Equilibrium correspondence of linear exchange economies

According to Mertens (Ref. 1), the set of equilibrium prices in a linear exchange economy is a convex polyhedral cone (after adding {0}). We give a constructive proof of this fact. Then, we establish a lower-semicontinuity property of the equilibrium price correspondence. The set of equilibrium allocations is a closed, convex polyhedron. We give a characterization of this set.