Hyperbolic discounting after class(1)

Hyperbolic discounting after class(1) - 1 How do we think...

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How do we think about welfare in these hyperbolic models where different selves disagree? If one self enjoyed procrastinating or over-indulging and later selves regretted it, which is right? Deep question with a shallow solution for our purposes: Think of beta as a problem. It represents present bias and is the source of dynamic inconsistency. So, when thinking of true, long run utility, sum all the delta-discounted consumption but ignore beta. Now, we have a lot of jargon summarized above. 2
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Sophistication vs. naivete could also be thought of as “insight” into the self-control problem I suppose. Knowing that future selves will have different preferences than now selves is important to decision making. Particularly, it means your strategy of what to plan to consume may change. 3
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Naifs and sophisticates have the same preferences, but different perception perfect strategies. If the sophisticate knows that a future self will be present-biased and do something she would not want, that may change her plan for what to do now. The naif never has such concerns because the naif does not anticipate that future selves will be present-biased. The following examples should help to make clear the difference between preferences and strategy. 4
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This problem deals with procrastination – the decision maker can pay a cost (the opportunity cost of missing a movie) or put it off until later, when the cost will be larger. Since δ = 1 in this problem, the ideal is skipping the mediocre movie and doing the report right away. You might wonder whether it is cool to just assume δ = 1. It is, for two reasons. First, all the action in the problem (any dynamic inconsistency and plans for such) is captured by β, so it would seem best to keep the problem otherwise computationally simple. Second, any stream of utilities with exponential discounting and δ < 1 (the “standard” case) can be rewritten in a consequentially equivalent manner as an alternate stream of utilities with δ = 1 (what would have been the delta discounted utility in that time period can be written as the instantaneous utility). 5
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This is the schedule of instantaneous utilities for each of the movies. Time consistent is completely straightforward. Skip the worst movie, in this case Mediocre, and end seeing Good, Great, and Depp for long run utility 5 + 8 + 13 = 26. The naif has different decision utility than the time consistent because he has β = .5, yet his strategy is the same. Since he does not anticipate future self-control problems, he simply compares each week the opportunity cost of skipping in the present versus skipping some future movie. As long as something out there looks worse, he doesn’t skip. At time Mediocre, Good has utility 5*.5 = 2.5 and thus looks like the one to skip (Mediocre has utility 3). At time Good, though, Good has utility 5 and Great has utility 8*.5 = 4, so he prefers to go to Good and wait to skip Great. At time Great, Great has utility 8 and Depp has utility 13*.5 = 6.5, so he prefers to see Great and ends up having to skip
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This note was uploaded on 04/04/2012 for the course PSYC 265 taught by Professor Jasondana during the Spring '12 term at UPenn.

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Hyperbolic discounting after class(1) - 1 How do we think...

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