Heterothetic Cobb Douglas: Theory and Applications

We study a class of preferences that we call Heterothetic Cobb-Douglas (HCD). They feature unitary own-price elasticity and non-unitary income effects so that differences in expenditure shares for a given good are solely due to income effects. HCD preferences generate a tractable demand system that can be introduced in standard general equilibrium models, yielding rich results. We illustrate HCD’s properties with different applications. First, we show that under HCD preferences, the money-metric cost of inflation in a cross-section of households can be computed with information on prices, expenditure shares, and total expenditures. Second, applied to growth theory, we show that HCD preferences strengthen and generalize the classic results by Kongsamut et al. (2001) and Foellmi et al. (2008). Third, when applied to economic geography and international trade, we show how HCD preferences yield new insights in the Krugman (1991) core-periphery model, the class of spatial economy models of Allen and Arkolakis (2014) and Redding (2016), and the monocentric city model (Alonso, 1964; Mills, 1967; Muth, 1969). Here, the combination of unitary own-price elasticity and equalization of utility over space plays a crucial role in making the analysis tractable.