### The Alchian-Allen theorem, and how we learn preferences

Apart from Alchian and Allen, Tyler Cowen is the only economist mentioned in the Wikipedia entry for the Alchian-Allen theorem. Is this because he is the pre-eminent commentator on that theorem in the contemporary economics world? Or just because he has a popular blog?

This post won't answer that question, but it is prompted by Tyler's thoughts on the theorem in his book, and in an interesting Econtalk podcast with Russ Roberts.

The theorem states that if a fixed unit cost is added to the prices of all products in a set, relative consumption will shift towards the most expensive one. Or more simply: high shipping costs lead to higher quality goods.

The classic example is apples. In Somerset (arguably the apple capital of Britain, for readers unfamiliar with its many joys) let's imagine a juicy, hand-picked, top quality Pink Lady apple costs £0.10; while a tasteless, mass-produced Golden Delicious costs £0.02. That's a fifth of the price! Local consumers of apples will therefore be likely to eat a fair number of Golden Deliciouses.

But when the apples are transported to London, with a £1 shipping and packing cost, the Golden Delicious now costs £1.02 and the Pink Lady £1.10. The (proportional) difference is almost nothing, and therefore Londoners should eat far more Pink Ladies. Of course they won't consume - in absolute terms - more than Somersetters, but the balance between the two varieties will be tipped much more towards the more expensive type.

Now this simplistic explanation ignores many factors such as the likely volumes of each product shipped, the apportionment of fixed costs and the higher margins that will be obtained by growers and retailers for the more desirable product - which will counter part of this effect. But the basic microeconomic insight is sound.

So if the theorem is sound, why then - as Tyler points out - does it not appear to be true*? In reality people seem to eat much better apples in Somerset than in London. The best lobster is found in Maine, not Nebraska; and do people in Australia really drink better Californian wine than people in California?

Well, in the last case I suspect they might. Again not in absolute terms, but certainly in relative ones. The cheapest Californian wines probably don't ever find their way to Australia (but then, do the most expensive ones?)

In any case, for many other products the insight doesn't seem to hold. If in London you want the best quality steaks, they will always come from Suffolk or Scotland, not Ireland or France.

Tyler hints at the answer in the podcast - it's about how we learn what tastes good. People who eat apples all the time have a much better knowledge of what is a top quality apple; the farmer who eats his own steak every day will develop a different set of preferences - and much higher standards - than the city-dweller who only gets it once a month.

So perhaps the theorem is true when comparing two individuals with identical preferences. If that beef farmer moves to the city perhaps she will want to eat only the best steaks available. But once we let the clock run and allow preferences to evolve over time, the effects of high consumption may lead to different long-run results.

Wine, being a more globalised product, lends itself to stable preferences, which differ less by location, and thus the theorem is more likely to hold. Indeed the relatively low shipping and storage costs of wine may indicate that the theorem only works when it doesn't work too well.

Two final thoughts.

There's a famous behavioural result showing that people are much more sensitive to relative than absolute prices. More people are willing to travel across town to get a \$25 saving on a \$100 microwave than a \$25 saving on a \$20,000 car. Perhaps the A-A effect is somehow at play here?

Secondly, just because Tyler says the theorem isn't true, does that mean it isn't? He, after all, lives in a city and famously travels all over the world sampling the food when he gets there. No wonder he gets the best of everything when he arrives; it doesn't mean that he's eating what the locals eat. As for that Maine lobster: want to bet that the people who consume the most expensive specimens are those from Chicago who spent \$1500 on their New England vacation?

Try this Google search if you want to see some empirical evidence. I'm left without any firm conclusions on whether the theorem really works, but with an extra insight at least into how preferences are created. Traditional microeconomics takes consumer preferences as an externally given, fixed set of utility functions; but to understand how the world really works we need to be able to incorporate changing preferences endogenously into our models.

* Note that Tyler says the theorem is true for cultural goods - he casts doubt on it only for food products, which are the traditional exemplar of the theorem.