Suppose agents live for three periods: youth, 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 hit, they become addicted. The payoffs are defined as follows:

Utility (hitting l addicted) : -10

Utility (hitting l not addicted) : 12

Utility (not hitting l addicted) : -27

Utility (not hitting l not addicted) : 0

(a) If = 1, in what periods will a time-consistent who enters youth not addicted

choose to hit? Demonstrate that this is the optimal consumption path.

(b) If = 1 and = 1/2, in what periods will a naive agent who enters youth not

addicted choose to hit?

(c) If = 1 and = 1/2, in what periods will a sophisticate who enters youth not

addicted choose to hit?

(d) Provide a discussion of the behavioral differences across types.