Question 3 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 gets bigger and requires even more effort to cut down. Specifically, suppose that the effort cost to cut down the tree in year t is c(t), where c(1) = 24, c(2) = 28, c(3) = 35, and c(4) = 46. Suppose that Mr. X is an exponential discounter with discount factor 8, 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: (i) For what & does Mr. X prefer cutting in year 1 rather than year 2? (ii) For what & does Mr. X prefer cutting in year 2 rather than year 3? (iii) For what o does Mr. X prefer cutting in year 3 rather than year 4? (b) As a function of 6, when is Mr. X's preferred time to cut down the tree? (c) Suppose Mr. X does not harvest the tree in year 1. From a year-2 perspective: (i) For what o does Mr. X prefer cutting in year 2 rather than year 3? (ii) For what o does Mr. X prefer cutting in year 3 rather than year 4? (d) Is there any o for which Mr. X would decide in year 2 to deviate from his initial year-1 plan