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c) Show that the equilibrium conditions in parts (a) and (b) are equivalent to the following equilibrium conditions from the social planner's problem:? 7 = BE Ct 1 It 91 = (1 - 6) K141 d) Solve this model using guess and verify. In particular, find the policy functions for Kit, It and Of (Hint: start by guessing that investment and consumption are a constant share of output). Briefly discuss how, and why, the responses of consumption and investment to TFP shocks vary with 6. e) Briefly explain how you would solve this model computationally using a linearization- based technique. Give one advantage of this method over Value Function Iteration.Question 3 (20 points) Consider the following decentralized business cycle model. The representative household makes consumption (C) decisions to maximize lifetime expected utility: E _ p' (In CL) (1) subject to their budget constraint: ath=mN+K + l, (2) where w is the real wage, / is hours worked, K is capital, / is investment, * is the rental price of capital and II are profits from firms. As usual, 0 0. Is this intuition (always) correct in this model and why?Question 2 (20 points) This question studies the co-existence of money and credit. Time is discrete with an infinite horizon. Each period consists of two subperiods. In the day, trade is bilateral and partially anonymous as in Kiyotaki and Wright (1991) (call this the KW market). At night trade takes place in a Walrasian or centralized market (call this the CM). There are two types of agents, buyers and sellers, and the measure of both is normalized to 1. The per period utility for buyers is u(g) + U(X) - H, and for sellers it is -q+ U(X) - H, where q is the quantity of the day good produced by the seller and consumed by the buyer, X is consumption of the night good (the numeraire), and H is hours worked in the CM. In the CM, all agents can turn one unit of labor into a unit of good. The functions u, U satisfy the usual assumptions; I will only spell out the most crucial ones: There exists X* c (0, co) such that U'(X*) = 1, and we define the first-best quantity traded in the KW market as q' = (q : u'(g") = 1}. Here we will assume that there are two types of sellers. Type-1 sellers, with measure 1 -o, never accept unsecured credit. Hence, in any meeting with this type of seller, the buyer must pay on the spot (quid pro quo) with money. In contrast, type-2 sellers, with measure o, accept money but they also accept unsecured credit, in the form of a promise by the buyer to repay the seller in the forthcoming CM with numeraire good. However, there is a credit limit: the buyer can credibly promise to repay only an amount up to O - 1. New money is introduced, or withdrawn if a 0, u"(c) 0, f"(@)