Stochastic Arrow-Debreu Economies. Aggregate Risk.

1. Dene an AJmWDebieu competitive equilibrium with time- trading (ADE) for this economy. Use the Jllowing notation: pa for the price of the good at t = I], and p1, hr the price of the good at date-state {1,3}, for s = A, B. Also, feel free to use the notation for the \"state-dependent interest rate\Stochastic Arrow-Debreu Economies - aggregate risk The purpose of this exercise is to get you to think about how market economies allocate aggre- gate risk across different people. Exercise 19. Consider the following Arrow-Debreu economy with time-0 trading. There are two dates, te {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 So is known to all agents, and S1 is a random variable, S1 6 {A, B}, with NA = Pr (S1 = A|So) and TB = Pr (S1 = B|So), with WA = TB = 1/2. There are two types of agents, indexed by i E {1, 2}. For any c = (Co, CIA, CIB) E R. preferences of an agent of type i E {1, 2} are represented by a utility function U' (c) : R3 - R, where as in the lecture notes, co denotes consumption at t = 0, and Cls denotes consumption at date-state (1, s). Specifically, assume the utility functions for the two agent types are: U' (c) = 1-n CO + B _ ( A B ) " $ 1 - 1 1 - n Cis , with n > 0 1-n U2 ( c ) = 1-1 - + B L' SE( A, B) " sCls. As in the lecture notes, let ed denote the endowment of the consumption good that agent i owns at t = 0, and let els denote the endowment of the consumption good that agent i owns at date-state (1, s). Assume Co 1 els = e1= = 1te ifs = A 1 -E ifs = B, where & E (0, 1/2)