Value Preserving Welfare Weights for Social Optimization Problems

Abstract

Social optimization problems typically maximize the sum of individual weighted utilities over feasible allocations that satisfy certain constraints. While social optimization problems are at the heart of economic analysis, it is not always clear how to choose individual welfare weights. In this paper, we propose a mechanism that determines individual weights for social optimization problems. We first provide a set of axioms which uniquely determine, for any welfare function (social or individual), the contribution of a bundle of goods to that welfare function. We then choose welfare weights so that the contribution of an individual’s initial endowments to social welfare is proportional to the contribution of that individual’s final consumption allocation to his own welfare. That is, we choose the weights so that the ratio of social to private contributions is the same across individuals. For complete markets, we show that these weights are equal to the well known Negishi welfare weights. However, our principle can also be applied to other contexts where the welfare theorems do not hold. We provide an optimal taxation example that illustrates our methodology. Our results suggest that the allocations and tax rates with the weights we propose can substantially differ from the ones obtained with a standard utilitarian social welfare function. In particular, the weights we propose mute the redistribution motive inherently present under utilitarianism. As a result, with high levels of inequality and positive government spending, the government predominantly taxes labor income with the weights we propose, while the utilitarian approach predominantly taxes capital income. Moreover, with no government spending, taxes are zero with the weights we propose, while the utilitarian approach taxes capital and subsidizes labor.