Problem 8.3: 3 Periods. (15 points) Consider an agent who lives for 3 periods and has preferences given by u(c1,c2,03) = x/c_1+0.5\\/c_2+0.25\\/E The agent has no initial wealth. Her after-tax income is equal to $10,000, $20,000 and $30,000 in period 1, 2, and 3, respectively. Assume that the consumer can freely borrow and lend at an interest rate of 5%. (a) Calculate the optimal level of consumption in each period. (b) Suppose the agent's income increases by $10,000 in period 1. Calculate how consumption in the three periods of life changes in response to this increase in income. Explain your answer. (c) Suppose the agent's income increases by $10,000 in period 3. Calculate how consumption in the three periods of life changes in response to this increase in income. Explain your answer. Why is your answer here different than the answer in the previous example? (d) Suppose the agent's income increases by $10,000 in all 3 periods of its life. Calculate how consumption in the three periods of life changes in response to this increase in income. Explain your answer. Why is your answer here different than the answer in the previous examples? Redo Problem 8.3 above under the assumption that the agent can only save and not borrow. Redo Problem 8.3 above under the assumption that the consumer has logarithmic preferences over consumption: u(c1, C2, C3) = In(c1) + 0.5 1n(c2) + 0.25 In(c3)