Alchian-Allen Theorem

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The Alchian-Allen Theorem was developed in 1964 by Armen Alchian and William R. Allen in the book University Economics (now called Exchange and Production ^[1]). It states that when the prices of two substitute goods, such as high and low grades of the same product, are both increased by a fixed per-unit amount such as a transportation cost or a lump-sum tax, consumption will shift toward the higher-grade product. This is true because the added per-unit amount decreases the relative price of the higher-grade product.

Suppose, for example, that high-grade coffee beans are $3/pound and low-grade beans $1.50/pound. Then high-grade beans cost twice as much as low-grade. But now add on a per-pound international shipping cost of $1. Now the effective prices are $4 and $2.50, so that high-grade beans cost only 1.6 times as much as low-grade. This difference will induce distant coffee-buyers to choose a higher ratio of high-to-low grade beans than local coffee-buyers. (Prices are illustrative only).

Another example, provided by Tyler Cowen in [1], is that the theorem, briefly, implies that Australians drink higher-quality Californian wine than Californians, and vice-versa, because it is only worth the transportation costs for the most expensive wine. He also related this theorem to long-distance relationships.

Colloquially, the Alchian-Allen theorem is also known as the “shipping the good apples out” theorem (Thomas Borcherding) or as the “third law of demand.”