Exercise 1 Consider the following 1-period economy with a single representative agent. The agent is at time t = 0 endowe

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Exercise 1 Consider The Following 1 Period Economy With A Single Representative Agent The Agent Is At Time T 0 Endowe 1 (365.65 KiB) Viewed 27 times

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) = 7, 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) 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. (b) Find the unique equilibrium state-price deflator (w) for any y. (c) Find the equilibrium risk-free rate Rf for different parameters y € [0.5, 2]. Present your results in a graph.
Consider the zero-net supply Asset 1 with state-contingent dividends given in Figure 2. D₁(₁): = 2 D1 (W₂) = 1 D1 (W3) = 0 Figure 2: State-contingent dividends of Asset 1. (d) What is the equilibrium price of Asset 1 for any parameter ? (e) Find the equilibrium expected excess return of Asset 1, E[R₁]-R¹, for different parameters 7 € [0.5, 2]. Present your results in a graph. Explain the economic intuition behind your results. Consider the zero-net supply Asset 2 with state-contingent dividends given in Figure 3. D₂(₁): = 1 D₂ (W2) = 2 D₂(W3) = 0 Figure 3: State-contingent dividends of Asset 2. (f) Find the equilibrium expected excess return of Asset 2, E[R₂]-R³, for different parameters 7 € [0.5, 2]. Compare your results to Asset 1 economically, using the assets' correlation with the agent's future endowment.