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The Alchian-Allen Theorem

October 12, 2011

The Alchian-Allen Theorem is a lesser known but still very interesting economic theory. It states that when a fixed cost is added to substitute goods, the more expensive one becomes relatively less expensive, and so people are likely to increase consumption of the higher quality good. I think the best way to illustrate the theorem is with examples.

Suppose there is a country that makes wine. They can make good wine or mediocre wine. Mediocre wine costs $5 to make and good wine costs $10. Suppose that shipping costs to foreign countries is $5 per bottle. The price of the wine in foreign countries is $10 for mediocre and $15 for expensive. The ratio of prices at home is 1:2, but abroad it is 1:1.5. Abroad, the more expensive wine is relatively less expensive, meaning foreigners will consume more of the expensive wine. Similarly, if shipping costs fall, foreigners will consume more of the cheaper wine.

When a drug is outlawed, people face a large fixed cost equal to the expected punishment. They not only have to pay higher money prices, but they also pay in the form of a potential prison sentence. Thus, in areas where alcohol is outlawed, people tend to drink either high concentration or high quality alcohol. It’s simply not worth the trouble to smuggle regular beer. Likewise, the THC content of marijuana has increased as more effort is spent trying to eliminate marijuana use. Paradoxically, because of the higher dosages, drug prohibition can actually increase the dangers associated with drug consumption by eliminating the low cost low concentration doses from the market.

The Alchian-Allen Theorem has profound explanatory power when applied to the internet. The harder it is to gain access to cultural elements, the higher the quality of those elements will be consumed. On the flip side, if it is easy to access culture, people will prefer to consume shorter lower quality pieces of culture. In the middle ages, people had to travel long distances to view concerts, which were performed by live musicians. Thus, the fixed costs of consumption were very high. If you bothered to pay a huge amount of money and time, you might as well view a long complex opera or symphony. On the flip side, when fixed costs are as low as a Google search, people prefer short YouTube videos of cats doing cute things. Don’t think that this means that the quality of culture has gone down.

When there are large fixed costs, an opera is only about 50% more expensive than watching a cat video. An opera would only have to bring a little more enjoyment to be worth doing.

With low costs (a mouse click), an opera is many times more expensive than a cat video. It would have to bring as much enjoyment as hundreds of cat videos to be worth consuming (graph not to scale).

While the average quality may have gone down, because there are so many people connected to one another than before, the quality of the highest skilled artists is higher than it was in the past. Additionally, there is an opportunity to create things which are far grander than was possible in the past, such as Wikipedia. Because people are able to take cell phone camera pictures, they take photos of things that are completely trivial, but when combined, paint a more detailed view of their life than was possible for even the most famous celebrities in the past.

Additional Material:
Sex, Drugs and the Alchian Allen Theorem
An EconTalk podcast with Tyler Cowen where he discusses the Alchian Allen theorem. It’s an hour long or so, but I enjoyed it. Here is a paper by Cowen and Tabarrock.
Catvertising.
When the fixed costs of hiring someone drops, people hire each other more often to do smaller jobs.
Marriage vs. Dating, more here.
The first LOLcats. HT Koettke.

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