Dave is considering quitting smoking. Assume that Dave lives three periods (indexed by 0,1,2), and that he might quit in period 0 or in period 1. If he does not quit, he will receive a consumption value of 3 in each of the first two periods, then consumption -30 in the third period. If Dave decides to quit he will receive a consumption value of 3 for any period he is smoking, consumption of -10 during the period that he quits, and consumption of 6 every period after quitting. (a) Assume Dave has linear utility of consumption, i.e., u(c) = c. Write down a table showing the streams of utility Dave will receive under each possible choice he could make. (b) Assume that Dave is an exponential discounter. Find the values of & that make Dave indifferent between each pair of choices Dave might make. (c) Given the choices that he has, for which values of & will Dave go with each of the options? (d) Can it be rational for Dave not to quit? Why or why not? (e) Now assume Dave is a beta-delta discounter, with the delta that made him indifferent between quitting at time 0 and quitting at time 1 (in part B), as well as a B = 0.4. Given his utility function, what will Dave choose to do in period 0? How about in period 1?