Consider the example of cleaning your dorm except now there are BOTH rewards and costs. Suppose you have , preferences with = 0.7

Consider the example of cleaning your dorm except now there are BOTH rewards and costs. Suppose you have β, δ preferences with β = 0.7 and δ = 1. You have to clean your room at some point over the next five days. Depending on which day you clean your dorm, your reward will be v_t and your cost will be c_t , where

(c1, c2, c3, c4, c5) = (45, 45, 45, 62, 87)

(v1, v2, v3, v4, v5) = (35, 45, 60, 60, 60)

There are two possible cases for when you receive these payoffs:

• Immediate costs: you incur the cost the day you do it, and receive the reward in the future.

• Immediate rewards: you receive the reward the day you do it, and incur the cost in the future.

For instance, if you do the activity on day 4, your cost is c4 = 62 and your reward is v4 = 60. For immediate costs, the cost of c4 = 62 is incurred on day 4 while the reward v4 = 60 is received sometime later. For immediate rewards, the reward v4 = 60 is received on day 4 while the cost c4 = 62 is incurred sometime later. Since we are assuming δ = 1, exactly when is later is irrelevant.

(1) Consider the case of immediate costs. When do naifs complete the task? When do sophisticates complete the task?

(2) Consider the case of immediate rewards. When do naifs complete the task? When do sophisticates complete the task?

(3) Suppose you are EDU with δ = 1. When is the best time for you to clean your room? How does your answer depend on whether it is immediate costs or immediate rewards? Contrast your answer with parts (1) and (2).