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.