# Good Grapes and Bad Lobsters: Applying the Alchian and Allen Theorem

## Article excerpt

I. THE THEOREM

The Alchian and Allen theorem states that adding a common charge to the price of two substitute goods increases the relative consumption of the higher quality good, real income held constant. The classic example of this theorem is from Alchian and Allen's [1964, 75] textbook University Economics.

Suppose that grapes are grown in California and that it costs 5 cents a pound to ship grapes to New York whether the grapes are "choice" or "standard" ... suppose further that in California the "choice" grapes sell for 10 cents a pound and the standard for 5 cents a pound... If grapes are shipped to New York, the shipping costs will raise the costs of "choice" grapes to 15 cents and of "standard" grapes to 10 cents. In New York the costs of "choice" grapes are lower relative to "standard" grapes (1.5 to 1) than in California (2 to 1)... New Yorkers faced with a lower price of "choice" grapes relative to "standard" will consume relatively more "choice" grapes than Californians will.

Alchian and Allen's theorem is solely about relative price effects and does not rely upon income effects or selection effects. It assumes that those most willing to pay the fixed charge do not have systematically different preferences and incomes as those not paying the charge. Furthermore, the theorem does not hold for corner solutions where the high- and low-quality goods are consumed by different classes of consumers, or equivalently, each consumer purchases only one unit of the good in question. We must then consider the different rates at which consumers of high- and low-quality goods decrease consumption when price changes. Purchasers of high-quality items need not reap more consumer surplus than purchasers of low-quality items.(1)

II. PER UNIT COSTS VERSUS FIXED AND SUNK COSTS

The Alchian and Allen theorem applies only when the costs are applied to each good on a per unit basis. Charging a single fee or fixed tax to allow consumption of the good to take place does not create a substitution effect. The fixed fee, once paid, is treated as a sunk cost and consumers face the same relative prices they faced initially. An increase in the cost of a "grape-shipping permit," for instance, will not have any direct effects on the quality of grapes.

Many of the examples of the Alchian-Allen theorem that have been given in the literature do not specify true per unit taxes. Umbeck [1980], for example, argues that an increase in the installation charge for phones will increase phone usage. But in this case the relevant charges are fixed. The installation or monthly service charge will increase current phone usage only if individuals are planning to go without a phone in future periods. In contrast, individuals who will continue phone service into the foreseeable future cannot minimize their monthly charges or their installation charges by increasing their phone usage now. Any change in behavior would be due to an income effect which is unpredictable.

A trickier problem is raised by Borcherding and Silberberg [1978, 133] who claim that

it does not matter if the goods are shipped to the consumers or the consumers are shipped to the goods. Going to Maine or the country involves a transport cost to people not from Maine or the country. What [the Alchian-Allen theorem] predicts, therefore, is that tourists in Maine will consume, on average, higher quality lobsters than the natives and similarly for city versus rural dweller's purchases of produce at roadside stands...if people who make a special trip to Maine in fact choose to eat "truly delectable" instead of inferior quality lobsters sold there, this confirms Alchian and Allen's thesis. (emphasis added)

When the tourists are transported, the Alchian-Allen theorem applies only if (1) the tourists are planning both high-quality and low-quality trips in the future, and (2) "high-quality lobster" is strongly and positively related to a "high-quality vacation" in Maine. …

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