2. Hyperbolic discounting
In one example that we discussed, David Laibson describes how hyperbolic discounting explains
why so many people amass large amounts of credit card debt while at the same time saving large
amounts of money for retirement.
For the purposes of this problem, a "period" is one year.
a) You are a student who has just started college. You are considering buying a new
television for your dorm room today which costs $1000. As a student, you have no
income, so in order to buy it, you have to use a credit card that charges 100% interest per
year (not compounding - just 100% each year on the original amount). You cannot pay
off the credit card until you graduate and get a job four years from now. You are a quasi-
hyperbolic discounter for whom $\beta = 0.2$ and $\delta = 1$. The television gives you $1000 worth
of utility, which you receive immediately upon buying it. Will you decide to buy the
television? Explain how you arrive at your solution.
b) As you start your new job, you are asked if you would like to enroll in a retirement
savings plan that will deduct $5000 from each paycheck. You are paid your full annual
salary once per year at the end of the year, so you do not receive your first paycheck until
one year from now. Your time preferences have not changed.
You plan on working for 20 years, then retiring. So, if you decide to enroll in the plan,
you can think of your payoff as -$5000 in each of these 20 years, and $0 if you do not
enroll in the plan. If you enroll, you earn a total of 20% interest on your retirement
savings on top of the saving itself (all 20 $5000 payments into the plan), which you
collect one year after retiring (so one year after you receive your final paycheck).
Given your time preferences, will you choose to enroll in the retirement plan? Explain
how you arrive at your solution.
c) Explain Laibson's argument behind why these choices are seemingly contradictory, but
can be explained by hyperbolic discounting. Explain how the problems in a) and b)
illustrate the logic behind his argument.
