Competitive Equilibrium in Affine Economies

Our approach is committed to suitably enriching the duality commodity-price at the level of a single structure instead of the classical usage of dual pairs. To this aim, we study economies having as commodity space the vector lattice of real affine continuous functions on a Bauer simplex playing the role of the price space. Furthermore, the initial endowment is a partition of the unity and the preferences are represented by valuation functions on the extreme points boundary of the price space. The main goal in this paper is the obtainment of a competitive equilibrium existence theorem.