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IN THE UNITED STATES DISTRICT COURT
EXPERT REPORT OF JERRY WIND. PRESIDENT. WIND ASSOCIATES Dated: June 14, 2000 COUNSEL FOR PLAINTIFF CARL SCHNEE
Judith M. Kinney (DSB #3643) Mark J. Botti
1041 Waverly ROad DENTAL LAB TECHNICIANS PREFERENCES AND TRADEOFFS FEBRUARY 29, 1999
TABLE OF CONTENTS Appendices
I. QUALIFICATIONS, BACKGROUND AND OBJECTIVES My qualifications, including a list of my publications and past testimony at trial and by deposition, are contained in my curriculum vitae. which is attached as Appendix H to this report. I am compensated at the rate of $750 per hour for my work in this case. As I understand the issues in this case, Dentsply International is the leading producer of artificial teeth in the U.S. market. Estimates of its current share ranges from 65 to 80 percent of the U.S. market. Currently, Dentsply distributes its teeth through dealers, and if a dealer adds a competitive line of prefabricated artificial teeth, Dentsply severs its relationship with that dealer. Other producers of artificial teeth, such as Vita and Ivoclar, have had a difficult time in penetrating the U.S. market. What is not known about this market is the role that the following marketing variables play in influencing dental laboratory technicians' choices of artificial teeth brands:
The objective of this study that I have been asked by the United States to conduct, is to produce an appropriate representative sample and generate data that will provide a basis for establishing empirically the relative importance of these factors and a basis for estimating the expected share of Dentsply and its competitors under various scenarios of the above two marketing variables. In addition to the data generated by the survey I conducted, which is incorporated into this report, I considered other documents including various documents generally describing the artificial tooth market, marketing and promotional materials for several brands of prefabricated artificial teeth, and the Complaint filed by the United States in this case. I designed and directed a study among dental laboratory technicians as a tradeoff conjoint study focusing on key variables associated with the product, distribution and price offerings of seven suppliers: Dentsply, Vita, Ivoclar, Myerson, Universal, Kenson and Justi. The study is designed as a conjoint analysis study that generates the data providing a basis for various types of modeling including the PRIDEM and PRIDEL Models. The paper documenting these models is included in Appendix A attached to this report. The study was designed as a TMT (Telephone recruitment, Mail follow-up and main Telephone interview) study. Universe The universe was defined as dental lab technicians responsible for the selection of plastic artificial teeth purchased by the lab for use in making dentures. Sample A representative national probability sample was selected from the universe of dental lab technicians responsible for the selection of plastic artificial teeth purchased by the lab for use in making dentures. The sample size included 274 respondents, one per laboratory. The sampling procedure involved 3 phases:
The detailed screening results are included in Appendix G. The main part of the questionnaire was Part B which consisted of a tradeoff exercise in which each respondent received 8 stimuli cards containing experimentally designed scenarios describing Dentsply and each of its competitors. Each competitor was named - Dentsply, Vita, Ivoclar, etc. The starting, or reference scenario - Exhibit 1 on the following page - showed base price and distribution for each supplier.1 Subsequent experimentally designed scenarios varied price and distribution mode for the various brands to measure the respondent tradeoffs. For each scenario, the respondent was asked to allocate 100 points across the suppliers, reflecting his/her total plastic tooth purchases from each supplier over the next three months given the distribution and price conditions shown. In addition, in Part A of the questipnnaire, a selected set of respondent background characteristics (lab size, shares of current tooth suppliers, years in business, etc.) and preferences were collected. Part A of the questionnaire and the instructions for responding to Part B are included in Appendix E. Exhibit 1: Sample Scenario Card
[This is the reference (C141) card sent to all respondents] Each respondent received 8 Scenario cards. The top card in each set is the reference card, C-141; the remaining cards represent a block of 7 (shuffled) cards drawn from a block of the master design (Appendix B). Exhibit 1, shows C-141, the reference card. The 140 experimental cards (numbered from C-1 through C-140) appear in 20 blocks of 7 cards each; their designs appear in Appendix B - the master experimental design. Appendix C contains seven illustrative stimuli cards. Pricing The first 8 columns of the master experimental design contain the pricing information for the 8 primary brands; the 4 Dentsply brands - BIOFORM IPN, BIOBLEND IPN, PORTRAIT IPN, TRUBLEND SLM, and Ivoclar SR VIODENT PE, Myerson DURABLEND SPECIAL RESIN, Universal VERILUX and Vita VITAPAN, respectively. The prices for Dentsply CLASSIC, Justi BLEND and Kenson RESIN are fixed throughout the design at the prices shown in the reference scenario, Card C-141, in Exhibit 1. The experimental prices for the 8 primary brands are shown in Exhibit 2. As noted, there are four price levels for each primary brand. As noted above, the 3 secondary brands have fixed prices - the same as those shown in Exhibit 1. Distributor Availability Exhibit 3 shows the master coding for availability. There are 7 levels for this variable. Columns 9 through 13 of Appendix B show the availability codes for the active products. Column 9 is applicable for all of the five Dentsply brands' availability. Columns 10 through 13 of Appendix B show the availability coding for SR VIVODENT PE, DURABLEND SPECIAL RESIN, VERILUX and VITA, respectively. Justi BLEND and Kenson RESIN both received an availability coding of: Yes - Yes - Yes throughout all of the experimental cards.
Exhibit 3: The Availability Attributes
The data collection was conducted at my direction by Guideline Research. The data collection consisted of a TMT design in which respondents were screened by telephone (screener questionnaire is included in Appendix D). Following that, they were sent by priority mail 2 envelopes consisting of a questionnaire (Appendix E) and 8 stimulus cards (one of the 20 blocks of the master design outlined in Appendix B and illustrated in Appendix C). Four to five days later they received a second telephone call and instructions on how to complete the forms. They were asked to return the completed forms and the stimuli to Guideline Research. The field instructions were prepared by Guideline Research and are included in Appendix F. Neither the interviewers nor the respondents were informed of the purpose or sponsor of the study. The data generated by the responses to Parts A and B of the questionnaire is incorporated into this report and contained, respectively, in the computer files titled "dental.as1" and "dental.as2." One method that can be used to analyze the data produced by this survey is the PRIDEM/PRIDEL model developed by Paul Green and Abba Krieger (and described in Appendix A). This model enables the user to "parse out" the effect of each experimentally manipulated variable on respondents' tradeoffs across suppliers. Respondent background attributes from Part A of the questionnaire are included in the model in order to examine their segmentation effects. The initial analysis focused on 3 scenarios:
The initial results produced by the PRIDEM/PRIDEL model for three key scenarios are included in Exhibit 4 on the following page. This model allows for the calculation of expected share for any scenario based on the factors and levels included in the study (and listed in Exhibits 2 and 3). Estimated Market Share Results for Ivodar and Vita Under Three Scenarios
This study, using conjoint analysis methodology, which is generally accepted and commonly used for assessing respondent's trade-offs among key marketing variables, was designed to generate data that allows analysis to:
The survey was conducted at my direction according to generally accepted professional scientific standards for survey research used in litigation in order to assure the objectivity of the entire process. The findings of the study using the PRIDEM/PRIDEL model as summarized in Exhibit 4 show that:
_______________/s/________________ Yoram Jerry Wind, Ph.D.
FOOTNOTES 1 The reference scenario card showed Vita VITAPAN as being available from a local dealer, because for some labs this is technically accurate; however, as I understand the facts, this is not the existing market condition for the majority of labs in the United States, and was not at the time the data was collected. This was, accordingly, adjusted for during the analysis (as discussed in section F, page 12).
BACKGROUND ARTICLE ON THE PRIDEM AND PRIDEL MODELS
European Journal of Operational Research 60 (1992) 31-44
Theory and Methodology Modeling competitive pricing and market share: Anatomy of a decision support system * Paul E. Green and Abba M. Krieger The Wharton School of the University of Pennsylvania, Steinberg Hall-Dietrich Hall, Philadelphia, PA 19104-6371, USA Received December 1989; revised July 1990 Abstract: Even with today's high emphasis on management decision support systems, relatively little has been published on the motivations, tribulations, and post mortems that generally accompany the development of such systems. This paper reports (in a mixture of narrative style and more formal model exposition) how a computerized decision support system for optimal price determination was developed, implemented, and finally applied to a broad range of industry problems. Keywords: Pricing; demand analysis; conjoint analysis; multiattribute preference 1. Introduction Product and service pricing is one of the oldest (and still very important) tools of the marketing executive. Each day business firms face questions like the following: 1. Competitor X has just increased its price by five percent. Should we match it, or stand pat? 2. How should we price our new product, which offers several technical advantages over current offerings? 3. How should we set prices among competing items in our current product line? Answers to these questions are hard to find for at least two reasons. First, given a set of existing prices and market shares for products in a competing product class, it is often difficult to predict new shares accurately if one or more prices were to change. Second, it is difficult to predict how competitors will react to others' price changes. Marketing researchers have dealt with the first question by proposing several new marketing research methods that show promise for augmenting information obtained from older approaches. Historically, the measurement of price-demand relationships has relied on statistical methods applied to either cross-sectional or time series data (e.g., Wittink, 1977). However, newer approaches, such as those based'on laboratory studies (Pessemier, 1960), instore experiments (Doyle and Gidengil, 1977), test market simulation (Silk and Urban, 1978), and willingness-to-pay surveys (Monroe and Delia Bitta, 1978) have received increased attention and, in some cases, commercial application. Even more recently, conjoint-based methods (Mahajan, Green, and Goldberg, 1982; Louviere and Woodworth, 1983; Wyner, Benedetti, and Trapp, 1984) have considered explicitly designed competitive product profile descriptions. Respondents either pick their preferred choice from the set of alternatives, indicate their likelihood of choosing each option, or state their preferences for alternative allocations of a common resource across products or activities competing for that resource (Carroll, Green, and DeSarbo, 1979). A prototypical procedure entailing tradeoff techniques is that proposed by Mahajan, Green, and Goldberg (MGG). Their survey data collection approach is a modification of one originally proposed by Jones (1975). Respondents are shown profile descriptions of P products, each with an associated brand name and price. Profiles are designed according to fractional factorials in which attributes and levels are idiosyncratic to each brand. Respondents allocate a constant sum (typically 100 points) across each stimulus option indicating the likelihood that they would choose each option, given the stated prices for each alternative. MGG employ a conditional logit model (Theil, 1969) to estimate parameter values that satisfy the following sum and range constraints: 1. The estimated probability of choosing some p-th brand ranges between zero and one. 2. The sum of the choice probabilities across all P brands (including an all-other-brands category, if appropriate) equals unity. While MGG discuss how their approach might be used in actual business situations, they also add that their experience with applying the model to real-world problems is quite limited. 1.1. Inputs from the business world As we mulled over the idea of adapting some of the conjoint methodology to the measurement and strategy issues related to optimal pricing, we sought the advice of several commercial marketing research firms. Gradually, a pattern emerged regarding their views about what managers would like to see in a price/demand model: 1. The approach should be able to utilize survey methods, similar to the kinds of buyer trade off data that are collected in applied conjoint studies. 2. The model should be able to consider not only the impact of price changes on market share but also the effect on share of non-price attribute changes on the part of any or all competitors. 3. The model should be able to make market share predictions at both the total market and individual market segment levels. 4. The model should be capable of examining interactions among different competitors' prices and non-price attribute levels. 5. The model should be 'decomposable' in the sense of allowing the client to focus attention on the behavior of a single product's share as a function of individual competitors' prices and non-price activities. 6. The model should be capable of being calibrated to actual starting (i.e., existing) market shares and prices. 7. The model should contain an 'optimizing' feature in which the user can find the best price for a given product, conditional on fixed prices for competitors and specified levels of all non-price attributes, self and competitors. 8. The model should be flexible enough to allow interpolation across discrete price points. 9. The model should be user friendly and, if possible, adaptable to a personal computer. With these desiderata in mind, we set about the task of constructing a suitable data collection method, parameter estimation technique, and price optimizing routine. 1.2. Borrowing from the past Fortunately, earlier work in componential segmentation (Green, Krieger, and Zelnio, 1989) led to the development of a conjoint model for forecasting buyers' likelihoods of purchase from information about product attribute preferences and buyer backgrounds (e.g., demographics, life styles, current brand usage, etc.). The PROSIT (PROduct SITuation) model contained a number of relevant features for the current effort, namely PROSITs ability to estimate parameter values for both product attributes and buyer attributes, as well as selected two-way, within-set and between-set interactions. Furthermore, PROSIT contained an optimizing feature wherein one could find the best product profile for a given market segment or the best segment for a given product. In the PROSIT model, all parameters are estimated as though each predictive variable is categorical (i.e., predictors are treated as dummy-variables in the spirit of conjoint analysis). The response variable is 'univariate' - typically, a buyer's subjective likelihood of choosing a specific and or service supplier as a joint function of product profiles (for that brand and competitive brands) and respondent background varibles. In contrast, our present problem emphasized an underlying continuous variable (i.e., price) and entailed a 'multivariate' response, namely, the respondent's subjective likelihood of choosing each of P products as a function of their product attributes, their prices, and the buyer's background attributes. Still, the earlier PROSIT model seemed like a good place to start. On the plus side, it had been successfully applied in a variety of industrial applications (particularly in the phamaceutical and computer industries) and had already been adapted for interactive, personal computer applications. 2. Decisions, decisions At this point we had a starting point for the PRIce-DEMand model (PRIDEM). However, a number of decisions still had to be made on adapting the PROSIT model for pricing and, in particular, incorporating a multivariate response variable, PROSIT was estimated by OLS dummy variable regression. Its optimizer employed a heuristic for finding optimal combinations of product and/or segment attribute levels from the full Cartesian product set of attribute levels. In contrast, our current interest centered on price optimization, conditional on given settings of all other attributes. 2.1 Handling the price attribute In keeping with conjoint methodology, it seemed appropriate to maintain the treatment of all attributes (including price) as categorical, encoded as dummy variables. From a pragmatic viewpoint this would allow us to use a portion of the same software already in place for fitting the PROSIT model. Second, we could avail ourselves of highly efficient, fractional factorial designs for setting up the product and price stimulus design that would estimate all main effects as well as selected two-way interactions. Moreover, these (orthogonal) designs are flexible enough to accommodate enough price levels (e.g., five in nine per brand) to approximate a continuous part-worth function rather closely. Why not just select a polynomial (e.g., quadratic) to represent part worths for the price variable? One of the problems with this approach is that the resulting curve is sensitive to error. In fact, il is possible that the fitted curve could depart rather markedly from the actual response associated with the experimentally designed price points. Clearly, with polynomial fitting there is no requirement that the curve 'go through' the response value observed at each discrete experimental price point. In contrast, by using splines we could make sure that the response function passed through the knots (i.e., price points). Furthermore, we could make the function smooth between each pair of knots so that simple (classical) methods ol optimization could be used to find the solution that maximized the sponsors contribution to overhead and profit (conditional on fixed prices for competitive products). Accordingly, we set up a computer routine for fitting one and two-dimensional splines where the knots represented the discrete price levels used in the original experimental design underlying the competitive product profiles. The Appendix describes this procedure. 2.2. Making the model multicariate A second problem with the adaptation of PROSIT to PRIDEM was how to deal with the multivariate response variable. The PROSIT model is fit by ANOVA-like, OLS regression. If the original PROSIT response variable were quantal (e.g., 1 or 0) or if the response were each respondent's subjective likelihood of purchase on a 0 to 1.0 scale, no attempt was made in PROSIT to transform it to a logit (as was done in Mahajan, Green, and Goldberg, 1982). Why not, then, set up a multinomial logit model with brand and product interactions, rather than fitting individual linear probability models and then finding market shares on a post hoc basis? We chose to maintain OLS fitting and the linear probability model for two reasons. First, the PROSIT model has a rather elaborate, built-in cross validation feature which we wished to retain for assessing the predictive accuracy of prices, market segments, and non-price attributes on a single products likelihood of purchase. This could be applied to each product, in turn, as a way to see if some part worth functions are poorly estimated. Second, despite the theoretical attractiveness of the multinomial logit (see Mahajan, Green, and Goldberg, 1982), we noted that Brodie and De Kluyver (1984) have reported that linear probability models, with post hoc adjustment (to respect non-negativity and sum constraints), have fared as well as the more complex multinomial logit models in terms of empirical market share validation. (Still, it should be mentioned that the current structure of PRIDEM could be reformulated in terms of a multinomial logit.) With these preliminary decisions made, it was then time to formulate the model. 3. The PRIDEM model To motivate our description of the PRIDEM model, consider a situation in which a pharmaceutical firm wishes to increase the price of its antihypertensive drug brand A. There are five other competing brands in the market niche of interest to brand A's producers: B, C, D, E, and F. The producers of brand A are able to estimate per-unit variable production/distribution costs for each of the six competitive brands. In designing the marketing research survey, brand A's producers considered four price levels each for brands A, B and C, three levels each for D and E, and two levels for the more remote competitor, brand F. In addition, they selected one three-level non-price attribute describing brand A's dosage schedule: once daily, twice daily, or three times daily. A conjoint orthogonal design of 64 profile descriptions was set up. Each respondent received eight of the profile descriptions, drawn from the master design. For each description the respondent was asked to allocate 100 points across the six competitive brands so as to reflect the proportion of hypertensive patients for whom each drug would be prescribed, under the stated conditions. (Prior to this task each respondent similarly evaluated a base-case profile showing the current prices of each brand and brand A's current dosage level of three times daily.) Figure 1 shows an illustrative stimulus card for one of the experimental conditions.
Figure 1. Illustrative stimulus card Respondents were classified, a priori, by five segment attributes: specialty (cardiologists versus general practitioners); age (under 35, 35 and older); type of practice (solo versus group): current brand favorite (brand A versus others): and patient load, within specialty (above median versus below median).1 3.1. Preliminaries In describing the PRIDEM model more formally, we first consider the question of estimating the market shares for each brand, as a function of manipulated product/price variables and respondent characteristics. Market shares are assumed to depend on three types of attributes: (a) market segment attributes; (b) non-price (e.g., product) attributes; and (c) price attributes. We let l1 , l2 ,...., lS denote the number of levels associated with each of the S segment attributes. In the illustrative problem these attributes describe the decision makers, such as specialty (cardiologist, general practitioner), age (under 35, 35 and over), and so on. Similarly, we let m1 , m2 ,...., mr denote the number of levels associated with each of the T non-price attributes. In the illustrative problem there is only one non-price attribute: dosage (once daily, twice daily, three times daily). Finally, the market shares are also
assumed to depend on the brands' prices. We
assume R n1 , n2 ,...., nR denote the number of levels of each of the R price attributes. To simplify notation, we further assume that the brands are ordered, so that brand i refers to the brand whose price is varying in price attribute i. Associated with each level of each price attribute an actual price (e.g., m dollars per day's therapy). Prices are denoted by: llrj r = 1, 2.....R: j = 1, 2.....n? We shall use i, j, and k to subscript attribute levels in general. 3.2. Segment components The segment attributes are used to define the universe over which the market shares are computed. We specify a segment by assigning selected attribute levels to the S segment attributes. We can combine segments by aggregation. More generally, we can construct any universe of interest by a set of non-negative segment weights. wsj, s = 1, 2.....S: j = 1, 2.....l, so that
In particular, a given segment with levels (i1 , i2 ,...., iS) is captured by setting wj?? for j = 1, 2.....S and wj?k = 0; otherwise. Through the use of weighting coefficients PRIDEM can select a specific weighted universe across all attributes with (say) weights of 0.7 and 0.3 for cardiologist and GP, respectively, and weights of 0.2 and 0.8 for under 35 years and 35 years or older, respectively. Given the five two-level background descriptors, described above, we have a maximum of 32 distinct segments. Later on, we shall describe how the 'optimal' price for each product is determined, given stated prices for all other brands. The optimal price will be defined by the value that maximizes contribution to overhead and profit, defined by the expression: Industry sales units • (price - variable cost/unit of brand p ) • (market share of brand p). (In applying the computer-based PRIDEM model, industry sales are usually set, for convenience, at 1.0.) 3.3. Market share model Associated with each brand p is an estimated market share f(p)(k; j, w) where k is a vector (of length R) of prices, j is a vector (of length T) of levels for the non-price attributes, and w is S vectors (of respective lengths l1 , l2 ,...., lS) denoting the universe of decision makers (i.e., the physicians). The function f(p) is obtained by first fitting a main effects model to the raw response data (i.e., the likelihood of prescribing the p-th brand in question) where the predictors are the S segment attributes, the T non-price attributes, and the R price attributes, all expressed as dummy variables. Selected two-way interactions are then added to the model in a sequential, stagewise manner (Green and DeSarbo, 1979). As noted above, interactions can be either within segment, non-price, or price attributes, or between segment, non-price, or price attributes. The fitting of main effects and interactions yields a set of regression-based functions h(p), p = 1, 2 ,..., P, one for each product, as a preliminary step toward obtaining f(p). We first discuss how each h(p) is obtained and then how it is adjusted to find f(p). The model is described, in part, by its L interactions. As noted earlier, interaction l* can be of several differing types: ( We have the combinations as shown in Table 1. Attribute levels with associated interaction
Describing the formal regression model for estimating each individual product's h(p) is a bit messy because of the large variety of possible interaction terms. We define h(p) as
where A(p) denotes the intercept term for product p's function,
3.4. Base-case calibration To calibrate each individual brand model, we adjust each h(p) obtained from the individual product regressions to a base-case profile. This is accomplished by finding h(p) for this profile and then multiplying all the parameters (A, B, C, D, E) by b(p)/h(p) where b(p) is the given market share for the base-case profile. Finally, we obtain the market share function f(p) from h(p) by normalizing the individual h(p) values by means of the function
where (x)+ = max(x, 0), wi = 3.5. Additional remarks As noted earlier, we fit each h(p) regressior function as a simple linear probability model in which predicted values need not obey a 0-1 range constraint; simple OLS regression is employed. Similarly, f(p) is obtained by a normalizing procedure which simply insures that all of the individual h(p) predicted values are non-negative. (As described earlier, other procedures, including multinomial logit, could be used.) It should also be pointed out that the sequential fitting of two-way interactions requires that attention be paid to the significance testing of additional terms. This is implemented by procedures described in Green and DcSarbo (1979). In addition, each individual h(p) model is cross-validated at each stage in the interaction fitting procedure. Cross-validated predictions are employed as the principal guide to the selection of appropriate interaction terms, once the main effects have been fitted. 4. Price interpolation and optimization There are two remaining aspects of the
model
that are not explained fully by (1) for h(p).
(Since
the discussion below applies to all p, we
now
omit the superscript.) We first note from
the
preceding discussion that market shares
can only
be predicted at the price levels 4.1. Interpolation procedure The solutions to both of these problems de
pend upon the method of interpolation
between
successive price levels
where A includes the intercept, and the main effects for segments and nonprice attributes and interactions that do not involve price attributes: g, includes the main effect for price attribute r and all interactions involving the r-th price attribute with a segment attribute or a non-price attribute: g refers to the interaction between the r-th and s-th price attributes (where g?? = 0 if this interaction does not appear in the model).
The function s is R-dimensional with
known values on a lattice of points 4.2. Finding the optimal value for price From discussion in the previous sections
(and the Appendix), we only need to
consider
where
and the objective function,
It is straightforward to solve (6) when
Z1 ( Hence, where We find the two points such that Z1( 5. A real-world application The PRIDEM model and decision support system have been implemented on both the main frame (Vax 8700) and the personal computer. A number of industrial applications have been made of PRIDEM over the past three years. We illustrate PRIDEM's application with an actual industry example involving two pharmaceutical companies' pricing strategies in the marketing of a diet supplement for use by hospital patients who have trouble swallowing traditional foodstuffs. (All data have been disguised to respect sponsor confidentiality.) 5.1. Study background For several years, only one pharmaceutical firm, hereafter called Alpha, had been marketing a special diet supplement for hospital patients with esophagus ailments. The product was designed for drinking (through a straw); it contained a balanced set of nutrients. More recently, a second firm, hereafter called Beta, had developed its own diet supplement. Several of its product properties differed from those of Alpha as well as its marketing and pricing plans. Prior to Beta's entry, Alpha's ongoing price for its diet supplement was $41 per day per patient. Beta believed that Alpha's short run monopoly could be upset by penetration pricing; accordingly. Beta introduced its product at only $38 per individual per day. The results were dramatic; in two years. Beta had penetrated the market to such an extent that the two firms' shares were 28% and 72%, respectively, for Alpha and Beta. At this point, Beta wondered whether its price was 'right' (in the sense of optimizing its contribution to overhead and profit) and what the implications might be if Alpha were to change its still-current price of $41. 5.2 Designing the conjoint surrey A conjoint study was designed to obtain data for use in the PRIDEM model. First, Beta personnel discussed possible non-price attributes that could affect market shares independently (or possibly interactively with price). Four such attributes were identified: 1. Packaging for Alpha: 4-ounce can (current) versus 6-ounce can (prospective); Beta's dosage was already at 6 ounces per can. 2. Extended contract price guarantee for Alpha: NO (current) versus YES (prospective); Beta had no price guarantee. 3. Concentration of amino acids for Beta: low concentration (current) versus high concentration (prospective); Alpha's concentration was already slightly lower than Beta's current concentration. 4. Educational aids for Beta: NO (current) versus YES (prospective); Alpha already had educational aids. In addition to the non-price attributes, Beta's management considered several possibilities for identifying market segments. Management settled on two primary segmentation bases: 1.Type of respondent (i.e., as an influence on which brand is purchased)
2. Size of hospital
Finally, Beta management estimated that variable costs for producing and distributing the diet supplement were about equal between the two firms; they estimated these costs at $19 per individual per day. A sample of 390 respondents was selected, according to the two stratifying criteria (profession and hospital size). All interviews were conducted by personal administration, following pre-arranged appointments. Respondents received honoraria for their participation. The conjoint portion of the interview was based on a master orthogonal experimental design of 50 profile cards. Each profile card contained information on brand names, non-price attribute levels under each brand name, and prices per patient day. The prices were drawn from the following sets:
Each respondent first received a 'base case' profile card, followed by five cards (balanced with respect to prices) from the overall orthogonal design. For each card, the respondent was asked to indicate what his/her recommendation would be to purchasing agents responsible for choosing the diet supplement supplier. Each respondent was asked to split 100 points (constant sum scale) between the two potential suppliers, reflecting their likelihood of recommending each. Other, background information, including the hospital's current use of diet supplements, respondent's role in the contract decision process, years of experience, etc., were also collected for cross-tabulation with the conjoint results. 6. Running the PRIDEM program Figure 2 shows a portion of the PRIDEM computer run for the problem described above. Illustratively, we input the base-case prices (as a control) and note, of course, the same market shares as originally read in (e.g., Alpha's share is 0.28). We also observe that the contribution to overhead and profit per patient day is $6.16 and $13.68 for Alpha and Beta, respectively. 6.1. Overall market analysis We next consider alternative pricing strategies, conditioned on the non-price attributes remaining at their original (current) levels. Suppose we wish to find Alphas optimal price at base-case levels. We enter instructions accordingly and find from Figure 2 that its optimal price is $36.19, a decrease from its current level of $41. If Alpha were to reduce its price, with no retaliation from Beta, its share would increase ten percentage-points (from a share of 0.28 to 0.38). Overhead/profit contribution would increase from $6.16 to $6.53. Next, we repeat the exercise for Beta, conditional on no change in Alpha price from its status quo of $41. In this case Betas optimum entails an increase in its price to $41 (which then happens to be at parity with Alpha). Beta's share would decline from 0.72 to 0.65 but its contribution would increase from $13.68 to $14.26.2 Next, we consider a unilateral strategic change by Beta - one that both improves its non-price attribute levels (from their current levels to their prospective levels) and decreases its price from the original $38 level to $34. Given no retaliation from Alpha, the net effect is to increase Beta's share to 0.868 and its contribution to $13.03. What should Alpha do if Beta drops to $34 and improves its non-price attributes? Assuming that Alpha's only short-run retaliation is price, the PRIDEM model finds that it should lower price from its starting level of $41 to $34 (at parity with Beta's new price). Next, we consider a case in which Alpha stays at $41 but Beta really drives down its price (to $28). Moreover, both firms improve their respective non-price attributes to level 2 (prospective levels). The net effect of these actions is that Beta's share markedly increases to 0.933 but its contribution drops substantially (to $8.39). 6.2. Selected segment analysis At this point we elect to stay with the same non-price parameters as described immediately above. But now we focus on a specific market segmenting variable-type of respondent: nurses, doctors, and pharmacists. PRIDEM shows that the effects on Beta's share differ by segment: 0.892 (nurses), 0.921 (doctors), and 0.982 (pharmacists). Their weighted average is 0.933. as noted above for the total market analysis.
Figure 2. Illustrative run of PRIDEM (Main-frame version)
6.3. Weighted segment analysis To round out the discussion, we also consider a weighted segment analysis for both type of respondent and hospital size. Illustratively, we assign weights of 0.5, 0.4, and 0.1 to nurses, doctors, and pharmacists, respectively. We assign weights of 0.8 and 0.2 to large and small hospitals, respectively. The net result of this parameter setting is a Beta share of 0.909 and an associated contribution of $8.18. These outputs are each lower than their total market counterparts.3 6.4. Dynamic changes Up to this point, our PRIDEM illustration did not explore sequential competitive retaliation. It is, however, a simple matter to use the program in such a way that in Round 1 Alpha initiates action; in Round 2 Beta answers in some fashion, and so on. By way of illustration, a sequence of actions was implemented, based on starting conditions of $41 (Alpha) and $38 (Beta) with all non-price attributes at their current levels. We assume that Alpha starts out as the price "leader," Beta follows suit, and so on (and each tries to optimize its contribution, conditional on the other's prices). For two such rounds, the results are as- can be seen in Table 2. At the end of two rounds - initiation and response - the prices are $36.19 and 39.83. with shares (contributions) of 0.43 ($7.38) and 0.57 ($11.90) for Alpha and Beta, respectively. Of course, given the ability of Alpha and Beta to collude (if no external competitor were present and if total demand were completely inelastic), they could drive up the prices as much as they liked. (Hence, we do not consider further price changing rounds lor this example.) The idea of an external competitor can he incorporated into the PRIDEM model by including a ( P + 1 )-st product with fixed prices and non-price attribute levels, and a starting share. Then, if Alpha and Beta tried to drive up their prices the external competitor would garner an increasing share of the market. 7. What have we learned? How did the study's sponsor react to the PRIDEM model? As we have frequently found in applied studies using the model, the sponsor explored the possibilities for non-price attribute changes. In this example, Beta management added a price guarantee and educational aids. These non-price changes were accompanied by a Beta price increase to $41 (at parity with Alpha). As of six months after Beta's changes, Alpha had not retaliated with either non-price or price changes. While we are not privy to the financial consequences of Beta's strategy, to the best of our knowledge market share remained relatively stable over the six months' time period in question. To date, the PRIDEM model has been used on several empirical applications, most frequently drawn from the pharmaceutical industry. The predictions made from the model have been, cross-checked, where possible, with time-series analyses of historical price changes. As is well known, analyses of such 'natural experiments' are fraught with difficulty. However, in the cases analyzed, the results have been roughly concordant with those obtained-from the model. The main advantages of the PRIDEM model over that proposed by Mahajan, Green, and Goldberg (1982) are twofold. First, market segment responses can be estimated by means of main effects parameters and interactions with price and non-price attribute levels. Second, the present model solves for optimal prices, conditioned on fixed levels for price and non-price attributes of competitive products (using variable cost data estimated by the sponsoring firm's financial department). Moreover, use of the model, as a decision support system, is straightforwardly implemented by non-technical personnel on either a main-frame of personal computer. There are several limitations to the model, as currently formulated and operationalized. First, the model deals with aggregated responses, where segment differences are measured by within- and between-set interactions. As Moore (1980) has illustrated, researcher-selected segmenting variables may not adequately capture full individual variation in attribute-level part worths. Second, the model does not make allowance for lack of respondent knowledge about actual prices; in some cases the model could overstate price sensitivity, since full comparative pricing information is shown to the respondents. Third, while the model can handle intra-product line pricing (in terms of within-firm competition), it does not consider joint production/distribution costs. 7.1. Action / reaction sequence As briefly described earlier, PRIDEM enables the user to examine action/reaction sequences, albeit in a rather simple way that does not consider changes in buyer preferences or other kinds of new information that might be obtained between successive rounds of price changes. Theoretical work by Hauser and Shugan (1983), Kumar and Sudharshan (1988) and Choi, DeSarbo, and Harker (1990) represent a very interesting topic to pursue in tandem with the measurement aspects of PRIDEM. To date, management's reaction to PRIDEM's potential for formulating 'dynamic' (action/reaction) strategies has been less than enthusiastic. In our experience managers are much more concerned with the interplay of non-price and pricing strategies, with priority given to the former. Bearing in mind that competitive retaliation to non-price actions is typically more difficult and less immediate, this emphasis is understandable. When managers do engage in action/reaction gaming, their interest usually does not extend to questions of long term equilibria but, rather, is focused on only two to three moves ahead. Again, we do not find these views naive and 'myopic'. Managers typically lack information regarding competitors' costs, motivations and intentions; moveover, they also face questionable assumptions regarding stability in buyers' perceptions and brand preferences over the time period under study. 7.2. Conclusions These are important caveats and represent opportunities for further research. 4 Hence, we consider the model and its associated decision support system as an interim effort that can (and should) be expanded, consistent with making sure that future versions can be operationalizcd in terms of accessible buyer preferences and cost data. If we have learned anything from the development of PRIDEM, it is the important fact that useful models must pay due attention to the kinds of measurements and data inputs one hopes to be able to obtain from the environment (e.g., marketplace). What has made PRIDEM work is the simple fact that conjoint data can be obtained in reasonably realistic ways from prospective buyers. Without this measurement linkage (and at the back end, a user-friendly computer system), PRIDEM could have easily joined the ranks of a large array of technically attractive models with few (or no) users. Appendix In this section we describe, in further detail, the spline fitting procedure that enabled us to interpolate between the discrete price points utilized in the experimental design. A.1. Fitting onc-dimensioual splines Let g be a function of one variable. Assume
that we know the value of g at Let g(k) denote the k-th derivative of x. We
know g( Then, from which All we need to specify exogenously is g(t) Linear interpolation is a special case of the above. Solving for (at0, a??) yields and A.2. Fitting two-dimensional splines Let g be a function of two variables.
Assume that we know the value of g at the
lattice of points ( for In a manner similar to the one-dimensional case, smoothness conditions and
t00 = g( and These four equations have the solution: and References Brodie, R., and De Kluyver, C.A. (1984), "Attraction versus linear and multiplicative market share models: An empirical evaluation", Journal of Marketing Research 21, 194-201. Carroll, J.D., Green, P.E., and DeSarbo, W.S. (1979), "Optimizing the allocation of a fixed resource: A simple model and its experimental test", Journal of Marketing 43, 51-57. Choi, S.C., DeSarbo, W.S., and Marker, P.T. (1990), "Product positioning under prior competition", Management Science 36, 175-199. DeSarbo, W.S., Rao, V.R., Sieckel, J.H., Wind. J., and Columbo, R. (1987), "A friction model for describing and forecasting price changes", Marketing Science ?. 299-319. Doyle, P., and Gidengil, B.Z. (1977), "A review of in-sture experiments", Journal of Retailing , 53, 47-62. Green, P.E., and DeSarho, W.S. (1979), "Componemial segmentation in the analysis of consumer tradeoffs", Journal of Marketing 43, 83-91. Green, P.E., Krieger, A.M., and Zelnio, R.N. (1988), "A componential segmentation model with optimal product design features", Decision Sciences 20, 22l-238. Greville, T.N.E. (ed.) (1969), Theory and Application of Spline Functions, Academic Press, New York. Hauser, J.R., and Shugan, S.M. (1983), "Defensive marketing strategies", Marketing Science 2, 319-360. Jones, D.F. (1975), "A survey technique to measure demand under various pricing strategies", Journal of Marketing 39, 75-77. Kumar, K.R., and Sudharshan, D. (19S8), "Defensive marketing strategies: An equilibrium analysis based on decoupled response functions", Management Science 34, 805-815. Louviere, J., and Woodworth, G. (1983), "Design and analysis of simulated consumer choice or allocation experiments: An approach based on aggregate data", Journal of Marketing Research 20, 350-367. Mahajan, V., Green, P.E., and Goldberg, S.M. (1982), "A conjoint model for measuring self- and cross-price/demand relationships", Journal of Marketing Research 19, 334-342. Monroe, K.B. and Della Bata, A.J. (1978), "Models for pricing decisions", Journal of Marketing Research 15, 413-428. Moore, W. (1980), "Level of aggregation in conjoint analysis: An empirical comparison", Journal of Marketing Research 1?, 516-523. Nagle, T. (1984), "Economic foundations for pricing", Journal of Business 57, 83-52?. Pessemier, E.A. (1960), "An experimental method for estimating demand", Journal of Business 33, 373-383. Rao, V.R. (1984), "Pricing research in marketing: The state of the art", Journal of Business 57, 839-860. Rice, J.R. (1969), The Approximations of Functions, Vol. 2, Addison-Wesley, Reading, MA. Robinson, B., and Lakhani, C. (1975), "Dynamic price models for new product planning", Management Science 21, 1113-1122. Silk, A.J., and Urban, G.L. (1978), "Pre-test-market evaluation of new packaged goods", Journal of Marketing Research 15, 171-191. Theil, H. (1969), "A multinomial extension of the linear logit model", International Economics Review 10, 251-259. Wittink, D.R. (1977), "Exploring territorial differences in the relationship between marketing variables", Journal of Marketing Research 14, 145-155. Wyner, G.A., Benedetti, L.H., and Trapp, B.M. (1984), "Measuring the quantity and mix of product demand", Journal of Marketing 48, 101-109.
FOOTNOTES * The authors would like to acknowledge the support of the Marketing Science Institute and the Wharton School's Sol C. Snider Entrepreneurial Center. 1 It should be noted that the approach does not require segment atributes to be dichotomous; however, the model implemented here assumes that all attributes are discrete. 2 To conserve on space, the analyses to follow are not shown in Figure 2. 3 By applying weights of 1 and 0, one can find results for each of the six possible segment combinations of respondent profession by hospital size. 4 For other illustrations of recent developments in pricing research, see DeSarbo et al. (1987), Nagle (1984), Rao (1984), and Robinson and Lakhani (1975). 0377-2217/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
MASTER EXPERIMENTAL DESIGN CARDS Nos. 1 - 140 ARRANGED IN 20 BLOCKS OF 7 CARDS EACH
ILLLUSTRATIVE STIMULI CARDS
C001
C002
C003
C004
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P price attributes; this allows for the
case in which a subset of size P - R of the P
brands does not vary with respect to price. We let
= 1 for s = 1, 2.....S.
) with 
.
are denoted by (
). For example, if q11 = 2, q12 = 3, u11 = 3, and w12 = 4, then the first
interaction is between the third non-price
attribute and the fourth price attribute.
denotes the main effect partworth for
level is of segment attribute s,
denotes the main effect partworth for
level jt of non-price attribute t.
denotes the main effect partworth for
level kr of price attribute r, and
(i, j, k; 
, 
, 
) is an entry in the
matrix associated* with interaction l*. The
specific entry depends on i, j, k, 
, 
,
and 
and h has
been previously adjusted to base-case market
shares, as described above. Note that if h(p) (i, j, k) = 0 for all p, then f(p) (k, j, w) = 1/P.
associated
with the price attributes. It is desirable to
be able
to interpolate, i.e., to predict market shares
at
prices 
, r = 1,..., R, that are not limited to
the
original 
, r = 1,..., R.
. To this
end, we assume that the weightings over
seg
ments and levels for non-price attributes
are fixed,
in any given run of the model. The
function, h,
can then be written as h(
,..... 
) where
, and (
) we can fit one and
two-dimensional splines respectively to these
functions, thus determining h. The Appendix
describes how this is done.
includes the assumed specified
values, for the prices of the remaining p - 1
products. Hence, the market share for
product p is
, can be
written as:
for j = 0, 1..... n - 1. Finally, we compare Z at these two points, provided that the points are in the appropriate
(
) to determine 
.
(i.e., at n + 1 knots). We want to interpolate to
find g(x) smoothly; 
. We approximate g(x) by a p-dimensional polynomial in
each
interval 
, i = 1.....n. Note that the
meaning of the variables here (e.g., p below) is different from that used in the
main text. That is,
for 
) and g(
) for smoothness we assume that 
for
k = 1,.... p - 1. This gives us p + 1 linear equations in p + 1 unknowns and hence ai0.....aip are determined. Specifically, let r1 = g(
, k = 1,..., p - 1. Let ai = ai0.....aip and
,...., g(p-t)
, 
), i = 1, j = 1,...,n. We want to interpolate to find g( x, y ) smoothly for all
x and y, 
and 
. We
approximate g( x, y ) by a polynomial in each
rectangle 
, 
. That is,
),
t01 = g(
. We then have four linear equations in
four unknowns
,
,
,
.
,
,
,
.