Household bargaining, spouses' consumption patterns and the design of commodity taxes

We study the role and structure of commodity taxes when consumption and labor supplies are determined through a bargaining procedure between spouses, and where an optimal income tax is also available. We focus on the question whether there should be differences in tax treatment between "female" and "male" products. When weights (as well as wages) differ across couples, the heterogeneity is multidimensional and the Atkinson and Stiglitz theorem does not apply. In addition, when the social welfare function is individual-based, spouses' social weights may differ from their weights within the couples. This brings about Pigouvian considerations which in themselves may justify commodity taxes. We show that the expressions for the tax rates include Pigouvian and incentive terms. Their roles are most apparent in the case where some goods are consumed exclusively by one of the spouses. Supposing, for instance, that the female spouse has the lower bargaining weight, we find conditions under which the Pigouvian term calls for a subsidization of the "female good", and a taxation of the "male good". The incentive term depends on the distribution of bargaining weights across couples. For instance, for the exclusive consumption case, when the weight of the female spouse increases with wages, the female good tends to be consumed in larger proportion by more productive couples. Consequently, the incentive term makes it a candidate for taxation. In this case the Pigouvian term is mitigated.