Reservation Price As a Range: an Incentive- Compatible Measurement Approach

TUO WANG, R. VENKATESH, and RABIKAR CHATTERJEE*

Drawing from the literature on buyers’ uncertainty in preference and product knowledge, the authors suggest and empirically test the proposition that a consumer’s reservation price for a product is more meaningfully and accurately represented as a range than as a single point. Given this conceptualization, they propose an approach for incentive-compatible elicitation of a consumer’s reservation price range (ICERANGE) that builds on Becker, DeGroot, and Marschak’s (1964) point-of-purchase method. Two empirical applications of the approach provide an assessment of its practicality and its predictive performance relative to current methodologies for reservation price elicitation. The results demonstrate that the proposed method significantly outperforms the benchmark approaches in terms of predictive validity and yields valuable incremental information about uncertainty in product valuation.

Reservation Price as a Range: An Incentive- Compatible Measurement Approach

Reservation price is a well-known and widely invoked customization and personalized pricing in several industries economic concept (Varian 1992). In common parlance, a (Choudhary et al. 2005), motivating accurate individual- consumer’s reservation price represents the maximum price level reservation price measurement. Second, marketing he or she is willing to pay for one unit of a good or service. researchers are applying recent methodological advances in Value pricing, product design, negotiations, and bundling areas such as experimental economics and Bayesian statis- are some substantive areas that depend on understanding tics to the measurement of reservation prices. Third, there is the reservation prices of individual consumers. a lack of consensus on the “right” way to measure (and, we Although the concept of reservation price has appeared in contend, even define) a consumer’s reservation price that the economics literature for well over a century (e.g., Dav- has left open avenues for further research. These factors, enport 1902), there is growing interest in advancing the especially the third, provide the motivation for our study. understanding and measurement of the construct, particu- For illustration, consider the following definitions of larly in marketing (Chung and Rao 2003; Jedidi, Jagpal, reservation price (italics added): and Manchanda 2003; Jedidi and Zhang 2002; Wertenbroch •“The minimum price at which [a consumer] would no longer and Skiera 2002). We attribute this interest to three factors. purchase the [product]” (Hauser and Urban 1986, p. 449). First, the advent of e-commerce has paved the way for mass •“The price at which a consumer is indifferent between buying and not buying the product” (Moorthy, Ratchford, and Taluk- dar 1997, p. 265). *Tuo Wang is Assistant Professor of Marketing, College of Business •“The price at or below which a consumer will demand one unit Administration, Kent State University (e-mail: [email protected]). R. of the good” (Varian 1992, p. 152). Venkatesh is Associate Professor of Business Administration (e-mail: [email protected]), and Rabikar Chatterjee is Professor of Business These three definitions differ from one another in the sense Administration (e-mail: [email protected]), Joseph M. Katz Graduate that in each case, the reservation price maps onto a different School of Business, University of Pittsburgh. The authors thank the late propensity to buy on the part of the consumer. They con- Dick Wittink and Russ Winer, the four anonymous JMR reviewers, Eileen verge only if the consumer’s propensity to buy transitions Bridges, Pradeep Chintagunta, Esther Gal-Or, John Hulland, Jeff Inman, Vijay Mahajan, Vikas Mittal, Vanitha Swaminathan, and doctoral students from a definite yes to a definite no at a single price point in Marketing at the Katz School for their helpful comments. They appreci- rather than over a range of values. ate the programming support from Leela Venkatesh and the help with data We propose that it is more reasonable to conceptualize a collection from Karen Page. The research has been funded by a grant from consumer’s reservation price as a range, with each of the the Katz Center for Industrial Competitiveness and two research grants definitions representing specific supports within the range. from the Office of the Dean at the Katz School. As we discuss in the next section, the literature on con- To read and contribute to reader and author dialogue on JMR, visit sumers’ preference uncertainty (e.g., Fischer, Luce, and Jia http://www.marketingpower.com/jmrblog. 2000) and performance/quality uncertainty (e.g., Rust et al. 1999) lends theoretical support to this proposition. If a con-

© 2007, American Marketing Association Journal of Marketing Research ISSN: 0022-2437 (print), 1547-7193 (electronic) 200 Vol. XLIV (May 2007), 200–213 Reservation Price as a Range 201 sumer’s reservation price for a particular product is a range indirect measure of utility (Hauser and Urban 1986) or “a tied to the probability of purchase rather than a point, the direct monetary measure of product value” (Kalish and Nel- seller’s best price for the consumer depends on this range son 1991, p. 327). and its mapping onto purchase probability. In other words, One commonality among the three definitions of reserva- ignoring the range in an individual consumer’s reservation tion price cited in the preceding section is that they link, at price when it exists is likely to lead to problems, such as least implicitly, the definition to the consumer’s probability suboptimal pricing. of purchase at a particular price point. The difference lies in The primary contribution of our study is methodological. the implied purchase probability: 0% in Urban and Hauser’s We propose an approach called ICERANGE, which is short (1986) definition, 50% in Moorthy, Ratchford, and Taluk- for incentive-compatible elicitation of the range in a con- dar’s (1997), and 100% in Varian’s (1992). The lack of consumer’s reservation prices. Our approach, which is tied to sensus goes beyond these three studies.1 actual choice and is motivated by Becker, DeGroot, and In our conceptualization, a consumer’s reservation price Marschak’s (1964; hereinafter BDM) point-of-purchase is explicitly tied to his or her probability of purchasing the methodology, is the first in the literature to measure con- good. On the basis of the implied probability of purchase in sumers’ reservation prices as a range. The range measure- current definitions, we identify the following three signifi- ment is significant because the theory of uncertainty and cant reservation price points: related literature in experimental economics (and other 1. Floor reservation price is the maximum price at or below areas) underscore the notion that the point representation of which a consumer will definitely buy one unit of the product reservation price is tenuous. The range characterization (i.e., 100% purchase probability). retains the point measure as a special case. We demonstrate 2. Indifference reservation price is the maximum price at which that ICERANGE performs better than multiple benchmarks a consumer is indifferent between buying and not buying in two studies in which participants (college students) had (i.e., 50% purchase probability). the opportunity to buy the product (Belgian chocolate in 3. Ceiling reservation price is the minimum price at or above one study and Australian wine in the other). The two studies which a consumer will definitely not buy the product (i.e., confirm the existence of the reservation price range. Fur- 0% purchase probability). thermore, data from the more elaborate chocolate study Our motivation for the range representation comes from support our premise that consumers’ reservation price the uncertainty literature and related work in experimental ranges are positively related to their respective levels of economics (e.g., Ariely, Loewenstein, and Prelec 2003), performance- and preference-related uncertainty. Although resource economics (e.g., Gregory, Lichtenstein, and Slovic the elicitation procedure for ICERANGE is somewhat more 1993), psychology (e.g., Jacowitz and Kahneman 1995), involved than that for BDM, we address possible related and marketing (e.g., Urbany, Dickson, and Wilkie 1989). concerns. This range conceptualization seems able to unify the vari- We elaborate on the conceptual and theoretical underpin- ous definitions of reservation price (as a range of thresh- nings of our range characterization in the next section. olds). We note that utility theory has axiomatically treated Then, we compare and contrast alternative routes to reser- reservation price as a single-point measure, under the vation price measurement and draw from this discussion to assumption that participants know their preference struc- propose ICERANGE. In the two subsequent sections, we tures with certainty (thus, there may be uncertainty related describe the applications in the chocolate and wine cate- to product performance but not to preference structure). Our gories. Our concluding section outlines the scope and impli- conceptualization allows for both sources of uncertainty. cations of ICERANGE, as well as the study’s limitations Next, we examine the theoretical bases for this and future research directions. conceptualization. CONCEPTUALIZING RESERVATION PRICE AS A Theoretical Underpinnings for Reservation Price as a RANGE Range We first review the alternative definitions of reservation The single-point representation of reservation price price and cite theoretical support for our contention that the requires the central assumption that a consumer knows with construct is better represented as a range of valuations. certainty how much he or she would be willing to pay for Establishing these bases for the range is an essential prereq- one unit of the product (Hanemann 1984). This is a strong uisite for motivating the ICERANGE approach. assumption because consumers may lack a well-defined Review and Synthesis of Extant Definitions preference structure or the cognitive ability to make such an assessment (Gregory, Lichtenstein, and Slovic 1993; Heiner The basic idea of reservation price is that there is a maxi- 1985), except perhaps in the most familiar contexts (Fis- mum price a consumer would be prepared to pay for one chhoff 1991). unit of a product (or service). Thus, the reservation price Conversely, the vast literature on consumers’ uncertainty represents a consumer’s value threshold. His or her propen- about product performance and individual preference sity to buy depends on whether the actual price is above, underscores that neither type of uncertainty is ever fully below, or equal to this threshold. As in much of the extant literature, we use the term “willingness to pay” interchange- ably with reservation price. The economics literature interprets reservation price as 1For example, the implied purchase probability is 100% in Kristensen the combined economic value to a consumer of all the bene- and Garling’s (1997) definition of reservation price, 50% in Casey and fits that would accrue from the product (Ryan and Miguel Delquie’s (1995) and Jedidi and Zhang’s (2002) definitions, and 0% in 2000). To marketers, the reservation price represents an Scherer’s (1980) definition. 202 JOURNAL OF MARKETING RESEARCH, MAY 2007 resolved in practice (Urbany, Dickson, and Wilkie 1989). a consumer’s reservation price as a range tied to the proba- Simon’s (1955) seminal theory of bounded rationality—that bility of purchase. To motivate our approach, we first people have limited capacity for processing information— review the extant approaches for reservation price measure- guides the work in this area. ment. Beyond the methodological differences and framing Buyers’ product performance uncertainty is due to imper- distinctions, these approaches differ in the types of biases fect information about the product’s quality or future per- they ignore or control for and the purchase probabilities formance. Although decision making under imperfect infor- onto which the estimates map. We position ICERANGE as mation demands greater cognitive resources (Shugan 1980), a “better” alternative for measuring individual-level reser- the nature and extent of the search is constrained by many vation price because it controls for at least two key biases factors, such as search cost and experience (e.g., Ratchford and is able to capture reservation price as a range. We 1982; Stigler 1961; Wathieu and Bertini 2005) and the con- briefly discuss the principal extant approaches and then sumer’s ability to do so (Simon 1955). In the presence of present ICERANGE. In the following two sections, we uncertainty, consumers consider not only the average (or present empirical demonstration of the superior perform- expected) outcome but also the entire range (Rust et al. ance of ICERANGE (along with evidence in support of the 1999). existence of a reservation price range). A consumer’s preference uncertainty, also referred to in the literature as choice uncertainty (e.g., Urbany, Dickson, A Comparison of Extant Approaches for Reservation Price and Wilkie 1989), is the consumer’s ambiguity over what Measurement exactly he or she wants (Luce 1959; March 1978), making We review three prominent direct elicitation methods for the consumer unsure of “what value to assign to the alterna- reservation price measurement at the individual level: direct tive” (Fischer, Luce, and Jia 2000, p. 88). Even when the self-explication (e.g., Park and Srinivasan 1994), Vickrey consumer has perfect information about a product, he or she (1961) auction (see also Hoffman et al. 1993), and BDM’s may still be uncertain about his or her own preference (1964) point-of-purchase procedure (see also Wertenbroch (March 1978). Parallel work in agricultural economics and Skiera 2002). For completeness, we also consider the draws on “ambivalence” (Ready, Whitehead, and Blomquist main indirect estimation methods: conjoint analysis (e.g., 1995) as when people make “difficult trade-offs.” Opaluch Jedidi and Zhang 2002; Kohli and Mahajan 1991) and and Segerson (1989) point out that the cost of overcoming choice experiment and related hybrids (e.g., Chung and Rao ambivalence may be prohibitively high. Preference uncer- 2003). Our empirical applications, which use chocolate and tainty may be attributed to various sources. For example, wine as the product categories, focus on direct elicitation preferences may be constructive (Bettman, Johnson, and methods. Given the hedonic nature of both products, the Payne 1990; Gregory and Slovic 1997), the choice situation conjoint-based indirect estimation methods would not be may be novel or unfamiliar (March 1978), or there may be appropriate. Extant studies point to differences in estimates attribute conflict within a single alternative when it is good across methods. These may be attributable to a combination in some respects but bad in others (Fischer, Luce, and Jia of factors, such as the differences in the purchase probabili- 2000). When a consumer’s preferences are uncertain, ties onto which the methods map, the biases that the meth- Dubourg, Jones-Lee, and Loomes (1997) argue in favor of a ods ignore or overcome, semantic differences among elici- “personal confidence interval” of his or her willingness to tation measures, and measurement error. pay. Two important types of biases examined in the reserva- In a related vein, experimental economists argue for a tion price literature arise from the absence of incentive threshold price up to which a consumer definitely buys the compatibility in elicitation due to the hypothetical nature of product, another threshold above which the consumer sim- the responses and the tendency of respondents to act strate- ply walks away, and a range of prices in which consumer gically. These biases, which we discuss subsequently, could response is more ambiguous (Ariely, Loewenstein, and lead to overbidding or underestimation of reservation price. Prelec 2003, p. 77). Loomes (1988) finds that people have The first is the absence of incentive compatibility due to regions of indifference instead of clearly defined indiffer- hypothetical response bias.2 An incentive-compatible mech- ence curves. The interval idea of these studies is also anism gives the respondent the incentive to respond truth- observed in the work of Jacowitz and Kahneman (1995) and fully (Lusk and Schroeder 2004). For example, incentive Luce, Jia, and Fischer (2003, p. 466). Recognizing the incompatibility arises when respondents are not responsible individual-level distribution, Li and Mattsson (1995) pro- for paying their stated (or inferred) reservation price. The pose eliciting a “postdecisional confidence measure” (i.e., a willingness to pay is higher in such cases than when respon- “subjective probability” measure) between 0% and 100% dents are required to pay (Posavac 2001). Cummings, Har- tied to reservation price elicitation. rison, and Rutström (1995), among others, show that this Taken together, this evidence, which is drawn from upward bias extends to other non-incentive-compatible diverse domains, lends strong theoretical support to the methods, such as open-ended and double-ended contingent notion of reservation price as a range rather than a single valuation. value. Our conceptualization formalizes this idea by specifically mapping this range onto purchase probabilities, in a choice context. 2Hypothetical response bias (Nape et al. 2003) exists when values THE ICERANGE PROCEDURE elicited in a hypothetical context, such as a survey, differ from those elicited in a real context, such as an actual purchasing situation. The usual Our primary objective is to propose a new, individual- concern with this bias is that people overstate their true valuation in hypo- level reservation price measurement approach that captures thetical settings. Reservation Price as a Range 203

The second type of bias is tied to strategic response. This cially Wertenbroch and Skiera 2002). The core distinctions arises when respondents anticipate a link between their of our article are that we draw on the theory of uncertainty response and the ultimate outcome and act to maximize to conceptualize individual reservation price as a range (in their utility by taking into account how their responses may contrast to the point representation in BDM), and our affect the decision (Carson, Groves, and Machina 1999). ICERANGE approach captures this reservation price range The direction of strategic response bias depends on the con- with associated purchase probabilities. As we show subse- text of elicitation. When consumers believe that stating a quently, ICERANGE predicts actual behavior better than higher reservation price will increase the likelihood of sub- BDM.4 sequently receiving a good, they are more likely to state a higher value than their true value (Posavac 2001, p. 95). Specifics of the ICERANGE Procedure Conversely, when anticipating a higher final price for a ICERANGE is tied to the point of purchase of the prod- product, buyers might state a value that is lower than their uct of interest. In the mold of Vickrey auction, BDM, and true reservation price. other direct elicitation methods, ICERANGE treats reserva- Although Vickrey auction is theoretically incentive com- tion thresholds as deterministic.5 The elicitation of reserva- patible, there is some evidence in the literature that it tion price information is followed in quick succession by induces overbidding (Kagel, Harstad, and Levin 1987). the “enforcement” phase, during which a respondent is Simple self-explication suffers from both kinds of biases either required to buy one unit of the product at an (see Monroe 1990; Posavac 2001). Unlike direct elicitation, incentive-compatible price or denied the opportunity to pur- indirect methods, such as conjoint analysis and choice chase. To avoid possible endowment effects, respondents experiments, avoid the increased attention to the pricing should not be paid any money for participation (Thaler question and mitigate the effect of strategic bias. At best, 1985). The point-of-purchase elicitation means that, as in these approaches are incentive neutral; they do not provide BDM, we are able to avoid the hypothetical response bias the respondent the (dis)incentive for (not) revealing the true by linking responses to real choice. willingness to pay. We believe that the BDM approach is The product (or brand) for which consumers’ reservation the “best” method among the available options because it prices are being ascertained is not in short supply. Thus, tackles the previously mentioned sources of bias (Plott and unlike in a Vickrey auction setting, the overbidding bias, for Zeiler 2005). The BDM approach provides for incentive example, is avoided by not making product choice a “com- compatibility by rewarding respondents for telling the truth petition” to be won (Kagel, Harstad, and Levin 1987). and penalizing them for lying (i.e., for over- or understating To control against strategic response, respondents are reservation prices). It addresses strategic bias by making informed that the seller has already set a price that is not respondents aware that there is no link between their stated disclosed to them. As a guarantee that the price will not be willingness to pay and the price they might need to pay dur- changed during the reservation price elicitation, this price is ing the enforcement phase of the procedure. written on an index card within a sealed envelope that is Another relevant issue is the probability of purchase onto placed in front of the respondent. In a slightly different which the reservation price measure (or estimate) implicitly vein, Wertenbroch and Skiera (2002) tell each respondent maps.3 Because the BDM and Vickrey auction procedures that the transaction price would be the one that the respon- are tied to real choice (i.e., the consumer must buy the good dent randomly picks from an urn. Our use of the secret, pre- if certain conditions are met), respondents may be expected selected price in a sealed envelope follows the work of to provide a value that corresponds to their floor reservation Schade and Kunreuther (2001). The price is revealed to the price with 100% purchase probability. Conversely, the respondent at the end of the study. nature of trade-off analysis in conjoint analysis and choice Ensuring incentive compatibility over a respondent’s experiments, which is tied to the indifference between buy- entire range of reservation prices forms the crux of ing and not buying, is likely to yield an estimate of reserva- ICERANGE. To achieve incentive compatibility, we must tion price that is close to the indifference reservation price, ensure that the respondent’s dominant strategy is to tell the with 50% purchase probability. To the extent that there is a truth over the entire range of purchase probabilities. We range in a consumer’s reservation price, the different clarify how we do so in our outline of the elicitation steps. approaches could measure distinct supports within the The respondent is given an opportunity to examine the range. product in factory packing and to use (or taste) a demon- We position the ICERANGE approach as one that is stration piece to gain familiarity. The elicitation involves rooted in theory and builds on the “best” characteristics of three steps to capture the respondent’s floor, indifference, the BDM approach (e.g., Wertenbroch and Skiera 2002). Our focus on incentive-compatible elicitation (in actual buying situations) and avoidance of strategic bias, as well as our choice of protocols, resembles those of BDM (espe- 4Our focus on ICERANGE distinguishes our study from that of Ariely, Loewenstein, and Prelec (2003) as well. Unlike theirs, our primary contribution is methodological. On the theoretical side, we build on Ariely, 3For illustration, the Vickrey auction, under which the respondents sub- Loewenstein, and Prelec’s proposal for the existence of the reservation mit independent sealed bids for a real product and the winning (i.e., high- price range by drawing from the literature on uncertainty and by linking est) bidder pays the second-highest price, arguably maps onto the floor specific supports within a consumer’s range to his or her purchase reservation price (i.e., 100% probability of purchase). This is because the probability. winning bidder (potentially any one of the respondents) must purchase the 5Rooting reservation price measurement in a random utility framework product, and the second bid could be only infinitesimally less than the is an alternative perspective, shared by indirect elicitation methods, such as highest bid. conjoint analysis and choice experiments. 204 JOURNAL OF MARKETING RESEARCH, MAY 2007 and ceiling reservation prices.6 The reservation price elicita- Our approach to operationalizing uncertainty by asking tion questions are accompanied by graphic representations respondents to pick a ball from an urn is supported by prior of the relationship between reservation price and purchase studies (Elliott and McKee 1995; Ellsberg 1961). Grether probability, so the idea is clear and intuitive to respondents and Plott (1979) take a slightly different route in which a (we describe the elicitation instrument in greater detail sub- random dart is thrown at a circle; the respondent “wins” if sequently). Details of each step are as follows: the dart hits a small shaded area within the circle. Novem- sky and Kahneman (2005) point to the conceptual similarity Step 1: A respondent is asked to state the maximum price A at or below which he or she would definitely buy the prod- between uncertain buying situations and a game of poker. uct (i.e., 100% purchase probability, equivalent to the We provide two additional clarifications. First, if the floor reservation price in our framework). To ensure respondent states the same reservation price for two or more incentive compatibility, the respondent is told that if the successive elicitations, the enforcement decision (to buy or price P (in the sealed envelope) is found at the end of forgo) is tied to the higher probability of purchase if the the study to be less than or equal to the respondent’s sealed price P equals the tied reservation prices. In other stated price A, he or she would be required to purchase words, a respondent cannot strategically lower his or her at price P. probability of purchase by keeping multiple reservation Step 2: The respondent is asked to reveal price level B at which price levels the same. Second, because the sealed price P he or she is indifferent between buying and not buying might fall between a respondent’s A and B levels (or the product (i.e., 50% probability of purchase, corresponding to the indifference reservation price). The between B and C, and so on), the respondent is shown respondent is informed that if the posted price P is later graphically the interpolation rule that would apply if the found to be equal to B, he or she must pick a ball from sealed price P were to fall between Xα and Xβ, the levels an urn containing one green ball and one red ball. If the corresponding to α% and β% probability levels (β > α). In respondent picks the green ball, he or she will be this case, he or she would be asked to pick a ball from an required to buy at the price P. If the respondent picks the urn corresponding to a probability of purchase equal to α + red ball, he or she will not have the opportunity to buy (β – α)(Xα – P)/(Xα – Xβ)%. For illustration, let α and β (Ellsberg 1961). That is, the respondent is made aware correspond to purchase probabilities of 50% and 100%. that P = B implies a draw from the urn with a 50% pur- Suppose that the sealed price P (in the envelope) is between chase probability. X and X (X > X ). The purchase probability at Step 3: The respondent is asked to state price level C at which 100 50 50 100 there is only a 10% (i.e., small) probability that he or price level P (based on the interpolation rule) is 50 + (100 – she would purchase the product. Because it is impossi- 50)(X50 – P)/(X50 – X100)%. (We discuss our verbal proto- ble to ask the respondent for an incentive-compatible col subsequently.) price level with a 0% purchase probability, we rely on Are these steps adequate to ensure that the respondent the price with the 10% purchase probability to extrapo- answers truthfully? Under the ICERANGE approach, the late the ceiling reservation price. If the posted price P respondents’ dominant strategy is to offer their true reserva- (in the sealed envelope) is later found to be equal to this tion price for any corresponding purchase probability of χ% price, the respondent will be asked to pick a ball from (0 ≤ χ ≤ 100). Because respondents must indicate price lev- an urn containing one green and nine red balls. The els X tied to their purchase probabilities χ%, not revealing respondent is required to buy at the price P (or forgo the “true” levels hurts the respondent. Specifically, under- purchase) if he or she picks a green (or red) ball. That is, P = C implies a draw from the urn with a 10% purchase estimating (overestimating) the true reservation price corre- probability. (As we discuss subsequently, we find from sponding to a given purchase probability means that the our applications of ICERANGE that we can approxi- respondent may have a less-than-ideal (more-than-ideal) mate the ceiling reservation price by extrapolating chance of being able to purchase the product at the revealed through the 100% and 50% purchase probability points price. In other words, incentive compatibility is maintained with no significant loss in predictive ability. Thus, to over the entire range. simplify the approach, Step 3 may be eliminated.)7 When the elicitation is complete, the envelope is unsealed and the respondent is subjected to the appropriate outcome as per the instructions (which serve as the “con- tract”). It follows from the foregoing description that the 6Alternatively, we could ask respondents for their purchase probabilities BDM procedure is nested within ICERANGE; the two at various price points. However, although both routes can be structured to approaches converge when the range of an individual con- avoid the strategic and incentive incompatibility bias, our approach is more sumer’s reservation prices is zero. efficient, requiring a small, fixed number of elicitation questions, given that the task is to elicit specific supports in the reservation price range cor- The Link Between Individual-Level Reservation Price responding to specific purchase probabilities (e.g., 0%, 50%, and 100%). Range and Uncertainty In contrast, the alternative approach would be more of an open-ended, “trial-and-error” process and would likely require additional questions. Previously, we cited the effect of the consumer’s degree 7Two optional steps that elicit the reservation prices D and E, which cor- of uncertainty with product performance and the level of the respond to the 75% and 25% purchase probabilities, respectively, may be added if the researcher wants to calibrate the response curve more accu- consumer’s preference-related uncertainty toward the prod- rately and if the respondents are deemed to have the time and resources to uct as motivation for our reservation price range conceptu- provide these values. The procedure to elicit D and E is as follows: If the alization. Thus, we posit the following: sealed price P matches D (or E), the respondent picks a ball from an urn containing three green balls and one red ball (or one green and three red •The greater a consumer’s uncertainty with the product’s per- balls). The respondent is required to buy (or forgo purchase) if he or she formance, the greater is his or her range in reservation prices picks a green (or red) ball. for the product. Reservation Price as a Range 205

•The greater a consumer’s preference uncertainty for the prod- The following steps are common to all methods. All uct, the greater is his or her range in reservation prices for the respondents were told a week in advance about the study on product. “consumers’ preferences for Galler chocolate.” They were APPLICATION OF ICERANGE: THE CHOCOLATE advised to come with approximately $10 in cash (i.e., well STUDY above the product’s price) because they would have an opportunity to buy the product. Respondents were not paid We conducted two studies that employ different products: to participate in any of the studies. We wanted to ensure that chocolate and wine. Several prior studies on consumers’ we did not create an endowment effect (Thaler 1985) that valuations have used chocolate (e.g., Bhatia and Fox- might contaminate the reservation price elicitation. Respon- Rushby 2003; Johannesson, Liljas, and O’Conor 1997; dents who were earmarked for the incentive-compatible Kaas and Ruprecht 2003) or wine (e.g., Horsky, Nelson, methods—ICERANGE, BDM, and Vickrey auction—were and Posavac 2004; Lynch and Ariely 2000; Nerlove 1995) specifically told that they might be required to purchase if as the product category. The primary objectives of the two the price was “acceptable” to them. On a given study day, studies together are (1) to demonstrate the practicability of each respondent was asked to taste a piece of the chocolate the ICERANGE approach and (2) to benchmark and to examine an unopened bar. No information about the ICERANGE’s performance relative to several alternative product’s typical retail price was provided. The data collec- direct elicitation approaches, including BDM and Vickrey tion for all methods included an elicitation phase and a auction, for different products. (As we mentioned previ- debriefing phase. For the three incentive-compatible meth- ously, conjoint-based indirect estimation approaches would ods alone, there was an additional enforcement phase in not be appropriate because of the hedonic nature of the which the respondents who were “required to buy” made products involved in both studies.) In the process, we the purchase. attempt to confirm the existence of the range in individual- Figure 1 documents the protocol and measurement proce- level reservation prices and to test its relationship with the dures for the various approaches. Panel 4 of the figure clari- individual-level performance and preference uncertainties. fies how we explained the measurements and implications The first study, which we describe in this section, of the intermediate purchase probabilities to the respon- involves 562 undergraduate students at two major U.S. uni- dents, including the interpolation of the probability corre- versities and uses as the product a premium brand of Bel- sponding to the envelope price P. gian chocolate, Galler. ICERANGE and BDM. We collected data for these two approaches in one-on-one interviews (see Wertenbroch and Data Collection Skiera 2002, p. 231). Respondents were randomly assigned Galler retails in the United States for $5.25 per 3.5-ounce to either the ICERANGE or the BDM group. They were bar at exclusive candy stores. Because the Galler brand is alerted that their responses would be binding in terms of the not available at most stores (indeed, none of our respon- ultimate purchase outcome, which depended on how their dents had heard of the brand before), the influence of refer- responses compared with the price inside a sealed envelope ence price effects on consumers’ reservation prices should (placed in front of the respondent). The interviewers also be weak at best. A salient feature of ICERANGE is its link- explained to respondents why it would not be in their inter- age to actual choice. Imported chocolates as the product est to over- or understate their valuations. These interview- category also ensures that respondents are likely to be in the ers (recruited from an undergraduate marketing research market,8 thus reducing “wasted” responses (from respon- class) were carefully trained and required to undergo sev- dents with no interest in purchasing the product at any rea- eral practice rounds. sonable price at the time of the study). In the elicitation phase, only respondents in the BDM We first collected the data for ICERANGE and BDM and group were asked to provide a single price representing randomly assigned 134 respondents to ICERANGE and 128 their maximum willingness to pay for the product, with a to BDM. Then, to benchmark ICERANGE against addi- follow-up option to revise their response (as in Wertenbroch tional methods, we went back to the same target population and Skiera 2002) until they reached a price level at which and randomly assigned a fresh set of respondents to these they were not willing to pay. Respondents in the methods: Vickrey auction = 104, the self-explicated floor ICERANGE group provided their floor, indifference, and reservation price measure = 54 (Varian 1992), the self- ceiling reservation prices, following the procedure we explicated indifference reservation price measure = 59 described in the previous section. ICERANGE respondents (Moorthy, Ratchford, and Talukdar 1997), and a “general” were also allowed to revise their floor reservation price esti- self-explicated measure that does not state the purchase mates, similar to those in Desaigues and Rabl’s (1995, on probability = 83 (Park and Srinivasan 1994). The greater contingent valuation) study and in BDM (Wertenbroch and number for Vickrey auction is because it is incentive com- Skiera 2002). Our results are based on these revised reser- patible, as is ICERANGE. Among the self-explicated meas- vation prices. Respondents were encouraged to review their ures, the general measure is the most commonly used and responses before they were “locked in” by the interviewer. thus was assigned more respondents. The option to revise reservation prices is a desirable feature because it tackles anchoring problems, if there are any. With ICERANGE, the review stage allows the respondents to reexamine their entire range and not be constrained by their first two responses on floor and indifference levels. The 8Studies have shown that the typical consumers of gourmet chocolate are “younger” (www.marketresearch.com/map/prod/112881.html). More- review offers respondents an added level of reassurance. over, although the retail price is at the high end of the range for chocolates, We structured the enforcement phase to aid benchmark- it is clearly affordable for undergraduate students. ing. To assess how well the respondents’ actual purchase 206 JOURNAL OF MARKETING RESEARCH, MAY 2007

Figure 1 PROTOCOL USED FOR ALTERNATIVE ELICITATION METHODS

A: Protocol for Respondents in the ICERANGE Group •For example, if the envelope price P corresponds to a 60% probability of purchase, you will be asked to pick a ball from an urn containing A Panel 1: Please reveal a price level at or below which you would three green balls and two red balls. definitely buy the bar of chocolate. Later, if the price in the envelope is found to be lower than or equal to this price A, you ••-If you pick a green ball, you will be required to buy at the price in the will be required to purchase at the envelope price. (For example, if envelope. your indicated price A is $100 and the envelope price is $99, you ••-If you pick a red ball, you will not be given the opportunity to buy. will be required to purchase the product at $99). Please state your price level A below: B: Protocol for Respondents in the BDM Group A: ______. For BDM respondents, there is a single reservation price elicitation question: Please reveal the price level A at or below which you will buy the bar of chocolate. (If the price in the envelope is found later to be lower than or equal to this price A, you will be required to purchase at the envelope price. Otherwise you will not be given the opportunity to buy the chocolate. For example, if your indicated price A is $100 and the envelope price is $99, Panel 2: Please reveal a price level B at which you would be indifferent you will be required to purchase the product at $99.) Please state your between buying and not buying the bar of chocolate. (At this price level A below: price, you are 50% likely to buy the product.) Later, if the price in A: ______the envelope is equal to this price B, you will be asked to pick a ball from an urn containing one green ball and one red ball. If you pick the green ball, you will be required to buy at the price C: Protocol for Respondents in the Vickrey Auction Group from the envelope. If you pick the red ball, you will not be given the opportunity to buy. (If, however, your price level B is the same Respondents placed a bid for a bar of Galler chocolate after reading the as your earlier price level A, the higher purchase probability following rules. associated with A will apply.) Please state your price level B •You gain the most by revealing the maximum price you are willing to below: pay for the product. B: ______•All bids are final. You will not be able to change your bid once the auction is closed. •We will collect all bids. The winner – to be announced in the next class – will be the highest bidder. If you are the winner, you will be required to purchase the chocolate at the second-highest bid. For example, if your winning bid is $100 and the second-highest bid is $99, you will pay $99 and receive a bar of chocolate. Please make your bid below: Panel 3: Please reveal a price level C at which you are only 10% likely to Bid: ______buy the bar of chocolate. Later, if the price in the sealed envelope is equal to this price C, you will be asked to pick a ball from an urn containing one green and nine red balls. If you pick the green D: Protocol for Respondents in the Self-Explication Groups ball, you will be required to buy at the price from the envelope. If Respondents were asked one of the following questions (depending on the you pick a red ball, you will not be given the opportunity to buy. group): (If, however, your price level C is the same as your earlier price level A or B, the highest associated purchase probability will For self-explication of floor reservation price: apply.) Please enter your price level C below: •Please reveal the maximum price P at or below which you will defi- C: ______nitely buy the bar of Galler milk chocolate at this moment. P: ______For self-explication of indifference reservation price: •Please reveal the maximum price P at which you would be indifferent between buying and not buying a bar of Galler milk chocolate at this moment. P: ______Panel 4: What if the envelope price P falls within the range of price points you have indicated before? For self-explication of general reservation price: •Please reveal the maximum price P that you are willing to pay for a bar of Galler milk chocolate at this moment.

P: ______Reservation Price as a Range 207 decisions correspond to their self-explicated reservation ing phase, following the same format as in ICERANGE or prices, each respondent was asked to pick one of five index BDM. cards with a different price level ($2.50, $2.75, $3.00, Self-explicated approaches. The measures corresponding $3.25, and $3.50) printed on their backs (thus hidden from to the three different self-explicated approaches are related the respondent). Respondents were assured that all five to the floor, indifference, and general reservation prices (see index card prices were weakly lower than the price in the Figure 1, Part D). Respondents were randomly assigned to sealed envelope. They were instructed to turn over the answer one of the three corresponding instruments. Under selected card to reveal the price and then declare whether these approaches, respondents were asked directly to state they would buy the chocolate at that price. A respondent their valuations, without corresponding precautions to choosing to buy paid the revealed price, received the choco- maintain incentive compatibility and avoid strategic biases late, and completed the final debriefing phase of the study. (i.e., the answers are not binding). After respondents turned The unmasking of the envelope price has no practical sig- in the questionnaires containing their reservation prices for nificance for these respondents. For respondents who did a bar of chocolate, they were informed of a “special offer not choose to buy at the price revealed on the index card price” and were asked if they wanted to buy the chocolate. (i.e., the special offer price), their stated valuations in the Again, this step aids benchmarking. Those who said yes elicitation phase were binding. Depending on how the collected a bar each after paying the price. The data collec- unmasked envelope price stacked against their reservation tion ended with debriefing. prices, they were required to buy or not to buy according to Results the procedure we discussed in the previous section. In the debriefing phase, we elicited feedback from Table 1 contains the mean reservation price estimates respondents to benchmark ICERANGE against other (and associated standard errors) from ICERANGE and the approaches on qualitative dimensions. We wanted to deter- five other approaches, as well as the shift in choice likeli- mine whether there are (dis)advantages with ICERANGE hood (SCL) measures that indicate predictive performance that go beyond predictive performance. Accordingly, we (we discuss this in greater detail subsequently). The mean surveyed respondents’ comfort levels with each approach, floor, indifference, and ceiling reservation prices (across the clarity of incentive compatibility, and the comprehen- respondents) from the ICERANGE approach for a bar of sion (or understandability). (We discuss the specific meas- Galler chocolate are $2.97, $3.48, and $4.19, respectively. ures and results in greater detail subsequently.) The mean range (difference between floor and ceiling reser- Vickrey auction. Respondents were informed of the rules vation prices) of $1.22 is significantly different from zero of the auction (see Figure 1, Part C). Special attention was (t = 10.60, p < .01), in support of our range conceptualiza- drawn to the rules that the bids would be final and binding tion. Furthermore, the mean indifference reservation price is and that the winner (i.e., the highest bidder) would pay the significantly greater than the mean floor reservation price second-highest bid price. They were told that the winner (t = 8.16, p < .01), as is the mean ceiling reservation price would be revealed in the following class. Soon after, the compared with the mean indifference reservation price (t = respondents submitted their “sealed” bids for a bar of 11.10, p < .01). Of the 134 respondents under ICERANGE, chocolate. In the enforcement phase, and before unsealing 106 characterized their reservation prices as a range rather their bids, the respondents were told about a special offer. If than as a point (we classified a range of $.50 or less as a they chose to buy the chocolate at this special price, their point [see Kagel and Levin 1993]).9 bids would be withdrawn from the auction and would no longer be binding. The special price, which was predeter- mined from a pilot study, was then revealed. Respondents 9Indeed, our approach allows respondents to give the same values for all who indicated that they would buy at the special price paid three reservation prices; that is, they could indicate a range of zero if they wanted. Of the 134 respondents for the chocolate study, 21% indicated a the money and collected a bar apiece. The bids of those who range of $.50 or less, demonstrating that respondents could and did exer- chose not to buy at the special offer price were included in cise the option of indicating the same or similar values for all three the auction. All respondents then participated in the debrief- thresholds.

Table 1 CHOCOLATE STUDY: RESERVATION PRICE ESTIMATES AND PREDICTIVE PERFORMANCE MEASURES

Self-Explicated (Total N = 196) ICERANGE (N = 134) BDM Vickrey Auction Floor Indifference General Floor Indifference Ceiling (N = 128) (N = 104) (N = 54) (N = 59) (N = 83) M ($) 2.97 3.480b 4.19 2.94 3.14 2.02 2.71 2.39 (SE) ($) 0(.14)(.17) 0(.21) (.15) (.27) (.12) (.42) (.16) Mean difference ($) .51a .71a (SE) ($) (.06)a (.06)a

SCL .126b .180 .307 .315 .337 .339 aSignificantly greater than zero (p < .01). bSignificantly less than the SCL for BDM (p < .10) and for all other methods (p < .05). 208 JOURNAL OF MARKETING RESEARCH, MAY 2007

For the BDM group, the mean reservation price is $2.94, The issue could be raised that the SCL measure favors whereas under the Vickrey auction procedure, it is $3.14. ICERANGE because this approach alone allows PCL and The self-explicated mean floor, indifference, and general SCL values anywhere between zero and one for a given reservation price estimates are $2.02, $2.71, and $2.39, respondent. With other methods, PCL and SCL values for respectively. As anticipated, we find that BDM yields an any respondent are dichotomous—zero or one, representing estimate closer to the ICERANGE floor reservation price; the miss rate (1 – hit rate). To address the concern that SCL indeed, they are not significantly different from each other might “handicap” the benchmark methods, we also com- (t = .14, p > .10). At the same time, the BDM estimate is puted the miss rate under ICERANGE. To do so, we used significantly lower than the indifference reservation price of the indifference price (50% purchase probability) as the cut- ICERANGE (t = 2.33, p < .05). off point. If the predicted purchase probability is less than Comparisons of ICERANGE’s predictive performance 50% (≥50%) under ICERANGE, the predicted choice is with those of the other approaches are based on the data treated as “not buy” (or buy). The miss rate for ICERANGE collected at the enforcement phase of the study. At the indi- of .112 is significantly less than that of BDM (miss rate vidual level, we compared the observed (i.e., actual) choice difference = .068, p < .10) and each of the other approaches for each respondent at the offer price with the predicted (p < .05). The results provide greater assurance for the use choice likelihood at that price from ICERANGE or an alter- of ICERANGE. We must emphasize that SCL is the more native approach, as applicable for the individual. Our spe- appropriate measure of predictive performance. cific measure of predictive performance is the SCL (Inman, Table 2 reports the average respondent evaluations of the McAlister, and Hoyer 1990), defined as SCLi = OCi – PCLi, different methods on three dimensions that were collected where SCLi is the SCL for respondent i, OCi is the observed in the debriefing phase of the study. Note that the superior choice indicator, and PCLi is the choice likelihood pre- performance of ICERANGE over BDM comes without sac- dicted by the model, all for the ith respondent. rificing the comfort level of the respondents in answering If the respondent buys (does not buy) at the special offer the reservation price elicitation questions. Furthermore, price, OCi is one (or zero), and PCLi from ICERANGE can there was no significant difference between the two meth- be anywhere between zero and one. Specifically, if the offer ods in terms of the clarity of incentive compatibility, though price is less (greater) than or equal to the respondent’s floor respondents appeared to think that the BDM method was (ceiling) reservation price, PCLi is one (zero). For any other easier to understand (the mean score of 3.85 for offer price, PCLi equals the estimated purchase probability ICERANGE is significantly lower than that of 4.39 for we discussed previously. Under the other methods, PCLi is BDM at p < .05). one (zero) if the offer price is less than or equal to (greater Furthermore, to test the postulates that a consumer’s than) the respondent’s stated reservation price. For any performance- and preference-related uncertainty are posi- approach, a lower SCL (averaged over respondents) implies tively related to his or her reservation price range, we devel- superior prediction. oped measures of performance- and preference-based ICERANGE provides the best predictive performance uncertainty as follows (for details, see Table 3): We draw with an SCL of .126. Next in our application is BDM with the six items from Urbany, Dickson, and Wilkie’s (1989) an SCL of .180, followed by Vickrey auction (SCL = .307), and Cordell’s (1997) studies. Principal components analysis self-explicated floor (SCL = .315), self-explicated indiffer- followed by Varimax rotation suggested two factors corre- ence (SCL = .337), and self-explicated general (SCL = sponding to performance- and preference-related uncer- .339). The predictive performance of ICERANGE is signifi- tainty, with reasonably strong convergent and discriminant cantly better than that of BDM (SCL difference = .054, p < validity. Next, we ascertained the strength of association .10) and each of the other approaches (p < .05). between respondents’ scores on each of these factors (as

Table 2 CHOCOLATE STUDY: RESPONDENTS’ EVALUATIONS OF METHODS ON KEY DIMENSIONS

Key Dimensions (Five-Point Scale: 1 = “Strongly Vickrey Self-Explicated Self-Explicated Self-Explicated Disagree,” and 5 = “Strongly Agree”) ICERANGE BDM Auction Floor Indifference General (1) Comfort level: “I am comfortable answering 4.38a 4.44 4.32 4.54 4.65 4.51 questions in this survey.”

(2) Clarity of incentive compatibility: “It is clear 4.14b 4.34 3.29 N.A. N.A. N.A. to me that I would benefit most by stating my true reservation price.”d

(3) Comprehension: “The procedure is easy to 3.85c 4.39 4.24 4.73 4.53 4.59 understand.”e aNot significantly different from corresponding measures for the other methods. bNot significantly different from the BDM measure but significantly higher than the Vickrey auction measure (p < .05). cSignificantly less than the corresponding measures for the other methods (p < .05). dAdapted from Wertenbroch and Skiera’s (2002) question, “Is it clear why it is in your best interest to state exactly the price you are willing to pay?” eAdapted from Wertenbroch and Skiera’s (2002) question, “Has this procedure been confusing for you?” Notes: N.A. = not applicable. Reservation Price as a Range 209 measures of performance and preference uncertainty) and us to evaluate the relative performance of ICERANGE their reservation price ranges as estimated by ICERANGE. using the (quicker) survey-based approach, in contrast to As we predicted, both preference uncertainty and perform- the one-on-one interviews used in the wine study. The ance uncertainty have significant, positive associations with results appear in Table 4. individual ranges in reservation prices (correlation coeffi- Again, we find strong support for the superior predictive cients of .276 and .236, respectively, p< .05). performance of ICERANGE, as measured by the SCL. Specifically, ICERANGE (SCL = .08) significantly outper- THE WINE STUDY forms both BDM (SCL = .29) and Vickrey auction (SCL = We conducted the second study with The Lucky Country .21), with p < .01 and p < .05, respectively. The SCL values brand of wine (a 55% Shiraz/45% Cabernet Sauvignon of BDM and Vickrey auction are not significantly different blend) from Australia that retails at approximately $15.00 from each other. Confirming the range characterization, the per 750 milliliter bottle, to replicate the performance of mean observed “range” in reservation prices under ICERANGE in a more expensive product category with ICERANGE of $4.92 is significantly greater than zero (p < “older” respondents—specifically, 91 part-time MBA stu- .01). Moreover, we find that both performance and prefer- dents. We focused on ICERANGE, BDM, and Vickrey auc- ence uncertainty are positively correlated (correlation coef- tion, the top three approaches from the chocolate category, ficients of .05 and .12), though in this case, the coefficients all of which provided for incentive compatibility (at least in are not statistically significant, perhaps because of the rela- theory). The protocol was essentially similar to that for the tively small sample size for ICERANGE in the wine study chocolate study; the only difference was that because of the (and possibly greater measurement error under the survey respondents’ time constraints, we used a questionnaire- format). Finally, the feedback from respondents in the based survey methodology (in lieu of one-on-one inter- debriefing phase indicates no significant differences views) to elicit respondents’ valuations. This also enabled between ICERANGE and BDM in terms of respondents’

Table 3 CHOCOLATE STUDY: CONVERGENT AND DISCRIMINANT VALIDITY OF THE MEASURES OF CONSUMERS’ PREFERENCE AND KNOWLEDGE UNCERTAINTY

Rotated Factor Loadings Factor 1a Factor 2b Measures (Five-Point Scale: 1 = “Strongly Disagree,” and 5 = “Strongly Agree”) (Preference Uncertainty) (Knowledge Uncertainty) U1: “I know exactly what kind of chocolate I want to buy.” .872 −.033 U2: “I know for sure which attributes of chocolate are important to me.” .676 .355 U3: “I know exactly how much I would like to pay for the chocolate.” .775 .205 U4: “I consider myself a knowledgeable person on chocolate.” .320 .559 U5: “I felt sure of the quality of the chocolate.” −.090 .872 U6: “I felt confident about my answers on the survey.” .426 .565 aVariance explained: 43.2%; coefficient alpha (U1, U2, U3) = .74. bVariance explained: 17.9%; coefficient alpha (U4, U5, U6) = .53. Notes: Factor loadings greater than .5 are in bold.

Table 4 WINE STUDY: RESERVATION PRICE ESTIMATES AND PREDICTIVE PERFORMANCE MEASURES

ICERANGE (N = 41) Reservation Price Type Floor Indifference Ceiling BDM (N = 31) Vickrey Auction (N = 19) Mean ($) 11.69 13.19 16.61 12.71 11.45 (SE) ($) 0(1.69)0(1.79) 0(2.23) 0(1.22) 0(1.55) Mean difference ($) 1.50a 3.42a (SE) ($) 0(.48)a 0(.67)a

SCL .08b 00.29 00.21

Respondent Feedback Measures 1. Comfort level 3.61c 03.81 04.16 2. Clarity of incentive compatibility 3.59c 03.58 03.42 3. Comprehension 3.41d 03.65 04.63 aSignificantly greater than zero (p < .05). bSignificantly less than the SCL for BDM (p < .01) and Vickrey auction (p < .05). cNot significantly different from corresponding measure for BDM and Vickrey auction. dNot significantly different from corresponding measure for BDM; significantly less than that for Vickrey auction (p < .01). 210 JOURNAL OF MARKETING RESEARCH, MAY 2007 comfort levels, comprehension, or clarity with regard to Research Contributions incentive compatibility. Reservation price is a key construct in understanding and DISCUSSION inferring consumer preference. We believe that our study contributes to this literature stream in the following ways: Overall, the two studies demonstrate the practicality of The primary contribution is methodological. ICERANGE is the ICERANGE procedure, at least among college-going the first methodology to measure reservation price as a respondents. Furthermore, we find strong support for the range. The (ICERANGE) approach is tied to real choice superior predictive ability of ICERANGE over multiple and guards against two common sources of bias. The sec- benchmarks. It performs significantly better across two ondary contributions are theoretical and empirical. Specifi- product categories and with undergraduate and MBA stu- cally, this study reconciles diverse definitions of reservation dents. Consistent with the conceptual framework, a respon- price with the range framework and establishes a link dent’s uncertainty levels in terms of product knowledge and between consumers’ uncertainties and reservation price personal preference are positively related to his or her range in reservation prices. ranges. The empirical contribution is from demonstrating We view ICERANGE as an approach that (1) integrates the superior predictive performance of ICERANGE, estab- the BDM method with the theoretically and empirically lishing the existence of the range in two different applica- supported idea of reservation price as a range of values on tions, and providing at least partial support for the link account of uncertainty, (2) avoids strategic bias and incen- between the level of uncertainty and the reservation price tive incompatibility bias, and, most important, (3) predicts range. choice significantly better than multiple extant methods Managerial Contributions across two categories. The wine application demonstrates that ICERANGE works well even under a survey format. If From a managerial perspective, we believe that respondents and interviewers have the time, we would rec- ICERANGE holds promise as a practical methodology for ommend personal interviews to make the process transpar- reservation price measurement. Our empirical study is ent and (at least in theory) reduce measurement error. encouraging in this regard, in terms of both its performance In an attempt to simplify ICERANGE further, we and its feasibility, notwithstanding the additional steps checked whether the reservation price elicitation tied to the involved compared with the BDM approach. Respondents 10% purchase probability level (arguably the most difficult stated that they were comfortable with the method and did part of ICERANGE) could be extrapolated from the floor not appear to find the additional questions difficult to and indifference reservation price elicitations, instead of understand or onerous. asking an additional question. We find that the extrapolated Although our empirical study used personal interviews reservation price for the 10% probability level is almost as for the elicitation process, we realize that such personal good as the measured value for both chocolate ($4.19 actual interviewing may not always be feasible in real-world versus $4.17 extrapolated, p = .85) and wine ($16.62 actual applications. With the objective of developing ICERANGE versus $17.32 extrapolated, p = .35). In addition, SCL val- as a practical tool for reservation price elicitation, we have ues based on extrapolations from the floor and indifferent designed an interactive online version of the approach, with reservation prices (i.e., not using the direct elicitations at a user-friendly graphic interface. This online version has the 10% probability level) exhibit no significant deteriora- undergone an initial pilot test with MBA students (in the tion. We suggest that when consumers are constrained in context of a consumer electronics product). Although the terms of time or cognitive resources, eliciting the floor sample size is too small to draw any statistically significant (100% purchase probability) and indifference (50% pur- conclusions, the online system worked smoothly, and chase probability) reservation prices according to the respondents were comfortable with it. Indeed, some of the ICERANGE format could suffice. participants believed that the idea of eliciting a complete range rather than just a single point made them more com- CONCLUSION fortable with ICERANGE than BDM. (The online interface A consumer’s reservation price for a product has tradi- has been posted on the second author’s Web site.) As we tionally been considered a single point. However, the litera- stated previously, the ability to estimate consumers’ reserva- ture on consumers’ uncertainty, which posits that consumers tion price ranges with reasonable accuracy (and minimal are not often sure of their own preferences and the perform- systematic bias) is valuable for managers who make pricing ance of the products they intend to purchase, suggests that decisions, particularly in a mass customization setting. this assumption, though analytically convenient, is practi- Clarifying the Scope and Limitations of ICERANGE cally weak. Against this backdrop, we attempted a synthesis of the literature to propose a conceptualization of a con- ICERANGE is arguably the most relevant for products or sumer’s reservation price as a range that is tied to purchase categories with which consumers have significant levels of probabilities. Extrapolating from this research, we develop performance- and/or preference-related uncertainty. an incentive-compatible elicitation procedure, ICERANGE, Incentive-compatible approaches, such as ICERANGE and to measure the range in reservation prices at the level of BDM, require consumers to “put their money where their individual consumers. Two empirical applications in the mouth is.” For the actual purchase to take place, the prod- chocolate and wine categories provide validation of the ucts, or at least their working prototypes, must be available ICERANGE methodology. for sale. Therefore, for new products that are still in the Reservation Price as a Range 211 design and development stage, conjoint analysis and its REFERENCES variants are likely to remain the preferred methods. 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