exciting to think of other applications of the Theorem. Perhaps longer-lasting holidays are associated with more decorations. This seems to fit Christmas being the most intensely decorated holiday I know of, and also the longest. Persons with shorter Christmas breaks should decorate less if this is true. This is in line with the Alchian-Allen Theorem, because putting up decorations is a "cost" (time sacrificed in order to celebrate Christmas) which does not vary with the length of the holiday.

*ceteris paribus*, more high-quality products should be consumed by those who really dislike the cost involved, and more low-quality products by those who do not mind it, or even like it.Because it is stated in such simple and general terms, it is exciting to think of other applications of the Theorem. Perhaps longer-lasting holidays are associated with more decorations. This seems to fit Christmas being the most intensely decorated holiday I know of, and also the longest. Persons with shorter Christmas breaks should decorate less if this is true. This is in line with the Alchian-Allen Theorem, because putting up decorations is a "cost" (time sacrificed in order to celebrate Christmas) which does not vary with the length of the holiday.

Armen Alchian was and remains one of my all-time favourite economists. It is so sad that he is not around to celebrate his 100th birthday, but at least he had a long and productive life. His Theorem with William Allen is just one of very many highlights of his career. I am sure to blog about more of this great economist's work in future.

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