Equal shadow wealth: A new concept of fairness in exchange economies

•This paper introduces a new notion of fairness in exchange economies and a measure of unfairness.•Agents have equal shadow wealth if a numeraire commodity is distributed so as to offset differences in the holdings of other commodities.•Inequality is measured as the deviation between the actual distribution of the numeraire and such an egalitarian distribution.•The new concept is contrasted with the notion of no-envy (Foley, 1967) and the envy-intensity measures of Chaudhuri (1986) and Diamantaras and Thomson (1990).•Sufficient conditions are established which ensure the existence of equitable and efficient allocations.

In this paper I introduce a new notion of fairness in exchange economies as well as a measure of unfairness. First, I consider the benchmark case in which agents have identical preferences, and I then extend the framework to allow for heterogeneous tastes. In both cases, I identify an appropriate egalitarian benchmark which requires that a numeraire commodity be distributed in such a way so as to offset differences in the holdings of other commodities. Inequality is then measured as the deviation between the actual distribution of the numeraire and such an ideal distribution. This renders a complete social ordering. Next, I contrast this notion of equal shadow wealth with the notion of no-envy (Foley, 1967) and with the envy-intensity measures proposed by Chaudhuri (1986) and Diamantaras and Thomson (1990). I also investigate conditions which ensure the existence of equitable and efficient allocations. The concepts developed here may be generalizable to a wide range of environments including economies with externalities and indivisible goods as well as relatively unstructured environments such as those involving abstract opportunity sets. In addition, this approach offers a simple method to measure multidimensional inequality.