Balanced equilibrium in pseudo-markets with endowments

In a variant of Hylland and Zeckhauser (1979)'s model that allows agents to start out with different endowments, we develop a pseudo-market procedure that allows the policymaker to decide to what extent individual endowment differences shall be balanced by the average endowment. Our procedure sidesteps the known non-existence problem of Walrasian equilibria, and finds an efficient and balanced individually-rational allocation. Envy in our procedure is justified in a utilitarian sense: an envying agent's endowment must make a lower contribution to standard weighted utilitarian welfare than that of the envied agent.