Rational Explanations for Flat-Rate Bias

Two primary rational explanations have been given for the flat-rate bias. The first supposes that consumers might not actually know the amount of use they are projected to have. Given this uncertainty about use, they might opt for the fixed-price plan to avoid the uncertain cost of consumption. For example, it may be that one occasionally uses a cell phone extensively, whereas in a normal month one might only use a few minutes. Expected utility theory suggests that a consumer may be willing to reduce the average payout of a gamble in return for eliminating the uncertainty. The flat-rate bias could be explained by the same phenomenon where consumers are willing to pay a larger amount on average to ensure that they are certain of the eventual total cost. In this case, although future use is a decision variable rather than an externally determined random variable, the value of the calls may be random. Thus, one might buy the fixed-price option because of the value of the option to place more calls without facing a penalty. Kridel, Lehman, and Weisman find that this appears to be a good explanation for many of the apparent mistakes in pricing choices.

Eugenio Miravete claims that there is little evidence of incorrect choices to begin with. He uses a survey of telephone customers’ anticipated and actual use of services in Kentucky to determine the extent of such errors. In fact, he finds that customers’ anticipated use was consistent with the pricing scheme they chose. Further, he finds evidence that customers respond to charges in a way that suggests they are trying to minimize their bill given their level of use. Thus, those who incorrectly predicted their use usually shifted to the correct service plan after discovering the error. He finds that less than 6% of customers commit the error of subscribing to a flat-rate service when they would have benefited by using another system. His explanation for the observed errors is that consumers are in transition and still discovering which is the best plan for them. He concludes that the rational model of pricing choice is the best model to describe behavior. Miravete finds that among those who choose the flat rate pricing, a majority overestimate their eventual use of the phone service. However, even if the phone-use data contain no direct or incontrovertible evidence of the anomaly, the data are consistent with the underlying behavioral tendencies that could lead to the anomalous behavior. Even if the anomalous behavior is not evident, a behavioral economist would find the consumer’s formation of use forecasts important in discerning the motivations for behavior.

History and Notes

Although there was ample evidence and discussion before his observation, Kenneth Train is credited with coining the term flat-rate bias in discussing telephone pricing plans in 1994. In coining this term he cited evidence from his own work from the 1980s. This bias has been noted in Internet subscriptions, software licensing, electricity use, and gym memberships. Not only is there evidence of the flat-rate bias, but there is also evidence that those subscribing through a flat rate are much less likely to abandon service. Thus, the service provider not only gets more money for the level of service, but it is also more likely to retain the customer. Thus there is substantial incentive for service providers to offer a flat-rate option for premium levels of use.

Transaction Utility and Consumer

Preferences in Reference

Often our perception of how good a deal we have achieved depends not only on the amount we are able to consume and the quality of the good itself but also on the context within which we make our purchase. In some contexts, items are expected to be more expensive than in other contexts. This leads consumers to display very different demand behavior depending upon the purchase context. Someone might refuse to purchase a good in one venue because it is too expensive, but the same person might purchase the good at an identical price when in a context where the price seems justified. Consumers might use cues from the environment or memory of previous transactions in similar contexts to form an idea of what is a fair price. A comparison used to aid in making a decision is called a reference point. For example, your reference point may be the price you have paid in the past at a particular establishment. If a hamburger has always cost $5 at a particular restaurant, that hamburger might feel like a particularly good deal if you could purchase it for $3. It might feel like a terrible deal if the price rose to $6. Thus the reference point can play an important role in determining the consumer’s transaction utility. The reference point may be influenced by the context. An identical hamburger at another restaurant might always be priced at $2. Here it might feel like you have been ripped off if they were to suddenly increase the price to $3.

EXAMPLE 2.6 Beverage Demand and References

Richard Thaler surveyed consumers about their intended behavior under a couple of different hypothetical scenarios. Each respondent saw only one scenario. The first asks you to consider that you are at the beach on a hot day and want to buy a bottle of your favorite beer. A companion offers to get you one from a run-down grocery store. Your friend asks how much you are willing to pay for the beer, saying she will buy it if the price is less than or equal to your stated willingness to pay. The second scenario is identical except that instead of a run-down grocery store, your friend is going to a fancy resort hotel. Note that both scenarios suggest that the respondent will receive their favorite beer, and thus the item itself is identical in both choices. Respondents were willing to pay much more for the beer from the resort than from the grocery store (median value of $2.65 versus $1.50). Moreover, because both scenarios involve consuming the beer on the beach with the friend after she returns, there is no chance that environmental factors could influence the utility the consumer derives from the beer. Thus, the willingness to pay for the experience was influenced by the context in which the purchase takes place.

EXAMPLE 2.7 Internet Auctions

Internet auctions often offer either a minimum bid or a price at which the potential buyer could forgo the auction altogether and buy the item outright—sometimes called a buy now price. Anna Dodonova and Yuri Khoroshilov examined how the listed buy now price affected bids on a jewelry auction website. They found several mass-marketed items that come up for auction regularly on the site that could offer valid comparisons of behavior. This allowed them to compare items that are identical in design and content and thus in market value. However, the buy now price varied among the auctions. When items were posted with higher buy now prices, bidders placed higher bids, signaling that they valued the item more highly than when they saw the identical item with a low buy now price. Somehow, the buy now price had influenced the bidders’ valuations, perhaps by creating a reference point.

Theory and Reference-Dependent Preferences

The response of consumers to context in forming consumption decisions tells us a lot about how transaction utility works. To use the notion of transaction utility in predicting behavior, we need to know the potential reference points that drive the decision behavior. Thus, a behavioral theory of reference points might suppose that the consumer considering the purchase of a good will be influenced by her transaction utility for the purchase given the context of the purchase, zx, pξ, where ξ represents the reference point in the given context. The consumer will also be influenced by the utility of consumption, as in equation 2.8. This particular theory contains very little predictive power because it does not tell us how the reference point was created or how we could determine it.

We could create a procedural rational model of reference point selection. For example, the reference price may be the average price the consumer had previously observed in a particular context (e.g., a resort hotel). This would tell us that the consumer considered previous observed prices in determining if the price was reasonable or not. If the price was higher than at previous resorts, the consumer would think it was a bad deal and have a lower transaction utility. If the price was lower than at previous resorts, the consumer would feel she had gotten a good deal. There is substantial evidence of the use of reference points in decision making. This concept is examined in several of the chapters in this book.

A pervasive problem with using reference-based behavioral theories is that we seldom have a theory describing why a consumer selects a particular reference point. One of the reasons for a lack of clarity in theory is that it can be difficult to test for differences in reference points empirically. In purchasing behavior, the formation of reference points may be particularly difficult to isolate. What is it that quintessentially separates a resort hotel from a run-down grocery store? How can we classify different purchasing locations or experiences into different categories? Does the presence of luxury items nearby signal that higher prices are to be expected?

Alternatively, some have found success in manipulating reference points. For example, the buy now price creates a very simple reference point. In this case, the bidder will purchase or not purchase the item but will judge the transaction utility of a potential purchase based on what price she pays relative to the buy now price. In this case, transaction utility may be written as zppbn, where pbn is the buy now price and where transaction utility is decreasing in p and increasing in pbn. By raising the buy now price, the consumer is more likely to be willing to purchase at a higher price because she will receive a greater transaction utility in addition to the same level of consumption utility.

For the manager trying to set prices within her store, the implication is that one can manipulate the reference point of the consumer and potentially receive higher prices and greater profit. Stores can list comparison prices for items that they are selling in order to induce customers to feel they are obtaining a good deal. We often hear of stores that perpetually mark items as on sale in order to induce this type of feeling. For example, consumers are more likely to buy an item marked “On sale for $2 regularly $4” than they are to buy the same item marked simply $2. The item may be the same price, but consumers feel they are getting a better deal in comparison to the regular price. Stores often manipulate regular and sale prices to take advantage of this behavior. Some stores that offer everyday low prices instead advertise their own price in relation to their competitors’ regular price to the same effect.

From a normative standpoint, transaction utility can lead consumers to make two types of mistakes. First, consumers might purchase items that they otherwise would not want, simply because they think they are getting a good deal. Second, consumers might fail to purchase things that would make them better off because the context suggests a lower reference price to them. In this case, a consumer might not purchase the $3 hamburger at a relatively cheap restaurant even though she would be willing to pay $5 for the same sandwich at a relatively more expensive restaurant. Normatively, consumers would receive higher consumption utility if they did not consider the transaction utility and made purchase decisions based on price irrespective of context. The difficulty in offering our consumers prescriptive advice is that we do not know which context represents true consumption preferences. Nevertheless, we are often given advice designed to combat such context-dependent preferences. For example, one should never use the snacks provided in your room at a high-end hotel: The markup is enormous.

Rational Explanations for Context-

Dependent Preferences

Two primary alternative explanations exist for reference-dependent preferences. First, it may be that the context itself conveys information. For example, bidders might not have substantial knowledge about the prices of jewelry and might look to the buy now price to learn something regarding the overall value of the item. Although this might not be the best way to research the price of a good, other ways may be prohibitively costly in terms of effort or time. In this case, it might not be the reference point that was manipulated but simply the bidder’s expectation of prices she may be able to obtain if she looked

the numerator—the marginal utility of good 1. This is an unlikely occurrence if we are holding x1* constant. Alternatively, good 1 may remain the same if the two goods are independent and if good 2 displays constant marginal utility.

Were we to assume p1 = 0, then equation 2.B is replaced by

or, after substituting the budget constraint

which implicitly defines the demand function. Totally differentiating equation 2.H with respect to x1* and p0 yields the relationship between fixed costs and demand for good 1

zero, implying that consumption of good 1 will not change with a marginal change in the fixed price of consumption.