Consider a model exactly like that in Question 1 where the person receives income $37,254 in period 1 and additional income $33,169 in period 2 - except let's now suppose that the person faces a liquidity constraint. Specifically, she can still save at an interest rate of 3%, but if she borrows, then she must pay an interest rate of 9%. (a) If the person wants to save, the relevant interest rate is 3\%. For what values of is it optimal to save? [Hint: You already know the answer from Question 1.] (b) If the person wants to borrow, the relevant interest rate is 9%. (i) Suppose the interest rate is 9%, and solve for the optimal c1 and c2 as a function of . (ii) If the interest rate is 9%, for what values of is it optimal to borrow? [Note: Please report your answer to 5 decimal points.] (c) Given the liquidity constraint, for what values of is it optimal to neither borrow nor save? [Hint: Two conditions must hold: (i) must be such that the person does NOT want to save at an interest rate of 3%, and (ii) must be such that the person does NOT want to borrow at an interest rate of 9%. (d) Draw three pictures that illustrate the three cases when it's optimal to save, when it's optimal to borrow, and when it's optimal to neither borrow nor save. Each picture should depict (i) the budget constraint, (ii) some indifference curves, and (iii) the optimal c1 and c2. Question 3 Suppose that Mr. Z has a tree growing in his yard that has become too large, and he must cut it down within the next four years. Cutting down the tree requires effort, and he would like to wait and cut down the tree later. However, each year that he delays, the tree gets bigger and requires even more effort to cut down. Specifically, suppose that the effort cost to cut down the tree in year is c(), where c(1)=13,c(2)=20,c(3)=32, and c(4)=55. Suppose that Mr. Z is an exponential discounter with discount factor , and that the only utility consequence of cutting down the tree is the disutility of effort experienced when the tree is cut