These three sub-questions are together one big problem.

1. Consider a model with five periods. Dave wants to buy an ihome in period 2, but is considering whether he should save up for it, or use his credit card. Dave's benefit from the ihome is $100, which he will receive in period 2, when he purchases it. All of his options affect when he pays for the ihome, and how much he pays. - if he saves up, he will pay $85 in period 1 (into his checking account) - if he uses his credit card and pays it off in period 3, he pays no interest, only $100. - if he uses his credit card and pays off the balance in period 4 , he will pay 20% interest, for a total cost of $120. - if he uses his credit card and pays off the balance in period 5 , he will pay two years of 20% interest, for a total cost of $144. The table below gives the time sequence of Dave's benefits and costs for the 4 options: Dave's discount factor =.95; he is present-biased, with =.85. Assume he is nave. a) At t=0, which of these option will Dave choose? show your calculations. b) At t=1, which of these options will Dave choose? Show your calculations. c) If Dave chooses credit, in period 3 will he decide to pay it off? Show your calculations. d) If Dave chooses credit and does not pay off in period 3, in period 4 will he decide to pay it off? Show your calculations. 2. If Dave is sophisticated, but has no options to restrain his choices, analyze what he will do. 3. Let's say Dave is sophisticated, and has two options in period 0 to control his behavior: i) cut up his credit card ii) trade in his credit card for a "charge card," which he will have to pay off in period 3 (charge cards must be paid off in full). In light of the answers to question 1, which of these options will he choose? Think carefully through what Dave can anticipate will happen in each of these scenarios