THE GENERALIZED ALCHIAN–ALLEN THEOREM: A SLUTSKY EQUATION FOR RELATIVE DEMAND

We generalize the Alchian–Allen theorem so as to account for income and endowment effects and provide two versions of a Generalized Alchian–Allen theorem: one for a unit cost component and one for a proportional cost component. Both versions provide a decomposition of an uncompensated change in the demand ratio of two goods into a substitution effect and an income‐endowment effect—and may thus be regarded as extensions of the familiar Slutsky equation for relative demand. Finally, we apply our results to the choice of real estates and to parental time allocation decisions, the latter providing implications for child care policies. (JEL D11, H21, J22, R21)