Sam is attempting to decide between reading two books this week and can only do one.

Sam's discounted utility is provided by the function below:

Your discounted utility is provided by the formula:

Discount(t) = ^t, t denotes periods, and each period is one day long.

Let's assume Sophistication: You are fully aware of your future self-control problems

Naivete: You are fully unaware of your future self-control problems.

Here are Sam's options:

Option 1: Read "Moby Dick" on Wednesday night (value: 14 utils)

Option 2: Read "Gone with the Wind" on Thursday night (value: 20 utils)

1. Suppose = 1and= 1. If Sam had made the choice on Wednesday, which option would Sam have chosen? If instead Sam had made the choice on Tuesday, what would Sam have chosen?
2. Now suppose = 0.5and= 1, and that Sam is fully nave. If Sam had made the choice on Wednesday, which option would Sam have chosen? If instead Sam had made the choice on Tuesday, what would Sam chosen?
3. Assume = 1 and =0.9. If Sam had made the choice on Wednesday, which option would Sam have chosen? If instead Sam had made the choice on Tuesday, what would Sam chosen?
4. Explain what it means intuitively for = 1 as in part (1), < 1 as in part (2), and =1 and <1 as in part (3)?
5. Suppose Sam has = 0.5and= 1, and Sam is fully sophisticated. Explain how a "commitment device" on Tuesday might change Sam's decision of whether to read on Wednesday. What is a realistic example of such a device in this scenario? What is the maximum that Sam would be willing to pay for the commitment device (assume each util can be interpreted as a dollar)?

Source: Practice Problems