For this question you are working with an individual who lives for two dates in pure exchange economy: - y1= income at time 1,y2= income at time 2 (both known with certainty). - a1= financial assets carried into the first date (time 1 ), a2= financial assets carried into the second date (time 2). - C1= consumption of the composite good at the first date, C2= consumption at the second date (choice variables). - r= per period interest rate (known with certainty). - Assumed constant, are applies to both savings and debt. - No transaction costs, taxes or other imperfections. - Utility function: - Lifetime Utility: U(C1,C2)=u(C1)+u(C2) - Period Utility: u(Ct)=ln(Ct) Part A: Write down the decision maker's optimization problem (hint: you need the objective function and the constraint). Part B: Compute first-order conditions. For this part, you should end up with Ci as a function of C2,r, and (or C2 as a function of r,, and C1 ). Part C: Finish solving the model. L.e., solve for Ci and C2 as a function of income, financial assets, beta, and the market interest rate. Hint: you need to use the first order conditions and the intertemporal budget constraint. Part D: Interpret your findings. Please try to focus your discussion on how and (1+r) impact the optimal consumption plan