A conditional demand approach to the Alchian-Allen effect

We explore the Alchian-Allen effect-that is, the effect of an absolutely equal increase in the price of two goods on their demand ratio-for conditional (viz. short-run) and unconditional (viz. long-run) demand functions. We show that the Alchian-Allen effect for unconditional demand equals its conditional counterpart (where the consumption level of a third good is held constant) if the two goods feature identical substitution elasticities with the third good. Remarkably, this result holds true for both Hicksian and Marshallian demand functions.