Exercise 1 Consider the following 1-period economy with a single representative agent. The agent is at time t = 0 endowed with eo = 1.5 and her future endowment at time t = 1 depends on the outcome of three possible economic scenarios as shown in Figure 1 Assume that the financial market is complete, i.e. the agent can obtain any future consumption plan given her budget constraint. e1(w1) = 3 e1(w2) = 2 e1(W3) = 1 Figure 1: State-contingent endowment of the agent. Each of the three states are equally likely. The agent's preferences are characterized by the utility function u(c) = 1, with > 0 and for 1 she has log utility. In addition she has time-additive expected utility with a time preference parameter 8 = 0.05. = (a) What is the agent's optimization problem in the complete market? Write the Lagrangian in terms of the consumption today, the state-contingent consumption and state-price deflator at time t = 1.