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 3 = 0.5 and 6 = 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?

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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 = 0.5 and 6 = 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?
Transcribed Image Text: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 = 0.5 and 6 = 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?
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