1. Let (2,1)?F. Since by Theorem 1, a competitive equilibrium allocation belongs to the core, (1,2) cannot be a competitive equilibrium allocation. However, (p,A) is a competitive equilibrium;Let N = {1,2} and suppose rk 1 (2) > rk
2. A theorem on connected graphs in which every edge belongs to a 1-factor
3. ) > rk 2 (1) and (1,2) / ? F. Then, there is no competitive equilibrium in this economy. Suppose (2,1) is a competitive equilibrium. If p(1) ? p(2) then, agent 2 prefers object '2' to object '1' and further object '2' is affordable to agent '2';Case 3: rk 1 (1) > rk