Albert has to clean his room on one of the the next 4 days. Cleaning on Day 1 has a utility cost of 18, cleaning on Day 2 has a utility cost of 30, cleaning on Day 3 has a utility cost of 48, and cleaning on Day 4 has a utility cost of 90. 1. Suppose Albert is a naive hyperbolic discounter with B = 0.5 and 6 = 1. On which day will Albert clean his room? 2. Suppose Albert is a sophisticated hyperbolic discounter with B = 0.5 and = 1. On which day will Albert clean his room? 3. Albert's friend Bill offers to act as a commitment device. On any of these four days, Albert can ask Bill to force him to clean on a particular day. But by doing so, Albert pays an additional utility cost of 8 on the day that he is forced to clean. For example, if on Day 3 Albert asks Bill to force him to clean on Day 4, then Albert incurs an additional cost of 8 on Day 4. Suppose Albert is a sophisticated hyperbolic discounter with B = 0.5 and 6 = 1. Will Albert use the commitment device? On which day will Albert clean his room?