Please help me with this question.

Q4. (18 points) Consider the Fisher's Model that we discussed in class: a consumer who lives for two periods, with income Y, in period one and income Yz in period 2. This consumer's lifetime (two-period) preferences are given by: U(C1, C2)= U(C1)+ BU(C2), Where U(C1)= C1 - =CY and, U(Cz)=C2 - = CZ , and B is the discount rate. The consumer maximizes his two-period utility. a) Write down the consumer's maximization problem, and set up the Lagrangian (4 points). b) Solve the problem and obtain the consumer's Euler equation. (4 points) Interpret the Euler equation. (2 points) c) Is your result different from Keynes' consumption theory? Explain it. (2 points) d) Suppose that Y, = $200, Yz =$100, C,= 150 ,and C2=160. What is the interest rate, r? (3 points) In equilibrium, how will the consumption decision of this consumer change if the interest rate increases? Explain it in words (3 points)