A naive hyperbolic discounter with a daily = 0:9 and = 1 has $10; 000 to invest for retirement, which is 30 years from today. Her utility function for wealth at retirement is u(w) = w. The money is currently sitting in account A, earning 0% interest. She can costlessly transfer it to account B, in which it would earn an interest of 3% per year (=.03/365 per day). However, if she exerts some effort, she can find an investment C in which her money would earn an interest of 5% per year. The effort cost of finding this account is e = 60. Every day, the agent decides to transfer it to account C, she has to pay the effort cost immediately. Assume that she cannot transfer the money from account B to account C.

a) Show that the agent leaves the money in account A, and plans to transfer it to account C tomorrow.

b) Show that she will keep doing this until sometime close to retirement, and then transfer the money to account B.

c) When will she transfer the money to account B? d) How would your answer to c) change if the cost of transfer e was lower? e) How would your answer to c) change if was lower?