Question 2: Suppose there is a desert with two people, Anya and Bryce, and two goods, rocks and sand piles. Let Anya's allocation of rocks and sand piles be denoted by (TA, 3A) and Bryce's by (TB, 33). Their respective utility functions are uA(rA,sA) = ri/zsh/z and uB('rB, 83) = rig/2 + 33 In total, there are 10 rocks and 10 sand piles in the market. Anya's endowment is 8A, a pair denoting her initial allocation of rocks and sand piles. Bryce's endowment 33 is the remaining rocks and sand piles. For Questions (3)(5), the prices of rocks and sand piles are p, and 193 respectively. You can ignore any corner solutilns in this problem. (1) Suppose Anya's endowment is 6,4 = (6, 6). Find M RSA and M RSB. Suppose Anya's endowment is 6,4, = (6, 3). Find M RSA and M R83. (2) Find the formula for the contract curve. This can be a function of 3A in terms of TA (the note above that you can ignore corner solutions means that you can ignore the part of the contract curve on the edge of the box). (3) Normalize p8 = 1 and nd p, and a pair of endowments 6A and eg that induce the competitive equilibrium allocation where (TA, 3A) 2 (6, 1.5). (4) Normalize p, = 1 and suppose 8,4 = (5,65). Find a price p,~ that induces a competitive equilibrium and nd the corresponding competitive equilibrium allocation. (5) Draw an Edgeworth box with the contract curve from Question (2); the budget line, endowment, and competitive equilibrium allocation from Question (3); and the budget line, endowment, and competitive equilibrium allocation from Question (4)