A person prefers to receive $100 today over $110 tomorrow but also prefers $110 in 31 days over $100 in 30 days. This pattern of preferences is...
AConsistent with exponential discounting because the person values earlier payments
BTime-inconsistent — the person's discount rate is higher for immediate trade-offs than for distant ones, which exponential discounting cannot produce
CRandom and uninterpretable
DConsistent with risk aversion but not discounting
Exponential discounting applies the same discount rate to all adjacent periods, so if $100 now is preferred to $110 tomorrow (a 10% premium is insufficient for one day's wait), then $100 in 30 days should also be preferred to $110 in 31 days (the same one-day wait). The reversal reveals that the discount rate between today and tomorrow is higher than between day 30 and day 31 — a declining discount rate that is the hallmark of hyperbolic discounting and the source of time inconsistency.
Question 2 True / False
Hyperbolic discounting implies that people always make poor decisions about the future.
TTrue
FFalse
Answer: False
Hyperbolic discounting describes a systematic pattern in preferences, not necessarily poor outcomes in all cases. When present bias causes problems (undersaving, procrastination, unhealthy choices), people can and do adopt commitment devices — pre-commitment strategies that restrict their future choice set to counteract anticipated present bias. Automatic payroll deductions for savings, deadlines for projects, and gym membership contracts are all commitment devices that reflect sophisticated awareness of one's own time inconsistency. The problem is real but not inescapable.
Question 3 Short Answer
What is a commitment device, and why does its existence provide evidence for hyperbolic discounting?
Think about your answer, then reveal below.
Model answer: A commitment device is a voluntary restriction on one's own future choices — like automatic savings deductions, prepaid gym memberships, or self-imposed deadlines — designed to prevent future temptation from overriding current intentions. Commitment devices provide evidence for hyperbolic discounting because a time-consistent agent (exponential discounter) would never pay to restrict their future options — they would simply execute their plan when the time comes. Only a person who anticipates that their future self will have different preferences (present bias) would rationally constrain that future self.
The demand for commitment is a revealed preference for self-control. Odysseus binding himself to the mast to resist the Sirens is the classic metaphor. In modern life, people who delete social media apps before exams, ask friends to hold them accountable for diet goals, or use apps that lock them out of their phone at bedtime are all demonstrating awareness of time-inconsistent preferences and using pre-commitment to manage them. An exponential discounter would have no need for such devices.