J Popul Econ (1988) 3:213-224 --Journal of Population Economics © Springer-Verlag 1988 Household composition and optimal commodity taxes Do demographic variables matter? Ran jan Ray* Department of Econometrics and Social Statistics, Faculty of Economics and Social Studies, Manchester University, Manchester MI3 9PL, United Kingdom Received March 29, 1988 / Accepted August 24, 1988 Abstract. This paper investigates conditions under which demographic vari- ables will have no impact on commodity taxes. We allow nonlinear and nonseparable preferences, a general demographic demand procedure, and a demogrant scheme linked to the number of children. Formulae for demo- graphic revision of tax estimates are presented in a form that can be easily ap- plied, and the only marginal data requirement is the number of children in the household. The paper extends an earlier exercise (Ray 1988) in avoiding the need for equivalence scales, and in using a demogrant scheme that is consis- tent with current practice in several European countries. The study confirms the robustness of the earlier discussion to the demogrant scheme adopted. 1. Introduction It is now widely accepted that optimal commodity taxes depend crucially on a household's demand response to changes in economic variables, most notably, prices and aggregate expenditure (Atkinson and Stiglitz 1980, Ch. 12, 14; Ray 1986) 1. What is not so widely appreciated, however, is that demographic vari- ables, namely, children in this paper may significantly affect the tax calculations via their effect on household expenditure pattern and price/expenditure elasticities. The empirical evidence on family budget data has established quite conclusively the significant influence of demographic variables on consumer de- mand. 2 Given the crucial role played by demand elasticities in optimal tax calculations, one should expect household composition or, more generally, demo- * I acknowledge, with thanks, the comments of two anonymous referees, but retain responsibility for errors that may remain. l See, also Sandmo (1987) for a recent unified interpretation of some of the well known results of optimal tax theory that highlight the crucial dependence of the tax rates on price and expenditure elasticities. 2 See, for example, Pollak and Wales (1981), Ray (1983)s' results on UK budget data.