2. Addiction {20 pts) Suppose agents live for three periods: youthJ middle age} and old age. In each period? agents choose whether to consume an addictive substance (to hit} or to refrain. Assume that the substance is so powerful that once the hit1 they become addicted. The payoffs are dened as follows: Utility (hitting I addicted} : 1l} Utility (hitting | not addicted} : 12 Utility (not hitting | addicted} : 2'i' Utility (not hitting I not addicted} : [l {a} If 5 = 11 in what periods will a timeconsistent who enters youth not addicted choose to hit":I Demonstrate that this is the optimal consumption path. {b} If 5 = 1 and g3 = 11.321 in what periods will a naive agent who enters youth not addicted choose to hit? {c} If 5 = 1 and ,3 = 1,32, in what periods will a sophisticate who enters youth not addicted choose to hit? {d} Provide a discussion of the behavioral differences across types