The Alchian-Allen Theorem | Hacker News Reader

The Alchian-Allen Theorem

azmytheconomics.wordpress.com

82 pointsczr8020 comments

I just checked out the wikipedia page of Armen Alchian and it appears that he died today http://en.wikipedia.org/wiki/Armen_Alchian.

I suppose somebody posted this after learning of his death. His theory appearing on the HN front page is a way to remember one of his achievements on the day of his passing.

That's what I figured.

I wrote the post in October of 2011, but people have reblogged it recently in response to Alchian's death.

Should it be called a theorem? It looks to me more like a theory, since economics is not an exact science like mathematics. According to Wikipedia, [1] a theorem is fundamentally deductive, in contrast with a scientific theory, which is empirical.

[1] http://en.wikipedia.org/wiki/Theorem

My guess is that it's a "theorem" in the sense that you could come up with some mathematical model of economics in which some translation of Alchain-Allen into a mathematical statement would be a provable mathematical theorem.

Alchain-Allen being true in most or every model of economics (as the Church-Turing thesis [1] is true in most models of computation), or being always true in reality, is a much more debatable question.

Real demand curves can be mighty pathological, for example, you can have D'(P) > 0 [2] if the good in question is something people buy to show off their wealth, and so actually like it to be more expensive.

[1] http://en.wikipedia.org/wiki/Church_Turing_Thesis

[2] Economists like to put demand on the horizontal axis and price on the vertical axis. That convention is insane, so I ignore it when I can.

Regarding [2], forgiving my ignorance in economics, how is that convention insane?

Typically, the independent variable is on the x axis and the dependent is on the y. Most modern economists consider price independent, hence the axes are reversed. The convention was created by Alfred Marshall and everyone has stuck to it ever since. I don't think it matters, since neither variable is causal. The "inputs" of the function are actually the supply and demand curves themselves and the output is both price and quantity.

It's more of a science-in-general thing: The near-universal [1] convention used in drawing graphs is to put the independent variable on the x axis.

If the independent variable is price, then your thought process will be: "If the price is $100, then there will be 1000 buyers. If the price is $150, then there will be 700 customers." It's easy to think about things that way.

If the independent variable is demand, then your thought process will be: "If there are 1000 people buying the product, it must cost $100. If there are 700 buyers, then it must cost $150." It seems counterintuitive to think in this way.

[1] Except in economics, of course!

Wikipedia article is actually written about Alchian–Allen effect rather then a theorem: http://en.wikipedia.org/wiki/Alchian%E2%80%93Allen_effect

The article is good, but I need to point the elephant in the room:

"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."

By that logic, more people could be watching opera videos on YouTube if they cared, since the opportunity cost is the same.

I'm inclined to believe the fact most people prefer cat videos is not because of availability, but because most people are mundane.

The way I understood it, the "cost" of watching an opera on YouTube is the time and mental effort it takes, which is many times greater than the time and mental effort it takes to watch a cat video.

Like, say you may derive more enjoyment from reading novels than Hacker News comments, but when you sit down to quickly eat breakfast you peruse Hacker News, even though great many high quality novels are also one click away.

> The way I understood it, the "cost" of watching an opera on YouTube is the time and mental effort it takes, which is many times greater than the time and mental effort it takes to watch a cat video.

The original analogy compared with the cost of watching an opera on the middle ages, but I get your point: people perceive the value of consuming copious amounts of mundane content to be greater than the reward to be gained from a single, more elaborate content.

Interesting. Would you say it's a race to the bottom of time and mental effort then? Cultural production and consumption is limited by the second law of thermodynamics? That sounds pretty hopeless.

The implication is actually that cat videos are more enjoyable per instant than opera. If that were not the case, people would always watch opera. But if there were a high fixed cost, such as a ticket price, or the mental energy required to pay attention, the opera becomes relatively attractive. Imagine driving to a movie theater and paying $10 to watch a 2 minute cat video. It would be absurd.

My point about the middle ages was that at that time, the fixed cost for all media consumption was high, so no one even considered short videos (preformances?). Now, when fixed costs are lower, you see a dramatically different pattern of consumption.

High cost/high benefit media is still around - just think about a long running tv show like Lost or Game of Thrones, where the audience is expected to put a ton of mental effort into the show. So I don't worry about a race to the bottom.

People prefer short-term gratification when it is available. "Mundane" isn't relevant. Wik Wheaton or Freddie Wu or someone explained that youtube audiences don't have short attention spans, but that they have demanding attention spans, and won't tolerate a 2 minute bit stretched out to 10 minutes.

By "increase consumption of the higher-quality good," is that in absolute terms, or relative to the lower-quality good?

Is there a concrete example of "reasonable" demand functions under which a fixed increase leads to an absolute increase of the higher-quality good?

(Original Author): Relative. In the wine example, if you add a fixed cost, total absolute consumption will decline, but relative consumption of the more expensive one will increase. Likewise, when fixed costs are lower, absolute consuption increases, as per the law of demand. People spend more time watching media in general now than in the Middle Ages, but cat videos are relatively more popular.

I know very little about economics. I will be happy to know if this 'theorem' is supported by experimental evidence (none were mentioned in the article). Otherwise it should really be called a hypothesis.

There are various formalizations of the Alchian–Allen effect that are theorems in the mathematical sense of the word in that they have been formally proved. See, e.g., http://www.cesifo-group.de/portal/pls/portal/docs/1/1219670.....

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