The Boadway Paradox Revisited: The Case of Compensated Equilibrium

The Boadway paradox, named after its discoverer, the well-known Canadian economist Robin Boadway, points at an inherent aw in the concepts of compensat- ing variation (CV) and equivalent variation (EV). A redistribution of endowments across agents has no e ciency impact. Nevertheless, the aggregate CV (EV) turns out to be non-negative (non-positive), and in general strictly positive (negative) for discrete redistributions. In this paper we draw on the concept of compensated equilibrium and show that in such a context a pure redistribution in a multi-agent, multi-commodity society causes the aggregate CV to equal zero (and coincide with the aggregate EV). Hence, the measure correctly re ects the fact that gainers are unable to compensate losers and still gain. Previous authors, claiming that they have resolved the paradox, have used Edgeworth boxes to arrive at a graphical result for a two-commodity, two-agent society. We also show that the CV based on compensated equilibrium correctly captures the sign of the value of marginal as well as non-marginal changes in endowments. The latter is not the case for the measure based on Marshallian concepts. In addition, the paper provides a generalization from a pure exchange economy to a production economy.