Take the model of risk sharing presented in class with with I agents and S states of nature. For an agent i denote yi0 her endowment at time t = 0, and ys i1 her endowment at time t = 1 in state s. Similarly, denote ci0 her consumption at time t = 0, and cs i1 here consumption at time t = 1 in state s. Assume that agent i is given by isoelastic utility with parameter , i.e., she wants to maximize c1 i0 1 1 SX s=1 s (cs i1)1 1 1 Agents can trade Arrow-Debreu securities in zero net supply: the AD security associated with state s has price ps. 1. Show that the first-order condition of agent i's optimization problem gives cs i1 ci0 = s ps 1 2. Denote Y0 the sum of individual endowments at time 0 and Y s 1 the sum of individual endowments at time 1 in state s. Using market clearing (i.e. that sum of individual consumptions is equal to the sum of individual endowment), show that Y s 1 Y0 = s ps 1