Naïve Procrastination
12
Except for a very select few, almost all federal taxpayers have the necessary materials in their hands to file their federal taxes by the middle of February. Nonetheless, every year, 40 million people in the United States wait until the week of April 15th (the federal deadline) to file their tax returns. This is just about a quarter of all tax returns filed in the United States. Most post offices remain open until midnight on April 15th just for this special class of procrastinators. Many of these procrastinators eventually receive tax refunds, and some refunds are substantial.
Waiting until the last minute can create a risk of missing the deadline. Those filing electronically might have their returns rejected for missing information or other errors. Sometimes communication lines go down in the waning hours of the 15th, overloaded by too many choosing to file at the same time. Those filing by mail often run into very long lines at the post office and risk missing the last opportunity to file. Moreover, putting off preparing taxes until the very last minute can create problems as taxpayers only realize that certain receipts or documents are missing once they have begun to fill out the forms. Ultimately, missing the deadline can result in financial penalties. So why do so many procrastinate until the last minute?
As teenagers and young adults we are bombarded with the advice to “never put off until tomorrow what you can do today.” Nonetheless, procrastination seems to be engrained into human behavior from our earliest opportunities to make decisions. We put off studying until we are forced to cram all night for the big test. We put off cleaning, maintenance, or other work until we are forced into action. Then we must complete tremendous amounts of work in a very short time. Procrastination becomes a problem when we prioritize activities that are not particularly important over those that have real and if not immediate at least long-term consequences. After one has been burned time after time by failing to study early or after a steady stream of financial emergencies that could not be covered by a meager savings, it would seem like time to stop procrastinating. A quotation attributed to Abraham Lincoln is, “Things may come to those who wait, but only the things left by those who hustle.” If that is so, why do we seem so apt to procrastinate? Some economists believe the answer lies in how we value today versus tomorrow versus the day after tomorrow.
Procrastination, like the hot–cold empathy gap described in Chapter 11, can result in timeinconsistent preferences. We might see others who went to work right away, look back on our actions, and consider that we have taken the wrong strategy. Firms interested in selling products can use customer procrastination to their own advantage through price discrimination or by
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NAÏVE PROCRASTINATION |
charging customers for services or the option to take some action that they will never exercise. In some cases, finding last-minute tax preparation is more costly than early preparation. In others, people might pay in advance for flexible tickets that they never actually find the time to use. This chapter introduces the exponential model of time discounting, the most common in economic models, and the quasi-hyperbolic model of time discounting. The latter has become one of the primary workhorses of behavioral economics. This model is expanded on in Chapter 13, where we discuss the role of people’s understanding and anticipation of their own propensity to procrastinate.
The Fully Additive Model
In Chapter 11, we introduced a general model of intertemporal choice when the consumer is deciding on consumption in two different time periods. In many cases that we are interested in, a consumer considers more than just two time periods. In some cases we are interested in planning into the distant future. This is often represented as a problem involving an infinite number of time periods, or an infinite planning horizon. We can generalize the model presented in equation 11.1 to the many-period decision task by supposing the consumer solves
maxc1, c2, U c1, c2, |
12 1 |
subject to some budget constraint, where ci represents consumption in period i. This model is general in the behavior that it might explain because it allows every period’s consumption to interact with preferences for every other period’s consumption. Thus, consuming a lot in period 100 could increase the preference for consumption in period 47. This model is seldom used specifically because of its generality. We tend to believe people have somewhat similar preferences for consumption in each period. Moreover, we often deal with situations in which consumption in one period does not affect preferences in any other period. Thus, when dealing with intertemporal choice with many periods, economists tend to prefer the fully additive model, assuming exponential discounting. This model assumes that
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U c1, c2, |
= u c1 + δu c2 + δ2u c3 + + δi − 1u ci + = |
T |
δi − 1u ci |
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i = 1 |
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12 2 |
where δ represents how the person discounts consumption one period into the future and where T could be 
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The fully additive model is based upon two fundamental assumptions. First, the consumer has stable preferences over consumption in each period. Thus, u
ci
can be used to represent the benefit from consumption in each time period i, often referred to as the instantaneous utility function. This may be more important in the case where u
.
has several arguments. For example, suppose that u
ci
= u
c1, i, c2, i
, where c1, i represents hours spent studying at time period i, and c2, i represents hours spent partying at time period i. Then the additive model assumes that the same function will
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The Fully Additive Model |
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describe the utility tradeoffs between partying and studying in every time period. Thus, whether you are three weeks from the test or one hour from the test, the student still has the same relative preference for studying and partying. Second, the consumer discounts each additional time period by a factor of δ, referred to as exponential time discounting. Consuming c next period will yield exactly δ times the utility of consuming c now. Moreover, consuming c two periods from now will yield exactly δ times the utility of consuming c next period, or δ2 times the amount of utility of consuming c this period. This coefficient δ, often referred to as the discount factor, may be thought of as a measure of patience. The higher the discount factor, the more the consumer values future consumption relative to current consumption and the more willing the consumer will be to wait.
The solution to a problem such as that in equation 12.2 occurs where the discounted marginal utility of consumption in each period is equal, δi − 1u′
ci
= k, where u′
c
is the marginal utility of consumption (or the slope of the instantaneous utility function), and k is some constant. Intuitively, if one period allowed a higher discounted marginal utility than the others, consumers could be made better off by reducing consumption in all other periods in order to increase consumption in the higher marginal utility period. Similarly, if marginal utility of consumption in any period was lower than the others, consumers would benefit by reducing their consumption in that period in order to increase consumption in a higher marginal utility period. This would continue until marginal utility equalizes in all periods. Thus, given the instantaneous marginal utility of consumption function, you can solve for the optimal consumption profile by finding the values for ci such that δi − 1u′
ci
= k for some k and such that all budget constraints are met. One way to picture this optimum is displayed in Figure 12.1. On each vertical axis is displayed the discounted marginal utility of consumption for one time period. Overall utility is optimized where consumption in each period yields the same level of discounted marginal utility (depicted by the horizontal line). The discount causes each successive curve to be less steep and to be scaled in toward the x axis by the discount factor. This results in declining consumption in each period.
Let us see how we can use this model to examine a simple choice. Suppose a decision maker is given a choice between consuming some extra now or a lot extra later. Suppose that to begin with a decision maker consumes c each period. Then, in addition to c, the decision maker is given the choice of consuming an additional x at time t or an additional
x′ > x at time t′ > t. The decision maker will choose x at time t if the additional utility of doing so, 
i
tδiu
c
+ δtu
c + x
>
i
t′δiu
c
+ δt′u
c + x′
, where the right side of
utility |
u'(c1) |
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δu'(c2) |
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δ2u'(c3) |
Discounted marginal |
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c1 |
c1 |
c2 |
c2 |
c3 |
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FIGURE 12.1
Optimal Consumption with More than Two Periods
Foresight: The Effect of Outcome Knowledge on Judgment Under Uncertainty.