Question 1 [16 points] Consider an exchange economy with three dates {t=0, 1, 2} and three agents {A, B, C} with utility functions: Ua=Cao + (1-1a)( Cart Ca2) Up=Cpo+Cpi1+ (1-/8)Cp2 Uc=Coot Cc1t Ce2 In questions (a) to (e) it 1s assumed that /3=1 and /p=1. The agents have the following endowments. Agent A owns an asset x at t=0 and nothing else at the other dates. Agent B owns w=100 at t=0 and nothing else at the other dates. Agent C owns w=100 at t=1 and nothing at the other dates. The asset pays off x at t=2 where X is either 0 with 0.8 probability or 500 with 0.2 probability. The risk free rate and repo rate are both zero. a) What is the expected payoff V of the asset? [1 Points] Suppose no agent can produce information. b) Suppose agent B owns the asset at t=1. What amount Lg can agent B borrow from agent C in a repo trade at t=1 and what is the haircut? [2 Points] c) In equilibrium, what amount L can agent A borrow from agent B at t=0? [1 Points] Now suppose agent C can produce private information about the true realization x at t=1 and the information cost is y=40. d) What is the maximal amount Lg that agent B can borrow from agent C with probability 1?7 What is the haircut? |2 Points] ) In equilibrium, what 1s the maximal amount L4 that agent A can borrow from agent B at t=0? And what is the haircut for agent A? Note, the strategy in question (d) above is not the only strategy that agent B can choose. [3 Points] (H) Suppose /4=0.1 and /g=1. In equilibrium what 1s the amount agent A wants to borrow from agent B? In addition, provide a verbal explanation for the results. [4 Points] (2) Suppose /4>0.1 What 1s the full set of {/g} such that there is no haircut when agent A borrows from agent B? If there is not enough information to answer this question, make further assumptions to answer it. In addition, provide a verbal explanation for the result. [3 Points]