The Generalized Alchian–allen Theorem: A Slutsky Equation for Relative Demand

Abstract

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)

Testing the Alchian–Allen theorem for three goods using the pseudo Poisson model

“…There were several recent attempts to generalize the AA theorem on different grounds. Minagawa and Upmann () do so accounting for income and endowment effects and provide two versions of a generalized AA 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.…”

“…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. Therefore, the theorems offered by Minagawa and Upmann () can be regarded as extensions of the Slutsky equation for relative demand.…”

“…Given the growth in product vertical differentiation in recent years, economists developed and refined general economic theory behind the AA theorem considering n ‐good qualities (e.g., Liu, ; Miljkovic, ; Minagawa & Upmann, ). Nonetheless, there has been only one study testing the AA theorem for more than two goods (Miljkovic, ).…”

Price Effects on Compound Commodities

“…This general implication has also practical relevance, for example, for tax policies. Governments often aim at reducing total consumption of demerit goods 2 Further details and development on this topic can be found in, e. g., Minagawa and Upmann (2015).…”