University of Washington
Generally speaking, models of equilibrium involve a game-like competitive structure that, in the case of concave utility functions, can be set up as a variational inequality. What's surprising is that the Lagrange multipliers for the budget constraints of the various "agents' in the economy can be used to generate weights for these agents which have a remarkable interpretation. The equilibrium allocation of resources coincides with an optimal allocation in the "collective" problem in which the weighted sum of the agents' utilities is maximized subject only to the constraint on total resource availability. Moreover, the equilibrium price vector comes out then as the multiplier vector for that constraint. This observation isn't just of theoretical interest. It might lead to an iterative scheme for computing an equilibrium in which collective optimization is executed with successive adjustment of the weights.
University of Washington