Question [1]: For each of the following pure exchange economies with 2 goods and 2 consumers, draw a well labelled representation of the Edgeworth Box and clearly indicate and/or describe the Pareto Set, i.e. the set of Pareto optimal allocations. Indicate the set of allocations that are only weakly Pareto optimal if there are such allocations. 1. us(x, y) = x + Vy; uB(x, y) = 8x + y; Total endowment (10, 20) 2. uA(x, y) = min{x, y}; uB(x, y) = x + 2Vy; Total endowment (10, 15) 3. uA(x, y) = min{x, y}; uB(x, y) = max{x, y}; Total endowment (20, 10) 4. The following requires calculus techniques and the Pareto Set may be hard (impossi- ble?) to draw precisely. Provide a 'rough line' indicating the key features only (like, does it start at origins? Does it lie above or below the main diagonal, or cross it? Are any boundary elements Pareto Optimal?) Supply a short argument / derivation to support your work. u(x, y) = x + 4In(y); uB (x, y) = 41n(x) + y; Total endowment (10, 10) 5. The following requires calculus techniques and the Pareto Set may be hard (impossi- ble?) to draw precisely. Provide a 'rough line' indicating the key features only (like, does it start at origins? Does it lie above or below the main diagonal, or cross it? Are any boundary elements Pareto Optimal?) Supply a short argument/ derivation to support your work. uf(x, y) = x1/3y2/3; uB(x, y) = x1/3y2/3; Total endowment (10, 20)