Question

1. We have considered hyperbolic discounting and self-control as it relates to one-time decisions (save for retirement, apply to college, building houses for pigs). In these cases, we face a one time immediate cost (go to HR, spend time on the application) and a lifetime of future benefits. Sometimes, instead, we face constant persistent temptation. For instance, as I am writing this test, my phone sits at arm’s length, tempting me with social media, games, videos, texting friends, and so on.

Consider a 4 period model, t=0, t=1, t=2, and t=3. In t=0, you are not studying or playing, you are just thinking about what you want to do. In t=1 and t=2, you must decide if you want to study or if you want to play on your phone in that period. In t=3, you earn the benefit from your studying.

In t=1 and t=2, the phone generates utility of 2. Studying generates no utility. In t=3, you get 3 utils for each period you studied and 0 utils for every period you spent on your phone. In other words, if you studied in both periods, you’d get 6 utils in t=3. If you studied in only one period, you’d get 3 utils in t=3. You are a hyperbolic discounter and β= 0.5 and δ=1.

1. Before you sit down to study, t=0, what do you plan to do? There is no cost and no utility in t=0, it’s just a planning period. To simplify, you have three choices: to study in both periods; play on your phone in the first period and study in the second period; or to play on your phone in both periods. Calculate the utility for Self 0 for each of those three possibilities. What does Self-0 plan to do?
2. When t=1 arrives, what does Self 1 prefer to do?
3. Given the choice made in t=1, what does Self 2 choose to do in t=2?
4. Explain the intuition. Do you see this behavior in yourself or others?
5. What is a commitment device that Self 0 could use, if they’re sophisticated? You can assume t=0 is immediately before t=1 (meaning, minutes not days).

Answer 1

Hyperbolic discounting happens when people show a preference for a reward that arrives sooner rather than later.According to hyperbolic discounting, valuations fall relatively rapidly for earlier delay periods (as in, from now to one week), but then fall more slowly for longer delay periods (for instance, more than a few days).

‍For example, in an early study subjects said they would be indifferent between receiving $15 immediately or $30 after 3 months, $60 after 1 year, or $100 after 3 years.

a) By assumption,if the problem set is not done in either period 0 or 1,then the problem set will be done in period 2. (It has to get done,since period 2 is the last period in the game.)

b) Self 1 prefers to use phone during that period.

c) Self 2 chooses to study

d) Instinct is our innate inclination toward a particular behavior (as opposed to a learned response).
• A gut feeling—or a hunch—is a sensation that appears quickly in consciousness (noticeable enough to be acted on if one chooses to) without us being fully aware of the underlying reasons for its occurrence.
• Intuition is a process that gives us the ability to know something directly without analytic reasoning, bridging the gap between the conscious and nonconscious parts of our mind, and also between instinct and reason.

e) If T is even,then sophisticates will do the project in even periods(and not in odd period)
If T is odd,then sophisticates will do the project in odd periods (and not in even periods)