Homothetic Non-CES Demand Systems with Applications to Monopolistic Competition

This article reviews homothetic non-CES (constant elasticity of substitution) demand systems and their implications when applied to monopolistic competition, to offer guidance to those looking for flexible and yet tractable ways of departing from CES. Under general homothetic symmetric non-CES, two measures, substitutability and love-for-variety, are introduced to identify the condition under which the equilibrium product variety is excessive or insufficient. Because homotheticity and symmetry alone impose little restriction to make further progress, we turn to the homothetic single aggregator (HSA) class. HSA is more flexible than CES and translog, which are its special cases, and yet equally analytically tractable, because all cross-variety interactions are summarized by the single aggregator. Under HSA, substitutability is increasing in product variety if and only if Marshall's second law holds, which is a sufficient condition for love-for-variety to be diminishing in product variety and for the equilibrium product variety to be excessive. Monopolistic competition under HSA remains tractable even under various forms of firm heterogeneity and in multi-market settings.