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lConsider the Fisher's Model that we discussed in class: a consumer who lives for two periods, with income 1'1 in period one and income 1"; in period 2. This consumer's lifetime [twoperiod] preferences are given by: \"(C1-Cz}= U(E'1)+ Utz}. 'Where U{C1)= c1 is: and, U(cz)= c2 is; . and a is the discount rate. The consumer maximizes his two-period utility. 3} Write down the consumer's maximization problem, and set up the Lagrangian {4 points}. l1} Solve the problem and obtain the consumer's Euler equation. {4 points} Interpret the Euler equation. [2 points) It} Is your result different from Keynes' consumption theory? Explain it. {2 points) d) Suppose that Y1 = 5200, Y; = Sl, C1= 151} ,and C2=l. 1What is the interest rate, r? {3 points) In equilibrium, llw will the consumption decision of this consumer change if the interest rate increases? Explain it in words (3 points)