Pareto optima, welfare weights, and smooth equilibrium analysis

The first part of this paper deals with the parameterization of the set of Pareto optima by utility levels and by the welfare weights. In the second part, the parameterization by the welfare weights is used to establish properties of the Negishi equation system associated with the finite general equilibrium model. This approach yields proofs of the regularity of the no-trade equilibria and of the existence of equilibria by a degree argument that are new. The formulation (and the proof) of these properties within the setup of the Negishi equation system plays a crucial role in extending these properties to the infinite horizon model with discounted utility functions.