Shipping the Good Apples Out: Alchian-Allen Theorem of Various Qualities

This paper explores conditions for which Alchian-Allen theorem–the finer quality product is relatively more purchased than the lower one in regions where additional costs are imposed–holds in models of various but finite qualities. In this paper, “finer qualities raise ratios to lower ones in response to transportation costs” defines the various qualities version of Alchian-Allen theorem. Then we find Alchian-Allen theorem holds if and only if consumptions of neighbor qualities are not so different and weighted averages of compensated elasticities by inverse of prices are decreasing in qualities. In order to provide plausible intuitions, some sufficiency conditions are also suggested.