This question asks you to reconsider the when-to-cut-a-tree problem (from Question 3 on Problem Set #4). Once again, suppose that Mr. X 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 geta bigger and requires even more effort to cut down. Specifically, suppose that the effort cost to cut down the tree in year 7 is c(), where c(1) = 24, (2) = 29, c(3) = 36, and c(4) = 48. Suppose that Mr. X has present bias with 3 = .8 and = .9, and that the only utility consequence of cutting down the tree is the disutility of effort experienced when the tree is cut.

(a) From a year.1 perspective, what are Mr. X's preferences over the four possible cutting dates?

(b) If Mr. X does not cut the tree in year 1, then, from a year-2 perspective, what are his preferences over the three remaining possible cutting dates?

(c) If Mr. X does not cut the tree in years 1 or 2, then, from a year-3 perspective, what are his preferences over the two remaining possible cutting dates?

(d) If Mr. X is naive, when will he cut the tree? () If Mr. X is sophisticated, when will he cut the tree?