Review the setup of Exercise 12. Assume you have time-inconsistent preferences ( = 0.5, = 0.5)

Review the setup of Exercise 12. Assume you have time-inconsistent preferences (β = 0.5, δ = 0.5) but are also a sophisticate.

a. Propose two realistic commitment mechanisms in this situation. One should be a authoritarian measure that harms the November 1 self, and one should be a Pareto self-improving measure that weakly benefits all three selves.

b. Suppose for whatever reason that these commitment mechanisms are not available.

Now, how much candy do you allot yourself on October 31 for consumption on October 31 in order to maximize your overall utility? Is this more or less candy than you would allot yourself if you were a naive beta-discounter? Explain the difference in these strategies in intuitive terms.

Data From Exercise 12.

It is October 31 (Halloween night), and thanks to a great pirate costume, you have pulled in a record haul during trick-or-treating – 1001 pieces of candy! Before bed, you have to decide how you will allocate your candy over the next three nights. Your parents have already declared that any un-eaten candy will be thrown away after November 2. On any given night, your utility from candy is u(x) = ln(x), where x is the number of pieces consumed that night. In the following exercises, U₀ and x₀ will represent your utility and candy consumption respectively on October 31. The subscripts 1 and 2 denote analogous quantities for November 1 and 2 respectively.