Consider a two period economy in which the representative consumer has nocontrol over his/her income y1 and y2. The lifetime utility function of therepresentative consumer is:u(c1, c2) = ln (c1) + c2 (3)The period 1 budget constraint of the consumer is given byP1c1 + A1 = Y1 + (1 + i)A0 (4)and the period 2 budget constraint faced by the consumer is given (in nominalterms) by:P2c2 + A2 = Y2 + (1 + i)A1 (5)where c1 and P1 is consumption and prices in period 1, respectively, and c2and P2 is consumption and prices in period 2, respectively, A0 is the savingat the beginning of period 1, A1 is the saving during period 1, and A2 is thesaving during period 2, i is the nominal interest rate, Y1 and Y2 are nominalincome in period 1 and period 2 respectively. You are given that the marginalutility of consumption in each period is strictly positive and diminishing. Basedon the concepts in the two period consumption-savings framework, answer thequestions that follow. (Make note of the specific functions and functional formsin the question and use them in your answers where required.)

Consider a two period economy in which the representative consumer has no control over his/her income y; and y,. The lifetime utility function of the representative consumer is: u(cy,c2) =1ln (1) + co (3) The period 1 budget constraint of the consumer is given by Pll + Al = Yl + (]. + !.)A(] (4) and the period 2 budget constraint faced by the consumer is given (in nominal terms) by: PQGQ + A-2 YQ + (]. s L)Al (5) where y and P; is consumption and prices in period 1, respectively, and c and P, is consumption and prices in period 2, respectively, Ay is the saving at the beginning of period 1, A, is the saving during period 1, and A, is the saving during period 2, 7 is the nominal interest rate, Y7 and Y5 are nominal income in period 1 and period 2 respectively. You are given that the marginal utility of consumption in each period is strictly positive and diminishing. Based on the concepts in the two period consumption-savings framework, answer the questions that follow. (Make note of the specific functions and functional forms in the question and use them in your answers where required.) Assume that the consumer starts out with no savings in the beginning of period 1, that is, Ay = 0. 1. It follows from the information given in the question that As should be 0. Explain why in not more than 1-2 sentence(s). [2] 2. Combine the period 1 and period 2 budget constraints to derive a lifetime budget constraint in nominal terms. [2] 3. Write the Lagrangian function for the consumer's lifetime problem using the lifetime utility function given to you in the question, and the lifetime budget constraint derived above. [2] 4. Derive the first order condition with respect to ;. [2] 5. Derive the first order condition with respect to ca. [2] 6. Using the FOCs derived above, derive the consumption-saving optimality condition for the consumer. Make sure you do not have any multipliers in your final answer. [2]