## Questions

1. Many have erroneously described hyperbolic discounting

as an extreme bias toward current consumption.

Describe why this is a false statement. Explain

intuitively what hyperbolic discounting does to decisions

involving intertemporal choice.

2. Naïve hyperbolic discounting leads people to make

plans that are never executed. However, there are many

reasons people might not execute plans. What other

reasons might lead someone to abandon a plan for the

future? What distinguishes plans that are not executed

owing to hyperbolic discounting from alternative

explanations for not executing plans? Do hyperbolic

discounters regret not executing their plans?

3. Many people display something like hyperbolic discounting.

Some businesses thrive on supporting this

sort of short-term excess. For example, several establishments

offer payday loans—short-term loans with

ultrahigh interest rates designed to be paid off the next

time the person is paid.

(a) Suppose you were considering opening such a

payday loan establishment. Given that hyperbolic

discounters often fail to follow through on plans,

how could you structure the loans to ensure payment?

Use the quasi-hyperbolic model to make

your argument.

(b) The absolute-magnitude effect suggests that people

are much closer to time consistency with regard to

larger amounts. How might this explain the difference

in the structure of consumer credit (or shortterm

loans) and banks that make larger loans?

(c) Lotteries often offer winners an option of receiving

either an annual payment of a relatively small

amount that adds up to the full prize over a number

of years or a one-time payment at a steep discount.

Describe how time inconsistency might affect a

lottery winner’s decision. How might the lottery

winner view her decision after the passage of time?

4. Harper is spending a three-day weekend at a beach

property. Upon arrival, Harper bought a quart of ice

cream and must divide consumption of the quart over

each of the three days. Her instantaneous utility of ice

cream consumption is given by U c =c0.5, where c is

measured in quarts, so that the instantaneous marginal

utility is given by 0.5c− 0.5.

(a) Suppose Harper discounts future consumption

according to the fully additive model, with the

daily discount factor δ= 0.8. Solve for the optimal

consumption plan over the course of the three days

by finding the amounts that equate the discounted

marginal utility of consumption for each of the

three days, with the amounts summing to 1.

(b) Now suppose that Harper discounts future utility

according to the quasi-hyperbolic discounting

model, with β =0.5, and δ=0.8. Describe the

optimal consumption plan as of the first day of the

weekend. How will the consumption plan change

on day two and day three?

(c) The model thus far eliminates the possibility that

Harper will purchase more ice cream. In reality, if

consumption on the last day is too low, Harper

might begin to consider another ice cream purchase.

Discuss the overall impact of hyperbolic

discounting on food consumption or on the consumption

of other limited resources.

5. Consider the diet problem of Example 12.3. Let

δ=0.99, ul =2, uh =1, γi =1 180 for all i, and

w=140. Suppose that initial weight in the first period

is 200. How high does β need to be before the person

will actually go on a diet rather than just planning to

in the future? Use geometric series to solve this

analytically.