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Essays on the effects of the consumer price-perceived quality heuristic : theoretical and empirical perspectives Lee, Freddy 2004

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ESSAYS O N T H E E F F E C T S OF T H E C O N S U M E R P R I C E - P E R C E I V E D Q U A L I T Y HEURISTIC : T H E O R E T I C A L AND E M P I R I C A L P E R S P E C T I V E S By FREDDY LEE BS Electrical Engineering (High Honors) University of Texas at Austin, USA 1995 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF D O C T O R OF P H I L O S O P H Y in THE FACULTY OF GRADUATE STUDIES FACULTY OF COMMERCE AND BUSINESS ADMINISTRATION We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June 2004 © Freddy Lee, 2004 Abstract The study of consumer behavior and the study of firm strategy using quantitative modeling are among the many successful research streams in marketing. While both traditions have proved fruitful, there exists an obvious "gap" between them. In particular, relatively few of the significant findings in the behavioral research stream have been incorporated into the modeling framework to study firm strategies. For example, while numerous behavioral studies suggest that consumers may not have perfect information and may employ judgmental heuristics when they make purchase decisions, most of the quantitative studies on product positioning have assumed, among other things, that consumers have perfect information about true product quality. The research "gap" between behavioral studies and quantitative research needs to be filled, since to derive practically useful managerial implications, a modeling framework needs to reflect market realities to the possible extent. The rich findings in consumer behavior thus provide a great opportunity to incorporate them into models of firm strategy, and examine how the optimal outcome is changed. Feinberg, Krishna and Zhang (2002) and Krishna (1994) are some examples of work done with this focus. This ii is especially important for the studies of product positioning, since consumer perception about product offerings is often the consequence of both economic and psychological factors. This thesis examines one aspect of consumer behavior that has received consistent recognition in the behavioral literature but has not been considered in a modeling framework. In particular, we examine the effect of the price-perceived quality heuristic on a monopolist's quality and price strategies. The thesis will comprise 7 chapters. For the first chapter, the research problem is defined and a literature review of the existing work done on price as a signal of objective quality and the relevance of the price-perceived quality heuristic is presented. In the second chapter, we introduce and define the price-perceived quality heuristic formulation. In the third chapter, in the context of a monopolist deciding on price and quality strategies, we propose that consumers in reality may not have perfect information about the quality of a product. Instead, the "perceived" quality depends upon both true quality, which can be communicated to the market through non-price advertising, and the price level, which serves as an index of quality in addition to the indication of monetary sacrifice. As the behavioral literature suggests, this is particularly true for products that are difficult to evaluate, at least initially. We are able to derive analytical results that provide a valuable addition to existing studies where a perfect information world is assumed (i.e., consumers know the exact quality level and do not use the price-perceived quality heuristic). Some results are highlighted here. First, the degree of suboptimality of inappropriately assuming only true quality information is shown to critically depend on both the significance of the price-perceived quality heuristic, and its interaction with the amount of true quality i i i information available to consumers. Second, and perhaps more importantly, the firm can improve its optimal profits by enhancing the relative availability of the true quality information as compared to perceived quality through advertising. However, such an improvement is constrained by the magnitude of the price-perceived quality heuristic and occurs in the model when there does not exist a strong correlation between the magnitude of price-perceived quality heuristic and the availability of true quality information. In other words, this occurs when the use of the price-perceived quality heuristic is primarily a behavioral primitive, as most of the existing studies suggest. If a strong dependence between the magnitude of price-perceived quality heuristic and the availability of true quality information is assumed in the model, the pattern of results reverses. A few welfare implications are also obtained. For instance, the greater dependence on price to judge perceived quality in an efficient solution and the greater availability of true quality information in a monopoly solution may actually hurt consumers. In the fourth chapter, an empirical study was designed to test our conclusions that for markets where the consumers rely more heavily on the price-perceived quality heuristic, a higher level of non-price advertising will lead to greater profits. Despite the limitations of the study, the results are consistent enough with our expectations. Thus our conjecture that the parameters for the price-perceived quality and true quality information are independent or, at most, mildly dependent is supported and the theoretical results obtained are significant and have relevant managerial implications. In the model extensions, the thesis investigated product and price strategies for a monopolist in a dynamic setting as well as with a product line. In the dynamic setup iv with two periods, we incorporate the main findings of prospect theory when modeling how consumers respond to the differences between anticipated (perceived) quality and actual (true) quality. Our analysis indicates that it is optimal for the monopolist to adopt a price skimming strategy when both the price-perceived quality heuristic is important and the true quality information is readily available. Otherwise it is actually optimal for the firm to provide a quality level that matches or exceeds the level necessary for purchase, adopting a pricing strategy dependent on the heterogeneity of the consumers. The inclusion of the prospect theory also provides a more accurate guideline for managers when they need to adopt the correct quality and price strategies under different market conditions. In the next extension, optimal product and price strategies for the monopolist with a product line are obtained. The results are analyzed for various different market conditions for the two products as well as against the monopolist single product solution. The monopolist is better off having a product line for most market conditions as the market coverage is bigger and the higher product can be used to extract surplus from the consumers. However, when both the strength of the price-perceived quality and the availability of true quality information are high, the single product solution is more optimal as the monopolist can charge a very high price for a high quality product to a small customer segment that is willing to pay high for quality. In the 6 t h chapter, we incorporate competitive effects and investigate the product and price strategies when firms in a duopoly correctly believe or incorrectly not believe that consumers adopt the price-perceived quality heuristic prior to purchase. A comparison between the equilibrium solution, the efficient solution and the monopoly v solution reveals that generally the equilibrium products are not efficiently positioned and the firm that is more profitable has a product closer to the monopoly product. Finally, we conclude and present directions for future research. Keywords: Monopoly, Price, Quality, Price-perceived quality heuristic, Empirical, Advertising, Duopoly. vi Contents Abstract ii List of Tables x List of Figures xii Acknowledgement xiv 1 Introduction 1 1.1 Research Problem 1 1.2 Literature Review 2 1.2.1 The Relevance of The Price-Perceived Quality Heuristic. .. 3 1.2.2 Product Positioning 10 1.3 Structure and Substantive Findings of the Thesis 11 2 Incorporating the Price-Perceived Quality Heuristic 16 2.1 Introducing the Price-Perceived Quality Heuristic 16 2.2 Defining Perceived Quality 19 3 Monopoly Core Model 24 3.1 Overview 24 3.2 Modeling Framework and Monopolistic Behavior 25 3.3 The Effects of Sp, 5S and Consumer Heterogeneity 27 3.4 The Cost of Ignoring the Price-Perceived Quality Heuristic 31 3.5 The Role of Non-price Advertising 33 vii 3.6 Welfare Implications 37 3.6.1 Efficient Solution and Welfare 38 3.6.2 Profit Maximization and Welfare 41 3.7 Summary 43 4 The Role of Non-price Advertising When Consumers Use the Price-Perceived Quality Heuristic: An Empirical Study 46 4.1 Overview 46 4.2 Hypothesis and Models 51 4.3 Data 55 4.4 Results 61 4.4.1 First Stage Analysis 62 4.4.2 Second Stage Analysis 63 4.5 Summary 66 5 Model Extensions 68 5.1 Monopoly Dynamic Product and Price Strategies 69 5.1.1 Model Framework 70 5.1.2 Results and Analysis 72 5.1.3 Summary 79 5.2 Monopoly Static Simultaneous Product and Price Strategies in a Product Line 80 5.2.1 Model Framework 81 5.2.2 Results and Analysis 83 5.2.3 Summary 88 viii 6 Duopoly Product and Price Strategies 89 6.1 Model Framework 92 6.2 Results and Analysis 98 6.3 Summary 109 7 Conclusions and Future Research 110 Bibliography H 7 Appendix 126 ix List of Tables 1.1 Summary of Gerstner (1985) results 5 1.2 Summary of Studies in Lichentstein and Burton (1989) 1 7 1.3 Summary of Studies in Lichentstein and Burton (1989) 2 8 1.4 Summary of Results in Peterson and Wilson (1985) 9 2.1 Summary Empirical Results from Erickson and Johansson (1985) 17 3.1 Analysis of Optimal Profits As 8P and 8S Changes 35 4.1 Tests of the Hypothesis 54 4.2 Descriptive Statistics 61 4.3 Cronbach Alpha Values 62 4.4 Exploratory Factor Analysis 62 4.5 Effects of Market Price, Frequency of Purchase and Ease of Evaluation of Products on Price-Quality Perception (Restricted Model) 63 4.6 Category Average Predicted Price-Perceived Quality Values 64 4.7 Effects of Price Quality Perception, Market Share and Market Size on Advertising Spending (Restricted Model) 65 4.7(a) Effects of Price Quality Perception, Market Share, Market Size, Firm Size, Primary Business, Market Share x Firm Size on Advertising Spending (Unrestricted Model) 66 x 5.1 Comparison of The Product Line Optimal Solutions (PLOS) and The Monopoly Single Product Solution (SPS) 86 6.1 Summary of the Efficient Solutions 95 6.2 Comparison between Different Solutions for Case 1 (a=0.1, b=0.9, a = \ ,SS =1) 102 6.3 Comparison of Case 4 Numerical Output (a=0.1, b=0.9, a = \, ds = dv =0.2) 106 6.4 Comparison of Case 4 Numerical Output (a=0.1, b=0.9, a = \, 8 =5 =0.9) 107 xi List of Figures 2.1 Price-perceived quality heuristic and Purchase Decision 18 3.1 Monopoly Market Coverage 25 3.2 The Effect of the Strength of the Price-Perceived Quality Heuristic on Optimal Prices 29 3.3 The Effect of the Strength of the Price-Perceived Quality Heuristic on Optimal Quality 30 3.4 The Effect of the Strength of the Price-Perceived Quality Heuristic on Market Coverage 31 3.5 Sub-optimal Profits When Failing to Consider Price-Perceived Quality Heuristic 32 3.6 Optimal Profits As a Function of ds 34 3.7 Optimal Profits As a Function of Ss (Advertising Cost Function) 37 3.8 Welfare Implication of the Efficient Solution (b = 1, a = 1) 39 3.9 Welfare Implication of the Efficient Solution with Perceived Quality (b = \,a = \) 40 3.10 Welfare Implication of the Monopoly Solution (b = O.S,a = 1) 41 3.11 Higher 8S Need Not Make Consumers Better Off in a Monopoly Solution . 43 4.1 Optimal Profits As a Function of Ss when 9 = 0.9 48 4.2 Sample Plots of Residuals vs Market Share, Primary Business xii and Brand Quality 55 5.1 Possible Market Scenarios in Two Periods 74 5.2 Optimal Monopoly Quality Strategy in A Two-period Model (a=0.1, b=0.9) 76 5.3 Optimal Monopoly Profit Levels in A Two-period Model (a=0.1, b=0.9) 76 5.4 Optimal Monopoly Quality Strategy in A Two-period Model (No Customer Satisfaction Carry over, a=0.1, b=0.9) 77 5.5 Optimal Monopoly Quality Strategy in A Two-period Model (Symmetric Customer Satisfaction Carry over, a=0.1, b=0.9) 78 5.6 Monopoly Product Line Market Coverage 81 5.7 Profit Levels of Products in Product Line vs Strength of the Price Perceived Quality Heuristic 83 5.8 Product Quality level vs Strength of Price-Perceived Quality Heuristic 85 5.9 Market Coverage vs Strength of Price-Perceived Quality Heuristic 85 6.1 Firms' Belief About Consumers' Adoption of the Price-Perceived Quality Heuristic 91 6.2 Consumer Segments in a Duopoly 94 6.3 Profit Levels of the Duopolists in Case 1 99 6.4 Market Coverage of the Products in Case 1 100 6.5 Margins of the Duopolists in Case 1 101 6.6 Profit Levels of the Duopolists in Case 4 (a=0.1, b=0.9) 104 6.7 Market Coverage of the Products in Case 4 (a=0.1, b=0.9) 105 xiii Market Coverage vs Strength of The Price-Perceived Quality Heuristic Case 4 xiv Acknowledgement I would like to take this opportunity to acknowledge the valuable and precious contribution to this work by the members of my dissertation committee: Professors Charles B. Weinberg (Dissertation Committee Chair), Thomas W. Ross (Committee Member) and Robert Krider (Committee Member). Chuck is the epitome of a great researcher, a great mentor and a great teacher. I consider myself to be very fortunate to be accepted into UBC and to be able to work with Chuck. His vision of research positioning, strength in methodology and collegial support of my progress in the PhD program is deeply engraved in my mind and serve as a model for me for the rest of my academic career. Of special mention is Professor Yong Liu. Yong has been my friend and research buddy from the day I began my PhD program. His encouragement and support during my most difficult times in the PhD program greatly enabled me to continue and complete this thesis. Special thanks to Tom and Bob for their many insightful suggestions which greatly improved the thesis. I sincerely thank my wife, Sharon, who has accompanied and persevered with me throughout the intense and pressurizing periods. Without her tender loving care, this thesis and much of my research work could not have been possible. xv Chapter 1 Introduction 1.1 Research Problem Consider the following headline from the Wall Street Journal (Page A2, December 4, 1996): "A jewelry-store owner instructs the shop clerk to cut prices on turquoise, to clear the merchandise. The clerk mistakenly raises prices instead. Quickly, all the merchandise sells, because unsophisticated buyers associate high prices with high quality." Not only will "unsophisticated" buyers do this, a perfectly rational buyer may use the price-quality heuristic as well, especially if complete information about product quality is unavailable (Stafford and Enis, 1969; Monroe and Krishnan, 1985; Erickson and Johansson, 1985; Zeithaml, 1988). Indeed, the phenomenon of using price to infer quality exists in many markets and for many consumers. Existing studies have shown that consumers are likely to adopt this heuristic when purchasing status-oriented products, durable goods, convenience products and products that are difficult to evaluate. 1 (Chao and Schor, 1988; Gerstner, 1985; Owen, Wright and Grif f in, 2000; Zeithaml, 1988). Research focusing on understanding and managing customers is receiving great attention from both business and academic fields. This naturally points to the value of incorporating important consumer behavior features into an analytical framework of marketing strategy and developing pragmatic implications from findings in consumer behavior. Although many behavioral studies have demonstrated the significant influence of the price-quality heuristic on purchasing decisions, little analytical work has considered it when formulating consumer utility and product choice. Research f i l l ing this gap is especially needed for such issues as pricing and product positioning, as incorporating the price-quality heuristic is l ikely to produce different marketing strategies. 1.2 Literature Review Since our goal is to investigate the effect of the price-quality heuristic on product positioning and pricing strategies, two groups of literature are of primary interest to us. The first comprises behavioral studies that demonstrate the existence of the price-quality heuristic in consumer decision-making, and the theoretical research on signaling, which point to the possibility that companies may be able to credibly convey product information through certain market mechanisms such as price and advertising. The second is the product positioning literature in marketing and economics, which concerns product differentiation and price competition. 2 1.2.1 The Relevance of The Price-Quality Heuristic The neoclassical economic approach assigns price a sole responsibility - to serve as an index of sacrifice in consumers' budget. The direct influence of this approach on analytical marketing models is that, not surprisingly, price always shows up as a negative factor in consumers' evaluation of alternatives. However, this is inconsistent with the findings of many behavioral studies. To the best of our knowledge, Scitovsky (1945) was the first to formally suggest that price was not only an index of sacrifice to consumers; but also an index of quality. Later on, a number of experimental studies showed that consumers typically infer a higher quality level from a higher price (see Monroe, 1973). Formulating the relationship between price and product quality has received a substantial amount of attention since the mid 1980s. For example, Monroe and Krishnan (1985) proposed a conceptual model in which price positively influence both the "perceived quality" of a product and its "perceived sacrifice." While perceived quality enhances a product's "perceived value," perceived sacrifice diminishes it. Eventually, price plays two roles in the evaluation process - both to increase a consumer's willingness to buy and to decrease it. This framework has been validated by several studies (Dodds and Monroe, 1985; Rao and Monroe, 1988; Zeithaml, 1988; Dodds, Monroe, and Grewal 1991; Chapman 1993). This work was extended by Erickson and Johansson (1985) who identified both direct and indirect paths for price's effect on consumer's intention to buy. They found that the traditional budget-constraint role of price exists without interfering with quality 3 beliefs or the overall product attitude. This, of course, is the negative effect of price on intention to purchase. A positive effect of price is shown to exist as well . However, this effect occurs as price enhances quality belief first, and then improve overall attitude, and finally increases a consumer's intention to buy. A simplified version of this is presented in Figure 2.1 in the next chapter, and used to support the consumer utility function in Section 2.2. Another relevant stream of research deals with the signaling effect of certain market mechanisms. Among these are price (e.g., Mi lg rom and Roberts, 1986; Bagwell and Riordan, 1991), advertising (e.g., Nelson, 1974; Schmalensee, 1978; Kihlstorm and Riordan, 1984; Mi lg rom and Roberts, 1986), reputation (e.g., Shapiro, 1982), warranties (e.g., Gal-Or, 1989), and product specific investment (e.g., Kle in and Leffler, 1981). The basic consideration of these studies is whether companies wi l l have the motivation to separate themselves from each other by offering distinctive signals to the marketplace. If such a motivation exists (i.e., a separating equilibrium occurs), then, for instance, a higher price w i l l indicate a higher quality product. Two important differences exist between our model and the signaling literature. First, it is a common practice in the signaling literature to start with aggregate market demand. Instead we start by formulating individual utility functions. Second, most of the signaling studies assume exogenous product features. For example, most papers assume two different quality levels (High and Low), and assign a priori one firm, or product, to High and the other to Low. We do not impose this constraint, and allow the product quality decision to be endogenous in a continuous space, together with price. 4 Price as a signal of objective quality has been shown to be a relatively weak signal by Gerstner (1985). Table 1.1 Summary of Gerstner (1985) Results Price - Objective Quality Correlations Durables Categories: 86 /?>0.5 12 13.95% 0<p<0 .5 57 66.3% p<0 17 19.8% Non durables Categories: , 59 p>0.5 3 5.08% 0< / o<0.5 31 52.5% p<0 25 42.4% For 86 durable product categories and 59 non-durable product categories, Gerstner found that only 14% of the former and 5% of the latter had very strong objective quality and price correlations (See Table 1.1). For the rest of the categories, a majority demonstrated very weak relationships and for other categories, the relationship was either non existent or negative. Riesz (1979) also replicated similar results with packaged food. In his studies, he provided evidence that the price-objective quality relationships are weak. Sproles (1977) also found that the price-objective quality relationship is generally weak and cannot be generalized across products and product categories. As the correlation on average is minimal with only some categories that are high, this further provides support that firms do not use a signaling approach when deciding on their product and pricing strategies. As such, customers in general might not be wise to rely 5 on price to gauge objective quality. However, as we discuss in the next paragraph, they often do. Lichenstein and Burton (1989) assessed the accuracy with which consumers perceive objective price-quality relationships. Results across four studies for durables and non-durables indicate that many people perceive quality from price. This price-perceived quality schema exists for all 4 studies (See Table 1.2) conducted by Lichenstein and Burton and can be seen from the 3 or 4 clusters concerning the use of the price-quality heuristic that are generated across all the studies. Study 1 and 3 utilized student samples while study 2 and 4 utilized shoppers. Taking the case of study 1, a three-cluster solution was shown to best summarize beliefs about the existence of price-quality relationships. On average, the subjects in all 3 clusters utilized a price-perceived quality schema (juall > 4.0). The authors used a comparative approach for the clusters and derived a cluster that has a higher overall mean (jiall =5.54, Adopt the Price-perceive quality schema), a cluster with a higher mean for the non-durables (jUND = 4.48, Adopt the Price-perceive quality schema for Non durables) and a cluster for the durables (jUD =5.39, Adopt the Price-perceive quality schema for non durables). These clusters are also found in study 4. In study 4, juall = 5.35 in the first cluster leads to the cluster that adopts the schema. In the second row, juND = 3.63 > juND =3.00in the third row, thus leading to a non durable price-perceived quality schema. Likewise, jilD = 5.21 in the third row > jUD =4.71 in the second row resulting in the durable price-perceived quality schema cluster. 6 Table 1.2: Summary of Studies in Lichentstein and Burton (1989) 1 Study 1 (N=220 students) Study 2 (N=156 Shoppers) Study 3 (N=220 students) Study 4 (N=152 Shoppers) 15 cat, 7ND, 8D 15 cat, 7ND, 8D 18 cat, 9ND, 9D 18 cat, 9ND, 9D Adopt PQ 74 (33.6%) 65 (41.7%) 30 (19.7%) Schema jUD =6.03* Mo =5-72* juD =5.60* jUND =5.05* ^ = 4 . 7 2 * ^ = 5 . 1 0 * Ma,, =5.54* MaU=522* M A „ =5-35* u>4.0= 15 8D 7ND //>4.0= 15 8D 7ND //>4.0= 18 9D 9ND Adopt 24 (10.9%) 31 (19.9%) 61 (27.7%) 63 (41.4%) Non Durable PQ Schema jUD =4.14* ^o=4.48* //D=3.40 / / „ D =3.90 UD =5.03* Mm =4-65* //D=4.71* MND = 3-63 / / a / / =4 .31* Matt = 3 - 6 5 Man = 4 - 8 4 * ^,,=4.17* U > 4.0 = 10 4D 6ND U > 4.0 = 4 2D 2ND a > 4.0 = 6 6D u> 4.0= 13 9D 4ND Adopt 122 (55.5%) 46 (29.5%) 86 (39.1%) 26(17.1%) Durable fiD =5.39* MD =4.72* / / D =5.52* Md=5.2\* PQ schema Mm =3-62 / / a „ = 4 . 5 0 * Mm = 2.96 / / a „=3 .84 Mm = 3 - 6 2 ^=4 . 5 7 * ^ D =3 .00 jUall=4.U* //>4.0 = 9 7D 2ND // > 4.0 = 7 7D > 4.0 = 17 9D 8ND //>4.0 = 9 9D Do not 14 (8.9%) 73 (33.2%) adopt PQ schema //0=1.69 MND =1-28 / / a „=1 .48 //> 4.0 = 0 fiD =4.50* Mm =2.70 Matt = ^ H> 4.0= 11 9D 2ND Others 33 (22%) Cat=Categori es, Study 1 & 2 Durables Study 1 & 2 Non Durables Study 3 & 4 Durables Study 3 & 4 Non durables D=Durables, Stereo Receiver Kitchen Trash Bags C D Player 12" frozen sausage ND=Non Durables V C R 19-inch portable color T V Peanut Butter Frozen French Fries 10 speed bicycle Stereo speakers pizza Half gallon vanilla ice Microwave oven Food Processor Clock Radio Laundry Detergent Dishwashing Liquid Washing machine Cooking range Gas B B Q grill cream Facial tissues box of 100 tea bags Blow Dryer Blender Fabric softener Oil popcorn popper 10-inch saucepan Drip Coffee maker (40 sheets) Spray cleaner (22 Oz) Oven Cleaner (16 Oz) Laundry bleach (40Oz) Club Soda (1 quart) • ~ The mean is more than 4, the mid point of the scale. Table 1.3 provides a clearer representation of the adoption of the price-perceived quality schema by the subjects in the 4 studies. The classification is done on the basis of 7 the average scores for each segment being more than 4 (the mid point of the scale). For study 1, all subjects adopted the price perceived quality schema with 55% for durable products only. For study 2 and 3, the clusters also revealed that a large portion of the subjects utilize the price-perceived quality schema especially for durables in study 3. Similar results are also obtained for study 4. These results clearly indicate that the price-perceived quality schema is adopted by consumers and is especially significant for durables. Table 1.3: Summary of Studies in Lichenstein and Burton (1989) 2 Study 1 Study 2 Study 3 Study 4 Adopt PQ Schema for Durables and Non Durables 44.5% 41.7% 27.7% 20% Adopt PQ Schema for Durables 55% 29.5% 72.3% 58% Adopt PQ Schema for Non Durables Do not Adopt PQ Schema 28% Empirical support for the existence of price-perceived quality schemas is also obtained from Peterson and Wilson (1985). In their study, 131 business students evaluated 22 durable and nondurable product categories. In the cluster analysis of the data, they found that 83.2% % of the total sample did have a stored price-perceived quality schema. Based on a scale that ranged from 1 (Strongly Disagree) to 6 (Strongly Agree) such that "the higher the price of the item, the higher the quality.", 3 of the clusters have a mean that is higher than 3. Table 1.4 summarizes these results. Consistent with the contention of Alpert (1971, p.131), these individuals made a priori judgments about the relationship between price and quality implying that the perceptions are based on a stored schema. These results thus provide strong evidence that consumers 8 have a preprogrammed price-perceived quality schema which they utilize when they evaluate product quality. Table 1.4: Summary of Results in Peterson and Wilson (1985) 22 Categories, 131 subjects Cluster 1 Cluster 2 Cluster 3 Cluster 4 # of Subjects 25 43 41 22 Cluster Means 4.32 3.88 3.68 2.89 # of Categories with means more than 3 22 17 17 11 As the previous studies have indicated, firms generally do not use price to signal objective quality and it may not be wise for customers to rely on price to signal objective quality. Although the signaling theory is extensively explored in existing literature, the previous studies mentioned have indicated that it may be less relevant in practice at least with regard to price. In this paper, we deviate from the signaling approach and focus on the behavioral primitive. From the consumers' standpoint, the price-quality heuristic may not accurately reflect firm behavior but it has been shown to exist in several empirical studies over both student and nonstudent samples. The price-quality heuristic we model is an inherent behavioral phenomenon which is not necessarily related to the firms' motivation to send a quality signal, as is the primary concern of the signaling studies. There thus exists a dilemma in which studies have shown that the price-objective quality relationship is often weak and yet data also supports the notion that consumers believe that price is related to quality, in at least some circumstances. This suggests that consumers may not learn from their purchases and frequently rely on the heuristic especially in situations which require much mental cognition or in which there exists an internal reference price/product. 9 1.2.2 Product Positioning Product positioning is concerned with a company's decision on product attributes. In particular, this may be the "type" or "quality level" of a product. Following the Hotelling (1929) tradition, numerous studies have examined the positioning issues for different market conditions (e.g., demand elasticity, distribution of consumer preferences, non-price competition). One of the common features of these models is that consumers are assumed to know product attributes. That is, consumers make purchase decisions based on perfect information of product offering and price. As Moorthy (1988) states, "consumers can observe the product qualities and prices available before they decide to buy" in a study of duopoly quality positioning and price decisions (p. 146). This may be truer for price than for quality. For many products, it is difficult for a consumer to judge the quality level before purchase and consumption (especially for the "experience" goods, as defined by Nelson, 1970), and consumers tend to combine both price information and the imperfect information about quality to make their inferences (Erickson and Johansson 1985). Depending on whether the horizontal attribute (i.e., taste) or the vertical attribute (i.e., quality) is the major focus, examples of studies employing this perfect information assumption include Mussa and Rosen (1978), who models one vertical attribute, Neven and Thisse (1990), who models a horizontal attribute and a vertical attribute, and Vandenbosch and Weinberg (1995), who model two vertical attributes. A typical consumer utility function, as used by Neven and Thisse (1990), takes the format of U -R + ts-(x-y)2 for a consumer whose willingness to pay for quality is t, and whose 10 taste is at x. For a product with quality level s and attribute y, this clearly states that the consumer knows all the information about the product when making purchase decisions. The premise of introducing the price-quality heuristic into this class of models is that both the optimal price and positioning strategy will change. 1.3 Structure and Substantive Findings of Thesis The second chapter will introduce the price-quality heuristic through existing literature and define the formulation of perceived quality from price in a quantifiable form. While some existing literature has indicated that the extent that consumers rely on price depends on the availability of true quality information, other literature has indicated that the price perceived quality heuristic is an inherent and stable schema. We will further develop our formulation of perceived quality along these lines. The third chapter examines how the price-quality heuristic influences a monopolist's product and pricing strategies. The most distinct features of our model are that price-quality association is explicitly considered in consumer utility functions. The model produces several results that should be of interest to marketing researchers and practitioners. First, the extent to which the monopolist achieves sub-optimal profit by using purely quality-information-based strategies (as most of the existing studies assume) in an imperfect information world is examined. The degree of this sub-optimality critically depends on both the significance of the price-quality heuristic, and its interaction with the amount of true quality information available to consumers. In general, the optimal result is surprising in 11 that not only should the monopolist raise price, but also quality, as reliance on the price-quality heuristic increases. Second, and more importantly, the monopolist can improve optimal profits by enhancing the relative availability of the true quality information as compared to perceived quality through the use of advertising. However, such improvement is constrained by the magnitude of the price-quality heuristic. This indicates that the effectiveness of non-price advertising is different in markets where consumers use price as the quality index to different extents. Thirdly, welfare implications pertaining to the efficient solution and the profit maximization scenario are also analyzed. • The introduction of the price-quality heuristic produces unexpected welfare results; namely, in the efficient solution that a social planner would adopt, total welfare is independent of the price-quality heuristic. However, consumers are worse-off when they rely more heavily on price to perceive quality. This is not surprising since consumer welfare depends on the true quality level, which can only be found out after purchase, and the social planner uses higher price to induce more consumers to buy. Similar patterns occur for the monopoly firm, but at a more significant level. For the monopolist, although it will earn sub-optimal profits if it adopts the non-heuristic strategies, consumers will benefit from such a "mistake." That is, compared with the case in which the monopolist adopts the heuristic strategies, consumer surplus increases when the non-heuristic strategies are applied to markets where consumers use the price-quality heuristic. Consumers served by a profit-maximizing monopolist are not necessarily better-off if more true-quality information is available. If there is very limited amount of true-quality information, more of it will 12 enhance consumer welfare. If there is already a fair amount of true-quality information, more of it will actually decrease consumer welfare due to a corresponding increase in true quality and price. In either case, the monopolist will have more profit. In the fourth chapter, we will empirically investigate whether firms make higher investments in non-price advertising especially in markets where the price-quality heuristic is emphasized. Theoretical results in the first study have indicated that non-price advertising is especially important when more objective quality information is available and consumers emphasize price in their perception of quality prior to purchase. With secondary data from Advertising Age, Standard and Poor's and Hoovers Annual Reports as well as primary data from a survey, we attempt to validate the theoretical hypothesis obtained. The results indicate that industry practice is largely consistent with the implications of the theoretical model. In the fifth chapter, we will introduce model extensions that build on the core model. Firstly, to understand the issues surrounding customer acquisition and retention, we examine the monopolist's product and price strategies in a two-period framework. The distinction between true quality and perceived quality allows us to incorporate the well-known value function of prospect theory into consumer utility functions (Hardie et al, 1993; Anderson and Sullivan, 1993; Putler, 1992) and consumer satisfaction is measured by the difference between the perceived quality (i.e., consumer expectation) and the true quality (which consumers know after consumption). We find that when consumers rely heavily on the price level and incorporate the limited true quality information in their perception of quality, the monopolist tends to use a price skimming strategy. The initial high price results in consumer dissatisfaction as the consumers 13 discover (after purchase) that the quality falls short of expectation. To obtain new sales, the monopolist reduces its price in the second period. By exploiting consumers in the first period, the firm is essentially emphasizing two different aspects of its profit: profit margin in the first period, and market coverage in the second period. Interestingly, this pattern is reversed when consumers either do not use the price-quality heuristic, or do not have true quality information readily available. In this case, it is actually optimal for the monopolist to provide a quality level that matches or exceeds consumer expectation. Essentially the firm is using the first period to induce trial, and then adapt its pricing strategy to extract profit from the satisfied customers, with precise results depending on the heterogeneity of the consumers. The inclusion of the prospect theory also provides a more accurate guideline for managers when they need to adopt the correct quality and price strategies under different market conditions. When the monopolist has a product line, the total profit is higher than when having a single product for most market conditions except for when the price-perceived quality heuristic is high and the true quality information is available. In this case, the monopolist is better off charging a high price for a single high quality product to extract surplus from the small number of higher end customers. In chapter 6, we incorporate competitive effects and investigate the product and price strategies when firms in a duopoly correctly believe or incorrectly not believe that consumers adopt the price quality heuristic prior to purchase. Equilibrium product and price strategies can be very different depending on how firms view the availability of quality information to the consumer prior to purchase. The effects of the price-quality heuristic on pricing strategy, product strategy, market coverage and profit levels are 14 analyzed. Results obtained are interesting and show that depending on market conditions, the better quality product (be it in the monopolist's product line or the higher quality firm), may not be the more profitable product. Likewise, the market coverage of the better quality product may or may not be higher than that of the lower quality product. A comparison between the equilibrium solution, the efficient solution and the monopoly solution reveals that generally the equilibrium products are not efficiently positioned and the firm that is the more profitable one has a product closer to the monopoly product. Chapter 7 concludes the thesis and suggests a number of potentially fruitful directions for future research. 15 Chapter 2 Incorporating the Price-Perceived Quality Heuristic 2.1 Introducing the Price-Perceived Quality Heuristic The Oxford American Dictionary defines quality as "a degree or level of excellence." By extension, perceived quality can be defined as the consumer's judgment about a product's level of excellence. Perceived quality is different from objective quality and involves a higher level abstraction which can be directly or indirectly derived. Summarizing, the previous research suggests price plays two roles in consumer evaluation. First, as neoclassical economics suggest, price serves as an expenditure term in the budget constraint. The theory of resource allocation says that a consumer needs to take price into consideration since it is a sacrifice of monetary resource, and that spending on one product necessarily decreases the possible purchase of another (e.g. Lilien and Kotler 1983, p.390). Therefore, price has a direct negative impact on purchase decisions. Second, for certain product categories consumers frequently use price as an indicator of product quality - a higher price is usually taken as an indication of higher 16 quality. A number of studies have demonstrated that this positive role of price on purchase decisions does not occur directly; instead, price helps form a perceived quality or quality belief, which then influences the intention to buy (e.g., Erickson and Johansson, 1985; Monroe and Krishnan, 1985). Table 2.1 summarizes the main findings from Erickson and Johansson (1985). The three equations below indicate that "(1) price affects intention positively through its positive effect on quality perception, through the positive effect of quality perception on attitude, and through the positive effect of attitude on intention, and (2) price has a negative and direct effect on intention, controlling for the attitude effect." (p. 198, Erickson and Johansson (1985)) Table 2.1 Summary Empirical Results from Erickson and Johansson (1985) Equation/V ariable Coefficient Est. t value Endogenous Variable: Attitude Price Belief 0.083 0.77 Quality Belief 0.672 5.29* Economy Belief 0.441 14.42* Familiarity 0.145 4.63* Intercept -0.037 -2.02* Endoeenous variable: Quality Belief Attitude 0.377 10.60* Price Belief 0.527 11.81* Actual Horsepower -0.002 -1.58 Actual Acceleration -0.020 -1.93** Actual Driving Comfort 0.116 2.81* Intercept 0.016 0.06 DV: Probability of Purchase Attitude 0.700 25.14* Price Belief -0.190 6.81* Intercept 0.010 0.85 * p=0.05, ** p=0.01 17 Figure 2.1: Price-Perceived Quality Heuristic and Purchase Decision Actual quality Price + / + • Quality belief + Purchase intention These two distinctive routes of the effect of price on purchase are presented in Figure 2.1. It allows us to construct a consumer utility function that incorporates the price-perceived quality heuristic and the traditional setups in which this heuristic is absent (e.g., Mussa and Rosen, 1978; Moorthy, 1984, 1988; Neven and Thisse, 1990). First, the "budget constraint" role of price suggests putting price itself directly in the utility function (as a negative term). Second, a perceived quality (sh) is formed based on both the true quality (s) and the price levels. In particular, sh p and sh s . In order to capture the phenomenon that consumers are not fully aware of the true quality of a product and very often unable to judge and appreciate the true quality, we assume that only a proportion of the true quality information can be utilized to form perceived quality. This is also consistent with existing studies which indicate that product quality information can never be fully conveyed or evaluated by the consumer prior to purchase. (Chang and Wildt (1996) and Shapiro (1982)). 18 2.2 Defining Perceived Qual i ty In our formulation of perceived quality, we introduce two parameters, 8P and ds. Parameter dp captures the heuristic value of price, while Ss indicates the availability of the true quality information. Note that two factors possibly contribute to the magnitude of 8S: to what extent the true quality information is made available to the market by the firm or by others, e.g. consumer reports, and to what extent a consumer is willing to rely on this information. In order to focus on issues of perception and information and the role of non-price advertising and to avoid modeling the psychological process that contribute to the "trust" or "distrust" between consumers and firms, we assume that consumers are willing to rely on true quality information to the extent that it is available to them. To concentrate on the price-perceived quality heuristic, we associate the meaning of Ss with the amount of true quality information available to consumers. Another benefit of this formulation is that we can investigate the role of non-price advertising, the principal effect of which is to increase 5S. Although empirical research, as summarized earlier, strongly supports the view that a substantial proportion of consumers rely on price as an indicator of quality in many product categories, there is more discussion as to how dependent that reliance is on the amount of other information that is available in the market. Zeithaml (1988) for example shows that the use of price as an indicator of quality depends on the availability of other cues to quality. The informational factors that affect the price-perceived quality relationship include when intrinsic cues to quality are readily accessible, when brand names provide evidence of a company's reputation, or when the level of advertising 19 communicates the company's belief in the brand. In this thesis, we constrain the scope to goods that are not purely search goods. A parsimonious way to capture this effect is as follows: sh=Sp(\-d8s)p + Sss 0<8p<\ 0<SS<1 (1) The formulation in equation (1) allows for dependence between the parameter for price and the parameter for true objective product quality where 6 captures the strength of this dependency. However, a formulation which implies the independence between the parameter of price and the parameter of quality is equally important. Mizreski, Golden, and Kernan (1979) contend that true covariation assessment is most likely to occur when consumers are first learning of a relationship between two variables, especially in extended information processing situations. However, consumers rapidly learn to generalize across situations perceived to be similar as they associate causes and effects (ie. price and quality). Consequently, by the time the consumers are adults, they are likely to perceive that they have sufficient experience and information base on which to make schema-based generalizations. Aspects of this issue have already been addressed in the attribution theory literature thus resulting in causal schemas. In equation (la), Sp is independent of ds as we believe consumers evoke a schema to assess the price-quality relationship. Alpert (1971) further suggests that these schemas may be further reinforced and supported by a history of "you get what you pay for" advertising. All these thus reinforce and reduce the likelihood of price-quality covariation assessment on a product category. 20 Hence another parsimonious setup allowing these (independent) effects is the linear function: sh=Spp + S,s (la) Thus from this point on, equations with an (a) will represent results or derivations from assuming the perceived quality formulation using equation (la). Existing studies (Chang and Wildt (1996) and Shapiro (1982)) have indicated that product quality information can never be fully conveyed or evaluated by the consumer prior to purchase. As such, to capture this aspect in our model, we set the upper constraint of Ss to be 1. Here we assume the consumer fairly interprets the available information and does not over or underestimate the product objective quality information.1 Therefore in the heuristic world the utility level that a consumer expects to receive is modeled as U = t(Sp(l-0Ss)p + Sss)-p (2) U=t(Spp + Sss)-p, (2a) where t is consumer type, and captures the heterogeneity of consumers in their willingness to pay for quality, t is assumed to be uniformly distributed on [a, b], 0 < a < b. A uniform distribution is assumed to concentrate on the key issue of price quality perception remove positioning possibilities due to non-uniformity and to simplify derivation. ' Such an effect could be modeled. For example, let the component of true quality that leads to perceived quality be kSss where k captures the distribution of consumers' interpretation of objective quality information. We implicitly have k=l in our model. Mathematically, even when k>l, our main results and findings hold. 21 As consumers cannot be fully aware of the quality of a product prior to purchase, firms that assume consumers do not use the price-perceived quality heuristic will have a consumer perceived quality level of sT = 8ss. While many existing studies have assumed perfect quality information for the consumers (8S =1), our model presents a more general representation of firms with this assumption. Thus the utility level in the true quality information only world is defined as U=t(Sss)-p (3) Except for the perceived quality factor, these utility functions are consistent with those in the literature (e.g., Moorthy, 1988). Since the overall effect of price is likely to be negative (otherwise there will not be a price ceiling in the market without introducing the income effect), we constrain our discussion to situations where 0 < tdp (1 - 68s) < 1 and 0 < 18p < 1 for any t2. Other assumptions are as follows: a) Consumers may purchase either one unit of the product or none, while the monopolist decides whether to cover the entire market. b) The monopolist has a single product with a single quality attribute. c) The consumers buy the product if the "expected" utility, which depends on perceived quality, is positive, or do not buy if it is negative. This implies a default substitute of zero quality and zero price. d) The marginal cost of producing one unit of product at quality s is as2 (a > 0). The quadratic cost function is assumed so that the marginal cost (of quality) can increase faster than the willingness to pay. This ensures that the optimal quality level the 2U =t(8p(l-08s)p + Sss)-p = (t(Sp(\-98s)-V)p + 8ss thus t(5p(l-05s)<land U — tSp p + t8sS — p = (t8p —l)p + t8s S thus t8p — 1 < 0 for negative overall effect of price. 22 monopolist can choose for consumer type t will not be infinite. Indeed the maximum quality level the monopolist may provide for t (without incurring a loss) is t5. a(l-t(Sp(\-eSs))) or tSs /[a(l - tSp)] respectively for the two formulations . Fixed cost is irrelevant to our analysis and assumed to be zero. 3 Marginal cost = CCS should exceed the willingness to pay ( = UH (0) ) so that quality offered will not be infinite. 23 Chapter 3 Monopoly Core Model 3.1 Overview For our core model, we formulate and design a model using a monopoly structure. As our primary research objective is to study the effects of the price quality heuristic, thus this objective dictate the appropriate assumptions and model. Competitive effects although important will be explored later as an extension rather than the primary model of concern so as to fully analyze the effects of the price quality heuristic. As in Shugan (2002), we believe the strong approximating assumption of no competitive response is sometimes better (as in this case), than the approximating assumption of pre-existing equilibrium behavior. We believe the creation and creative use of monopoly power will serve our purpose well here. This is also consistent with the many popular economic models with many marketing applications in which the decision maker is modeled as a monopolist. Some examples include principal-agent models (Holmstrom 1979), contracting models (Nalebuff and Stiglitz 1983), franchising models (Brickley and Dark 1987) and even economic models of consumers (Thaler and Shefrin 1981). 24 3.2 Modeling Framework and Monopolistic The assumptions made in the previous chapter allow for the formulation of a monopoly model as in Figure 3 .1. Figure 3.1: Monopoly Market Coverage 1 b ti a Consumer heterogeneity in their willingness to pay for quality is distributed between a and b. tj is the indifferent consumer between buying and not buying the product.4 Market coverage is the region represent by (b -1{). The monopolist's profit function is thus given by YV = (p-as2)(b-tx) (4) where tj is the lower boundary of the market served by the monopolist, and can be solved from tlsh - p = 0 . Note that if t{ > a , the monopolist does not cover the whole market. If it decides to cover the whole market, r, will need to be set at a. It is then straightforward to solve for the market-covered and market-not-covered optimal strategies analytically. 4 tj is endogenous to the model and implies that U=0. 25 When the market is fully covered, tx=a. From equation ( 1 ) , P = adcs ada-eds)-\ and the optimal strategy is to set product quality at ad. 2(\ + aSp 68s -a8p)a and sell at p*c = i2Sj 2(1 + adp68s -aSpfa provided b < a(a68p5s +3-aSp)/2. When the market is not fully covered, it holds thattx = pish. We then obtain closed form solutions , 5,{Abdp8S? -4bSpS, + AS, --j2^(4bSp0S, -4bSp -SbSfiS, -%b~S~p + 5)<5,2)((4b5peS, -4bSp-^9 + &b8peS, -Zb5p) * (.tybS^S)-1 + 0S, +bSp-2bSp6Ssfa) and (5) s„,. = Ss(3 + 4bSp6ds -Ab8s -^9 + SbSp0Ss-SbSp Za(b82e28] -8p+8p08s +b8p '08,) (6) Similarly from equation (la), p = as8s 1(1 -aS ). The optimal strategy is then to set product quality at s*c = aSr a o. 2a(l-a8p) , and sell at p*c 2cc(\-aSpf When the market is not fully covered, it holds that tx = pi'sh. We then obtain these closed form solutions Pnc* = (4bSp -4 + ^j-SbSp + 2(9-Sb8p)u2 + \o\-3 + 4bSp+ J9-$bSp) 32aS2p(l-bSpY (5a) and ^ ( ^ - 3 / 4 + ^ 9 - 8 ^ / 4 ) 2a8p(\-b8p) (6a) 26 As the main results from both formulation of perceived quality are similar, especially when 6 <~ 0.655, to reduce repetitive representations, the results and implications from equation (la) will be further discussed from this point onward ie. Our model considers situations whereby the parameters of price and true objective quality information are either independent or moderately correlated. 3.3 The Effects Of SP9 Ss and Consumer Heterogeneity The degree of consumer heterogeneity is measured by b - a (0 < a < b < 1). When b is large enough6, i.e., b > a(3-adp)/2, the monopolist will not cover the entire market; it only serves the customers with willingness to pay greater than t\*. Otherwise it will find it optimal to serve all the customers, and the substitute's market share is zero. When only true quality information is assumed to be utilized by consumers, the monopolist's market-covered solution is to sell qualityads 12a at price a28s 212a. This is conditional on b<3a/2. The market-not-covered solution is to sell bSs /(3a) at price 2b2Ss2 /(9a) provided that b>3a/2. Putler et al (2004) investigated expenditure in many product categories including clothing, home entertainment, entertainment, sports and recreation as well as reading materials and printed matter. In all the categories, within the available household spending data, some households did not make an 5 We numerically found the limit of the dependence of the parameters that will give us the similar main findings and results. Thus our model holds for product categories in which the parameters are independent and moderately dependent. 6 * t > a for market to be not covered. 27 expenditure. For example, for women's and girls' wear, 10.1% of households had zero expenditure while for bicycle maintenance and repair, 94.1% of households had zero expenditure. Given these results, we focus most of our discussion on the case when the market is not fully covered. Comparing the results between the true quality information case and the heuristic case, it appears that the market can be less heterogeneous [(b-a)is smaller] for the optimizing monopolist not to cover the whole market when consumer use the price-quality heuristic. That is, a(3-a8p)/2<3a/2. The reason, as this inequality suggests, has to do with the fact that considering price as a positive signal for quality gives the monopolist a chance to charge a higher price, everything else equal, so as to extract more surplus from the upper end of the market. Figure 3.2 shows how pnc changes with 8 . As expected, higher 8p induces higher pnc when the monopolist takes advantage of the heuristic. However, only when b is comparatively large is this change in pn* managerially important. A lower b limits the ability of the firm to capitalize on this behavior. Even though a higher 8p enables the monopolist to charge a higher price, its ability to do so while still maintaining sales is limited. This is opposite to the situation where b-a is large, in which case the monopolist can extract the surplus from the higher end of the market by increasing pn* to a greater extent. 28 Figure 3.2: The Effect of the Strength of The Price-quality Heuristic on Optimal Prices (a = 1,8s = 0.5) * Pnc 0:6" / 0:5- . / 0:4-•i .0:3-•••/ / 0.2-•0.1-0 . : : :V ° : 4 deltal £ = 0 . 8 O.B 0.8 1 8, Further investigation reveals that when b-a is small, the effect of true quality information (Ss) on pn* is much more significant, because the effect of 8 is minimal. However, when b-a is large, pn* is sensitive to both 8p and 8S, and increases when either of them increases ( > 0 and > 0). 88 88 p s The pattern of changes in optimal quality level when 8p and 8S change is similar * 8s 8s to that of pnc (see Figure 3 .3 i.e. >0and >0) . These results provide two 88 88 p s insights on monopolistic behavior. First, the price-quality heuristic does matter in a market where consumer's willingness to pay for quality is high. Second, as market conditions (in terms of 8 and 8S) change, at the optimal the monopolist will raise its price, and, while not obvious, this needs to be supported by an improvement in quality as well. 2 9 Figure 3.3: The Effect of the Strength of the Price-quality Heuristic on Optimal Quality (a = 1,5S = 0.5) 0.5-/ / / / / * 0.4- / / / 0.3-0.2-0 ' 0 2 ' ' °: 4 : delta! D- 3 O.B . 1 £ = 0.8 The market coverage of the monopolist is given by (b -pIsh), and it declines when the price-quality heuristic is stronger (See Figure 3.4). Recall that as 8 increases, the monopolist will respond with an increase in price. Simultaneously, this induces a higher level of perceived quality. However, the corresponding increase in true quality is not enough to offset the overall negative impact of the price increase. Thus some consumers with lower willingness to pay will not buy. 30 Figure 3.4: The Effect of the Strength of The Price-quality Heuristic on Market Coverage (a= 1, 5S = 0.5) 0.2E-0.24^  \ ^ Market Coverage 0.22: .0,2-•0;1B-0:16 X X .0.14- \ \ 0.12; \ \ 0 : 0-2-'.-•'•••.M deltal'°-'B • 0 8 " 1' 8 P £ = 0.8 3.4 The Cost Of Ignoring The Price Quality Heuristic A natural question one may ask, then, is what happens if the real situation is one where consumers use the price-quality heuristic in an imperfect information world, as many behavioral studies suggest, but the monopolist ignores this heuristic and proceeds as if consumers care only about true product quality (8ss), as most of the existing models do although they assume 8S = 1. It will be sub-optimal, but to what extend does this depend on factors such as 8p and 8S ? To examine this question, we compare the results derived in Section 3.3 with those derived if one had assumed quality only information (i.e., U =tSss-p). 31 Recall that with quality only information, the monopolist's market-not-covered solution is to sell quality bds /(3a) at price 2b2Ss2 /(9a), provided that b>3a/2. Let us * * denote these solutions by qt and pt . If the true world is such that consumers are not fully informed about quality and use the price-quality heuristic, this strategy wi l l lead to a sub-optimal profit level Kh(q*,p*t) where subscript h indicates a heuristic/imperfect information world. The degree of sub-optimality in 7th(q*,p*t) turns out to be nonlinear in both the price-quality heuristic and the true quality information. Specifically, the degree of sub-optimality (measured by the difference between 7th(q*,p*) and 7Th*, the optimal profit level the monopolist can achieve by acknowledging the heuristic world) is most severe when Sp is very large 7. This sub-optimality is made more severe when Ss is very large. Figure 3.5 plots the situation for Ss = 0.5. Figure 3-5: Sub-optimal Profits When Failing to Consider Price-quality Heuristic (ft = 0.8, a= 1,8,= 0.5) .0.03-/ * / 7lh .0:025-0 02-0 01- 7C h(Pt¥ ,S t*) o:op5- TkiPt , s t ) ti:'; :V'W\';'•'.'••:'d,'4'-' UB : " 0.8' ' 1 7 With the inclusion of price into the perceived quality level, this creates a demand shifting effect. The difference in profit levels between 7tt (pt, st ) and 7th (qt ,pt), as in Figure 3.5, accounts for this effect. 32 The factor that drives this result is, of course, how different a monopolist's assumption of the consumers' utility function is from the real imperfect information world. In an imperfect information world, consumers shift some of their judgment basis from the true quality information to the price-quality association. In essence, firms assume consumers have U=tSss-p when in fact they have a utility of U - t(Spp + Sss) - p in an imperfect information world. The above results show the degree to which a monopolist achieves sub-optimal profits when using only a true quality information strategy in an imperfect information world. A firm that fails to recognize that consumers adopt the price-quality heuristic will certainly follow sub-optimal strategies and be less profitable than firms that acknowledge that. When consumers emphasize the price-quality heuristic (dp ~ 1), the difference in profitability for such a firm can be substantial. 3.5 The Role of Non-price Advertising As shown in Figure 3.6, the optimal profit (n*h) increases as the intensity of the price-quality heuristic effect (measured by 8p) increases. This happens because as Sp increases, the optimal price increases at a rate that is faster than the rate of quality increase (and thus the cost associated with it), resulting in an increasing profit margin that more than compensates for the drop in demand. Similarly, as the true quality information improves (i.e., Ss increases), 7t*h also increases. However, the extent of such improvement is constrained by the magnitude of the price-quality heuristic. When 8p is high, a small increase in 8S will cause the 33 monopolist to improve its quality by a small amount, and then charge a much higher price. A very high profit level is then obtained. In this case, price and quality are actually increased proportionally resulting in no drop in market coverage (See Table 3.1). When 8 is low, the monopolist's ability to increase optimal profits for a higher 8S is much more limited. These results are shown in Figure 3.6 by the optimal profit curves with different slopes; higher 8 results in steeper curve for n*h. Figure 3.6: Optimal Profits As a Function of $ = 0.9 From Equation (la) From Equation (1), 6 — 0.6 34 Table 3.1: Analysis of Optimal Profits As 5p and 8S Changes:-Rescaled Values Reliance on the Price-Quality Heuristic Quality Knowledge 8p=0.1 8P=0.5 8P=0.9 88=0.1 p=0.022 s=1.51 margin=0.227 coverage=100 n=0.092 p=0.065 s=2.55 margin=0.06 coverage=74.3 n=0.195 p=1.23 s=ll.ll margin=1.23 coverage=24.76 n=i.23 5S=0.5 p=0.57 s=7.54 margin=0.57 coverage=100 n=2.29 p=1.62 s=12.8 margin=l .6 coverage=74.3 n=4.86 p=30.86 s=55.56 margin=30.86 coverage=24.76 n=30.9 8S=0.9 p=1.84 s=13.57 margin=1.84 coverage=100 n=7.44 p=5.25 s=22.5 margin=5.25 coverage=74.3 n=15.75 p=100 s=100 margin=100 coverage=24.76 n=ioo 35 The implication of this result is both managerially relevant and empirically testable. The magnitude of Ss captures the extent to which the true quality information is available to the market. While there are a number of information sources that may influence Ss, such as word-of-mouth and publicity, the main marketing tool is non-price advertising. Assuming advertising is effective, a higher level of non-price advertising will result in higher consumer awareness. Therefore a firm may influence the magnitude of 8S through its expenditure on non-price advertising. The relationship between 8S and 7t*h, which is constrained by Sp, implies that in a market where the price-quality heuristic is strong, the monopolist will tend to spend more on non-price advertising to achieve greater profits. As we indicate below, this proposition can be empirically tested. The results illustrated above assume that non-price advertising is affordable. As we believe this is a reasonable assumption, we will include an advertising cost function in the objective function of the monopolist and determine the impact of advertising cost. Consider the case where Ss (the proportion of true quality information available to consumers) is determined by the level of non-price advertising. The monopolist's profit function with advertising cost is given by n = (p-as2)(b-t,)-g(Ss) Cl) where t\ is the lower boundary of the market served by the monopolist and ^(^is a convex advertising cost function. Assuming that g{Ss) is properly scaled, (7) can be solved from t1sh— p = 0. Solving the equations analytically, and retaining the assumption that 0 < 8S < 1, we obtained results as in Figure 3.7(a), which assumes a (convex) power function g(8s) = /3{8s + P2S*, while Figure 3.7(b) assumes g(Ss) - -yln(l- Ss), adopted from 36 Meurer and Stahl (1994). Depending on the convexity of the advertising cost function, the profit curves yield optimal^ at different levels. In both situations, the maximum profit is achieved at a higher level of Ss when Sp becomes higher. Figure 3.7: Optimal Profits As a Function of Ss (Advertising Cost Function) (/?, = 0.001, & =0.05, y = 0.007) Based on our analysis of these two advertising cost functions, we conclude that the monopolist will find it optimal to invest in non-price advertising (i.e. to increase 8S) especially for product categories where the price-quality heuristic is high. We will empirically test this proposition in Chapter 4. 3.6 Welfare Implications In this section we examine whether considering the price-quality heuristic in a positioning model brings new insight for welfare issues. We will first look at the efficient solutions that a social planner would adopt, and then compare it with the monopoly solutions. 37 3.6.1 Efficient solution and welfare The efficient solution maximizes the total surplus in the market. For consumer t the total surplus amounts to ts-as2 (since consumer surplus is ts - p and the producer surplus is p-as2). The efficient product for consumer t is thus the product s/he will choose if all feasible products were sold at marginal cost. The aggregated total surplus is given by Recall that with quality only information, tx =p/Sss, and under imperfect information, r, = p I sh. Although the total surplus for any individual consumer is not affected by price, the aggregate total surplus in the market-not-covered case is. Indeed, this total surplus will decrease (and a smaller market will be served) when the price increases. The efficient solutions are as follows. The market is not fully covered when b>3a. The optimal strategy a social planner takes is to set pe = 3b2Ss /[9a(3-bSp)] and se =b/(3a). This leads to 2b/3 of the market being covered. As expected, the market is more likely to be covered in the efficient solution than in the monopoly solution. This reflects the social planner's focus on total welfare, as opposed to the monopolist's sole interests in its profits. Rather than taking into consideration how many consumers are served, the monopolist chooses to position its product to extract greater surplus from consumers who have higher willingness to pay. b (8) 38 Figure 3.8 plots the level of surpluses that the efficient solution provides. Interestingly, the total surplus is entirely independent of whether the consumers adopt the price-quality heuristic or not. This suggests that from a social planner's point of view, to what extent the consumers infer quality from price is not a major concern. The social planner is shifting surplus between the consumers and the firm when Sp changes. In Figure 3.8, the change in consumer surplus is accompanied by an equal amount but opposite change in firm profits. Figure 3.8: Welfare Implication of the Efficient Solution (b = 1, a = 1) 0.12.1 £s = 0.8 4 = 0.5 The dependence on the price-quality heuristic turns out to be a negative strategy for the consumers, even in the efficient solution. Figure 3.8 shows that regardless of the weight on true quality information, consumer welfare decreases as Sp increases. This occurs because the social planner has to shift some surplus to the producer to maintain total welfare. If it does not do so (i.e., if it does not allow the producer to increase price 39 to take advantage of the greater price-quality heuristic), the gain for consumers will be insufficient to compensate for the loss for the producer. Moreover, the degree of this welfare shift depends on 8S. The higher the 8S, the more significant this shift becomes. Indeed, the producer will be allowed to make positive profits only when both 8p and Ss are high. If we look at the level of consumer surplus for different values of 8S (Figure 3.8 shows the comparison between 8S = 0.5 and 8S = 0.8), it appears that consumer surplus is lower overall when 8S is higher. That is, consumers are worse-off when they know more about the true quality! The reason for this unexpected result is that when consumers are more informed, the producer tends to enhance quality. Then the surplus allocation between them results in a very high price level, which leads to a greater gain for the producers and a corresponding loss for the consumers. The total surplus if computed using perceived quality is given by b j(tsH -as2)dt (8a) h Figure 3.9: Welfare Implication of the Efficient Solution with Perceived Quality , (b = l . q = I) , 0:044-0.4L . 0.3; .6:642-• 0;04: ;;0:038; /0;1r T S u , D.;sisSiP 2;/,;'';;;:/.;.j.qy''''' ' ;'B';x/:';'Vv0'8:'''':':.: ; 0" 8, 0.2 ' 'o'4 ' 0.6 ' •  0.B " A 40 From Figure 3.9, the main difference between solving with SH in the objective function is that the total surplus and consumer surplus increase as Sp increases. This is due to the higher price and quality level at high Sp which in turn lead to a higher level of perceived quality and total surplus. 3.6.2 Profit maximization and welfare As discussed in pervious sections, a monopolist will earn greater profits when either Sp or Ss increases. Our analysis of the welfare results further indicates that this greater profit comes at the expense of consumer welfare; consumer surplus unambiguously decreases when Sp increases. Because of the different objectives of a social planner and a profit-maximizing monopolist, the degree of this change is greater than that of the efficient solution, Figure 3.9: Welfare Implication of the Monopoly Solution (b = 0.8, a = 1) 0.06-Consumer Surplus 0.05-0.04-/ CS„(pT,sT) (Non Heuristic Solution) 0.03-0.02-CSH (Heuristic Solution) 0.01 - • — C S | i with Su in obj I ' m i . l i n n 0 WW* .1 _ Ii _ A 0.5 0.6 = 0.5 • ' i ' ' i,.'o (Heuristic Solution) Ii./ U.o 41 If the optimal solution in the quality only information world (i.e., qt and pt ) is applied to the imperfect information world, total surplus is higher than if the monopolist * * applies the heuristic-based solutions (qh and ph ), especially when the price-quality heuristic effect and the true quality information effect are comparatively high (See Figure 3.9) . For the monopolist, although it will earn sub-optimal profits if it adopts the non-heuristic strategies, consumers will benefit from such a "mistake." That is, compared with the case in which the monopolist adopts the heuristic strategies, consumer surplus increases when the non-heuristic strategies are applied to markets where consumers use the price-quality heuristic. Solving with SH in the objective function, the consumer surplus is the lowest because of the higher price associated with a higher Sp and profit level. Furthermore, consumers served by a profit-maximizing monopolist are not necessarily better-off if more true-quality information is available. If there is very limited amount of true-quality information, more of it will enhance consumer welfare. If there is already a fair amount of true-quality information, more of it will actually decrease consumer welfare due to a corresponding increase in true quality and price (See Figure 3.10) . In either case, the monopolist will earn more profits. The consumer surplus in the heuristic world is also always lower than in the quality information only world as when firms know that consumers utilize the price-quality heuristic, price could be raised higher resulting in more sacrifice for the consumer. 42 Figure 3.10. Higher 8S Need Not Make Consumers Better Off in a Monopoly Solution (ft = 0.8, a = 1) 0.012; Consumer / \ 0.01- Surplus .. / : \ 0.008: / \ 0.005 : / 0.004; 0.002; ' ' ' o.Y ' ' 0.2' ' ' 0.3' ' ' b.4 '•' o.'s' '. ' b.'e' ' ' b> 4 = 0.5 3.7 Summary The judgmental heuristics that consumers adopt in decision-making should play an important role when firms decide on market strategies. Firms generally do not use price as a signal of objective quality, as evident by existing literature, and consumers are probably not wise to solely rely on price as an indicator of the true quality. We deviate from the signaling approach of objective quality through price and focus on the behavioral primitive of the consumers. In this chapter, we examined the effect of the price-quality heuristic on a monopolist's quality and price strategies. Based on existing behavioral findings, we conjecture that consumers perceive the quality of a product by looking at its price level and also any information about the true quality. Research 43 suggests two alternative approaches as to how the perceived quality effect can be modeled. One allows for the dependence of the reliance on the price quality heuristic on the availability of true objective quality information while the other acknowledges the existence of schemas that are inherent and stable in the consumers. As we show, the main findings are similar for both cases. Together with the degree of consumer heterogeneity in willingness to pay for quality, the price-quality heuristic effect and availability of true quality information influence the price, quality, and welfare levels. In brief, the greater the consumers' reliance on the price-quality heuristic, the higher the price and the quality that the optimally behaving monopolist wi l l provide. If a monopolist ignores the market condition that consumers refer to price when forming the perceived quality, the monopolist w i l l achieve suboptimal profits, the extent of which depends on the reliance on the price-quality heuristic and the amount of true information available. We also find that higher reliance in the heuristic motivates the monopolist to invest more heavily on non-price advertising, which enhances the true quality information effect, in order to receive greater profits. This is however constraint by the magnitude of the price-quality heuristic. These results were obtained when the parameters for price and true quality information are independent or at most, mildly dependent. We had also assumed that advertising is affordable. Even when the advertising cost is included in the objective function, it does not alter the main findings. We wi l l empirically validate these results and our conjecture of the price and true quality information parameters in the next chapter. 44 Interesting welfare implications are also obtained. Higher dependence on price in an efficient solution and higher availability of true quality information in a monopoly solution may actually hurt consumers. 45 Chapter 4 The Role of Non-price Advertising When Consumers Use the Price-Perceived Quality Heuristic: An Empirical Study 4.1 Overview In this chapter, we examine the relationship between the price-perceived quality heuristic and investment in non-price advertising. The motivation for this study comes from one of the analytical results obtained in chapter 3. Specifically, a firm's profitability varies with the strength of the price-perceived quality heuristic, and this variation is constrained by the availability of true quality information. As Figure 3.6 shows, optimal profits increase when Ss (the parameter for the availability of true quality information) becomes higher, and the rate of this increase is greater when Sp (the price quality heuristic) is larger. The primary reason for this result is that as Ss increases and 8p is high, the profit margin increases without loss of coverage (See Table 3.1). The high values of 8p enable the firm to charge a high price for high quality, and consumers still purchase it. However, at lower levels ofSp, some consumers no longer want to 46 purchase a high quality product, even i f the price is not raised in proportion to the quality increase. These results always hold when the price factor and true quality information, combined to form the perceived quality levels, are either mildly dependent upon each other (i.e., as in equation (l),sh = 8p(\-68s)p + Sss, f?<~0.65, see footnote 4) or completely independent from each other (i.e., as in equation ( la), sh = 8pp + 8ss). If they are strongly dependent (i.e. 0 >~ 0.65), optimal profits still increase as 8S becomes greater. However, different from the case when 6 is moderately low, the rate of this increase becomes greater the lower 8 is. The reason this reversal of pattern occurs is that a strong correlation between the effects from price and true quality damps the effects of 8p; in the extreme where 6 = 1, 8p loses its impact entirely when the true quality information approaches perfect information (i.e., as 8S approaches 1). Figure 4.1 provides an illustration of the optimal profits where 6 is very high at 0.9. It shows that the lower 8„ gives a higher marginal rate of change in profits ( ^  H ) when 8S is high. _ . , z _ „ SLVH SLVH 8TI*H , For example, when os =0.8, > > . In comparison, higher 8 leads to a higher marginal rate of change in profits as 8S increases in Figure 3.6, when 6 is not very high. 47 Figure 4.1 Optimal Profits As a Function of Ss when 6 = 0.9 0.02-i 0.0181 o.oi 6-; y Sp = 0.9 /% <$ = 0.5 / <5j, = 0.1 0:014^  0.012-0 01 6.008-0:006^  0.004-0:002." 0^  • os "8. One of the managerial implications of these results is that a firm will find it more profitable to invest in non-price advertising (i.e., to reveal more information about the true quality, thus to increase 8S) in a market where the price-perceived quality heuristic is stronger (i.e., a higher 8p), compared with the case where Sp is lower, if the use of price to infer quality is independent from or at most, mildly dependent on the amount of true quality information. That is, the use of price-perceived quality heuristic is more of an intrinsic behavioral tendency by consumers, not entirely the consequence of being unaware of true quality levels. On the other hand, if the use of price-perceived quality heuristic is essentially derived from the lack of quality information, then a firm will find it more profitable to invest in non-price advertising to enhance Ss when the overall level of the price-perceived quality heuristic is weaker (i.e., a lower Sp). As we discuss in detail in the following paragraphs, there are reasons, both theoretical and empirical, to support either direction. Then, from a managerial point of view, what should be the optimal strategy of advertising becomes an empirical question, 48 and the answer, not surprisingly, is likely to be dependent upon specific markets or industries. As a result, these patterns that uniquely link optimal strategy to parameter values provide an interesting opportunity to empirically examine whether firms invest more in non-price advertising when the price-perceived quality heuristic is stronger or weaker. If the finding shows that the advertising expense is greater when Sp is larger, then it provides additional (and empirical) support for the conjectures in equation (1) and (la) (i.e., entirely independent or at most, mildly dependent parameters), at least for the markets that are empirically examined. At a more general level about perception and stimuli, there is agreement among researchers that "perception depends not only on the physical stimuli but also on the stimuli's relation to the surrounding field and on conditions within the individual" (Kotler 1997, p. 185). In the context of price-perceived quality heuristics, this suggests that there is more to perceived quality than the information about true quality itself. Earlier research has identified correlations between perceived quality and a few extrinsic factors such as price levels (Scitovsky 1945, Jacoby and Olson 1985, Gorn, Tse and Weinberg 1991), brand name (Andrews and Valenzi 1971, Jacoby, Olson, and Haddock 1971), and store name (Wheatley and Chiu 1977, Szybillo and Jacoby 1972). For instance, Gorn, Tse and Weinberg (1991) study the negative effects of zero price (free) and exaggerated prices on perceived quality of services, and find that when the tested services are offered for free and for exaggerated prices, they are perceived as lower in quality than when they are offered in a normal price range. The explanation for these correlations, not 49 surprisingly, needs to go beyond the availability of information and look at intrinsic consumer behavioral tendencies. Relatively little attention has linked advertising spending to perceived quality levels, with the notable exceptions of Kirmani and Wright (1989) and Kirmani (1990 and 1997). In these studies, the authors find a positive relationship between perceived advertising expense and perceived quality using laboratory experiments. More recently, Moorthy and Zhao (2000) further add to this literature by showing the effect of advertising on perceived quality. They find that advertising expenditure and perceived quality are generally positively correlated even after accounting for objective quality, price and market share - for both durable and nondurable goods. This empirical study intends to extend the existing studies in the following ways. First, our study goes in the opposite direction of Moorthy and Zhao (2000): we test the (positive/negative) effect of 8 on firms' spending on non-price advertising, as a result of strategic optimization behavior. Second, we use market data that include a number of established brands and their advertising expenditures. Third, the data set we use enables us to control a number of important factors related to firms' behavior, namely market share, market size, firm size, and the popularity of brand name. The existing studies, as discussed in detail below, suggest that these variables play a role in advertising decisions, and thus should be controlled as covariates. Finally, a few studies such as Gerstner (1985), Dodds, Monroe and Grewal (1991), and Zeithaml (1988) have found that list price, durability, and ease of evaluation of the product categories appears to have significant impact on the levels of perceived quality. As a result, we incorporate these 50 factors in the empirical specification to examine the effect of the price-perceived quality heuristic on non-price informative advertising. 4.2 Hypothesis and Model The theoretical results from the third chapter (and the first section of chapter 4) suggest that a strategically-behaving firm will want to control the availability of the true quality information available to consumers. A primary way of doing so is through non-price advertising. Further, it is found that the optimal amount of advertising expenditure should be positively correlated with the magnitude of the price-perceived quality heuristic, if such magnitude is not strongly influenced by the amount of true quality information. That is, if the price-perceived quality heuristic is primarily an intrinsic consumer feature and not highly dependent upon a consumer's real knowledge about a product's objective quality. IT the degree of such dependence is very high, then we should observe a negative correlation between advertising expenditure and price-perceived quality heuristic. As we discuss earlier in the thesis, numerous studies have found that the use of price-perceived quality heuristic is a behavioral primitive, goes beyond the consequence of information availability, and can be product and market dependent. These findings will be further supported by this study if our empirical study shows that advertising expenditure and the price-perceived quality heuristic is indeed positively correlated. As a result, we use the following as the major hypothesis: H i : Firms invest more in non-price advertising in markets where belief in the price-perceived quality heuristic is higher. 51 We test this hypothesis using advertising expenditure for a number of established brands. In addition to the price-perceived quality heuristics, it is necessary to control other variables that existing studies have shown to influence advertising spending. These include the size of the market, the size of the firm in terms of annual sales, the market share of the firm, the brand name perception and whether the firm is primarily engaged in that product category. Below we summarize a few studies that found specific correlations between these factors and advertising, and then provide further hypothesis. Nelson (1974) and Schmalensee (1978) found that better brands spend more on advertising especially when consumers respond to advertising. Dodds, Monroe and Grewal (1991) and Zeithaml (1988) suggest that products that are harder to evaluate will invoke a price-perceived quality heuristic. Gerstner (1985) and Lichenstein and Burton (1989) have indicated that quality-price relations are product-specific, with frequently purchased items displaying weaker relations than non-frequently purchased items. As a result, the secondary hypothesis for this study will be: H2: Consumers will more strongly adopt the price-perceived quality heuristic for items with higher market prices. H 3 : Consumers will more strongly adopt the price-perceived quality heuristic for items which have a lower frequency of purchase. H 4 : Consumers will more strongly adopt the price-perceived quality heuristic for items which are difficult to evaluate. To test our hypotheses, we use a 2 stage cross-sectional regression to estimate the model specified at the brand level as price-perceived quality perception is influenced by prices of the products, the frequency of purchase for the products and the ease of evaluation of the products; factors which are exogenous to the advertising budget. 52 Doing so allows us to correct for bias due to the endogeneity of the price-perceived quality perception on advertising budget. For the first stage regression, the dependent variable is the price-perceived quality association and the independent variables are market price, frequency of purchase and the ease of evaluation of the product in that category. The first stage model is specified as: Spi =/3Q+/3lPi + B2FQt + &EVAL, + e{ (9) 8 i is the category Spi is category i's price quality perception level Pj is category i's average market price for medium size products FQj is category i's frequency of purchase EVALj is category i's ease of evaluation For the second stage regression, the dependent variable is the advertising budget and the independent variables include the predicted price-perceived quality level, market share, total market size, firm size (annual sales) and brand quality perception at the brand level. The second stage model is specified as: A]k =/}4+/]5MSjk + 06MTk +j31 SP + ejk (10) Ajk = /34 + (35MSjk + &MTjk + B1 SP + fitPRIj + 09Bj + /310F;+£jk (10a)9 where we have omitted the category subscript to avoid clutter. Here j is the brand 8 Another first stage unrestricted model that was specified and tested involved interaction terms of the main effect variables. A test o f the restricted model versus the unrestricted model (F2,379=1.4605<4.68) shows no significant differences between the two models. Furthermore, existing theories do not provide an explanation for the interactions. 9 A s the model in equation (10) is not significantly different from the model in equation (10a), we wi l l apply the parsimonious model for the regression. 53 k is the year of data Ajk is brand fs advertising spending for year k MSjk is brand fs market share for year k MTk is total market size for year k is brand fs firm size in terms of annual sales for year k PRIj dummy variable to indicate whether brand j is the primary brand of firm is brand fs quality level perception sP is category predicted price quality perception level from stage 1 The correspondence between our hypotheses and the coefficients of the model is summarized in Table 4.1. Table 4.1 Tests of the Hypothesis Hypothesis Test Hi /?7>0 H 2 A > o H 3 /?2<0 H 4 In all the regressions, a plot of residuals versus the independent variables was used to check for heteroskedasticity. All plots of residuals against independent variable (See Figure 4.2) except for Market Share are approximately symmetric around zero and indicated that all the independent variables do not demonstrate any heteroskedasticity. 54 To test whether heteroskedasticity does exist for Market Share, we performed a White's test10 and the results provided no evidence of heteroskedasticity for Market Share. Figure 4.2 Sample Plots of Residuals vs Market Share, Primary Business and Brand Quality m Market Share i •2 0.0 .2 Primary Business .6 & 1.0 1.2 °! lis I ' " " I "8 4.3 Data Our study involves a regression analysis on both secondary and primary data. Secondary data was collected from sources like Advertising Age, Standard and Poor's Industrial Survey and Hoover's Annual Reports. Our preliminary search found 250 brands in over 35 product categories. As the theoretical results from the third chapter support the hypothesis that firms invest more in non-price advertising especially for markets in which the price-perceived quality heuristic is important, we chose product categories that involve predominantly non-price advertising and very little price advertising (eg. Athletic Footwear and Shampoo). As we are interested in price-perceived quality perceptions, product categories that primarily involve the horizontal differing tastes of consumers were excluded (eg. Soft Drinks, Cigarettes, Beers) too. Product categories that may not be familiar to the subjects (eg. RX prescription drugs) 1 0 The White's test is usually used as a test for heteroskedasticity. In this test, a regression of the squares of the residuals is run on the variables suspected of causing the heteroskedasticity, their squares, and cross products. When n*R2 < %2, we fail to reject the null hypothesis. 55 were excluded as well. Eventually we were able to shortlist 10 categories in which our major requirements are met. A pilot test was conducted in which 37 subjects completed a questionnaire which included 15 brands in 5 product categories out of the possible 10. Subjects were students and staff members of the university and were invited to complete one questionnaire each. They were also told to write any questions or suggestions they have pertaining to completion of the questionnaire. Preliminary results from this survey indicated that the theoretical hypothesis from the third chapter is supported; however, we were not able to replicate two of the relationships in extant literature between price and price-perceived quality perception as well as ease of evaluation and price-perceived quality perception. This could mainly be attributed to the limited subject pool and product categories. One product category, cereals, was found to be unsuitable as the price-perceived quality and brand quality perception were susceptible to differing tastes among the subjects rather than the true perception measurement. Some other examples of minor problems in the pilot tests include not labeling the center point of the 9 point scale as "neutral" and excluding purchase by "other family members" in measuring the frequency of purchase as products like toothpastes or shampoos often could be purchased by another member of the respondent's family. Subsequently for the full test version, we targeted to increase the subject pool to a total of 100, expanded the product categories under survey to all the categories that have been short listed and dropped the "Cereals" category. All these product categories are also likely to be used and/or owned by the subjects in addition to the primary constraint that advertising for such categories is primarily non-price in nature. All the reported 56 minor problems were addressed and fixed so as to obtain more accurate responses from the subjects. Although we had a sign up of about 90 participants eventually, due to events beyond our control, about 15% were unable to show up. The survey was conducted in a laboratory among 77 Commerce undergraduate students. The respondents were randomly assigned a questionnaire to complete. There were 10 versions of the questionnaires each having 5 different product categories (15 brands) out of 9. Measures within categories were also randomly ordered to reduce order effects. Price-perceived Quality Perception. We measured consumers' price-perceived quality perception directly through a laboratory survey. The respondents filled out a questionnaire asking their level of agreement with the statement, "For (a product category), the higher the price of the product, the higher the quality of the product" (9 = strongly agree, 1 = strongly disagree) for each product category (cf. Lichtenstein and Burton 1989 and Peterson and Wilson 1985). Two other measures that assess the respondent's opinion of price to overall quality of the product category are also included to determine overall reliability in this construct, namely:- "To what extent do you think that price reflects/is a reliable indicator of the overall quality of (product category) prior to purchase" (9 = very well/reliable, 1 = Not at all). Respondents also reported their confidence in their judgments (on a 9 point scale). Pechmann and Ratneshwar (1992) suggested that both the content of a person's belief and the strength of that belief could be important independently. Adopting Moorthy and Zhao (2000) approach, we use the confidence data to weed out judgments where the respondent was not confident. This method of eliminating doubtful data is used for all subsequent measures in the 57 questionnaire. Only ratings where the subject was at least 50% confident will be retained and used in the analysis. For all constructs that had multiple measures, the average of the three measures will be computed and recorded. For eliminated data, we will enter the final sample average to substitute the weeded data. Market Price. We obtain the average product category price by sampling a few prices of the mid-size range products for bath tissue, shampoo, toothpaste, laundry detergent, diapers and paper towel. For athletic footwear, PDA and toothbrush we sample a few prices for models in the mid-tier range for other categories. Prices were obtained from the local grocery store as well as from online sources. As the analysis involved prices in different years, we assume a 5% inflation and derived the prices over the years from 1995 from the 2002 price. This is reasonable as we are only concerned about the product category price ranking rather than absolute figures. Prices were converted to USD at a rate of 0.65. Frequency of Purchase. This measure is an indication of the durability of the product category and is obtained directly from the respondents. They are to indicate on an interval scale how often they or their family purchase products in the category (1 implies "once in a few years" while 9 indicate "once in a few days"). If they or their family do not purchase products in that category, another similar question follows in which they are asked to enter their views about how often others purchase those products in the category. 58 Ease of Evaluation. The ability of the respondents to evaluate the product category prior to purchase was measured by having the subjects indicate their level of agreement with the statement, " For (Product Category), it is very difficult to evaluate quality in this product class prior to purchase" (9= strongly agree, l=strongly disagree) for each product category (cf. Lichtenstein and Burton 1989). The first question is reversed scored as the next two other questions pertaining to respondent's ability to assess the overall quality are presented with the higher number indicating ease of evaluation; "To what extent are you able to assess the overall quality of (product category) prior to purchase?" (9 = Very Able and 1 = Not at all). The three measurements will be validated for reliability in this construct (Table 4.5). Advertising Spending. Annual advertising spending data are obtained from Advertising Age for the years from 1995 to 2001, availability depending on the brand and product category. For certain brands, advertising expenditures are missing for certain years while others are recorded as zero as the amount is not substantial. To be consistent in our regression, we chose brands in a product category where all brands have the same data for the same number of years. As some parent companies have multiple brands, to avoid repeated data in Market Share and Firm Size, we randomly chose 3 brands of different parent companies (when possible) for the 9 product categories resulting in a total of 27 brands. Market Share, Total Market Size and Firm Size. Between-firm factors such as the market share and firm size are also controlled in the model. Market Share data are 59 collected from Advertising Age starting in 1995 at the brand level. Some brands do not have data available for some years and we will include whatever is available for those brands. For Firm Size, data is collected from Standard and Poors' Industrial Survey and Hoover's annual reports to correspond with the available Market Share data from 1995 to 2001. A reasonable representation of firm size is total annual sales of the parent company owning the brand. Total Market Size is extracted directly. To control for the multiple offerings of big parent companies, another parameter PRIMARY is introduced to indicate whether the brand is the primary brand for the parent company. Primary Business. This is a dummy variable to control for multiple offerings within a firm. When the brand in question is the main brand for the parent company, PRIMARY will be 1 and 0 otherwise, (eg: PRIMARY = 1 for Nike Shoes from Nike Corp, while PRIMARY = 0 for Pampers from Proctor and Gamble.) Brand Quality. This is a measure capturing the consumer's overall evaluation of the product at the brand level. We adopt a 3 item 9 point scale (Kempf and Smith (1998) p.329 & 332, MacKenzie and Lutz (1989) and Smith (1993)) that requires the subject to indicate whether their level of brand quality perception is Bad/Good, Inferior/Superior and Unfavorable/Favorable. As mentioned earlier, the respondents also reported their confidence in their judgments (on a 9 point scale). In total, we selected 27 brands over 9 product categories which largely utilize non-price as compared to price advertising and in which data for a few years are available for the previous variables mentioned. 60 4.4 Results Descriptive statistics on the nine product categories are given in Table 4.2. Table 4.2 Descriptive Statistics Product Average Price for Mid Years Data Categories Size/Tier Product (USD) Available Athletic Footwear 42.03 1996 44.14 1997 Bath Tissue 3.58 1995 3.76 1996 Shampoo 1.95 1996 2.05 1997 PDA 247.51 2000 Toothpaste 1.16 1996 1.22 1997 1.34 1999 1.41 2000 Toothbrush 1.99 1999 Laundry Detergent 4.81 1999 Diapers 6.77 1995 7.11 1996 8.64 2000 9.07 2001 Paper Towel 1.79 1995 1.89 1996 Tests were also performed to check the reliability and discriminant validity. Table 4.3 lists the Cronbach's alpha for the 3 constructs (Price-perceived quality perception, Ease of evaluation and Brand quality perception) and is a good indication of the reliability of the measures. From Table 4.4, we can also see that the Factor Analysis with Varimax rotation revealed three distinct components for all the measures thus indicating good discriminant and convergent validity for the constructs. 61 Table 4.3 Cronbach Alpha Values Construct a Price-perceived quality perception 0.9303 Ease of Evaluation 0.9105 Brand Quality 0.9219 Table 4.4 Exploratory Factor Analysis Rotated Component Matrix 1 2 3 PQ 1 0.919 PQ 2 0.942 PQ 3 0.916 EVAL 1 0.881 E V A L 2 0.929 EVAL 3 0.918 BRAND 1 0.930 BRAND 2 0.935 BRAND 3 0.927 Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 4 iterations. b Values that were less than 0.30 were dropped 4.4.1 First Stage Analysis Table 4.5 shows the regression results for the first stage analysis. For the first stage analysis, the data consist of 77 (subjects) * 5 (categories) = 385 unique primary observations. The predicted price-perceived quality perception value will be combined by taking the average so as to get industry-specific estimates in the second stage analysis. This will remove individual differences. With category price-perceived quality perception as the dependent variable, the main effects of market price, frequency of 62 purchase and ease of evaluation of the product are found to be significant. For price, the positive coefficient indicates that for product categories with higher market prices, price-perceived quality perception is more important. The negative coefficients for frequency of purchase and ease of evaluation of the products means that firstly, for product categories that are purchased more frequently, the price-perceived quality perception wi l l be lower and secondly, for product categories that are easier to evaluate, the price-perceived quality perception wi l l decrease as well. The F value for this model is significant and the adjusted R 2 is 0.444. Thus the results obtained support H 2 , H 3 and H 4 . Table 4.5 Effects of Market Price, Frequency of Purchase and Ease of Evaluation of Products on Price Quality Perception (Restricted Model). Dependent Variable = Price-perceived quality Perception Coefficient t-value (Constant) 8.319 38.027** Price 5.497E-03 7.772** Frequency of Purchase -0.187 -2.850** Ease of Evaluation -0.436 -9.087** N 385 Adjusted R2 0.444 F 103.3** **indicates significance at the 1% level. No evidence of heteroskedasticity was found as well from a White test. 4.4.2 Second Stage Analysis The results of the second stage regression based on the combined category average of the predicted price-perceived quality perception (see Table 4.6) obtained from the first stage regression along with other control variables are shown in Table 4.7. 63 Table 4.6 Category Average Predicted Price-Perceived Quality Values Category Predicted P-Q Average PDA 7.44 Athletic Footwear 7.17 Shampoo 6.34 Toothpaste 5.98 Diapers 5.68 Toothbrush 5.37 Paper Towels 5.17 Bath Tissue 5.00 Laundry Detergent 4.84 *9-point scale There are 9 (industry-level estimates for the categories) * 3 (brands) * 2.1 (average number of years) = 57 unique observations. The F value for this model is significant and the adjusted R 2 is 0.442. The coefficient for price-perceived quality perception (predicted) is positive and significant after controlling for between f irm factors, thus supporting hypothesis H i . Market share and Total Market size also have similar effects and these suggests that firms which have a bigger share or when the market is bigger in size, w i l l spend more on non-price advertising. The most parsimonious model is used as other control variables like brand quality perception, f irm size and primary business do not improve the model significantly. 64 Table 4.7 Effects of Price Quality Perception, Market Share, Firm Size and Brand Quality on Advertising Spending (Restricted Model). Dependent Variable = Advertising Spending Coefficient t-value (Constant) -72.38 -17.099** Market Share 0.980 25.268** Price-perceived quality (predicted) 12.597 2.714** Market Size 4.336E-03 2.387* N 57 Adjusted R 2 0.442 F 15.757** **, indicates significance at the 5, 1% level. No evidence of heteroskedasticity was found as well from a White test.. Table 4.7 (a) gives the results from the unrestricted model. As the F value for the „ (0.477 - 0.442) 1(6-3) two models, F, s n = — = 1.115 < 4.20 at 1 %, we fail to reject the null 3 5 0 (l-0.477)/(57-6-l) implying the two models are not significantly different. In view of a parsimonious model, only results from the parsimonious model as in equation (10) are discussed. 65 Table 4.7(a) Effects of Price Quality Perception, Market Share, Market Size, F i rm Size, Primary Business, Market Share x F i rm Size on Advertising Spending (Unrestricted Model). Dependent Variable = Advertising Spending Coefficient t-value (Constant) -93.16 -3.133** Market Share 1.286 3.675** Price-perceived quality (predicted) 9.865 1.786** Market Size 4.903E-03 2.580* Firm Size 8.33E-04 2.032* Primary Business 26.803 2.321 Share x Firm Size -5.32E-07 -0.031 N 57 Adjusted R 2 0.477 F 9.519** **, *indicates significance at the 5, 1% level. No evidence of heteroskedasticity was found as well from a White test.. 4.5 Summary Gerstner (1985), Dodds, Monroe and Grewal (1991), Zeithaml (1988) found that there exists a relationship between the product market price, frequency of purchase and product ease of evaluation to price quality perception. As a secondary finding to our main investigation, our secondary hypothesis results are able to replicate those of earlier studies and thus reduce the issue of external validity of our primary data collection through a questionnaire and contributed to the generalization of existing theory. Our results from the analysis of 9 product categories over 27 brands show a clear, positive relationship between price-perceived quality perception and advertising spending, after taking into account exogenous variables like market price, frequency of 66 purchase, ease of evaluation and controlling for between firms factors like market share and total market size. Theoretical results derived from the third chapter indicated that the profits of a firm increases when the availability of true quality information is increased. This increase is even more significant when the price-perceived quality heuristic is more important. Non-price advertising can increase the availability of true quality information to consumers and such advertising spending is even more critical when the price quality heuristic is emphasized. Our results thus support and empirically validate these theoretical findings and the conjectures as in equation (1) and (la) where price and true quality information are independent, or at most mildly dependent, in forming the perceived quality. Although our findings are limited by the presence of missing advertising and market share values, the small consumer sample and the number of product categories, the results obtained are consistent enough with theory and intuition to suggest that they may not be exceptional. Hence our theoretical and empirical findings bear significant managerial implications for the effect of non-price advertising especially in markets where the price-perceived quality heuristic is important. 67 Chapter 5 Model Extensions In this chapter, we examine two extensions to the model presented in Chapter 3. Recall that the model we analyzed so far has a monopolist firm, in response to a varying degree of price-perceived quality heuristic, makes optimal price and quality decisions. While focusing on the static case of one product enables us to highlight several significant strategic interactions, such as that between profit margin and market coverage, it is necessary to examine the effect of price-perceived quality heuristic in a dynamic setting, and with multiple products. As a result, we examine two extensions in this chapter of the thesis. First, we consider a monopolist in a dynamic setting where consumers have the opportunity of repurchasing. Such an extension provides a convenient opportunity to incorporate the effects of consumer satisfaction (from the first purchase) on subsequent purchase decision. The concave value function of the Prospect Theory becomes a useful framework to model consumer satisfaction (and dissatisfaction) when the revealed quality exceeds (falls short of) expectations. Second, we consider a monopolist with multiple products. The context we choose to conduct this study is product line decisions, which is not only an important decision for managers, but also attracted long lasting interests from researchers (see, e.g. Moorthy 1988 and Dobson and Kalish 1988). 68 5.1 Monopoly Dynamic Product and Price Strategies The analytical results obtained in Chapter 3 illustrated the importance of incorporating the price-perceived quality heuristic into strategic decisions, and examines the mechanism of how the heuristic is linked to consumer demand and thus price-quality decision. A natural extension would be to look at the dynamic issues associated with consumer purchases. Specifically, if consumers are given the chance of repurchase, if they are willing to, how their evolving knowledge about product quality affects the firm's price and quality choice? In the literature, Jen and Southwick (1969) and Chen and Jain (1992) developed dynamic monopoly models in which the implications of dynamic monopoly behavior and strategies are very important when determining pricing policies. Our goal in this extension is to develop a model that explores how decisions can be made for pricing and quality of a product optimally over time. Consumers tend to be most uncertain about product quality when they buy the product for the first time. As a result, this will be when the price-perceived quality heuristic is most likely to be used. When consumers have consumed the product, they will be able to evaluate the product and have more true quality information about the product. Thus the consumer repurchase decision will be influenced by whether their expected quality levels have been met in the first purchase. 69 5.1.1 Model Framework We look at a two period product-price model for the monopolist. The monopoly chooses its quality level (fixed for both periods) in the first period and price levels in both periods. In the first period, all consumers make judgment of the perceived quality based on information about price and the true quality. The consumers do not anticipate the second period. Some of these myopic consumers will buy and others will not. In the second period, the true quality information is totally revealed to the market. This assumption removes the difficulty of setting a specific information diffusion process and allows us to concentrate on the key dynamic issues surrounding the price-perceived quality heuristic and the availability of true quality information. Moreover, for the consumers who purchased the product in the first period, their satisfaction level will depend on whether the perceived level of quality is higher or lower than the true quality, which they find out upon consumption. Consumers are dissatisfied if they had perceived a higher level of quality prior to purchase relative to the true quality, while those who have perceived a lower level of quality relative to the true quality will be satisfied. This phenomenon resembles the findings from the reference-price literature (Hardie et al, 1993; Anderson and Sullivan, 1993; Putler, 1992) where researchers have suggested an asymmetric utility function for consumer evaluation at below or above the reference point. LaTour and Peat (1979) and LaBarbera and Mazursky (1986) have also researched satisfaction/disatisfaction as part of a dynamic cognitive process. They found that a high level of satisfaction results in a greater difference between outcome and the comparison level which yields a higher intention to repurchase the brand. The tendency that consumers react more significantly to loss (i.e., 70 dissatisfaction) than to gain (i.e., satisfaction) and the shifting of reference points can be traced back to the original work in Prospect Theory of Kahneman and Tversky (1979). As a result, the period one experience will influence a consumer's period two decision. As before, consumers' perceived quality and utility function in the first period are given by s*M - Spp\ + Ss s* and U = tsfl-p]. Those consumers with s* > s*M are satisfied with the period one purchase as they had a lower quality perception than that realized. The difference between the utility based on perceived quality and that based on true quality is given by AUS =Uactual - Uperceived -t(s-shl)u. When these consumers make purchasing decisions in period two, their period two utility function is assumed to be U =ts-p2+yfMJ\ (9) The last term in the equation is the carry-over effect of period one experience. The square-root transformation is used to capture the decreasing level of utility over the "gains" in quality.1 2 For consumers who are dissatisfied (i.e., s* < s*hl if they purchase in period one), the difference in the level of utility is AUd = Uperceived - Uaclual = t(shl - s). To capture the asymmetric responses of being satisfied and being dissatisfied, we assume the following period-two utility for a dissatisfied consumer: U = ts-Pl-lJAUd (10) " 0 < AtV^ < 1 while it is not so obvious for AUd , the optimal solutions for the different parameters constraint it to zero and one. 1 2 The square-root specification and the cubic-root specification are adopted only to capture the concave and asymmetric shape of the value function in prospect theory. They are not essential to the results we derive. 71 Figure 5.1 shows the ten possible scenarios that could possibly appear for the monopolist, from period one to period two. The line segment [a,b] represents the entire market, and the vertical bold line segments represent consumers who purchase. The ten possible scenarios are configured as follows. Scenarios starting with H (i.e., H-1, H-2, H-3, H-4, H-5) have the first period true quality higher than the perceived quality (s* > s*hl). That is, a consumer will be satisfied if s/he purchases. Then there are five different patterns of market coverage that could happen in period two. Scenarios starting with L are featured with dissatisfied consumers in period one (s* < s*H). Since the dynamic model is not solvable analytically, we derive the optimal strategy numerically (by conducting a dense grid search on 10,000 parameter sets.13 We search the exogenous parameters of a, b, 8p and Ss in small increments of 0.1 resulting in 104 possible parameter sets. Constraints derived analytically are taken into consideration for the computational process as well. 5.1.2 Results and Analysis The key results of the dynamic model are concerned with the monopolist's pricing patterns over time. Scenarios H-2, H-4, and L-5 turn out to be the 3 possible optimal strategies depending on the parameter values. 1 3 In our model, we are able to solve analytically for p2 given values of 5 and pj. Using numerical process to solve models with similar setups is common in the literature. See, for example, Moorthy (1988) and Kalra et al. (1995). The numerical process was done using R, and some sample algorithms are attached in Appendix A. The numerical run on a 1.5Ghz computer took approximately 4 weeks and the outputs are analyzed and summarized in the next section. 72 Scenarios H-2 and H-4 occur when either Sn or S, is low. In these situations, the P 5 monopolist provides a quality level that exceeds consumer perception in period one. This implies that the firm is actually not exploiting its information asymmetry in the market, and is "giving away" quality to consumers (despite the cost for quality)! This happens not only because the overall weight that a consumer puts on perceived quality is lower (so that the monopolist has to charge a comparatively lower price), but also because consumer satisfaction is comparatively more important in the consumer utility function. The monopolist then changes its price in the second period to capitalize on the positive residue of consumer satisfaction. As illustrated by scenario H-2, depending on the magnitudes of dp and 6S, the price can be increased while increasing market coverage. If the price is not raised very high, the satisfaction factor and the quality will keep all the existing customers and also attract new buyers to the market. This moderate price is especially important when the consumers are very heterogeneous as the monopolist can extract more surplus from the upper end of the market. Interestingly, price can be lower when the consumers are not so diverse (i.e. b-a<0.5). For a firm using the H-2 pricing strategy, it actually puts more emphasis on the profit from the second period, and using the first period to induce trial. On the other hand, in scenario H-4, the market coverage decreases as a result of setting a high price. Some consumers who purchase in period one will drop out in period two, and no new buyers will enter the market. In this scenario, the monopolist can still charge a high price and extract the surplus from the higher consumer segment resulting in the second period being more profitable despite the decrease in market coverage. 73 Figure 5.1: Possible Market Scenarios in Two Periods Period 1 H-1 H-2 Period 2 H-3 H-4 H-5 b b b 11 b bl 1 b< tl ti ti ti 1" t22 t22 I . 1- t22 Period 1 L-1 L-2 S*>S h* Period 2 L-3 L-4 b b I b 1 b 1 _ bi ti ti 1" ti ti t22 t22 1. 1-s*<sh* = Market Coverage L-5 Scenario L-5 suggests that in a two period setting, the firm may actually charge a high price in the first period so that the true quality level falls short of consumer expectations. This is possible when consumers put emphasis on the price-perceived 74 quality heuristic and have available true quality information (i.e., when 8p and Ss are both high). As consumers are dissatisfied after they purchase and know the true quality, the f irm has to lower its price in the second period to achieve positive sales 1 4 . However, this lower price is not low enough to compensate for consumer dissatisfaction. A l l of period one consumers drop out in period two. The new lower price wi l l , on the other hand, attract some consumer who did not buy in the first period to the market. The monopolist emphases the first period profit, which is greater than that it receives in the second period. The pricing pattern is more in line with a price skimming scheme, but for a very different reason than that traditionally advocated. Figure 5.2 and 5.3 summarize the two different dominant quality strategies and profit levels as illustrated in the two shaded regions for all ranges of consumer heterogeneity. Subject to rounding errors, the boundaries for the two strategies appear identical. In Figure 5.2, the f irm "under performs" when both Sp and Ss are very high. The f irm here is focusing on the short term period 1 profit and has no incentive to provide a quality level higher then what the consumers need to purchase the product. This strategy is optimal for durables as it does not require the consumer to repurchase frequently. The f irm "over performs" when both 8p and 8S are low. The f irm here is focusing on long run profitability (period 2) and hence has an incentive to provide a quality level beyond what is needed for the consumers to purchase. This strategy is optimal for non-durables as it requires the consumers to repurchase frequently. The ethics of such policies can be examined. 75 Figure 5.2: Optimal Monopoly Quality Strategy in A Two-period Model (a=0.1, b=0.9) Region where only one Quality Strategy exists 0 0 76 Consider the case when we do not incorporate the customers' period 1 purchase satisfaction levels and the second period consumer utility level is independent of the first period price, (i.e. U2=ts - p2) Figure 5.4: Optimal Monopoly Quality Strategy in A Two-period Model (No Customer Satisfaction Carry over, a=0.1, b=0.9) Region where only one Quality Strategy exists Figure 5.4 shows that the region where the firm "under performs" (i.e. when Sp + Ss>~1.0) is now bigger and the region that the firm "over performs" (i.e. when S + Ss <~1.0) is smaller. These strategies are different from those illustrated in Figure 5.2, which is a better approximate for practitioners as it considers the consumers' period 1 satisfaction carry over effect. Next consider the case when we take into account the consumers' purchase satisfaction levels from period 1. Previously, we considered the value function of the Prospect Theory which has an asymmetric shape associated with it when defining the consumer utility. If we were to relax that property and instead assume symmetric 77 satisfaction/dissatisfaction utility functions (i.e. Us =ts- p2+ ^AUS and Ud =ts- p2 -^AUd ), the results are as shown in Figure 5.5. Figure 5.5: Optimal Monopoly Quality Strategy in A Two-period Model (Symmetric Customer Satisfaction Carry over, a=0.1, b=0.9) Region where only one Quality Strategy exists 0 0 8P 1 Similar to Figure 5.4, the region where the firm "under performs" (i.e. when Sp + ds >~1.0) is now bigger while the region that the firm "over performs" (i.e. when S +SS<~\SS) is smaller. These strategies are also different from those illustrated in Figure 5.2. Thus when firms take into account the asymmetric nature of the consumers utility function in period 2 (i.e. take into account the Prospect Theory), they should only "under perform" at high £ pand Rvalues instead of over a broad range of market conditions to achieve optimal profits. The application of prospect theory in including the consumers' satisfaction and dissatisfaction in the second period utility function causes a forward looking firm to take 78 into account the second period price and quality levels when considering the first period strategies. The resulting different strategies are a better guide to managers than if the firm had assumed that the second period purchase decisions are independent of the first period purchase, or if satisfied and dissatisfied consumers react alike. 5.1.3 Summary In a two period dynamic model, our analysis shows only 3 outcomes are possible in period 2. Firstly, the monopolist can serve all period 1 customers and some of the customers who were not served by raising or lowering prices dependent on the consumer heterogeneity. Secondly, the monopolist can also serve some of the higher customers from period 1 who are satisfied and are willing to pay high prices for the same product. This occurs when the firm "over performs" in the first period. Thirdly, the monopolist can serve non-period 1 customers by lowering price after he/she has "under performed" in the first period and had charged a high price. The impact of including the Prospect Theory into long term product strategies also cannot be ignored as excluding it will lead to sub-optimal strategies under the same market conditions. From a managerial perspective, providing a quality level that surpasses consumers' expectation appears to be an optimal strategy but only under certain market conditions. When consumers purchase a product that exceeds their expectations, they will be satisfied and in turn, this will result in repeat purchase and leads to long term profitability. This strategy is especially important for non-durables. However, when consumers adopt the price-perceived quality heuristic and have available true quality information, a price slamming strategy will lead to higher short run profitability. In this case, such a strategy will be optimal for durables that do not require frequent repurchase. 79 5.2 Monopoly Static Product and Price Strategies In A Product Line Product line design is an issue that has long attracted attention from managers and researchers alike15. It is a critical decision, for example, as firms introduce products into new markets, introduce products into existing markets, or modify their product lines. Since targetability, the ability to predict if the customer is a potential switcher and addressability, the ability to contact the customers individually are imperfect, a firm has no way of price discriminating. (Chen, Narasimhan and Zhang (2001) and Blatterg and Deighton (1991)). Having a product line will better fulfill the needs of the customers and this in turn allows the firm to charge different prices for these products while satisfying these customers. On the other hand, costs associated with adding and producing the additional products in the product line, as well as the adverse effects of the additional products on the demand for existing products ("cannibalization"), may affect the total profit to the firm from this product line as well. The tradeoff between these factors determines how the products should be positioned and at what prices. While the problem is of great importance in practice, there are not many published quantitative studies on the subject of product line design. The primary reason may be the computational complexity of solving the problem mathematically (Dobson and Kalish 1988). This is due to the discrete nature of the variables and the interdependencies among the various segments. Most of the work in this area has 1 5 Product line in this extension is a line of products that differ in one vertical attribute (i.e. quality). 80 focused on the case of a single product, where the problem of where to position the product and how much to charge for it can be solved optimally. Shocker and Srinivasan (1979) reviewed models on evaluation and generation of single product concepts. In this extension, we further develop the framework in chapter 3 and present a model that allows a monopolist to simultaneously decide on the pricing and quality strategy when consumers rely on the price-perceived quality heuristic and true quality information availability to perceive product quality prior to purchase. A similar product line setup was first proposed by Moorthy (1988) who uses the framework from Mussa and Rosen (1978). Our model, although similar in the setup, provides the monopolist with a better approximation to practical pricing and quality decisions as we take into account the behavioral aspects of the consumer. 5.2.1 Model Framework Following the same framework as presented in chapter 3, our model allows for a monopolist to have two products in a product line. One product is superior in quality to the other and the monopolist makes simultaneous pricing and product quality decisions. Figure 5.6: Monopoly Product Line Market Coverage 1 b Better Quality 1 Product 1 - t 2 B Lower Quality • Product • t i Market Coverage a 81 Figure 5.6 illustrates the monopoly product line setup and market coverage. As in previous chapters, consumer heterogeneity is uniformly distributed between b and a. ^ is the indifferent consumer between buying the product of higher quality or the product of lower quality. tx is the indifferent consumer between buying the product of lower quality or not buying. We concentrate on the more interesting case when the market is not covered. (As mentioned in chapter 3, Putler et al 2004 find that most product categories do not have full market coverage). Thus we allow for consumers who have less willingness to pay for quality not buy either product in the setup. The utility of the consumer is given by Ux - tsHx - px (where x=l,2 with 2 representing the better quality product) and t2is obtained by equating the utility functions of the two groups of consumers, tx is obtained by equating Ux = tsm - px to 0. The profit function of the monopolist is II = (/>, - as2 )(t2 -tx) + (p2 - as22 )(b -t2) (11) where fo-tf) is the market coverage for the lower quality product and (b-ti) is the market coverage for the higher quality product. The monopolist's profit maximization problem was solved numerically using a dense grid search of 10,000 parameters. The exogenous variables included the consumer heterogeneity parameters (a,b), the price-perceived quality heuristic (5 ) and the availability of true objective quality information (Ss). Constraints that were analytically derived were included in the computation as well (e.g. a<tx = ^ <t2 <b). SPPx+Sss\ Sp(p2- px) + Ss(s2-sx) 82 5.2.2 Results and Analysis Profit Levels The monopolist w i l l have the highest level of total profit when both Sp and Ss are high. Wi th a product that is of high quality in which the consumers know more about the true objective quality, the monopolist can take advantage of the strength of the price-perceived quality heuristic adopted by consumers to charge a high price and extract maximum surplus from the consumers. Further analysis of the consumer heterogeneity reveals that when the consumers are more diverse in their willingness to pay for quality, the better quality product w i l l be more profitable as it can extract more surplus from consumers who are wil l ing to pay for quality. When more objective product quality information is available to the consumers, both products w i l l be more profitable. This is expected as consumers wi l l have better knowledge about product quality and be wil l ing to pay the corresponding price associated with the quality level. Figure 5.7 illustrates the profit level for the two products as the price-perceived quality heuristic increases in strength. Figure 5.7 Profit Levels of Products in Product Line vs Strength of the Price Perceived Quality Heuristic Profit Levels t o ' y • Product O C D P ' -' P '. • Higher Quality Product ^ ^ " O . • o • oL-. ' • C N • • •' O . -'. O V ^ • ^ j J J ^ ^ ^ ^ ^ r f * ^ ^ ^ ^ ^ ^ ^ ^ ^ Lower Quality Product ".'/.;;vl':./.;\v • . I;.-/ . ) . ' . . . . 1 ,1.0; 83 We can see that > and ^ 1 < 0 for higher values of Sn. This is consistent SS SS SS p P p p with expected results as when the strength of the price-perceived quality heuristic is strong, the better quality product will be able to sustain a higher price in view of the corresponding quality level resulting in a bigger margin. Quality and Price Levels The better quality product will always have a price level higher than the lower quality level product regardless of market conditions. The quality level of both products increases with low Spand decreases with high£ p . Figure 5.8 illustrates this phenomenon. This implies that when consumers strongly adopt the price-perceived quality heuristic, the firm can actually take advantage of that and use price to generate a higher perceived quality level to induce purchase while lowering true objective quality. Similar results are also obtained when Ss changes. These results hold especially when the consumers are very heterogeneous in their willingness to pay for quality. However, when consumers are very homogeneous, > 0 and > 0, quality will also increase &>P 5 5 P monotonically with Ss as it is difficult to use price to extract surplus from the consumers who are very willing to pay for quality and the firm will need to correspondingly increase the quality. Price of the products, on the other hand will always increase when either £ s or <?p increases, irrespective of consumer heterogeneity. i.e. *L>oA>oA>Oand^->0. SSp 'SSp 'SSS 88, 84 Figure 5.8: Product Quality level vs Strength of Price-Perceived Quality Heuristic P r o d u c t Q u a l i t y v s D e l t a _ p ' 2 -• : . : CO • 'j. J- H i g h Q u a l i t y P r o d u c t 'N*. • Cu . O I s -• • • ' . i . i 1 1 1 0 . 2 ; 0 . 4 p : 6 0 . 8 1 . 0 D e l t a _ p . ? J = 0 ' 1 . b = 0 . 9 . D e l t a _ s = 0 . 9 Market Coverage When consumers do not rely on the price-perceived quality heuristic or rely heavily on the price quality heuristic, the higher quality product will dominate the market. However, when consumers moderately rely on the price-perceived quality heuristic, the lower quality product will dominate the market (See Figure 5.9). Figure 5.9: Market Coverage vs Strength of Price-Perceived Quality Heuristic Market Coverage o C N _ <o o C N O 00 O — p Low Quality Product High Quality Product s s , -:;J: 0.8 1.0 85 The intuition from these results is that when consumers rely heavily on the price-perceived quality heuristic, a higher price on the better quality product will generate a much higher perceived quality level resulting in more market coverage for the better product. However, when consumers rely less on the price-perceived quality heuristic, the tradeoff between margin and coverage will determine the total profitability of the monopolist. The lower quality product will have a higher coverage but lower margin while it is vice versa for the higher quality product. In Figure 5.9, when consumers do not rely on the price-perceived quality heuristic, because the availability of quality information is high ( 8S = 0.9), consumers will prefer the higher quality product as the price difference is small compared to when 8 is big. Table 5.1 Comparison of The Product Line Optimal Solutions (PLOS) and The Monopoly Single Product Solution (SPS) (a=0.1, b=0.9,) PLOS Price Low, High /SPS PLOS Quality Low, High /SPS PLOS Coverage Low, High /SPS PLOS Margin Low, High /SPS PLOS Profit Low, High /SPS PLOS t, /SPS Sp =0.9,6, =0.9. PLOS 0.4, 1 0.3, 0.625 0.0858, 0.1793 0.31,0.609 0.0266, 0.1092 0.6349 SPS 2.8909 1.20227 0.11525 1.44545 0.1665892 0.78475 8 =0.9,8S = 0.3 PLOS 0.125, 0.425 0.2, 0.5 0.1087, 0.0667 0.085,0.175 0.0092. 0.0117 0.7246 SPS 0.3212 0.40076 0.11525 0.160606 0.0185099 0.78475 «S,=0.3,*,=0.9 PLOS 0.15,0.35 0.225, 0.45 0.1558, 0.1381 0.099, 0.1475 0.0155. 0.0204 0.6060 SPS 0.255176 0.35720 0.2589 0.127588 0.033032 0.64110 <yp=0.3,<J,=0.3 PLOS 0.025, 0.05 0.1,0.175 0.1667, 0.0667 0.015, 0.0194 0.0025, 0.0013 0.667 SPS 0.02835 0.119065 0.2589 0.014176 0.003670 0.641101 Consider the product line optimal solutions and the monopoly single product solutions as given in Table 5.1. When we compare the profit levels of the monopolist 86 over 4 different market conditions, the monopolist wi l l actually be more profitable having a product line for most market conditions except when both 8p and Ss are high. In the latter case (row 1), because the total product line market coverage (0.0858+0.1793=0.2651 > 0.11525) is bigger than in the single product solution and the price is also lower for both products (0.4 and 1 vs 2.8909), the monopolist with the product line is unable to extract the surplus with a high price (margin) from the high consumer end unlike when there is only 1 product. 1 6 Although the monopolist with only 1 product also has higher quality (marginal cost) (1.20227) compared to 0.625 of the high product in the product line, the high price creates a margin (1.44545) that is sufficient to generate more profits despite the smaller market coverage. For the other market conditions (when Sp and Ss are not high, rows 3-8), the product line is the more profitable strategy for the monopolist. The higher product of the product line always has a higher price, a higher quality level, a higher margin and a lower coverage than the single product. The lower product, on the other hand, has a lower price, a lower quality level, a lower margin and a lower coverage that the single product. However, when both 8p and 8S are small, the lower product actually has a higher margin. The optimal solutions from the product line, in most market conditions, allow the monopolist to cater to the needs of 2 different consumer segments and thus extending total market coverage while charging a high price with the higher quality product to extract surplus from the consumers who are wil l ing to pay more for quality. Only when consumers rely heavily on the price-perceived quality heuristic and have available true 1 6 As the numerical search routine searches for the two best products for the product line case, the results obtained do not rule out the possibility of having one product in the product line priced out of the market and having the other product match the one product solution. 87 quality information that only having a single product will be more profitable. The monopolist here is free to charge a very high price for a high quality product only to a small segment of the consumers who are willing to pay more for quality. 5.2.3 Summary In this extension, we investigate the monopolist simultaneous price and product decisions in a product line where the products differ only in one vertical attribute (quality). Results indicate that regardless of market conditions, the better quality product will always be more profitable than the lower quality product, especially when the reliance on the price-perceived quality heuristic is strong. However, this does not mean that the monopolist should abandon the lower quality product. When consumers do not rely so heavily on the price-perceived quality heuristic, the lower quality product actually has higher market coverage than the higher quality product although the margin is smaller. The price and quality of the better quality product will always be higher and that allows the monopoly to increase its total market coverage under different market conditions and maximize its profit. When compared to the single product solution, the monopolist will find it optimal to have a product line in most market conditions (i.e. when 8 and 8S are not high) by having a large total market coverage and using the higher product to extract consumer surplus. However, when Sp and 8S are high, having only a single high quality product at a high price to extract the surplus from the small upper segment of consumers is more profitable for the monopolist. 88 Chapter 6 Duopoly Product and Price Strategies The previous chapters of this thesis examine the behavior of a monopolist in a number of settings: the monopolist in a static game, the monopolist in a dynamic model, and the monopolist with a product line. In this chapter, we examine the competitive outcome for a duopoly market, where two firms compete on product quality and price. The model structure and methodology follow the spatial competition tradition established by the seminal work of Hotelling (1929) and the subsequent work that he inspired. In Hotelling's model, two firms compete on store location and price. The study suggests that the equilibrium strategy is for each firm to choose a location at the center of the market, leading to a Principle of Minimum Differentiation. The argument is that for any location of one firm, the other firm has an incentive to move toward its opponent in order to expand the territory under its exclusive control. D'Aspremont, Gabszewicz and Thisse(1979) have shown that this argument is flawed. The original Hotelling model does not consider the possibility of firms choosing prices that are sufficiently low to drive the competitor out of the market. If such undercutting strategies are allowed, then a (pure strategy) price equilibrium does not exist as the two firms are 89 close enough to each other. Thus nothing can be said about the location equilibrium. When d'Aspremont et al (1979) modify Hotelling's model by changing the distance function to enable the price equilibrium to exist at all product positions, they find that each firm's equilibrium product strategy is to locate at one end of the market, maximally differentiated from its competitor. The model used in this chapter assumes that firms differentiate themselves on the quality dimension and ceteris paribus, every consumer prefers a higher quality implying they have an identical ideal point of infinity quality. As a result, consumers' ideal points are homogeneous under equal prices. Furthermore, we assume that a higher quality product costs more to produce than a product that is of lower quality. Also, consumers differ in their willingness to pay for quality. Existing literature that explored models of this nature includes Moorthy (1988) and Kalra et al (1998), assumes that consumers always have perfect information about the product prior to purchase. When consumers adopt the price-perceived quality heuristic, firms will have to develop equilibrium product quality and price strategies based on their beliefs about the consumer. Specifically, Figure 6.1 illustrates the four possible scenarios that may arise. 90 Figure 6.1 Firms' Belief About Consumers' Adoption of the Price-Perceived Quality Heuristic. Firm I's Belief about Consumers' Adoption of Price-Perceived Quality Heuristic NOT ADOPT ADOPT Case 1 Case 2 NOT ADOPT / / l f X\x(pT,sT) y , \ \ Yl2(pT,sT) )/ n2(pT,sT) Firm 2's Belief ^ ADOPT Case 3 HI(PT>ST) U2(PH>SH) J = Current literature assumed consumers have perfect information = Current model extension In Figure 6.1, the circled area indicates firms optimize based on the assumption that consumers have perfect information about product quality. This is the situation modeled by most of the existing studies. The other cells indicate the gap in the literature that has not been addressed. In chapter two, we assumed a generalization of the true quality information available to the consumer prior to purchase and that the consumer will utilize the true quality information depending on the availability (sT = Sps). Moorthy (1988) and Kalra et al (1998) investigate product and quality strategies with consumers having perfect information (sT = s ,Sp = 1). We relax the assumption and 91 investigate how the availability of true quality information (Sp) will impact the firms' strategies (as indicated in Case 1 with the dotted circle). Essentially we hope to derive results when both firms believe or do not believe that consumers use the price-perceived quality heuristic in a one-period choice structure. A drawback of raising the price to take advantage of the price-perceived quality heuristic is the possible decrease in total demand. As a result, how the balance between these two factors influences firms' equilibrium strategies depends directly on each firm's belief on whether consumers use the price-perceived quality heuristic or not. 6.1 Model Framework In this section, we lay out the model formulation and discuss the main assumptions. We characterize the consumer perception of quality in the same fashion as in chapter 3 and derive the demand in a duopoly setting. a) There are two firms, indexed 1 and 2, and they each choose a product from the quality interval [0, oo). b) Let si be quality of the product of firm 1 with price /^and S2 the quality of the product from firm 2 with price p2. The consumer's perception of the firms' product quality is defined as shi = 8ppi +Ssst where i=l, 2. If a firm realized the existence of the price-perceived quality heuristic, it will take s/,, as the perceived quality in the consumer's mind when she makes purchase decisions. However, if a firm does not believe that consumers adopt the price-perceived quality heuristic, it will simply assume the consumers have a quality perception ofshi =Ssst, and the price-perceived quality heuristic plays no role. (See 92 chapter 2 for the discussion on parameters 8 and 8S) Again, even though all consumers value higher levels of quality, they are heterogeneous in the willingness to pay for incremental quality and this is captured by the marginal willingness to pay for quality, t, distributed uniformly over the interval [a,b] to remove positioning possibilities due to non-uniformity. c) Consumers may purchase either one unit of the product from either firm or not buy at all. d) The marginal cost of producing one unit of product at quality st is as2 (a > 0). The quadratic cost function is assumed so that the marginal cost (of quality) can increase faster than the willingness to pay. This ensures that the optimal quality level the monopolist can choose for consumer type t will not be infinite. Indeed the maximum quality level either firm may provide for t (without incurring a loss) is t8s /[a(l-t8p)]i7. Fixed cost is irrelevant to our analysis and assumed to be zero. e) 8p and 8S are exogenous and apply to both firms. To characterize each firm's market, we identify two consumer segments [tt,t2]. Firm fs market, M,-, is defined as the set of consumer types who get greater surplus from its product-price offering than from the other firm's offering and the substitute. That is, def M,. ={te [a,b]: tshi - p. > tshj - p. for 7=0, 1} for i= 1, 2 To further define the two market segments, we adopt the framework from Moorthy (1988) in his Proposition 1, which asserts that the boundaries of a firm's market 1 7 Marginal cost = OS2 should exceed the willingness to pay ( p^ = UH (0) ) so that quality offered will not be infinite. 93 segment are the consumer types who are indifferent between the firm and its neighbors (provided these neighbors have a market). The firms' market segments stack up in the order of the firms' perceived product qualities18: a firm with a higher perceived quality product has the segment with a "higher" willingness to pay for quality. PROPOSITION 1. Let (sx,px) and (s2,p2)be the product and price offerings of the two firms such that 0 < shl < sh2. Then i's market (i=l,2) can be characterized as: !• ski ^ shj a n d Pi > Pj => M i = ® 2. su < shj, te Af,.,r'€ Afy. => f < f , 3. If M, ^ ®, then M • = [r,, tM ], where u is either the lower consumer type a or the consumer who is indifferent between i and the next lower quality product with a nonempty market. ti+i is either the higher consumer type b or the type indifferent between i and the next higher quality product with a nonempty market. From proposition 1, the market segment for each firm can be specified as in Figure 6.2. Figure 6.2 Consumer Segments in a Duopoly Higher b Segment 2 Perceived Quality — t2 Lower Perceived + Segment 1 Quality ll a Market Coverage 1 8 The perceived quality ranking need not be the same as the true quality ranking. Existing literature had the market segmented based on true objective quality. 94 As discussed in chapter 3, when tx =a, the entire market is covered for the monopolist. Likewise in a duopoly, when tx = a , the duopolists cover the entire market. Since our primary focus is on the effect of competition on the duopolists' behavior taking into account the price-perceived quality heuristic, we shall limit the framework to one where the market is sufficiently diverse, that is, — is sufficiently large (See Table 6.1 for a tx> a ) - so that the duopolists do not sell to some consumers whose willingness to pay for quality is sufficiently low. Table 6.1 summarizes the efficient solutions for Case 1 and Case 4, in comparison with the perfect information solution derived in Moorthy (1988). The efficient solution has the biggest coverage or smallest tj. (i.e. tj>a or b>5a is the most restrictive constraint with respect to the monopoly or duopoly solution) Table 6.1 Summary of the Efficient Solutions Moorthy Case 1 Case 4 1988 Sl b b b 5a 5a 5a S2 2b 2b 2b 5a 5a 5a Pi b2 b2ss S2b2 25a 25a 5a{5-bSp) P2 Ab1 4b*Ss 2Ssb2(10-3Spb) 25a 25a 5a(Spb-5)(3Spb-5) Coverage 2 2b 2b 2b 5 5 5 Coverage 1 2b 2b 2b 5 5 5 h b b b 5 5 5 95 Consumers will always adopt the price quality heuristic in making purchase decisions. However, the firm may or may not believe that consumers do that. The consumer's utility function from the firm's perspective is thus dependent on the beliefs of the firm. If a firm believes that the consumers utilize the price-perceived quality heuristic, it will take the utility as U=t(SpPi+S,Si)-Pi i=l,2 (13) when formulating its strategies. If the firm does not believe that consumers use the price-perceived quality heuristic, then the utility is U = t(S,Si)-Pi i=l,2 (14) Denoting firm 2 as the firm with higher perceived quality, demand is thus obtained by locating the indifferent consumer in buying from firm 2 and firm 1, as well as the indifferent consumer in buying from firm 1 and not buying. Case 1: When Both Firms Do Not Believe that Consumers Adopt the Price-Perceived Quality Heuristic In this case, both firms incorrectly believe that the indifferent consumer between firm 2 and firm I's offerings is obtained by solving U2 =t(Sss2)-p2 =t(S1sl)-p1 = Ul A similar approach ( f (^ s 5,)-p x =0) is assumed for the indifferent consumer in deciding to buy from firm 1 or not buy. Hence, the firm incorrectly conclude that t2 - ——— and f, = . Thus the demand for firm 2 is b-t2 and the demand for 5s(s2-s,) Sss, firm 1 is t2—tl. 96 The firms make decisions about price and quality according to: n 2 =(p2-as22)(b-t2) (15a) n, = (px-as2x)(t2-tx) (15b) Although the firms make their decisions in this manner, customers actually choose the products based on the following utility functions, Ut = t(dppi + 8ssi )-/?,•, as in Case 4. In Case 1, should both firms have the same quality level (sx - s2), the profit function will be discontinuous at px = p2 (similar to the results in Moorthy 1988). This discontinuity is a consequence of consumers having the same perception of the true quality and can only choose between the products on the basis of price. The only possible equilibrium in this case is that both firms charge a price that equals the marginal cost and thus make zero profit. Case 4: When Both Firms Believe that Consumers Adopt the Price-Perceived Quality Heuristic Both firms correctly believe that the indifferent consumer between firm 2 and firm l 's offering in this case is obtained by solving u i =t(Spp2+S,s2)- p2 = t(SpPx+Sssx)- px =£/, A similar approach is assumed for the indifferent consumer in deciding to buy from firm 1 or not buy. Hence, the firm correctly conclude that t2 = Pi-Pi and tip(P2-Pi) + # s ( s 2 - s i ) t, = SPPl + SsSl The demand for firm 2 is b-t2 and the demand for firm 1 is 12 - tx. 97 The profit functions according to which the firms based their price and quality decisions are the same as in equations (15a) and (15b). Different from Case 1, if the firms have the same product quality s{ = s2 consumers may still have different perceptions of the product quality if the prices are different between the firms. Indeed, this may allow the lower quality product to be priced higher and perceived as the better product. As the objective functions of both Case 1 and 4 do not allow closed form solutions, a numerical search is conducted with a dense grid search on 10,000 values in the possible range of the parameters.19 The exogenous variables included the consumer heterogeneity parameters (a,b), the price-perceived quality heuristic (Sp) and the availability of true objective quality information (Ss). Constraints (e.g. tj and ti) that were analytically derived were included in the computation. 6.2 Results and Analysis Case 1 The effects of the availability of true objective quality information (8S) on the firms' product and price strategies are investigated. When Ss increases, the quality and price of both products increase for the entire range of consumer heterogeneity. To see the intuition behind this result, consider the case when b=0.9 and a=0.1. Figure 6.3 shows the equilibrium profits for these parameter values as <^  changes. When Ssis 1 9 Setups of this nature in Moorthy (1988) and Kalra et al (1998) were also analyzed through numerical analysis. The computational software used was R and the total time taken for the program batch run was approximately 6 weeks on a 1.5Ghz computer. Sample program codes are included in the Appendix. 98 sufficiently small (8S <~ 0.85), the firm providing the lower quality product is more profitable than the higher quality competitor. Only when SS > 0.8, does the higher quality product earn significant profits As shown in Figure 6.3, when consumers do not have enough product quality information, they are not willing to buy any products and as a result the firms earn minimal profit. As SS gets larger, its impact becomes more significant for the 2 differentiated products. When SS is not sufficiently high (0.2 < SS <0.85), the lower quality product is more profitable since the willingness-to-pay for higher quality is still not met by perceived quality, and as a result the market share of the higher quality product is still minimal. In other words, the higher quality firm may set the equilibrium price such that UL > UH for all potential buyers. Here, consumers are able to derive greater positive utility from the lower priced lower quality product. When SS > 0.8, the higher quality firm attracts more buyers and becomes more profitable than the low-quality firm when SS >=0.85 as consumers now have more information about the product to help form perceived quality. Figure 6.3 Profit Levels of the Duopolists in Case 1 Product Profit vs Delta_s . L D ' 4_j O • Z 3 " Q O i CL o Low Quality Product ^< • .1 - / v • o 1— - - / CL High Quality Product / 5S o 99 As Figure 6.3 shows, the cross-over of profitability occurs when consumers know the true quality very well (Ss - 0.85). In this situation, as illustrated in Figure 6.4, the lower quality product loses market share significantly as the higher quality product attracts more customers. Figure 6.4 Market Coverage of the Products in Case 1 Product Coverage vs Delta_s 5S 0.2 .- / : ;£#.:- . 0.6 0.8 1.0 Delta_p, a=0 1. b=3.9. delta_s=0.5 To further illustrate this relationship, consider the case when£> = 0.9. When 8S -0.8 tx -0.324074 and t2 -0.9 and when Ss -0.9, r, -0.31746 and t2 -0.83333. Here, the total market coverage has increased as Ss increases, and the market that is not covered is now [a,0.31746] compared to[a,0.324074]. However, the increase of 0.0066 for the entire market is not split between the two firms. In fact, the lower quality product has lost some of the higher consumers who are willing to pay for quality to the higher quality product. Thus with more quality information being available, the coverage of the higher quality product is now 0.0667. 100 Figure 6.5 Margins of the Duopolists in Case 1 Product Margin vs Delta_s f : 2 ; :\;v;:;^  0.8 1.0 Figure 6.5 further illustrates the margins of the two products. Although the higher-quality product always has a higher margin (despite a higher marginal cost), the availability of product quality information eventually determines its profitability because of higher equilibrium prices and whether it meets the preference of the consumers. In Moorthy (1988), perfect information for the consumer was assumed prior to purchase and is the situation when ds = 1 in case 1. With reference to Moorthy (1991), our main results are consistent with his findings in terms of profitability, coverage and margin rankings. When Ss -1, the higher quality product is more profitable, has a lower coverage than the lower quality product but has a higher margin. The equilibrium prices, margins and profits for case 1 when Ss -1 are summarized in Table 6.2: 101 Table 6.2 Comparison between Different Solutions for Case 1 (a=0.1, b=0.9,a = \, S=\) Case 1 Equil ibrium Solution Efficient Monopoly 2 0 pL = 0.0625 p„ = 0.085938 pL =0.0324, pL =0.1296 p = 0.18 sL =0.21875,*w -0.25 sL =0.18, sH =0.36 =0.3333 cov erageL ~ 0.4643, cov erageH =0.15 cov erageL = 0.4, cov erageH = 0.4 coverage =0.6777 mwginL = 0.014648, marginH =0.023438 margin^ =0,margmw =0 mwginL = 0.09 YlL = 0.0068, n„ =0.0110 n t - o , n H =o n„ =0.027 /, = 0.2857 f, =0.2 f, = 0.333 The efficient locations of the products are — for the lower quality product and 5a — for the higher quality product (see Table 6.1). The product equilibrium here is not 5a efficient. Taking the situation when Ss = 1, b = 0.9 and a = 1, the efficient products are 0.18 and 0.36 while the equilibrium products are 0.21875 and 0.25 respectively. As a result of the product inefficiency, coverage efficiency is affected as well. The market left uncovered is [a,0.2857], which is larger than that of the efficient solution, which is [a,0.20]. However, it is smaller than the market left uncovered in the monopoly solution, which is [a, 0.333]. The equilibrium coverage is larger than in the monopoly case 1 The monopoly solution here is based on sH=^s. 102 because of lower margins due to price competition. The higher quality product is more bS profitable because it is closer to — - ~ 0.333 (see footnote 20). Thus if given a choice 3a when Ss ~ 1, either firm would prefer to have the higher quality. However, when Ss <~ 0.85, then having the lower quality product will be better as the limited availability of information makes that the preferred choice of the consumers. Case 4 The two parameters of interests now are ds and 8p, and the focus would be on their impact on the equilibrium results. Both firms here correctly know that consumers use the price-perceived quality heuristic (U = t(8pp + 5ss)- p). When either Ss or Sp increases, the price and quality of both products increase. While the price increase with SsL H op is expected, the quality of both products increase as well with op ( ' > 0 and p SsLH SU, — — > 0). Further examination of the equilibrium results indicate that > 0 and 85s 8pxSp2 > 0 (See Appendix). These in turn imply that both price and quality for the two firms are strategic complements (Tirole p. 208). In order to illustrate whether being a higher quality firm or lower quality firm is more profitable, Figure 6.6 summarizes the profitability of the two products in response to the values of both parameters. 103 Figure 6.6: Profit Levels of the Duopolists in Case 4 (a=0.1, b=0.9) 1 When 8S is relatively high and the strength of the price-perceived quality heuristic is strong, the product with the higher quality will be more profitable. On the contrary, the lower quality product will be more profitable when both parameters are low. The explanation of this result comes from the market coverage and profit margins received by the two firms. Figure 6.7 illustrates market coverage when consumers do not have access to product quality information and do not rely on the price-perceived quality heuristic, then the quality difference between the two products is less apparent and not so valued, and hence the cheaper lower quality product (because of lower cost) will be the preferred choice for many consumers. Thus despite the small margin, the bigger market coverage will enable higher profitability for the lower quality product. The market boundaries in Figure 6.6 (and in Figure 6.7, to be discussed below) are obtained by plotting 8S and 8p at 104 0.1 intervals with the parameter indicator (i.e. Higher profit firm =1, 2 (for firm 1,2) or higher coverage firm =1,2 (for firm 1,2). Figure 6.7: Market Coverage of the Products in Case 4 (a=0.1, b=0.9) Region indicating the firm with bigger coverage 0 0 Figure 6.7 summarizes the market coverage of the two firms as Sp changes. There appears to be an increasing market coverage shifting from the lower quality product to the higher quality product as consumers' reliance on the price-perceived quality heuristic increases. As the price increases to take advantage of the strength of the price-perceived quality heuristic, the demand of both products drops. However 5coverageL > 8cov erageH and hence the decrease in the coverage of the lower quality product is more rapid as 8 increases. Figure 6.8 specifically illustrates the changes in market coverage as Sp increases at Ss = 0.7 105 Figure 6 . 8 : Market Coverage vs the Strength of The Price-Perceived Quality Heuristic Case 4 2 1 Product Coverage (ds=0.7)vsDelta_p I I 1 I . . - • U • Op v.; ;V;; : ^2V^ 04 C.6 0.8 ' 1.0 Delta_p. a=C.1 b=0.9, delta_s=0.7 Consider the product equilibrium results when b=0.9, a=Q.l, oc=\, Ss = 8p =0.9 and when S=Sn= 0.2. The results are as follow: Table 6 . 3 : Comparison of Case 4 Numerical Output (a=0.1, b=0.9, a = 1, Ss = 8p = 0.2) Case 4 Equilibrium Solution Efficient 2 2 Monopoly 2 3 0 . 2 pL =0 .01 p t f - 0 . 0 1 5 p L =0 .0006722 , pH =0.028645 p - 0 . 0 1 0 2 4 6 5 ^ «0.09,s H = 0 . 1 2 sL = 0 . 1 8 , ^ - 0 . 3 6 cov erageL ~ 0.1910, cov erageH =0.1857 cov erageL = 0.4, cov erageH =0.4 coverage =0 .273864 marginL - 0 . 0 0 1 9 , m a r g / n w - 0 . 0 0 0 6 marginL ~0,maxginH = 0 marginL = 0 . 0 0 5 1 2 3 3 nL = 0 .0004072 ,n w =0 .00011142 n L =o,n„ - o YlH = 0 . 0 0 1 4 0 4 tt = 0 . 5 2 3 2 7 6 f, = 0.2 tx = 0 . 6 2 6 1 3 6 Plots are pre-smoothing. See Table 6.1. Monopo ly Solution when s H = S p + Ss s 106 Table 6.4: Comparison of Case 4 Numerical Output (a=0.1, b=0.9, a = 1, Ss = 8p = 0.9) Case 4 Equilibrium Solution Efficient24 Monopoly 0.9 pL =0.77 pH =0.775 = 0.034797, pH = 0.21223 p = 2.89090 s t = 0.865, sH =0.87 sL = 0.18,sw =0.36 •5^=0.2 = 1 -20227 coverage^ =0.03228, coverage,, =0.3444 coverage L = 0.4,coverageH =0.4 cov erage ~ 0.11525 margin L = 0.021775, marginH =0.0181 marginL ~0,margmw = 0 margin L =1.445454 I"IT = 0.0007028, n„ = 0.0062336 n L =o , n „ =0 n „ =0.16658 r, = 0.523276 f, = 0.2 «! =0.626136 Similar to Case 1, the equilibrium products are not efficient. When Ss=8p= 0.2, the lower quality product is more profitable as it is closer to the best single monopoly product position of -0.0715. Market coverage is smaller than the efficient product coverage but bigger than the one product case of a monopolist. As expected, the monopolist is the most profitable compared with either firm in a duopoly. Similarly, when £ s =Sp= 0.9, the higher product is more profitable as it closer to the best single monopoly product position at approximately 1.2. Here the monopoly single product again has the smallest market coverage, followed by the equilibrium products and then the efficient products. Although the margins for both firms are small when ds -8p= 0.2, the market coverage for both firms is bigger than when it is at 8S =Sp - 0.9. Likewise, the monopolist is the most profitable. See Table 6.1. 107 From a managerial perspective, understanding the market conditions, adopting the correct beliefs about consumers, and then applying appropriate product and price strategies appear to be critical. When firms in the market do not believe that consumers adopt the price quality heuristic (Case 1), the availability of the product quality information will determine which product has the better coverage and profitability. The lower quality product is more profitable when there is little product quality information and the higher quality product is more profitable when consumers have available almost perfect product quality information. This resembles Moorthy's (1988, 1991) results, but it only holds when 8S is relatively high. Furthermore, the market coverage for the higher quality product is always smaller than that of the lower quality product. However, the market coverage of the higher quality product can be higher than the lower quality product when firms believe consumers adopt the price-perceived quality heuristic (Case 4). This occurs for high Sp and Ss values. Depending on the market conditions, the higher quality product firm may be more profitable than the lower quality product especially when consumers utilize the price-perceived quality heuristic and there is sufficient true quality information available. The lower quality product will be more profitable when the consumers do not have adequate true quality information and do not rely heavily on the price-perceived quality heuristic. 108 6.3 Summary In this extension, we introduce competition by investigating two firms that do not believe in one case and believe in another case that the consumers use the price-perceived quality heuristic prior to purchase. As existing literature had assumed perfect information for a duopoly with consumers not using the price-perceived quality heuristic, we relaxed that assumption and investigate this case as well for the purpose of comparison. The analysis of both cases indicate that depending on the level of price-perceived quality heuristic and the availability of true quality information, either the superior or inferior product may receive greater profits. A comparison between the equilibrium solution, the efficient solution and the monopoly solution reveals that generally the equilibrium products are not efficiently positioned and the firm that is the more profitable one has a product closer to the monopoly product. 109 Chapter 7 Conclusion and Future Research The study of consumer behavior and the study of firm strategy using quantitative modeling are among the many successful research streams in marketing. While both traditions have proved fruitful, there exists an obvious "gap" between them. In particular, relatively few of the significant findings in the behavioral research stream have been incorporated into the modeling framework to study firm strategies. For example, while numerous behavioral studies suggest that consumers may not have perfect information and may employ judgmental heuristics when they make purchase decisions, most of the quantitative studies on product positioning have assumed, among other things, that consumers have perfect information about true product quality. The research "gap" between behavioral studies and quantitative research needs to be filled, since to derive practically useful managerial implications, a modeling framework needs to reflect market realities to the greatest possible extent. The rich findings in consumer behavior thus provide a great opportunity to incorporate them into models of firm strategy, and examine how the optimal outcome is changed. This is especially important for the studies of product positioning, since consumer perception 110 about product offerings is often the consequence of both economic and psychological factors. This thesis examines one aspect of consumer behavior that has received consistent recognition in the behavioral literature but has not been considered in a modeling framework. In particular, we examine the effect of the price-perceived quality heuristic on a monopolist's quality and price strategies. Based on existing behavioral findings, the model acknowledges that consumers perceive the quality of a product by looking at its price level and also any information about the true quality. Together with the level of consumer willingness to pay for quality, the price-perceived quality heuristic effect and the true quality information availability influence the price, quality, and the welfare levels that occur in the market. The analysis shows that if a monopolist ignores the market condition that consumers refer to price when determining perceived quality, the monopolist will achieve suboptimal profits, the extent of which depends on the reliance on the price-perceived quality heuristic and the amount of true quality information available. For the optimal solutions, the higher the strength of the price-perceived quality heuristic, the higher the optimal price, quality and margin but the tradeoff is a drop in market coverage. We also find that a higher reliance on the heuristic motivates the monopolist to invest more heavily in non-price advertising, which enhances the availability of true quality information This is, however, constraint by the magnitude of the price-perceived quality heuristic and occurs in the model when there does not exist a strong correlation between the magnitude of price-perceived quality heuristic and the availability of true quality information. In other words, this occurs when the use of the 111 price-perceived quality heuristic is primarily a behavioral primitive, as most of the existing studies suggest. If a strong dependence between the magnitude of price-perceived quality heuristic and the availability of true quality information is assumed in the model, the pattern of results reverses. That is, a lower reliance on the heuristic by consumers motivates the monopolist to invest more heavily in non-price advertising. An empirical study was designed to test our conclusions that for markets where the consumers rely more heavily on the price-perceived quality heuristic, a higher level of non-price advertising will lead to greater profits. Despite the limitations of the study, the results are consistent enough with our expectations. Thus our conjecture that the parameters for the price-perceived quality and true quality information are independent or, at most, mildly dependent is supported and the theoretical results obtained are significant and have relevant managerial implications. A few welfare implications are also obtained. For instance, the greater dependence on price to judge perceived quality in an efficient solution and the greater availability of true quality information in a monopoly solution may actually hurt consumers. In the model extensions, the thesis investigated product and price strategies for a monopolist in a dynamic setting as well as with a product line. In the dynamic setup with two periods, we incorporate the main findings of prospect theory when modeling how consumers respond to the differences between anticipated (perceived) quality and actual (true) quality. Our analysis indicates that it is optimal for the monopolist to adopt a price skimming strategy when both the price-perceived quality heuristic is important and the true quality information is readily available. Otherwise it is actually optimal for 112 the firm to provide a quality level that matches or exceeds the level necessary for purchase, adopting a pricing strategy dependent on the heterogeneity of the consumers. The inclusion of the prospect theory also provides a more accurate guideline for managers when they need to adopt the correct quality and price strategies under different market conditions. When the monopolist has a product line, the total profit is higher than when having a single product for most market conditions except for when the price-perceived quality heuristic is high and the true quality information is available. In this case, the monopolist is better off charging a high price for a single high quality product to extract surplus form the small higher end customers. For the final model extension, we incorporate competitive effects and investigate the product and price strategies when firms in a duopoly correctly believe or incorrectly not believe that consumers adopt the price quality heuristic prior to purchase. A comparison between the equilibrium solution, the efficient solution and the monopoly solution reveals that generally the equilibrium products are not efficiently positioned and the firm that is more profitable has a product closer to the monopoly product. Future Research Directions We conclude the thesis by highlighting several areas where future research appears to be potentially fruitful. First of all, we have focused on only one of the many behavioral findings that deserve attention from analytical research, namely the price-perceived quality heuristic. Other significant behavioral factors may be suitable for similar treatment. Among these factors, reference price has received most of the attention. It has been incorporated into a microeconomic framework (Putler 1992) and used in empirical models of consumer purchase behavior (Kalyanaram and Little 1988; 113 Raman and Bass 1988; Lattin and Bucklin 1989, Chang, Siddarth and Weinberg 1999). It will be interesting to examine the role reference price plays in an analytical framework of firm strategies. For example, as two firms compete on price and product attributes, how does each firm's pricing behavior influence the formation of reference prices, and thus the competitive outcome. Other significant features of consumer behavior that deserve attention include phenomena such as mental accounting, regret and comparison and/or intertemporal choice. Including the psychological process that contribute to "trust" and "distrust" between consumers and the firm with regards to quality information is another area that warrants further investigation as well. In the context of price-perceived quality heuristic, an important area for future research concerns the product line extension strategy. As a popular business practice, product line extension is perceived to be less risky than brand extension, and has attracted a lot of research attention (Miguel Villas Boas 1998). The relevance of the price-perceived quality heuristic to product line extensions becomes obvious as consumers do not know the true quality of the new extension item, know only the quality of the existing product, and observe the price levels of both. It is perceivable that as consumers consider a new product, for which they do not have much information, they will rely on what they know about the existing product in the same product line. The most visible factor of the new product is price, which provides a natural hint to the consumers about the difference between the new product and the existing product. To capture the diffusion process of a new product (i.e., from being new and unknown to being familiar to consumers), we should also look at repeat purchase in this extension. Many existing studies have assumed a forward-looking firm that plans for all the items in its product line 114 simultaneously. Research here can capture the "sequential" nature of the product line extension and stay closer to reality that firms develop a new product based on what already exists in its product line. In the empirical study of this thesis, we directly measured the price-perceived quality heuristic construct, as in Lichtenstein and Burton (1989), in a single cross-sectional survey of a student sample. Another approach will be to indirectly measure it by computing the relationship between price and the measured perceived quality level. Research into demographic and socioeconomic characteristics that can affect this relationship will also bear significant implications on a firm's pricing and quality decisions. An immediate feasible empirical extension would be to enlarge the survey sample size to assess the generalizability of the current findings using nonstudent consumers. Demographic and socioeconomic data can be collected and analyzed for moderating effects. The same sample could also be surveyed over time to investigate the stability of the price-perceived quality heuristic to further support the schema consumers adopt as proposed by Mizreski, Golden and Kernan (1979). Zhou, Su and Bao (2002) found that there are significant differences in the use of price to infer quality over different markets, namely between the China and US markets. Similarly, people from these two markets can be surveyed. Main results from these empirical extensions that are similar to our current study will further add to the robustness of our model. In the monopoly dynamic extension, our main findings indicated that a firm is better off "giving away" free quality under certain market conditions and "under performing" under other market conditions. While Lichtenstein and Burton (1989) had indicated the relative strengths of the price-perceived quality heuristic correspond to 115 different product categories, advertising spending can be a proxy to the availability of quality information. Together, the market conditions for the different strategies can be empirically defined. Collecting longitudinal data from sources like Consumer Reports, Consumer reviews, Advertising Age, Hoovers annual reports and Standard and Poor's industrial index, we can test whether the theoretical strategies derived can be empirically validated. This approach can also be used to validate the main findings as in Case 4 of the duopoly extension. Firms with the higher quality product are expected to be more profitable and have higher market shares especially when quality information is available and the consumers rely.heavily on the price-perceived quality heuristic. Likewise, firms with the lower quality product are expected to be more profitable and have higher market shares especially when quality information is not readily available and the consumers do not rely heavily on the price-perceived quality heuristic. 116 Bibliography Alloy, L., and Naomi Tabachnik, (1984), "Assessment of Covariation by Humans and Animals: The Joint Influence of Prior Expectations and Current Situational Information," Psychological review, 91 (1), 112-149. Anderson, E., Sullivan, M. (1993), " The Antecedents and Consequences of Customer Satisfaction for firms," Marketing Science, 12(2): 125-144. Andrews LR. and E.R. Valenzi (1971). 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It II ff IIII tilt II IlititWll It nil II ttittrfttt IIIIIIII llitlt tt II tl tftl tl Hit IIII It II It II tl ItTT n<-10 #number of steps parastep<-0.1 paral<-fsetpara(parastep)$paraalphal #paral <-fexocon(para 1 a) #alpha=l #44-11IIIIIIIIII III] IIIIIIIIIIIIIIIIII It II It It IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII it II HIT IIII lift ttfiffitftifit rr ii If iiii II ti Ii ti it it ti if it tl it ft Ii itittrnil Ii ii tilt ITTT n if p<-ncol(paral) zzl<-"okl" zz2<-"fcore" __"5 - "44-44-41 If.4i44.44.444444.44 II It II41 H If IIIIIIIIIIIIIIIIIIIIIIIIIIII1144-'' It It If IflJ TTTTTTIIII tt tt It tl ti It tttl It tl tl It tl jl ti 91 ft It tl ft It tl Tt zz4<-"ok4" zz5<-"done" z<-l 8 #output columns out<-matrix(rep(0,z), 1 ,z) #to rbind later, ID, 5exo, 3dv,3 pis,2 ts,2 coverage for(i in l:p){ outcore<-fcore 1121a(paral,i,n,z) out<-rbind(out,outcore) print(zz3) print(zz2) print(i) I 126 Dynamic Asymmetric Satisfaction Model - Function fcore for(i in l:n){ s<-smin+i*sc ####tf#####P A 11 "*>.<:h* ##################### TTn II II 11 II 11 11 II II V A i l I I S > I1 TTfl II If 11IIII IIIIll IIIIII II IIII IIIIII IIII #exo check if(((l-a*dl) !=0)&& ((l-b*dl) !=0)){ for (j in l:n){ plmax<-d2*s*b/(l-b*dl) p 1 min<-d2*s*a/(l -a*d 1) p 1 c<-(p 1 max-p 1 min)/n pl<-plmin+j*plc if ((plmin<pl) && (pl<plmax)){ sh<-dl*pl+d2*s if(s>sh){ for (k in l:n){ sh<-dl*pl+d2*s p2max<-s*pl/sh p2min<-s*a p2c<-(p2max-p2min)/n p2<-p2min+k*p2c if ((p2min<p2) && (p2<p2max)){ dent<-8*sA2 numtl <-s-dl *pl-d2*s+8*s*p2 numt2<-(sA2-2*s*d 1 *p 1 -2*d2*sA2+l 6*p2*sA2+d 1 A2*p 1 A2+2*dl*pl*d2*s-16*dl*pl*s*p2+d2A2*sA2-16*d2*sA2*p2)A0.5 t21 <-(numtl -numt2)/dent tl<-pl/sh t22<-p2/s if (t21!="NaN"){ if ((pl/sh<t21) && (t21<b)){ pi 1 <-(pl -alpha*sA2)*(b-tl) pi2<-(p2-alpha*sA2)*(b-t21 +tl -t22) pi<-pil+pi2 if (pi>piholdll){ piholdl 1 <-pi hold11t,2]<-s holdll[,3]<-pl holdll[,4]<-p2 holdl 1 [,5]<-piholdl 1 }}}}))))) res<-rbind(holdll,holdl2,holdl3,holdl4)holdl5,hold21,hold22,hold23,hold24,hold25) res<-fsortmat5(res) ##########output with coverage#########3 outmat<-matrix(rep(0,z), 1 ,z) 127 Dynamic Asymmetric Satisfaction Model - Exogenous Parameters # Filling in parameter matrix###### n<-round(l/step) set<-rep(0,n) values<-matrix(set,n, 1) valuesa<-matrix(set,n, 1) for(i in l:n){ i f ( i= l ) f values[i,]<-0+step }else{ values[i,]<-values[i-l,]+step } I if (values[n,]>l){ values[n,]<-l } valuesa<-values valuesa[n,]<-l #11IIII II II II II II II tt tt tt UM Hit MM MMMMMMMMM tt tl tt tt lllllllllllrllllllilllli~tfllllll ItffIIII tftfUttitft Hit ttttit set<-rep(0,5) parahold<-matrix(set,5,1) set<-rep(l,6*nA5) para<-matrix(set,6,nA5) #### 5th row ALPHA############ j<-0 repeat { for (i in l:n){ para[5,n*j+i]<-valuesa[i,] ) j<-j+l if (j=nA4) break } #11 i111 fillIIII1111 Lilill Lllill till 1111 it 11 tlIIli tt tt~tttt tt ff tt tt it tttttt tt ttititittttt'tttt tt ttit #### 4th TOW d2^ Tr^ fr/W if ii il ii ii ii"ii j<-0 repeat { for (i in l:n){ para[4,((nA2)*j+(l+n*(i-l))):(((nA2)*j+(n*i)))]<-values[i,] ) j<-j + 1 if(j==nA3) break } # 1111 It IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIMII HUM IIII Hit IIIITrtl It ttttTfitttttitittttttrttTtttttTf #if(i==l){ #para[4,(9*j+1 ):(9*j+3)]<-values[i,] #) #if(i==2){ #para[4,(9*j+4):(9*j+6)]<-values[i,] #} #if (i==3){ #para[4,(9*j+7):(9*j+9)]<-values[i,] #} #} #j<-j+l #if(j=27) # break ) 128 Simultaneous Product Line Model - Gr id Search Function function (paral,i,n,pmin,smin,pmax,smax,z) { a<-paral[l,i] b<-paral[2,i] dl<-paral[3,i] d2<-paral[4,i] alpha<-paral[5,i] ID<-paral[6,i] flag<-0 l<-z set<-rep(0,l*l) case<-matrix(set, 1,1) casehold<-matrix(set,l ,1) count<-0 set<-rep(0,l*5) res<-matrix(set, 1,5) sc<-(smax-smin)/n pc<-(pmax-pmin)/n sl<-0 s2<-0 pl<-0 p2<-0 pi<-0 pihold<-0 for (i in 1 :n) ( sl<-smin+i*sc for (j in 1 :n) { s2<-smin+j*sc for (k in 1 :n) ) pl<-pmin+k*pc for (m in 1 :n) { p2<-pmin+m*pc shl<-dl*pl+d2*sl Sh2<-dl*p2+d2*s2 if(shl<sh2)( t2<-(p2-pl)/(dl*(p2-pl)+d2*(s2-sl)) tl<-pl/(dl*pl+d2*sl) if ((dl *(p2-pl)+d2*(s2-sl))!=0){ if ((t2>tl) && (tl>0) && ((b-t2)>0) && ((t2-tl)>0)) { pihold<-(pl -alpha*sl A2)*(t2-tl )+(p2-alpha*s2A2)*(b-t2) flag<-2 if (pihold>pi){ pi<-pihold casehold[l,7]<-pl casehold[l,8]<-sl caseholdf l,9]<-p2 casehold[l,10]<-s2 casehold[l,l l]<-pi casehold[ 1,12]<-(pl -alpha*s 1 A2)*(t2-t 1) casehold[ 1,13]<-(p2-alpha*s2A2)*(b-t2) casehold[l,14]<-(t2-tl) casehold[l,15]<-(b-t2) caseholdf 1,16]<-d 1 *p 1 +d2*s 1 casehold[ 1,17]<-d 1 *p2+d2*s2 caseholdf l,18]<-flag ) } }} if(shl>sh2){ 129 Simultaneous Duopoly Model - Grid Search Function function(paral ,i,n,z,step 1 ,step) { a<-paral[l,i] b<-paral[2,i] dl<-paral[3,i] d2<-paral[4,i] alpha<-paral [5,i] ID<-paral[6,i] pmin<-0 smin<-0 pmax<-l smax<-1 zz<-"####l done, going to 4####" zzl <-"#### 4 done ####" set<-rep(0,l*z) outl<-matrix(set,l,z) out4<-matrix(set, 1 ,z) outholdl<-fcasel(a,b,dl.d2,n,pmin,smin,pmax,smax,stepl,step) if (nrow(outholdl)>l){ outcorel<-t(as.matrix(fcleanout(outholdl))) )else{ outcore l<-as.matrix(outhold 1) ) print(zz) outhold4<-fcase4(a,b,dl ,d2,n,pmin,smin,pmax,smax,stepl ,step) if (nrow(outhold4)> 1) { outcore4<-t(as.matrix(fcleanout(outhold4))) }else{ outcore4<-as.matrix(outhold4) } print(zzl) outl[,l]<-paral[6,i] outl[,2:6]<-paral[l:5,i] out 1 [,7:21 ]<-outcore 1 [, 1:15] out4[,l]<-paral[6,i] out4[,2:6]<-paral[l:5,i] out4[,7:21 ]<-outcore4[, 1:15] return(outl,out4) } 130 Appendix B Chapter 6 Product Strategic Complement Analysis Verifying strategic complementary strategies for case 4 with 5 random exogenous parameters. Sni _ Sppxs2 ~ S p P \ s \ + <W ~s]Spp2 -2Sssxs2 +dpp2s2 +Sss22 + s5pas2s2 opx6p2 (6pp2+8ss2-Sppx-Sssxf ^s(p2- px)(asxSpp2-cxsxSppx + asxdss2-5spx) (Spp2+Sss2-Sppx -<5>,)3 -ds($pPis2 ~ S p P \ s \ -Sss\ ~ s \ S p P i + 2Sssxs2 + s P P i s 7 ~s.ssl +2Spaslsx -28pasl) bpx5p2 (Spp2+Sss2-Sppx-Sssx)3 dTl2 = 25s(p2- px)(as2Spp2-as2Sppx +as2Sss2-Ssp2) SsxSs2 (Spp2+Sss2-Sppx-Sssx)3 Sp 0.2 0.5 0.4 0.8 0.9 0.3 0.9 0.4 0.4 0.3 Pi 0.023438 0.195313 0.03125 0.085938 0.0625 P2 0.03125 0.21875 0.164063 0.11719 0.140625 Si 0.132813 0.398438 0.054688 0.242188 0.210938 S2 0.164063 0.4375 0.226563 0.3125 0.34375 m < >o Spx8p2 316.62 31.64 58.23 45.385 14.1654 m < >0 SsxSs2 254.33 223.7 145.71 121.30 21.803 >o dpxbp2 65.94 6.67 19.504 4.1034 2.0784 dsx8s2 11.09 18.48 4.2148 4.0708 1.5642 131 mx SsxSs2 sn2 ATHLETIC FOOTWEAR Price-Perceived Quality: 1) For ATHLETIC FOOTWEAR, the higher the price of the product, the higher the quality of the product. What is your opinion? Please circle a number below. 1 2 3 4 5 6 7 8 9 Stronqlv Disaqree Neutral Stronqlv Aqree 2) To what extent do you think that price reflects the overall quality of ATHLETIC FOOTWEAR prior to purchase. Please circle a number below. 1 2 3 4 5 6 7 8 9 Not at All Neutral Very Well 3) To what extent do you think that price is a reliable indicator of the overall quality of ATHLETIC FOOTWEAR prior to purchase. Please circle a number below. Not at All Neutral Very Reliable 4) On a scale of 1 to 9, how certain are you of these beliefs? Please circle a number below. 1 2 3 4 5 6 7 8 9 Not at All Neutral Very Certain 133 Frequency of purchase: ATHLETIC FOOTWEAR 1a) For ATHLETIC FOOTWEAR, please indicate, on average, how often do vou or your family members buy products in this category. Please circle the appropriate answer. 0 NO, I do not buy Athletic Footwear. (Please answer question 1b if you choose 0) 1 Once in a few years 2 Once a year 3 Once in a few months 4 Once a month 5 Once in a few weeks 6 Once a week 7 Once in a few days 8 Once a day 9 More than once a day 1b) ONLY ANSWER IF YOU CHOSE 0 IN QUESTION 1a) Please indicate, on average, based on your impression, how often people who had purchased ATHLETIC FOOTWEAR before buy products in this category. Please circle the appropriate answer. 1 Once in a few years 2 Once a year 3 Once in a few months 4 Once a month 5 Once in a few weeks 6 Once a week 7 Once in a few days 8 Once a day 9 More than once a day 134 Evaluating ATHLETIC FOOTWEAR: 1) For ATHLETIC FOOTWEAR, it is very difficult to evaluate quality in this product class prior to purchase. What is your opinion with regards to this statement? Strongly Disagree Neutral Strongly Agree 2) To what extent are you able to evaluate the overall quality of ATHLETIC FOOTWEAR prior to purchase? Please circle a number below. 7 8 Not at All Neutral Very Able 3) To what extent are you able to assess the overall quality of ATHLETIC FOOTWEAR prior to purchase? Please circle a number below. Not at All Neutral Very Able 4) On a scale of 1 to 9, how certain are you of these beliefs? Please circle a number below. 1 2 3 4 5 6 7 8 9 Not at All Neutral Very Certain 135 BRAND QUALITY - ATHLETIC FOOTWEAR - Nike 1) On a scale of 1 to 9, how would you rate Nike on overal l qual i ty? 1 2 3 4 5 6 7 8 9 Bad Neutral Good 1 2 3 4 5 6 7 8 9 Inferior Neutral Superior 1 2 - 3 4 5 6 7 8 9 Unfavorable Neutral Favorable 1a) On a scale of 1 to 9, how certain are you of these beliefs? Please circle a number below. 1 2 3 4 5 6 7 8 9 ^ ; * Not at All Neutral Very Certain 136 BRAND QUALITY - ATHLETIC FOOTWEAR - Reebok 2) On a scale of 1 to 9, how would you rate Reebok on overall quality? 1 2 3 4 5 6 7 8 9 Bad Neutral Good 5 6 7 8 Inferior Neutral Superior 6 7 8 Unfavorable Neutral Favorable 2a) On a scale of 1 to 9, how certain are you of these beliefs? Please circle a number below. 1 2 3 4 5 6 7 8 9 Not at All Neutral Very Certain 137 BRAND QUALITY - ATHLETIC FOOTWEAR - Adidas 3) On a scale of 1 to 9, how would you rate Adidas on overal l qual i ty? 1 2 3 4 5 6 7 8 9 < • Bad Neutral Good 1 2 3 4 5 6 7 8 9 < • Inferior Neutral Superior 1 2 3 4 5 6 7 8 9 < • Unfavorable Neutral Favorable 3a) On a scale of 1 to 9, how certain are you of these beliefs? Please circle a number below. Not at All Neutral Very Certain 138 

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