Consider a one good, 2 periods (t-1,2) Arrow Debreu economy with 2 investors indexed by i-A, B. There are 2 states of the world indexed by $1.2 and they have equal probability. The agents consume and receive endowment only at the second period. There is no endowment or consumption in the first period, though agents can trade in the first period. 1 The endowments for agent A ise1 = (1.2) (.e. I unit the of the consumption in state I and 2 units of the consumption good in state 2) and the endowment for agent Bise" = (2, 1). If agent A consumes the consumption plan c (c.) and agent B consumes the planc" (c) the utility for agent A is given by U^(c^) = log(em) + log(e) And the utility function for agent B: U"(c") = -log(e) + log(c) Q2. A Characterize the set of Pareto optimal allocations between the two agents. (Hint: You may need to consider the social planner with the weight