The Alchian-Allen theorem and the law of relative demand: The case of multiple quality-differentiable brands

The Alchian-Allen theorem of “shipping the good apples out” (the AA theorem) is based on a law of relative demand which states that as the price ratio of one good to another becomes larger, the demand for the former good becomes smaller relative to the demand for the latter good. However, both the AA theorem and the law of relative demand have only been discussed in the context where a commodity group has just two quality-differentiable versions. This paper defines relative demands and investigates their properties for the more general situation where a commodity group consists of more than two similar but quality-differentiable brands. The results obtained extend the AA theorem and the law of relative demand.