Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones

In this paper, we consider an economy with infinitely many commodities and market failures such as increasing returns to scale and external effects or other regarding preferences. The commodity space is a Banach lattice possibly without interior points in the positive cone in order to include most of the relevant commodity spaces in economics. We propose a new definition of the marginal pricing rule through a new tangent cone to the production set at a point of its (non-smooth) boundary. The major contribution is the unification of many previous works with convex or non-convex production sets, smooth or non-smooth, for the competitive equilibria and for the marginal pricing equilibria, with or without external effects, in finite-dimensional spaces as well as in infinite-dimensional spaces. In order to prove the existence of a marginal pricing equilibria, we also provide a suitable properness condition on non-convex technologies to deal with the emptiness of the interior of the positive cone.