2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

The value of delay

Kiss from a movie star 120 volt electric shock

Time delay

FIGURE 12.10

The Prospect-Theory Value Function with Intermediate Loss Aversion

Source: Loewenstein, G. “Anticipation and the Valuation of Delayed Consumption.” Economic Journal 97(1987): 666–684, John Wiley & Sons, Inc.

Courtesy of University Relations

at Northwestern University

Robert H. Strotz (1922–1994)

Ph.D., University of Chicago, 1951

Held faculty positions at Northwestern University and University of Illinois at Chicago–Navy Pier

Robert Strotz was born in Illinois and spent almost all of his career at Northwestern University. After completing his undergraduate work in economics in 1942, at the tender age of 20, he was drafted into military service during World War II. He spent much of his service in Europe, where he served in army intelligence. Part of his service included using econometric

and statistical models to estimate the necessary supplies to support the occupied German population. His interest in econometric techniques led him to continue his training in Europe for several years following the war. Following this period of training he returned to the United States to earn his Ph.D. He was hired by Northwestern University four years before he finished his Ph.D. His contributions to economics include welfare theory, economic theories of behavior, and econometrics. Many of his works are concerned with foundational principles of welfare economics: Is utility measurable? How should income be distributed? Additionally, he made substantive contributions to the practice and interpretation of econometrics. His explorations of behavioral models of dynamic choice can truly be considered an offshoot of his interest in welfare economics. The general model he proposed has become a foundation point for modern behavioral economists examining time-inconsistent preferences. Strotz served on the editorial board for many of the most highly regarded journals in economics, including a 15-year stint as editor of Econometrica. He also served for a time as chairman of the Federal Reserve Bank of Chicago. In 1970 he was named president of Northwestern University, where he contributed substantially to the growth and vitality of that institution. Some see Strotz’s leadership as key in attracting the faculty and endowment that made Northwestern one of the top research universities in the world.

T H O U G H T Q U E S T I O N S

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

R E F E R E N C E S

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 Uc = 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.

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.

Ainslie, G.W. Picoeconomics. Cambridge, UK: Cambridge University

Press, 1992.

Benzion, U., A. Rapoport, and J. Yagil. “Discount Rates Inferred from Decisions: An Experimental Study.” Management Science

35(1989): 270–284.

Bishop, J.A., J.P. Formby, and L.A. Zeager. “The Effect of Food Stamp Cashout on Undernutrition.” Economic Letters 67(2000): 75–85.

Loewenstein, G. “Anticipation and the Valuation of Delayed Consumption.” Economic Journal 97(1987): 666–684.

Loewenstein, G. “Frames of Mind in Intertemporal Choice.”

Management Science 34(1988): 200–214.

Loewenstein, G., and D. Prelec. “Anomalies in Intertemporal Choice: Evidence and an Interpretation.” Quarterly Journal of Economics

107(1992): 573–597.

Odum, A.L., G.J. Madden, and W.K. Bickel. “Discounting of Delayed Health Gains and Losses by Current, Neverand Ex-Smokers of Cigarettes.” Nicotine & Tobacco Research 4 (2002): 295–303.

Strotz, R.H. “Myopia and Inconsistency in Dynamic Utility Maximization.” Review of Economic Studies 23(1955-56): 165–180.

Thaler, R.H. “Some Empirical Evidence on Dynamic Inconsistency.”

Economics Letters 8(1981): 201–207.

Wilde, P.E., and C.K. Ranney. “The Monthly Food Stamp Cycle: Shopping Frequency and Food Intake Decisions in an Endogenous Switching Regression Framework.” American Journal of Agricultural Economics 82(2000): 200–213.