Abstract
Both the “law of one price” and Bertrand’s (J Savants 67:499–508, 1883) prediction of marginal cost pricing for homogeneous goods rest on the assumption that consumers will choose the best price. In practice, consumers often fail to choose the best price because they search too little, become confused comparing prices, and/or show excessive inertia through too little switching away from past choices or default options. This is particularly true when price is a vector rather than a scalar, and consumers have limited experience in the relevant market. All three mistakes may contribute to positive markups that fail to diminish as the number of competing sellers increases. Firms may have an incentive to exacerbate these problems by obfuscating prices, thereby using complexity to make price comparisons difficult and soften competition. Possible regulatory interventions include: simplifying the choice environment, for instance by restricting price to be a scalar; advising consumers of their expected costs under each option; or choosing on behalf of consumers.
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Notes
Of course, in many cases consumers make good choices, and market competition is effective. However, this article focuses on problems rather than successes. For a discussion of settings in which competition can be the only protection that consumers need, see for instance Armstrong (2008).
Woodward and Hall (2012) study the market in 2001. Since then, updated good-faith disclosure regulation has restricted partition pricing so that brokers may no longer quote multiple fees, such as an “origination fee”, a “funding fee”, or a “document processing charge”, without also reporting the sum. Moreover, since 2011, new regulations restrict commissions that lenders may pay brokers and increase brokers’ fiduciary responsibility to borrowers (Federal Reserve Board 2010). It would be interesting to know how Woodward and Hall’s (2012) results would differ under the new regulations.
Lack of search and unawareness of conflicts of interest are widespread in retail finance. Chater et al. (2010) find in a survey of 6,000 Europeans who had recently purchased a retail investment product that: (1) 66 % consulted only a single investment provider or advisor; and (2) that more than half believed that their provider or advisor gave completely independent and unbiased advice.
Grubb (2015c) provides a recent overview of the evidence for overprecision, whereby individuals underestimate the uncertainty surrounding their own forecasts. The law of small numbers asserts that “the law of large numbers applies to small numbers as well” (Tversky and Kahneman 1971). Belief in the law of small numbers leads to overinference from small samples (Rabin 2002).
As I use the terms, partition pricing and drip pricing are both pricing practices that describe the price of a product or service using several distinct fees that must be summed to compute a total price. Unlike hidden add-on fees, these distinct fees cannot be declined and are all communicated prior to a purchase decision. Partition pricing communicates all the distinct fees at the same time, while drip pricing reveals them sequentially through the shopping process. For instance, if a shipping fee is posted next to a product price, it is an example of partition pricing; whereas if it is not revealed until adding the product to the shopping cart, it is an example of drip pricing. Note that these terms are often used more broadly by other researchers. For instance, Morwitz et al. (2013) include drip pricing as a special case of partition pricing, and Shelanski et al. (2012) include add-on pricing as a type of drip pricing.
Wilson (2010) provides an alternative explanation that works when firms’ search costs are independent. In contrast to Ellison and Wolitzky (2012), Wilson (2010) assumes that: (1) consumers can observe how time consuming it will be to learn a firm’s price; (2) consumers can choose to begin their search at a firm with transparent prices (low search costs); and (3) firms choose obfuscation levels before prices. In this setting, Wilson (2010) shows that obfuscation can be more profitable than transparency by providing commitment to softer price competition in the second stage of the game.
Specifically, Ellison and Wolitzky (2012) assume that consumers make inferences about \(\tau \), which affect expectations about search costs at other firms, by observing the sum \(\tau +t_i\).
Consumers are typically uncertain about future data usage and hence the final cost of a data plan. As one might expect, experimental evidence shows that individuals are more likely to choose a dominated lottery when the description of available alternatives makes dominance non-transparent (Tversky and Kahneman 1986).
Miravete (2013) finds mixed results about whether foggy pricing increases or decreases with additional competition due to entry.
Figures are computed by multiplying Table 3 row 11 by Table A7 row 5. Naturally, a larger fraction (19–31 %) switch to tariffs that raise their bills without necessarily being dominated.
For a reference on stochastic choice, random utility, and spatial models see Anderson et al. (1992).
Given two firms, the model is equivalent to a Hotelling line duopoly in which 1/2 of customers are jointly located with each firm at either end of the line. Bachi (2014) extends the analysis to more general definitions of similarity, including ratio similarity, which states that two prices are similar if neither is more than \(d\%\) larger than the other.
In that case, choice probabilities correspond to those of “a random utility model with tastes distributed according to a mixture of different extreme value distributions” (Matějka and McKay 2012).
Carlin’s (2009) model endogenizes the number of informed and uninformed consumers in Varian’s (1980) model of sales. By increasing the number of consumers who choose randomly, complexity in Carlin’s (2009) model can be interpreted as increasing either search costs or price confusion. In contrast to Gabaix et al.’s (2013) model, Carlin’s (2009) model assumes that if firm 1 makes its price more complex, it directly reduces the number of consumers who can compare prices between firms 2 and 3. Gu and Wenzel (2014) analyze a duopoly version of Carlin’s (2009) model with asymmetric firms.
Flow fees are charged as a percent of income rather than of contributions. As contributions are 6.5 % of income, the equivalent “load fee” (on contributions) is \(1/0.065\approx 15\) times the flow fee.
Piccione and Spiegler’s (2012) model can be reinterpreted as a spatial competition model where: (1) frames correspond to locations; (2) each consumer i can costlessly travel a maximum distance \(d_i\) but no further; (3) consumers’ maximum travel distances, \(d_i\), are uniformly distributed on [0, 1]; and (4) travel distance between locations are given by the comparability structure. The key difference from a standard spatial competition model is that consumer locations are not exogenous to firm location choices. Rather 1/2 of consumers co-locate with each firm, wherever firms choose to locate. Piccione and Spiegler’s (2012) model is generalized by Spiegler (2014).
These results are not surprising in light of the literature on spatial competition. It is well known in models of spatial competition that firms will differentiate to soften price competition and raise profits, and that when locations and prices are chosen simultaneously equilibrium must be in mixed strategies (Anderson et al. 1992). Moreover, we may re-interpret spatial competition models as models of competition with framing effects by reinterpreting random utility shocks or travel costs as utility irrelevant decision errors. Much of this literature, however, focuses on the case in which prices are chosen after frames (Anderson et al. 1992; Eiselt et al. 1993). While appropriate for the original applications of these models, this assumption seems less realistic when a location is reinterpreted as a price frame.
All three models are compatible with simple partition pricing. Suppose firms choose a product price \(p_1\) and an unavoidable shipping charge \(p_2\) that sum to the total price \(p_{total}=p_1+p_2\). Each model can be applied by equating the frame with the shipping charge, and the model’s scalar price with the total price, which is independent of the shipping charge. In the Mexican social security context, however, price cannot be reduced to a scalar “total price” because investors have heterogeneous balances and incomes, and hence should place different weights on balance and flow fees. Thus the price is neither a scalar nor independent of the frame.
With a zero balance fee, those who accrue formal sector earnings early in life would cross-subsidize those who accrue them late in life. With a zero flow fee the direction of the cross-subsidy would be reversed. Which fee is set to zero could affect the level of competition.
The market pass-through rate measures the fraction of an infinitesimal increase in marginal cost that is passed on to consumers in higher prices. The pass-through rate is equal to 1 in a perfectly competitive market with perfectly elastic supply.
It is possible for overconfidence or other systematic biases to raise equilibrium markups. Overconfidence increases markups, for instance, if the market pass-through rate is less than 1 (Grubb 2015c). Alternatively, if only some consumers are overconfident, and these are less price sensitive than the unbiased, then an adverse selection problem arises for firms and softens competition (Grubb 2015b). It is not clear whether either of these two mechanisms might help explain why prices remained high after CONSAR’s fee index was introduced.
In this case outcomes will be similar to those in many other models of biased beliefs, such as those surveyed by Grubb (2015c) that fall under the umbrella of overconfidence.
Kőszegi and Szeidl (2013) develop a related model of endogenous focus but apply it to analyze individual choice behavior rather than equilibrium firm pricing. Spiegler (2014) presents an example that endogenizes salience quite differently. He assumes that firms determine salience of an attribute by the weight that it is given in marketing messages.
Osborne (2011) separately identifies switching costs from learning, which is an additional source of inertia for rational consumers who choose between untested and possibly differentiated experience goods.
Honka (2014) observes individual level data about both the firms searched and switching decisions. Luco (2014) observes not only new and current investors, but also lapsed investors. Importantly, whereas current investors avoid both search and switching costs by keeping their current fund administrator, lapsed investors can only avoid search costs because they must fill out paper work even if they do not switch.
This is Piccione and Spiegler’s (2012) primary interpretation.
For instance, Clerides and Courty (2014) document strong inertia in package size choice of laundry detergent and other packaged goods. Many regular consumers of a full-size package fail to switch to purchasing two half-size packages of the same brand on the same shelf when doing so would be cheaper due to price promotions. Clerides and Courty (2014) argue, however, that this can be explained by rational search behavior (or equivalently rational inattention) by considering the cost of the 10 seconds that it might take to compare prices.
Such market designs have been implemented in a variety of markets, such as privatized social security in Mexico (Duarte and Hastings 2012) or retail electricity in Texas (Hortaçsu et al. 2015), and have been approximated in other markets, such as in the Affordable Care Act health insurance exchanges (Kaiser Family Foundation 2013).
Interventions may help some consumers become savvy and make good choices, while others remain non-savvy. The remaining non-savvy may still benefit through equilibrium price reductions in the case of search externalities or be harmed through equilibrium price increases in the case of ripoff externalities (Armstrong 2015). The models that are surveyed in this article typically involve search externalities, so interventions that increase consumer savviness help all consumers. It is worth noting, however, that the same interventions, such as facilitating expert advice, are proposed to aid consumers who mis-weight elements of price or other product attributes. Biases that lead to mis-weighting of product attributes can create ripoff externalities between savvy and non-savvy consumers, in which case interventions that increase consumer savviness might harm some consumers (Armstrong 2015).
The hiring of 100,000 sales agents by Mexican Afores comes to mind as an example (Hastings et al. 2013, fig. 1).
Rather than restricting the use of complex prices, a milder intervention would be to require either firms or a regulator to offer at least one simple option in addition to any complex alternatives. Unfortunately, Spiegler (2011) predicts that such policies will be ineffective.
Bar-Gill’s (2012) book contains a complementary discussion of disclosure requirements for such “total-cost-of-ownership” measures.
In markets with individual specific pricing, such as for mortgages or car insurance, price quotes would also be required to be easily sharable.
See Kamenica et al. (2011) for a discussion of other issues that are relevant to practical RECAP implementation.
The scope for such inefficiency is perhaps larger for differentiated products, as a biased quality index could also distort quality provision. For instance, Dranove et al. (2003) document that the introduction of cardiac surgery report cards in New York and Pennsylvania distorted medical care provision and worsened health outcomes. Nevertheless, other quality indexes, such as Los Angeles’ restaurant hygiene grade cards, have been very successful (Jin and Leslie 2003).
My thanks to Amelia Fletcher for pointing out that price-engine recommendations may be biased in the same manner as overconfident consumers. The conclusion that three-part tariffs could be used to exploit data-limited price engines is related to results in Spiegler (2006a). In particular, Spiegler’s (2006a) results may be interpreted as showing that firms should make consumers’ bills highly variable from one month to the next when consumers compare options based on a single prior bill from each firm.
Unfortunately, the program does not select a sensible default and hence does not serve low-income enrollees well. First, default enrollment or switching is into a randomly chosen plan among those with premiums below a threshold. Second, the plan premium is not a good measure of expected costs, which also depend on deductibles, coinsurance rates or tiered copayment rates, plan formularies, and drug prices. (Drug prices matter due to deductibles, coinsurance, and the “doughnut hole”. The doughnut hole is a gap in Medicare Part D coverage that lies between the initial coverage limit and the catastrophic-coverage threshold.) Moreover, the threshold that determines whether a plan’s premium is low enough to be included as a random default for low-income enrollees is manipulable by insurers. Thus, as well as implementing poor default choices for low-income enrollees, the program has driven up prices (Decarolis 2015).
Evidence from the introduction of smart thermostats shows that consumers can be happy to automate consumption choices and that doing so can substantially affect energy use (Harding and Lamarche 2015).
From the perspective of firms, it seems that automatic switching should be comparable to eliminating search costs, consumer price confusion, and switching costs all at once. Eliminating search costs and consumer price confusion should lower equilibrium prices, and the prevailing view is that eliminating switching costs will as well.
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I am grateful to Mark Armstrong, Ben Handel, and Rani Spiegler for careful reading and many helpful comments on an earlier draft. I also thank Vera Sharunova for her excellent research assistance.
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Grubb, M.D. Failing to Choose the Best Price: Theory, Evidence, and Policy. Rev Ind Organ 47, 303–340 (2015). https://doi.org/10.1007/s11151-015-9476-x
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DOI: https://doi.org/10.1007/s11151-015-9476-x