Value Preserving Welfare Weights for Social Optimization Problems

Social optimization problems maximize the weighted sum of individual utilities over feasible allocations that satisfy certain constraints. In this paper, we propose a method that determines endogenous individual weights for such problems. We …rst provide three axioms which uniquely determine, for any welfare function, the contribution of a bundle of goods to that welfare function. We then de…ne weights to be value preserving (VP) if the contribution of an individual’s initial endowments to the social welfare function is proportional to the contribution of the …nal consumption allocation to that individual’s welfare function. That is, the selected weights set the ratio of the social value of one’s endowment to the private value of one’s …nal allocation equal across individuals. We show that VP weights coincide with Negishi weights and the corresponding VP allocations coincide with Walrasian allocations in Arrow-Debreu economies. In contrast to Negishi weights, VP weights can also be used in economies with distortionary taxes or incomplete markets where the welfare theorems do not hold. As an application, we show how VP weights can be computed numerically in the context of a standard optimal taxation problem. We also compare the optimal tax scheme under VP weights with the one under exogenously assumed equal weights. By muting the redistribution motive inherent in the equal weights assumption, VP weights can highlight the aspects of optimal tax schemes that derive from taxation motives other than redistribution. Finally, we show how to extend our general methodology for computing social welfare weights to other normative principles of justice. Keywords: Social Welfare Function, Heterogeneous Households, Redistribution, Optimal Taxation JEL Classi…cation: D63, E62, H21 We would like to thank Marina Azzimonti, Dirk Krueger, Fransesc Ortega, Victor Rios-Rull, Warren Sanderson and Matthew Weinzierl for useful comments and suggestions.