Wealth concerns and equilibrium

Most properties of the classical general equilibrium model without externalities fail to extend to the wildest forms of consumption externalities. The recent interest for wealth concerns, a kind of externality associated with herding behavior and other-regarding preferences, motivates a study of the general equilibrium exchange model with those externalities. The diffeomorphism of the equilibrium manifold with a Euclidean space, the smoothness and properness of the natural projection and its non-zero degrees are shown to hold true for endowment spaces with variable total resources. Other properties of the classical exchange model without externalities are fragile in the sense that they do not resist the introduction of wealth concerns even in models where consumers preferences are represented by the simplest forms of utility functions like the log-linear (or Cobb-Douglas) functions. The most notable fragile properties are the uniqueness and regularity of equilibrium at equilibrium allocations and the stability of no-trade equilibria.