The collective allocation of commodities in a democratic society: a generalization

Abstract

Lovell, in a recent article in this journal, probed the properties of a majority rule equilibrium. His conclusions, although insightful, are dependent upon his assumptions about the utility function. If individuals have constant marginal utility of income, Lovell shows that resorting to the democratic process may lead to overproduction of publicly distributed goods. If preferences are characterized by a Cobb-Douglas utility function, all voters will prefer the same level of governmental services in a democratic setting; under private production, consumption would increase with income. Lovell also shows that if individuals have a CES utility function and if the elasticity of substitution between "public" and private goods is less than unity, then per capita consumption of the publicly provided good is less than what per capita consumption of that good would be, were it privately produced and sold. In this note, these and other conclusions are shown to be special cases of the more general conclusion that in a democracy richer residents will demand higher levels of collective goods than their poorer neighbors only if the income elasticity of demand for governmental services exceeds the elasticity of substitution between collective goods and privately consumed goods. If the income elasticity exceeds the elasticity of substitution, then under rather innocuous assumptions about the income distribution, resorting to public provision of goods can be shown to reduce the level of services provided. Thus, it is the relative size of the income elasticity and the elasticity of substitution that determine the characterization of majority rule. The model can be used to examine the impact of deductability provisions for local tax assessments, mergers, and revenue pooling on the allocation of governmental goods; the model can also provide a framework for predicting