On the complexity of market equilibria with maximum social welfare

Abstract. We consider the compu-tational complexity of the Market equilibrium problem by exploring the structural properties of the Leontief exchange economy. We prove that, for economies guaranteed to have a mar-ket equilibrium, nding one with max-imum social welfare or maximum indi-vidual welfare is NP-hard. In addition, we prove that counting the number of equilibrium prices is #P-hard