Exercise 2. Consider the following Arrow-Debreu economy with time-0 trading. There are two dates, t E {0,1}. At date t = 1 there are two states of the world, denoted "A" and "B" Formally, the state of the world at date t is denoted St, where 50 is known to all agents, and 81 is a random variable, S 0 {A, B}, with #A = Pr (S = A|So) and T = Pr (S = B|So), with TA TB= 1/2. There are two types of agents, indexed by i= 1,2. The preferences of an agent of type i are represented by 1-n Co 1-7 +BElA.B) Ts with >0 U' (c) 1- 1 1-n Co U2 (e) 1 -1 'se{A,B} The endowments are 1 1+e ifs Al 1-e ifs B, eis= where &E(0,1/2). 1. Define an Arrow-Debreu competitive equilibrium with time-0 trading (ADE) for this economy Use the following notation: po for the price of the good at t = 0, and pis for the price of the good at date-state (1, s), for s = A, B. Also, feel free to use the notation for the "state-dependent interest rate", R, = po/Pls 2. Find the solution to the individual utility maximization problem that agent 1 solves in the ADE 3. Find the solution to the individual utility maximization problem that agent 2 solves in the ADE. (Make sure the solution to the problem contemplates all possibilities, including cases where the nonnegativity constraints on consumption at date t = 1 may bind.) 4. Prove that the prices together with the allocation = dA 1 2E 1 2E