a Exercise 1 Consider the following 1-period economy with a single representative agent. The agent is at time t O 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. ei(wi) = 3 ei(w2) = 2 e1(W3) = 1 w3 Figure 1: State-contingent endowment of the agent. Each of the three states are equally likely. 1-7 The agent's preferences are characterized by the utility function u(c) = , with y > 0 and for y = 1 she has log utility. In addition she has time-additive expected utility with a time preference parameter 8 = 0.05. a (c) Find the equilibrium risk-free rate Rf for different parameters y (0.5, 2). Present your results in a graph. a Exercise 1 Consider the following 1-period economy with a single representative agent. The agent is at time t O 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. ei(wi) = 3 ei(w2) = 2 e1(W3) = 1 w3 Figure 1: State-contingent endowment of the agent. Each of the three states are equally likely. 1-7 The agent's preferences are characterized by the utility function u(c) = , with y > 0 and for y = 1 she has log utility. In addition she has time-additive expected utility with a time preference parameter 8 = 0.05. a (c) Find the equilibrium risk-free rate Rf for different parameters y (0.5, 2). Present your results in a graph