The Progressivity of Equalization Payments in Federations

We investigate the conditions under which an inequality averse and additively separable welfarist constitution maker would always choose to set up a progressive equalization payment scheme in a federation with local public goods. A progressive equalization payment scheme is defined as a list of per capita net (possibly negative) subsidies – one such net subsidy for every jurisdiction - that are decreasing with respect to jurisdictions per capita wealth. We examine the question in a setting in which the case for progressivity is a priori the strongest, namely, all citizens have the same utility function for the private good and the public good, inhabitants of a given jurisdiction are all identicals and are not able to move accross jurisdictions. We show that a necessary and sufficient condition that the objective function of the constitution maker must satisfy to favour a progressive equalization payment scheme for all distributions of wealth and all population sizes is to be additively separable between each jurisdiction’s per capita wealth and number of inhabitants. When interpreted for a mean of order social welfare function, this condition is shown to be equivalent to additive separability of the individual’s indirect utility function with respect to wealth and the price of the public good. Some implications of this restriction to the case where the citizen direct utility function is additively separable are also derived.