furniture. For example, auto dealers often emphasize the amount of the monthly payment rather than the total cost. It sounds much cheaper to buy a car for “only $450 a month” than for “only $37,000.” Old commercials for charitable organizations often suggested that for just the cost of a cup of coffee each day, one could help others in need. Read, Loewenstein, and Rabin mused, “Imagine the response to the plea that your donation will cost ‘only $350 per year, no more than the cost of a small refrigerator.’”

Narrow Bracketing and Motivation

There is evidence of yet another way narrow bracketing can lead to higher overall utility. In some cases, narrow bracketing may be used as a self-control device. On the surface, this seems counterintuitive after a lengthy discussion on how narrow bracketing can lead to addiction and poor behavior. However, we often observe people intentionally using narrow bracketing to achieve very large goals. For example, many addicts try to avoid the object of their addiction “one day at a time.” Similarly the common adage states that great journeys begin with a single step. In both of these examples, the object is to break down a difficult and apparently insurmountable task into very small and doable tasks. It might sound very difficult for addicts to cease their addictive behavior for the next 40 years. Stopping for a day is much more achievable. As well, bracketing too broadly can make it difficult to verify progress on a goal. If one’s goal is to save $5,000 in a year, it may be easier to splurge in the interim because there is so much time left until the goal must be reached. Alternatively, if the goal is to save $210 from every paycheck, one quickly knows if one is on track and whether there is room to splurge and still meet the goal.

Behavioral Bracketing

Read, Loewenstein, and Rabin suggest several potential causes of bracketing and factors that can affect bracketing behavior. Among these are social heuristics, the timing of decisions, limits on cognitive capacity, and motivation. It is easy to see how joint decisions can quickly become so complex as to require someone to narrowly bracket decisions to create any reasoned response. Food consumption is a convenient example. Optimizing would require that a diner take into account all the food decisions she will make together. But, in a day one person makes an average of 200 to 300 food decisions (what to eat, when, where, etc.). It would take too much time and energy to consider these problems together. Thus, it is not particularly clear that one would be better off for having done it.

The rational model does not consider the cognitive costs of such an optimization problem. The timing of decisions makes sequential bracketing natural. We are somewhat forced to think through a decision when it is placed in front of us. Thus, we often make decisions as they arise, bracketing decisions by sequence. Returning to our food example, we would decide on breakfast in the morning, not considering our later meals. Around noon we would be forced to decide what to eat for lunch. Here our decision on breakfast might influence our decision because we are more or less hungry or feel more or less guilty about our level of consumption that morning. But we do not consider dinner at the time we decide on lunch. If the sequence of decisions is one of the primary drivers of bracketing, then our decisions are much more backward looking than forward looking.

Social heuristics clearly play a role as well. Social heuristics include cases in which society has, by convention, bracketed certain decisions or items together. Thus, we have conventions on the number and timing of meals throughout the day. Such conventions can influence the types of choices we make. For example, Read, Loewenstein, and Rabin find that people indicate a desire to consume more bread pudding when asked separately how much they would eat each weekday and each weekend day than if they were simply asked how much they would eat on each day in a week. Bracketing the weekend separately might induce people to think of this as an opportunity to make some exceptions to their normal routine and consume more of those things they normally try to limit.

History and Notes

The issue of bracketing has lurked in the economics and marketing literatures for quite some time, but the question of bracketing was first raised in a serious fashion by Itamar Simonson regarding the sequencing of choices. Issues such as the peanuts effect and segmenting of decisions were raised in passing by Richard Thaler, Daniel Kahneman, and Dan Lovallo, among others, in proposing mental accounting and other behavioral economic phenomena. Later these concepts were formalized by Daniel Read, George Loewenstein, and Matthew Rabin, whose work much of this chapter is based upon. These models have been very valuable in solving a puzzle in the addiction literature. Addicts display compulsive and binging behavior, but there is also evidence that they respond to monetary incentives to stop the addictive behavior. This is inconsistent with most other psychology-based models of addiction because these models suppose that the behavior ignores the monetary consequences of their actions. Alternatively, financial incentives might allow the narrowly bracketed decision to lead away from addictive substances, thus bringing the melioration optimum in line with the overall optimum.

The general rule would guide the consumer to use broader brackets when it is feasible. This leads to better decisions in nearly all cases. However, there are some clear exceptions, such as when using narrow bracketing to motivate behavior (like quitting an addiction) or if the cognitive decision costs of broad bracketing are overwhelming. The types of bracketing you as a marketer might want to induce depends substantially on the types of products you are selling. Goods that cost substantial amounts up front, but that provide delayed benefits, are more likely to be purchased using broad bracketing. Thus, universities often tout the longterm benefits of being an alumnus and the strength of their alumni organizations. Alternatively, goods that provide substantial benefits now (potentially with greater costs in the future) are better sold using narrow bracketing. Thus, automobiles are sold for their visual appeal, the feel of driving, and other things that can be experienced now.

or, completing the square in the second term,

u′ w μ − 1 + u″ w wzE z − μ 2 + μ z − μ − z − μ

6E

= u′wμ − 1 + u″wwzσ2 = 0

where σ2 = E z − μ2 . The value σ2 is commonly called the variance of z, and it measures how dispersed the values of z are. Thus the higher the value of σ2, the more risky is the investment. The result in (6.E) follows because Ez − μ = μ − μ = 0. Thus, the first-order condition results in

where RA = − u″u′, is the coefficient of absolute risk aversion.

Advanced Concept

Bracketing the Portfolio Problem

For now, let us suppose that v in equations 6.16 and 6.18 is continuously differentiable. This will allow us to again use a Taylor series expansion to approximate the decision rule and compare behavior with broad and narrow bracketing. Thus, we are omitting the possibility of loss aversion, which involves a function that is kinked at the reference point. equation 6.19 yields first-order conditions given by

As before, we will approximate the marginal value function using a first-order

Taylor series expansion around the mean. This yields

which can be rewritten as

Here, σij = E zi − μizj − μj is the variance of investment i, when i = j, and the covariance of investment i and j when they are unequal. Thus, solving (6.I) yields

If instead, we suppose that decisions are narrowly bracketed, equation 6.21 has first-order conditions

Again we can use the Taylor series approximation from equation 6.H, only now y = xizi, and Ey = xiμi. Thus, we can rewrite equation 6.K as