1. Let o3 denote the exogenously given initial asset position of individual i. Households at each node 3* can trade a full set of Arrow securities. Denote their prices by qs', 3H1}- Dene a sequential markets equilibrium. 2. Let the utility function take the form = lcr U[c] {EH log(c) if o' = 1 Let endowments of both households satisfy 6309*) = 36: (3*): that is, household 2 has three times the endowment of household 1 at every node. Also assume that a}, = {1% = I]. Compute the unique sequential markets equilibrium. 3. Take an arbitrary node a1 in period t = 1. Calculate the price of a risk free bond, traded at s:l that pays off one unit of consumption in period t = 4. If you could not solve question 2, state your results in terms of the Gil-9E: 3H1}- 4. Suppose you have solved the social planner problem 22 Z Bis )Utcilis {sin r=o a=o ,tEsr s.t. 13*}+C{3*) = mist] where the planner attaches equal weights to both consumers. IDutiine an algorithm of how to nd initial asset positions (om) such that the solution to the social planner problem is [together with the appropriate prices) a sequential markets equilibrium given these asset positions. What can you say about the sign of a and what about the sign of a3? Note that you do not have to perform any calculations for this question, but you do have to justify your