Volume bundle pricing for tied goods and untied goods in the marketplace

Volume bundle pricing for tied goods and untied goods in the marketplace | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Volume bundle pricing for tied goods and untied goods in the marketplace Kwanho Suk This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7625937/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract This research examines how firms apply quantity discounts to tied versus untied goods in volume bundles, focusing on shaving razors and shaving cream. Tied goods require joint use (e.g., razors and blades), while untied goods are consumed independently (e.g., shaving cream). We test whether bundling discounts differ across these categories. Market data from major online retailers show consistent discounts for shaving cream bundles but not for razor bundles. Findings indicate quantity discounts are less common for tied goods, highlighting product interdependence as a key factor shaping firms’ pricing strategies. tied goods bundling quantity discount captive pricing Figures Figure 1 Figure 2 Figure 3 Introduction Pricing strategies are among the most fundamental levers firms use to shape consumer demand and capture value from products (Nagle & Müller, 2018 ). A well-documented strategy is the use of quantity discounts, in which the per-unit price decreases as bundle size increases. Quantity discounts have been widely observed across categories of consumer nondurables such as beverages, detergents, and packaged foods (Gerstner & Hess, 1987 ; Iyengar & Jedidi, 2012 ). Such discounts appeal to consumers’ sensitivity to marginal savings and enable firms to increase sales volumes, promote stockpiling, and reduce per-unit distribution costs (Gupta, 1988 ; Neslin & Shoemaker, 1989 ). However, not all products are equally likely to feature quantity discounts. In particular, tied goods are products in which a durable primary good requires complementary consumables to achieve full functionality, and they often follow different pricing logics from stand-alone nondurable goods (Adams & Yellen, 1976 ; Chintagunta, Gopinath, & Venkataraman, 2018 ). For example, a razor handle has little utility without compatible razor blades. In such markets, firms frequently employ captive pricing strategies, keeping the durable primary product relatively inexpensive while maintaining high margins on the complementary consumables (Hartmann & Nair, 2010 ; Shapiro, 1995 ). This contrasts with untied goods, such as shaving cream, which function as self-contained nondurables and are therefore more likely to exhibit conventional quantity discounting. The current research examines how firms apply quantity discounts differently to tied and untied goods in volume bundling, using shaving razors and shaving cream as focal cases. We hypothesize and empirically test whether volume-bundling pricing systematically differs across these two categories. It is expected that quantity discounts will be less prevalent for tied goods because consumers tend to be less attentive to the costs of complementary consumables than to the upfront price of the durable. This reduced sensitivity weakens firms’ incentives to pass along per-unit savings in larger bundles, since profitability can instead be extracted in the aftermarket. By contrast, for untied goods, consumers anticipate and respond to conventional per-unit savings in larger bundles, reinforcing firms’ incentives to apply systematic quantity discounts. To test this prediction, this research analyzes market data from major online retailers in the United States and Korea, comparing how firms employ quantity discounts in razor bundles versus shaving cream bundles. This research contributes to the literature in three ways. First, it extends the literature on quantity discounts by showing that their application is contingent on whether products are tied or untied. Second, it provides empirical evidence on the captive pricing of razor blades, a longstanding case in marketing and industrial organization, by comparing it against a functionally related but untied product. Third, by using cross-national market data, it offers insights into the generalizability of these pricing patterns across cultural and institutional contexts. Theory and hypothesis Tied and untied goods Tied goods are products intended for joint use, where the value of the primary good depends on the complementary product (Chintagunta et al., 2018 ; Hartmann & Nair, 2010 ). The primary good is typically a durable item, sold either alone or bundled with complementary products, which take the form of nondurables (e.g., razors and blades, printers and ink cartridges, coffee machines and pods) or services (e.g., e-book readers and subscriptions). By contrast, untied goods are more common in markets. These products are complete and consumed independently, without requiring a complementary component to deliver value (e.g., toothpaste, shampoo, packaged food). Unlike tied goods, untied goods provide value on their own, making them the predominant form of consumer product (Bakos & Brynjolfsson, 1999; Stremersch & Tellis, 2002 ). Given the distinctive characteristics of tied goods, the discussion below concentrates on consumer decision-making and pricing strategies in tied-goods contexts. Consumer decisions of tied goods purchase A unique property of tied goods is that consumers make simultaneous decisions regarding both the primary and complementary products (Hartmann & Nair, 2010 ; Stremersch & Tellis, 2002 ). When purchasing tied goods, consumers must evaluate the costs and benefits of both the primary durable and complementary consumables. For example, buyers of a single-serve coffee machine also consider the price, availability, and quality of compatible coffee pods when making their decision (Chintagunta et al., 2018 ). Prior research suggests that consumers tend to focus more more on the durable component of the purchase (i.e, the primary good) than on the complementary consumables. For example, consumers tend to overweight the characteristics and costs of the durable product (e.g., printers, razors, video game consoles) while underweighting the ongoing expenditures for the tied goods such as ink cartridges, blades, or game software (Stremersch & Tellis, 2002 ). This asymmetry in attention can lead to suboptimal decision-making, where consumers underestimate the long-term cost of ownership associated with tied-goods systems. Consequently, firms strategically exploit this bias by setting lower prices on the durable component and recouping profits through higher margins on the complementary goods (Schmalensee, 1984 ). Pricing of tied goods The pricing of tied goods is often governed by the practice of captive pricing, in which firms sell the durable primary good at a relatively low price and generate profits through high margins on the complementary consumable. Classic economic theory explains this strategy as a form of price discrimination: by subsidizing the durable, firms expand adoption and subsequently extract consumer surplus through repeat purchases of the tied consumable (Adams & Yellen, 1976 ; Schmalensee, 1984 ). This mechanism is especially profitable when consumers exhibit heterogeneous usage rates of the complementary good, allowing firms to align revenues with intensity of use rather than charging a uniform premium on the durable alone (Nalebuff, 2004 ). For firms, captive pricing is a deliberate strategic approach to setting prices across the durable and its consumables. By lowering the price of the durable good, firms accelerate adoption and expand the installed base, while higher margins on the consumables provide a steady revenue stream over time (Chintagunta et al., 2018 ; Hartmann & Nair, 2010 ). This decision involves balancing short-term losses or thin margins on the durable against long-term profits from repeat purchases of tied goods, making the durability–consumable price ratio a central element of competitive strategy. Firms also recognize that consumers evaluate tied goods as a system rather than as independent products, which allows them to shift profitability from the upfront purchase to the aftermarket without necessarily undermining demand (Stremersch & Tellis, 2002 ). Therefore, captive pricing is not merely a tactic of discounting or bundle design, but a forward-looking strategy for acquiring customers, locking them into the firm’s ecosystem, and maximizing lifetime value through consumable sales (Shapiro, 1995 ). Volume Bundling Bundling refers to offering two or more products for sale as a single package at a single, typically discounted, price. The type of bundling examined in this paper is volume bundling, which refers to the practice of offering multiple units of the same product in a package at a lower price per unit than if each unit were purchased individually. Unlike mixed bundling, which combines heterogeneous products, volume bundling involves homogeneous items (e.g., multi-packs of beverages, bulk groceries). This strategy is widely applied across consumer packaged goods, subscription services, and digital products. From a theoretical perspective, volume bundling is a form of second-degree price discrimination that enables firms to segment consumers based on purchase quantities and usage intensity (Adams & Yellen, 1976 ; Stremersch & Tellis, 2002 ). Volume bundling takes on distinct forms depending on whether the products involved are tied or untied. For untied goods, volume bundling typically appears as homogeneous bundles in which multiple identical units are packaged together and sold at a discounted per-unit price. Examples include multipacks of soft drinks or family-sized household products. Research shows that this form of bundling can stimulate stockpiling, increase perceived value, and accelerate consumption (Wansink & Deshpandé, 1994). By contrast, volume bundling of tied goods typically takes the form of packages that vary the number of complementary components included with the primary durable. For instance, a razor handle may be bundled with two, four, or ten blades. The underlying logic of this practice extends the tying strategy: firms price the durable attractively to promote adoption, while structuring complementary-unit bundles in ways that influence usage intensity and lock consumers into the aftermarket (Adams & Yellen, 1976 ; Nalebuff, 2004 ). Quanity diccount for tied-goods and untied-goods volume bundles A central determinant of the effectiveness of volume bundling is the pricing strategy applied to the bundle. For tied goods, consumers are generally less sensitive to the costs of complementary goods than to the price of the primary durable. Therefore, pricing strategies for tied goods are expected to differ from those for untied goods. In particular, the extent to which firms apply quantity discounts is likely to vary across the two categories. Quantity discounts, also referred to as volume discounts, involve price reductions that lower the per-unit cost of products sold in larger quantities (Gerstner & Hess, 1987 ). Market studies indicate that the vast majority of products (over 85 percent) are sold with such discounts (Clerides & Courty, 2017 ; Gerstner & Hess, 1987 ). This widespread pattern has become a pricing norm, driven both by cost efficiencies (Manning, Sprott, & Miyazaki, 1998 ; Maxwell, 1995 ) and by consumer expectations that larger bundles should carry lower per-unit prices. Consistent with this logic, Iyengar and Jedidi ( 2012 ) demonstrate that consumers’ marginal willingness to pay declines as quantity increases. For untied goods, the commonly observed pattern of quantity discounts is expected to hold. Larger bundles (e.g., an eight-pack of beverages) are typically sold at a lower per-unit price than smaller bundles (e.g., a two-pack). In these cases, a clear and consistent pattern of decreasing per-unit prices as bundle size increases is expected. For tied goods, however, the logic of quantity discounting is more nuanced. Discounts are assessed with respect to the per-unit price of the complementary component, such as the per-blade cost in razor bundles. Although, in principle, larger bundles could provide lower per-unit prices, systematic quantity discounts are less likely to emerge for tied goods. Two factors can contribute to this pattern. First, consumers tend to focus more on the upfront price of the durable than on the ongoing costs of the consumables, which diminishes firms’ incentives to design bundle pricing strategies that emphasize marginal savings on complements. Second, the effective cost of complements in tied bundles is less transparent. Unlike untied goods, where the per-unit price is typically salient, consumers of tied goods must compare across bundles to infer the unit cost of the consumable. This added complexity not only reduces buyers’ ability to perceive savings but also weakens sellers’ motivation to structure discounts around them. Taken together, these dynamics make quantity discounts less prevalent in tied-goods markets. H1 Quantity discounts in volume bundles are less prevalent for tied goods than for untied goods. Methodology Overview This empirical study analyzes market data to examine how firms offer quantity discounts differently for shaving razor bundles and shaving cream bundles. Shaving razor bundles, which include a durable product (razor handle) and complements (razor blades), represent tied goods. Shaving razors were selected because they are a classic example of tied goods utilizing captive pricing strategies. Additionally, shaving razors provide a useful case for examining the variation in blade quantities within a single brand or model. For example, the same razor models are offered with one, two, or four blades (see, Fig. 1 ). By contrast, shaving cream represents untied goods. Shaving razors and shaving cream were selected because they are commonly used together in the same consumption context and are frequently produced by the same manufacturers, which helps to control for brand-level differences. [Insert Fig. 1 about here] The analysis examines the relationship between bundle size and selling price using data collected from online retailers. For razor bundles, the focus is on whether the number of blades is associated with both the total selling price and the per-blade cost. For shaving cream, the analysis explores the relationship between the number of units in a bundle and both the total selling price and the per-unit price. As suggested by H1, quantity discounts are expected to be less common for shaving razor bundles than for shaving cream bundles. When quantity discounts are present, two patterns are anticipated: (1) the relationship between bundle size and total selling price should be increasing but concave, and (2) the relationship between bundle size and per-unit price should be negative. Any deviation from these patterns would suggest that quantity discounts are not systematically applied. Data Razor bundle Information on razor blade bundles was collected from three major online retailers in May 2024. Two of the retailers were based in the United States and one in Korea. Our search focused on brand/models (e.g., Gillette Mach3) that offered multiple bundle types in terms of the number of blades included (e.g., 1-, 2-, and 4-blade bundles). A total of 20 brand/models that provided variation in blade quantities per bundle were identified. A set of bundles was defined as a unique brand/model even when the same manufacturer’s brand was sold across different stores. Across these 20 brand/models, price information was collected for 176 product bundles. For each item, both the selling price and the number of blades were recorded. Descriptive statistics for the razor bundle data are presented in Table 1 . [Insert Table 1 about here] To facilitate analysis, prices were normalized and the price per blade was calculated for items within the same razor brand/model. This normalization controlled for brand-level price variability, ensuring that comparisons reflected relative pricing patterns rather than absolute brand differences. First, the base price for each brand/model was defined as the selling price of the basic bundle, which consisted of a razor handle with a single blade. For example, if the basic bundle was priced at $ 10.00, this amount served as the reference point for subsequent calculations. Second, the standardized price for each larger bundle was calculated as its selling price relative to the base price. Thus, a two-blade bundle priced at $ 10.99 yielded a standardized price of 1.09 (i.e., $ 10.99/ $ 10.00). This allowed bundles of different sizes to be compared on a common scale. Finally, the price per blade was derived to capture the marginal cost of additional blades beyond the basic bundle. This was computed as the difference between the standardized price and 1 (the base) divided by the number of additional blades. In the example above, the two-blade bundle produced a per-blade price of 0.09 (i.e., [1.09 − 1.00]/[2 − 1]). This measure provided a standardized index of the incremental cost of complementary components across bundle sizes. The full normalization process is illustrated in Table 2 . [Insert Table 2 about here] Shaving cream Data on shaving cream products were collected in June 2024 from the same three major online stores where the razor bundle data were sourced. A total of 43 distinct brand/models were identified, with variations in the number of product units. A unique brand/model was defined when the same producer's brand was sold in bundles of different quantities. Across these 43 brand/models, data on selling price and unit quantity (i.e., bundle size) were collected for a total of 441 individual items. The descriptive statistics are presented in Table 3 . [Insert Table 3 about here] Using the price and quantity data, both standardized selling prices and per-unit prices were calculated within each brand/model. First, the base price was defined as the selling price of the single-unit product. Second, the standardized price for each multi-unit bundle was computed relative to the base price, allowing direct comparison across bundle sizes. Finally, the price per unit was derived from the standardized price to capture the relative cost efficiency of larger bundles. Results Bundle size and selling price The relationship between bundle size and selling price was analyzed separately for razor and shaving cream bundles. 1 Figgure 2A shows the relationship between the number of blades in a bundle and the standardized selling price for razor bundles. Figure 2 B presents the relationship between the unit quantity and the standardized selling price for shaving cream bundles. [Insert Fig. 2 about here] Razor bundle The relationship between the number of blades in a bundle and the standardized price was analyzed by regressing the standardized price of the items on the (mean-centered) blade-quantity and its squared term (blade-quantity 2 ). The squared term was included to capture a quadratic relationship. Nineteen brand/model dummies were included as control variables. The results of the polynomial regression showed that the blade-quantity coefficient was significant ( b = 0.292, t (154) = 20.44, p < .001). As expected, bundles with more blades generally had higher selling prices. However, the blade-quantity 2 term was not significant ( b = − 0.003, t (154) = 1.58, p = .117). This result indicated that razor blades included in the bundles did not provide significant quantity discounts. Table 1 A presents the results. Additionally, the relationship between blade quantity and standardized price was analyzed separately for the US and Korean retailers (Table 4 A). For the US retailers, the result was statistically the same, showing that only the blade-quantity coefficient was positive and significant ( p < .001). For Korean data, both blade-quantity ( p < .001) and blade-quantity 2 ( p = .041) coefficients were significant. The negatively significant blade-quantity 2 indicated that quantity discounts for larger-volume blades were observed only in the Korean market. [Insert Table 4 about here] Shaving cream bundle A polynomial regression examining the relationship between the number of shaving cream units in a bundle and the standardized price showed significant results for the unit-quantity coefficient ( b = 0.508, t (393) = 18.36, p < .001) and unit-quantity 2 coefficient ( b = − 0.003, t (393) = 5.28, p < .001). This pattern indicated that the relationship between bundle size and selling price is increasing and concave, revealing a significant quantity discount. Separate analyses for the US and Korean data showed the same pattern, with positive and significant unit-quantity coefficients ( p < .001) and negative and significant unit-quantity 2 coefficients ( p < .002). Table 4 B presents the results. Bundle size and price per unit The relationship between bundle size and price per unit for shaving razor and shaving cream bundles was also examined. This analysis did not include bundles containing only a single unit, as they were used as the base price. Figure 2 displays scatterplots showing the association between bundle size and price per product unit for razor bundles (Fig. 3 A) and shaving cream bundles (Fig. 3 B). Razor bundle The influence of the number of blades in the bundle on the price per blade was tested using a regression analysis with blade quantity, blade quantity 2 , and brand/model dummies as independent variables. Table 5 A shows the results. The blade quantity coefficient was not significant ( b = 0.003, t (114) = 0.44, p = .661). This finding indicated that the price per blade did not decrease as bundle size increased, providing no evidence of quantity discounts. The blade quantity 2 was negative and significant ( b = − 0.002, t (114) = 2.18, p = .032), indicating a concave relationship. The analyses conducted separately for the US and South Korea did not show evidence of quantity discounts either. The blade quantity coefficient was significant for both the US data ( p = .506) and the Korean data ( p = .346). [Insert Table 5 about here] Shaving cream bundle A regression analysis that examined the relationship between bundle size and price per unit for shaving cream data showed that the unit-quantity coefficient was negative and significant ( b = − 0.021, t (297) = 3.83, p < .001). This result indicated that the price per unit tended to be lower for larger bundles, revealing significant quantity discounts. The unit-quanity 2 coefficient was positive and significant ( b < 0.001, t (297) = 3.01, p = .003), suggesting that the marginal change of quantity discounts was smaller as the bundle size increased. Separate analyses for the US and Korean data showed the same pattern, with negative and significant unit-quantity coefficients ( p < .010) and positive and significant unit-quantity 2 coefficients ( p < .033). The results are presented in Table 5 B. General discussion and conclusions Summary of findings The market data analysis focused on bundle pricing strategies for razor blades and shaving cream, chosen as representative products for tied and untied goods. The findings revealed that quantity discount, commonly practiced for bundle pricing, was observed for shaving cream bundles but not for razor bundles, providing support for H1. The absence of quantity discounts for razor bundles may reflect a greater focus on the cost of the durable product rather than on complementary items. By contrast, quantity discounts for shaving cream bundles align with conventional pricing approaches for untied goods. Contributions First, it advances research on quantity discounting by demonstrating that its application depends on whether goods are tied or untied. While prior studies have documented consumer responses to bulk discounts in nondurables (Gupta, 1988 ; Neslin & Shoemaker, 1989 ), this research shows that the pricing of tied goods deviates from this pattern. Second, it extends work on bundling and captive pricing (Adams & Yellen, 1976 ; Schmalensee, 1984 ; Stremersch & Tellis, 2002 ). Razors illustrate how firms maintain margins on complementary consumables by avoiding quantity discounts, while shaving cream exemplifies how conventional bundling strategies apply to stand-alone nondurables. Our results thus provide empirical validation of long-standing theoretical claims about aftermarkets and captive goods (Shapiro, 1995 ). Third, by using cross-national retail data, we provide evidence of generalizability. Despite institutional and cultural differences between the United States and Korea, the observed contrast between razors and shaving cream was largely consistent across markets. This suggests that the tied versus untied distinction is a robust determinant of pricing practices, transcending specific market contexts. Finally, the study offers managerial implications. For tied goods, firms may sustain profitability without offering discounts on complements, while for untied nondurables, consumers expect and respond to conventional quantity discounts. Managers should therefore consider product interdependence when designing bundle sizes and discount policies. Limitations and Future Research This research has several limitations that suggest avenues for future inquiry. First, the data were restricted to online retailers in two countries and to a single product category. Future research should examine whether the findings generalize across other tied-good systems (e.g., printers and ink, coffee machines and pods) and across broader retail environments, including offline settings. Second, the analysis focused on observed pricing practices rather than consumer responses. Experimental studies could test how consumers perceive fairness, value, or exploitation in tied versus untied discount structures, and whether price transparency (e.g., explicit per-unit labeling) moderates these effects. Third, this study did not evaluate whether the differential application of volume-bundling strategies actually translates into higher profitability for firms. Future research should investigate the profit implications of discounting versus non-discounting practices, examining whether avoiding quantity discounts in tied goods enhances long-term margins, consumer lock-in, and aftermarket revenues compared to conventional discounting strategies in untied goods. Table 1 Descriptive statistics of shaving razor bundles Category N Average Price Average Blade Quantity Country USA (USD) 82 20.59 (11.11) 4.37 (4.03) Korea (KRW) 94 27,495.96 (17,500.68) 5.56 (4.97) Brand Gillette 134 20.82 (11.04) 3.95 (3.82) Schick 29 19.40 (12.86) 5.00 (4.64) Dorco 13 20.98 (8.02) 7.80 (3.83) Blade Quantity 1 blade 40 11.57 (5.09) 2 blades 48 13.45 (4.61) 3 blades 5 28.96 (0.03) 4 blades 13 23.90 (8.57) 5 blades 13 25.08 (6.50) 6–9 blades 25 30.08 (10.02) 10 blades 7 30.08 (9.81) 10 + blades 25 36.35 (11.85) Notes : Standard deviations are in parentheses. Average prices are presented for US data only, except for the data by country. Table 2 Examples of market data and price indices Market Data Price Indices Price [1] Blade quantity [2] Base price [3] Standardized price [4] = [3]/ [1] Price per blade [5] = ([4]–1)/ ([2]–1) $ 10.00 1 10.00 1.00 $ 10.90 2 10.00 1.09 0.09 $ 13.00 4 10.00 1.30 0.10 $ 15.60 8 10.00 1.56 0.08 Table 3 Descriptive statistics of shaving cream bundles Category N Average Price Average Unit Quantity Country USA (USD) 168 29.27 (28.14) 6.80 (10.76) Korea (KRW) 273 22,421.25 (23,533.24) 4.82 (8.47) Brand Gillette 228 31.78 (31.54) 8.29 (12.40) Schick 87 16.77 (6.08) 2.57 (1.40) Nivea 126 25.75 (18.01) 3.40 (2.68) Unit Quantity 1 unit 96 9.63 (4.12) 2 units 83 16.15 (4.41) 3 units 97 19.47 (1.81) 4 units 43 24.36 (10.10) 5 units 17 39.21 (10.81) 6–9 units 53 33.36 (10.57) 10 units 4 56.80 (0.00) 10 + units 48 71.13 (38.71) Notes : Standard deviations are in parentheses. Average prices are presented for US data only, except for the data by country. Table 4 Influence of quantities on standardized selling price A. Razir bundle All Data US South Korea Blade-quantity 0.292 (0.014) * 0.325 (0.024) * 0.277 (0.016) * Blade-quantity 2 − 0.003 (0.002) − 0.002 (0.003) − 0.005 (0.002) * Constant 2.072 (0.245) * 2.150 (0.280) * 1.673 (0.095) * R 2 .868 .860 .895 N 176 82 94 B. Shaving cream All Data US South Korea Unit-quantity 0.508 (0.028) * 0.438 (0.023) * 0.609 (0.038) * Unit-quantity 2 − 0.003 (0.001) * − 0.005 (0.001) * − 0.003 (0.001) * Constant 1.869 (1.497) 1.976 (0.905) * 3.262 (0.364) * R 2 .773 .861 .836 N 441 168 273 Notes : Dummy coefficients are not presented. * p < .05. Table 5 Influence of quantities on price per unit A. Razor All Data US South Korea Blade quantity − 0.003 (0.006) − 0.006 (0.009) 0.008 (0.009) Blade quantity 2 − 0.002 (0.001) * − 0.002 (0.001) − 0.002 (0.001) Constant 0.285 (0.134) 0.212 (0.144) 0.123 (0.062) R 2 .460 .372 .478 N 136 60 76 B. Shaving cream All Data US South Korea Unit quantity − 0.021 (0.005) * − 0.019 (0.005) * − 0.023 (0.009) * Unit quantity 2 0.000 (0.000) * 0.000 (0.000) * 0.000 (0.000) * Constant 0.323 (0.387) 0.314 (0.276) 1.265 (0.088) * R 2 .539 .542 .508 N 345 132 213 Notes : Dummy coefficients are not presented. * p < .05. Declarations Ethical approval Not applicable. Conflicts of interest The author declares no conflicts of interest. Funding This work received no external funding. Author Contribution Author A has colleced and analyzed data, and wrote the whole manuscript. Data Availability The data will be posted on public data repository. References Adams, W. J., and J. L. Yellen. 1976. “Commodity Bundling and the Burden of Monopoly.” Quarterly Journal of Economics 90 (3): 475–98. Bakos, Y., and E. Brynjolfsson. 1999. “Bundling Information Goods: Pricing, Profits, and Efficiency.” Management Science 45 (12): 1613–30. Chintagunta, P. K., S. Gopinath, and S. 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Deshpandé. 1994. “Out of Sight, Out of Mind: The Impact of Household Stockpiling on Usage Rates.” Marketing Letters 5 (1): 91–100. Footnotes Combining razor and shaving cream bundle data and analyzing interaction was not appropriate because of the differing nature of bundling between the two products and the disparity in the average price per quantity. Additional Declarations No competing interests reported. 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Suk","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVRIiWNgGAWjYBACCQYGZoYPB+D8BOK0MM4gWQszD0laJPvPGBvbnLHJ52c/wPjhB0NaPkEt0hI5xsk5N9IsZ/YkMEv2MORYNhDSIifBY3w458NhA4MDCQzSDAwVBgRtkeM/Y3zYAqjF/vwD5t9EaZFmADqM4QbQFokENqAtOYS1SM5IKzbsOZNmIHHjYZtlj0EaYS0S5w9vlvhxzMaAvz/58I0fFcmEtSABxgYGBpI0jIJRMApGwSjACQDGkjXUBWpxEgAAAABJRU5ErkJggg==","orcid":"","institution":"Korea University","correspondingAuthor":true,"prefix":"","firstName":"Kwanho","middleName":"","lastName":"Suk","suffix":""}],"badges":[],"createdAt":"2025-09-16 05:08:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7625937/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7625937/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":93718153,"identity":"db3099e7-89ba-42eb-975b-403a7fa71124","added_by":"auto","created_at":"2025-10-16 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20:36:16","extension":"xml","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":80413,"visible":true,"origin":"","legend":"","description":"","filename":"c0211d88ecfe49c291b174c1a797294f1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7625937/v1/866134ce54448a421b1052b0.xml"},{"id":93717786,"identity":"fde14007-6269-41a1-8b86-f0cbed71cbd4","added_by":"auto","created_at":"2025-10-16 20:36:16","extension":"html","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":85038,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7625937/v1/8b26d39052186b9309ec807d.html"},{"id":93717776,"identity":"da86e066-a7aa-427d-955d-abbefa1e1f90","added_by":"auto","created_at":"2025-10-16 20:36:15","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":239099,"visible":true,"origin":"","legend":"\u003cp\u003eShaving razor bundles with varying blade quantities in the marketplace\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7625937/v1/6bb8b73d716150e9fe414c08.jpeg"},{"id":93717779,"identity":"b17e89f1-4df9-4974-9726-1a6fa3325129","added_by":"auto","created_at":"2025-10-16 20:36:15","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":144849,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between unit quantity and standardized price for razor bundle (A) and shaving cream bundle (B)\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7625937/v1/d1729befa7ff901480fd3df2.jpeg"},{"id":93717781,"identity":"17aeb286-ee3d-46c5-8abb-608bd770cf3b","added_by":"auto","created_at":"2025-10-16 20:36:15","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":146674,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between unit quantity and price per unit for razor bundle (A) and shaving cream bundle (B)\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7625937/v1/9a74f6404b9f71f1365eaae1.jpeg"},{"id":93718285,"identity":"6ecf4f11-409b-4b80-9824-ed9ed2b65c90","added_by":"auto","created_at":"2025-10-16 20:52:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1374861,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7625937/v1/4d31431b-d01b-41bb-8a48-82853b671a7f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Volume bundle pricing for tied goods and untied goods in the marketplace","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePricing strategies are among the most fundamental levers firms use to shape consumer demand and capture value from products (Nagle \u0026amp; M\u0026uuml;ller, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). A well-documented strategy is the use of quantity discounts, in which the per-unit price decreases as bundle size increases. Quantity discounts have been widely observed across categories of consumer nondurables such as beverages, detergents, and packaged foods (Gerstner \u0026amp; Hess, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Iyengar \u0026amp; Jedidi, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Such discounts appeal to consumers\u0026rsquo; sensitivity to marginal savings and enable firms to increase sales volumes, promote stockpiling, and reduce per-unit distribution costs (Gupta, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Neslin \u0026amp; Shoemaker, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1989\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eHowever, not all products are equally likely to feature quantity discounts. In particular, tied goods are products in which a durable primary good requires complementary consumables to achieve full functionality, and they often follow different pricing logics from stand-alone nondurable goods (Adams \u0026amp; Yellen, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1976\u003c/span\u003e; Chintagunta, Gopinath, \u0026amp; Venkataraman, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). For example, a razor handle has little utility without compatible razor blades. In such markets, firms frequently employ captive pricing strategies, keeping the durable primary product relatively inexpensive while maintaining high margins on the complementary consumables (Hartmann \u0026amp; Nair, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Shapiro, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1995\u003c/span\u003e). This contrasts with untied goods, such as shaving cream, which function as self-contained nondurables and are therefore more likely to exhibit conventional quantity discounting.\u003c/p\u003e\u003cp\u003eThe current research examines how firms apply quantity discounts differently to tied and untied goods in volume bundling, using shaving razors and shaving cream as focal cases. We hypothesize and empirically test whether volume-bundling pricing systematically differs across these two categories. It is expected that quantity discounts will be less prevalent for tied goods because consumers tend to be less attentive to the costs of complementary consumables than to the upfront price of the durable. This reduced sensitivity weakens firms\u0026rsquo; incentives to pass along per-unit savings in larger bundles, since profitability can instead be extracted in the aftermarket. By contrast, for untied goods, consumers anticipate and respond to conventional per-unit savings in larger bundles, reinforcing firms\u0026rsquo; incentives to apply systematic quantity discounts. To test this prediction, this research analyzes market data from major online retailers in the United States and Korea, comparing how firms employ quantity discounts in razor bundles versus shaving cream bundles.\u003c/p\u003e\u003cp\u003eThis research contributes to the literature in three ways. First, it extends the literature on quantity discounts by showing that their application is contingent on whether products are tied or untied. Second, it provides empirical evidence on the captive pricing of razor blades, a longstanding case in marketing and industrial organization, by comparing it against a functionally related but untied product. Third, by using cross-national market data, it offers insights into the generalizability of these pricing patterns across cultural and institutional contexts.\u003c/p\u003e"},{"header":"Theory and hypothesis","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eTied and untied goods\u003c/h2\u003e\u003cp\u003eTied goods are products intended for joint use, where the value of the primary good depends on the complementary product (Chintagunta et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hartmann \u0026amp; Nair, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). The primary good is typically a durable item, sold either alone or bundled with complementary products, which take the form of nondurables (e.g., razors and blades, printers and ink cartridges, coffee machines and pods) or services (e.g., e-book readers and subscriptions).\u003c/p\u003e\u003cp\u003eBy contrast, untied goods are more common in markets. These products are complete and consumed independently, without requiring a complementary component to deliver value (e.g., toothpaste, shampoo, packaged food). Unlike tied goods, untied goods provide value on their own, making them the predominant form of consumer product (Bakos \u0026amp; Brynjolfsson, 1999; Stremersch \u0026amp; Tellis, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Given the distinctive characteristics of tied goods, the discussion below concentrates on consumer decision-making and pricing strategies in tied-goods contexts.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eConsumer decisions of tied goods purchase\u003c/h3\u003e\n\u003cp\u003eA unique property of tied goods is that consumers make simultaneous decisions regarding both the primary and complementary products (Hartmann \u0026amp; Nair, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Stremersch \u0026amp; Tellis, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). When purchasing tied goods, consumers must evaluate the costs and benefits of both the primary durable and complementary consumables. For example, buyers of a single-serve coffee machine also consider the price, availability, and quality of compatible coffee pods when making their decision (Chintagunta et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003ePrior research suggests that consumers tend to focus more more on the durable component of the purchase (i.e, the primary good) than on the complementary consumables. For example, consumers tend to overweight the characteristics and costs of the durable product (e.g., printers, razors, video game consoles) while underweighting the ongoing expenditures for the tied goods such as ink cartridges, blades, or game software (Stremersch \u0026amp; Tellis, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). This asymmetry in attention can lead to suboptimal decision-making, where consumers underestimate the long-term cost of ownership associated with tied-goods systems. Consequently, firms strategically exploit this bias by setting lower prices on the durable component and recouping profits through higher margins on the complementary goods (Schmalensee, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1984\u003c/span\u003e).\u003c/p\u003e\n\u003ch3\u003ePricing of tied goods\u003c/h3\u003e\n\u003cp\u003eThe pricing of tied goods is often governed by the practice of captive pricing, in which firms sell the durable primary good at a relatively low price and generate profits through high margins on the complementary consumable. Classic economic theory explains this strategy as a form of price discrimination: by subsidizing the durable, firms expand adoption and subsequently extract consumer surplus through repeat purchases of the tied consumable (Adams \u0026amp; Yellen, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1976\u003c/span\u003e; Schmalensee, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1984\u003c/span\u003e). This mechanism is especially profitable when consumers exhibit heterogeneous usage rates of the complementary good, allowing firms to align revenues with intensity of use rather than charging a uniform premium on the durable alone (Nalebuff, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2004\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eFor firms, captive pricing is a deliberate strategic approach to setting prices across the durable and its consumables. By lowering the price of the durable good, firms accelerate adoption and expand the installed base, while higher margins on the consumables provide a steady revenue stream over time (Chintagunta et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hartmann \u0026amp; Nair, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). This decision involves balancing short-term losses or thin margins on the durable against long-term profits from repeat purchases of tied goods, making the durability\u0026ndash;consumable price ratio a central element of competitive strategy. Firms also recognize that consumers evaluate tied goods as a system rather than as independent products, which allows them to shift profitability from the upfront purchase to the aftermarket without necessarily undermining demand (Stremersch \u0026amp; Tellis, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Therefore, captive pricing is not merely a tactic of discounting or bundle design, but a forward-looking strategy for acquiring customers, locking them into the firm\u0026rsquo;s ecosystem, and maximizing lifetime value through consumable sales (Shapiro, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1995\u003c/span\u003e).\u003c/p\u003e\n\u003ch3\u003eVolume Bundling\u003c/h3\u003e\n\u003cp\u003eBundling refers to offering two or more products for sale as a single package at a single, typically discounted, price. The type of bundling examined in this paper is volume bundling, which refers to the practice of offering multiple units of the same product in a package at a lower price per unit than if each unit were purchased individually. Unlike mixed bundling, which combines heterogeneous products, volume bundling involves homogeneous items (e.g., multi-packs of beverages, bulk groceries). This strategy is widely applied across consumer packaged goods, subscription services, and digital products. From a theoretical perspective, volume bundling is a form of second-degree price discrimination that enables firms to segment consumers based on purchase quantities and usage intensity (Adams \u0026amp; Yellen, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1976\u003c/span\u003e; Stremersch \u0026amp; Tellis, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2002\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eVolume bundling takes on distinct forms depending on whether the products involved are tied or untied. For untied goods, volume bundling typically appears as homogeneous bundles in which multiple identical units are packaged together and sold at a discounted per-unit price. Examples include multipacks of soft drinks or family-sized household products. Research shows that this form of bundling can stimulate stockpiling, increase perceived value, and accelerate consumption (Wansink \u0026amp; Deshpand\u0026eacute;, 1994).\u003c/p\u003e\u003cp\u003eBy contrast, volume bundling of tied goods typically takes the form of packages that vary the number of complementary components included with the primary durable. For instance, a razor handle may be bundled with two, four, or ten blades. The underlying logic of this practice extends the tying strategy: firms price the durable attractively to promote adoption, while structuring complementary-unit bundles in ways that influence usage intensity and lock consumers into the aftermarket (Adams \u0026amp; Yellen, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1976\u003c/span\u003e; Nalebuff, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2004\u003c/span\u003e).\u003c/p\u003e\n\u003ch3\u003eQuanity diccount for tied-goods and untied-goods volume bundles\u003c/h3\u003e\n\u003cp\u003eA central determinant of the effectiveness of volume bundling is the pricing strategy applied to the bundle. For tied goods, consumers are generally less sensitive to the costs of complementary goods than to the price of the primary durable. Therefore, pricing strategies for tied goods are expected to differ from those for untied goods. In particular, the extent to which firms apply quantity discounts is likely to vary across the two categories.\u003c/p\u003e\u003cp\u003eQuantity discounts, also referred to as volume discounts, involve price reductions that lower the per-unit cost of products sold in larger quantities (Gerstner \u0026amp; Hess, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1987\u003c/span\u003e). Market studies indicate that the vast majority of products (over 85 percent) are sold with such discounts (Clerides \u0026amp; Courty, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Gerstner \u0026amp; Hess, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1987\u003c/span\u003e). This widespread pattern has become a pricing norm, driven both by cost efficiencies (Manning, Sprott, \u0026amp; Miyazaki, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Maxwell, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1995\u003c/span\u003e) and by consumer expectations that larger bundles should carry lower per-unit prices. Consistent with this logic, Iyengar and Jedidi (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) demonstrate that consumers\u0026rsquo; marginal willingness to pay declines as quantity increases.\u003c/p\u003e\u003cp\u003eFor untied goods, the commonly observed pattern of quantity discounts is expected to hold. Larger bundles (e.g., an eight-pack of beverages) are typically sold at a lower per-unit price than smaller bundles (e.g., a two-pack). In these cases, a clear and consistent pattern of decreasing per-unit prices as bundle size increases is expected.\u003c/p\u003e\u003cp\u003eFor tied goods, however, the logic of quantity discounting is more nuanced. Discounts are assessed with respect to the per-unit price of the complementary component, such as the per-blade cost in razor bundles. Although, in principle, larger bundles could provide lower per-unit prices, systematic quantity discounts are less likely to emerge for tied goods. Two factors can contribute to this pattern. First, consumers tend to focus more on the upfront price of the durable than on the ongoing costs of the consumables, which diminishes firms\u0026rsquo; incentives to design bundle pricing strategies that emphasize marginal savings on complements. Second, the effective cost of complements in tied bundles is less transparent. Unlike untied goods, where the per-unit price is typically salient, consumers of tied goods must compare across bundles to infer the unit cost of the consumable. This added complexity not only reduces buyers\u0026rsquo; ability to perceive savings but also weakens sellers\u0026rsquo; motivation to structure discounts around them. Taken together, these dynamics make quantity discounts less prevalent in tied-goods markets.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eH1\u003c/strong\u003e\u003cp\u003eQuantity discounts in volume bundles are less prevalent for tied goods than for untied goods.\u003c/p\u003e\u003c/p\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eMethodology\u003c/h2\u003e\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\u003ch2\u003eOverview\u003c/h2\u003e\u003cp\u003eThis empirical study analyzes market data to examine how firms offer quantity discounts differently for shaving razor bundles and shaving cream bundles. Shaving razor bundles, which include a durable product (razor handle) and complements (razor blades), represent tied goods. Shaving razors were selected because they are a classic example of tied goods utilizing captive pricing strategies. Additionally, shaving razors provide a useful case for examining the variation in blade quantities within a single brand or model. For example, the same razor models are offered with one, two, or four blades (see, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). By contrast, shaving cream represents untied goods. Shaving razors and shaving cream were selected because they are commonly used together in the same consumption context and are frequently produced by the same manufacturers, which helps to control for brand-level differences.\u003c/p\u003e\u003cp\u003e[Insert Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e about here]\u003c/p\u003e\u003cp\u003eThe analysis examines the relationship between bundle size and selling price using data collected from online retailers. For razor bundles, the focus is on whether the number of blades is associated with both the total selling price and the per-blade cost. For shaving cream, the analysis explores the relationship between the number of units in a bundle and both the total selling price and the per-unit price.\u003c/p\u003e\u003cp\u003eAs suggested by H1, quantity discounts are expected to be less common for shaving razor bundles than for shaving cream bundles. When quantity discounts are present, two patterns are anticipated: (1) the relationship between bundle size and total selling price should be increasing but concave, and (2) the relationship between bundle size and per-unit price should be negative. Any deviation from these patterns would suggest that quantity discounts are not systematically applied.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\n\u003ch3\u003eData\u003c/h3\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eRazor bundle\u003c/h2\u003e\u003cp\u003eInformation on razor blade bundles was collected from three major online retailers in May 2024. Two of the retailers were based in the United States and one in Korea. Our search focused on brand/models (e.g., Gillette Mach3) that offered multiple bundle types in terms of the number of blades included (e.g., 1-, 2-, and 4-blade bundles). A total of 20 brand/models that provided variation in blade quantities per bundle were identified. A set of bundles was defined as a unique brand/model even when the same manufacturer\u0026rsquo;s brand was sold across different stores. Across these 20 brand/models, price information was collected for 176 product bundles. For each item, both the selling price and the number of blades were recorded. Descriptive statistics for the razor bundle data are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e about here]\u003c/p\u003e\u003cp\u003eTo facilitate analysis, prices were normalized and the price per blade was calculated for items within the same razor brand/model. This normalization controlled for brand-level price variability, ensuring that comparisons reflected relative pricing patterns rather than absolute brand differences.\u003c/p\u003e\u003cp\u003eFirst, the base price for each brand/model was defined as the selling price of the basic bundle, which consisted of a razor handle with a single blade. For example, if the basic bundle was priced at \u003cspan\u003e$\u003c/span\u003e10.00, this amount served as the reference point for subsequent calculations.\u003c/p\u003e\u003cp\u003eSecond, the standardized price for each larger bundle was calculated as its selling price relative to the base price. Thus, a two-blade bundle priced at \u003cspan\u003e$\u003c/span\u003e10.99 yielded a standardized price of 1.09 (i.e., \u003cspan\u003e$\u003c/span\u003e10.99/\u003cspan\u003e$\u003c/span\u003e10.00). This allowed bundles of different sizes to be compared on a common scale.\u003c/p\u003e\u003cp\u003eFinally, the price per blade was derived to capture the marginal cost of additional blades beyond the basic bundle. This was computed as the difference between the standardized price and 1 (the base) divided by the number of additional blades. In the example above, the two-blade bundle produced a per-blade price of 0.09 (i.e., [1.09\u0026thinsp;\u0026minus;\u0026thinsp;1.00]/[2\u0026thinsp;\u0026minus;\u0026thinsp;1]). This measure provided a standardized index of the incremental cost of complementary components across bundle sizes. The full normalization process is illustrated in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e about here]\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eShaving cream\u003c/h2\u003e\u003cp\u003eData on shaving cream products were collected in June 2024 from the same three major online stores where the razor bundle data were sourced. A total of 43 distinct brand/models were identified, with variations in the number of product units. A unique brand/model was defined when the same producer's brand was sold in bundles of different quantities. Across these 43 brand/models, data on selling price and unit quantity (i.e., bundle size) were collected for a total of 441 individual items. The descriptive statistics are presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e about here]\u003c/p\u003e\u003cp\u003eUsing the price and quantity data, both standardized selling prices and per-unit prices were calculated within each brand/model. First, the base price was defined as the selling price of the single-unit product. Second, the standardized price for each multi-unit bundle was computed relative to the base price, allowing direct comparison across bundle sizes. Finally, the price per unit was derived from the standardized price to capture the relative cost efficiency of larger bundles.\u003c/p\u003e\u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003eBundle size and selling price\u003c/h2\u003e\u003cp\u003eThe relationship between bundle size and selling price was analyzed separately for razor and shaving cream bundles.\u003csup\u003e1\u003c/sup\u003e Figgure 2A shows the relationship between the number of blades in a bundle and the standardized selling price for razor bundles. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB presents the relationship between the unit quantity and the standardized selling price for shaving cream bundles.\u003c/p\u003e\u003cp\u003e[Insert Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e about here]\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003eRazor bundle\u003c/h2\u003e\u003cp\u003eThe relationship between the number of blades in a bundle and the standardized price was analyzed by regressing the standardized price of the items on the (mean-centered) blade-quantity and its squared term (blade-quantity\u003csup\u003e2\u003c/sup\u003e). The squared term was included to capture a quadratic relationship. Nineteen brand/model dummies were included as control variables. The results of the polynomial regression showed that the blade-quantity coefficient was significant (\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.292, \u003cem\u003et\u003c/em\u003e(154)\u0026thinsp;=\u0026thinsp;20.44, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001). As expected, bundles with more blades generally had higher selling prices. However, the blade-quantity\u003csup\u003e2\u003c/sup\u003e term was not significant (\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.003, \u003cem\u003et\u003c/em\u003e(154)\u0026thinsp;=\u0026thinsp;1.58, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.117). This result indicated that razor blades included in the bundles did not provide significant quantity discounts. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA presents the results.\u003c/p\u003e\u003cp\u003eAdditionally, the relationship between blade quantity and standardized price was analyzed separately for the US and Korean retailers (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA). For the US retailers, the result was statistically the same, showing that only the blade-quantity coefficient was positive and significant (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001). For Korean data, both blade-quantity (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001) and blade-quantity\u003csup\u003e2\u003c/sup\u003e (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.041) coefficients were significant. The negatively significant blade-quantity\u003csup\u003e2\u003c/sup\u003e indicated that quantity discounts for larger-volume blades were observed only in the Korean market.\u003c/p\u003e\u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e about here]\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003ch2\u003eShaving cream bundle\u003c/h2\u003e\u003cp\u003eA polynomial regression examining the relationship between the number of shaving cream units in a bundle and the standardized price showed significant results for the unit-quantity coefficient (\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.508, \u003cem\u003et\u003c/em\u003e(393)\u0026thinsp;=\u0026thinsp;18.36, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001) and unit-quantity\u003csup\u003e2\u003c/sup\u003e coefficient (\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.003, \u003cem\u003et\u003c/em\u003e(393)\u0026thinsp;=\u0026thinsp;5.28, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001). This pattern indicated that the relationship between bundle size and selling price is increasing and concave, revealing a significant quantity discount. Separate analyses for the US and Korean data showed the same pattern, with positive and significant unit-quantity coefficients (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001) and negative and significant unit-quantity\u003csup\u003e2\u003c/sup\u003e coefficients (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.002). Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB presents the results.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\u003ch2\u003eBundle size and price per unit\u003c/h2\u003e\u003cp\u003eThe relationship between bundle size and price per unit for shaving razor and shaving cream bundles was also examined. This analysis did not include bundles containing only a single unit, as they were used as the base price. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e displays scatterplots showing the association between bundle size and price per product unit for razor bundles (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA) and shaving cream bundles (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\u003ch2\u003eRazor bundle\u003c/h2\u003e\u003cp\u003eThe influence of the number of blades in the bundle on the price per blade was tested using a regression analysis with blade quantity, blade quantity\u003csup\u003e2\u003c/sup\u003e, and brand/model dummies as independent variables. Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA shows the results. The blade quantity coefficient was not significant (\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.003, \u003cem\u003et\u003c/em\u003e(114)\u0026thinsp;=\u0026thinsp;0.44, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.661). This finding indicated that the price per blade did not decrease as bundle size increased, providing no evidence of quantity discounts. The blade quantity\u003csup\u003e2\u003c/sup\u003e was negative and significant (\u003cem\u003eb\u003c/em\u003e = \u0026minus;\u0026thinsp;0.002, \u003cem\u003et\u003c/em\u003e(114)\u0026thinsp;=\u0026thinsp;2.18, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.032), indicating a concave relationship. The analyses conducted separately for the US and South Korea did not show evidence of quantity discounts either. The blade quantity coefficient was significant for both the US data (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.506) and the Korean data (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.346).\u003c/p\u003e\u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e about here]\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\u003ch2\u003eShaving cream bundle\u003c/h2\u003e\u003cp\u003eA regression analysis that examined the relationship between bundle size and price per unit for shaving cream data showed that the unit-quantity coefficient was negative and significant (\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.021, \u003cem\u003et\u003c/em\u003e(297)\u0026thinsp;=\u0026thinsp;3.83, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001). This result indicated that the price per unit tended to be lower for larger bundles, revealing significant quantity discounts. The unit-quanity\u003csup\u003e2\u003c/sup\u003e coefficient was positive and significant (\u003cem\u003eb\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001, \u003cem\u003et\u003c/em\u003e(297)\u0026thinsp;=\u0026thinsp;3.01, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.003), suggesting that the marginal change of quantity discounts was smaller as the bundle size increased. Separate analyses for the US and Korean data showed the same pattern, with negative and significant unit-quantity coefficients (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.010) and positive and significant unit-quantity\u003csup\u003e2\u003c/sup\u003e coefficients (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.033). The results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\u003ch2\u003eGeneral discussion and conclusions\u003c/h2\u003e\u003cdiv id=\"Sec21\" class=\"Section3\"\u003e\u003ch2\u003eSummary of findings\u003c/h2\u003e\u003cp\u003eThe market data analysis focused on bundle pricing strategies for razor blades and shaving cream, chosen as representative products for tied and untied goods. The findings revealed that quantity discount, commonly practiced for bundle pricing, was observed for shaving cream bundles but not for razor bundles, providing support for H1. The absence of quantity discounts for razor bundles may reflect a greater focus on the cost of the durable product rather than on complementary items. By contrast, quantity discounts for shaving cream bundles align with conventional pricing approaches for untied goods.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\u003ch2\u003eContributions\u003c/h2\u003e\u003cp\u003eFirst, it advances research on quantity discounting by demonstrating that its application depends on whether goods are tied or untied. While prior studies have documented consumer responses to bulk discounts in nondurables (Gupta, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Neslin \u0026amp; Shoemaker, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1989\u003c/span\u003e), this research shows that the pricing of tied goods deviates from this pattern.\u003c/p\u003e\u003cp\u003eSecond, it extends work on bundling and captive pricing (Adams \u0026amp; Yellen, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1976\u003c/span\u003e; Schmalensee, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Stremersch \u0026amp; Tellis, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Razors illustrate how firms maintain margins on complementary consumables by avoiding quantity discounts, while shaving cream exemplifies how conventional bundling strategies apply to stand-alone nondurables. Our results thus provide empirical validation of long-standing theoretical claims about aftermarkets and captive goods (Shapiro, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1995\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThird, by using cross-national retail data, we provide evidence of generalizability. Despite institutional and cultural differences between the United States and Korea, the observed contrast between razors and shaving cream was largely consistent across markets. This suggests that the tied versus untied distinction is a robust determinant of pricing practices, transcending specific market contexts.\u003c/p\u003e\u003cp\u003eFinally, the study offers managerial implications. For tied goods, firms may sustain profitability without offering discounts on complements, while for untied nondurables, consumers expect and respond to conventional quantity discounts. Managers should therefore consider product interdependence when designing bundle sizes and discount policies.\u003c/p\u003e\u003cdiv id=\"Sec23\" class=\"Section3\"\u003e\u003ch2\u003eLimitations and Future Research\u003c/h2\u003e\u003cp\u003eThis research has several limitations that suggest avenues for future inquiry. First, the data were restricted to online retailers in two countries and to a single product category. Future research should examine whether the findings generalize across other tied-good systems (e.g., printers and ink, coffee machines and pods) and across broader retail environments, including offline settings.\u003c/p\u003e\u003cp\u003eSecond, the analysis focused on observed pricing practices rather than consumer responses. Experimental studies could test how consumers perceive fairness, value, or exploitation in tied versus untied discount structures, and whether price transparency (e.g., explicit per-unit labeling) moderates these effects.\u003c/p\u003e\u003cp\u003eThird, this study did not evaluate whether the differential application of volume-bundling strategies actually translates into higher profitability for firms. Future research should investigate the profit implications of discounting versus non-discounting practices, examining whether avoiding quantity discounts in tied goods enhances long-term margins, consumer lock-in, and aftermarket revenues compared to conventional discounting strategies in untied goods.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDescriptive statistics of shaving razor bundles\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCategory\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAverage Price\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eAverage Blade Quantity\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCountry\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUSA (USD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e20.59 (11.11)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.37 (4.03)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKorea (KRW)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e27,495.96 (17,500.68)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e5.56 (4.97)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBrand\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGillette\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e134\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e20.82 (11.04)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.95 (3.82)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchick\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e19.40 (12.86)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e5.00 (4.64)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDorco\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e20.98 (8.02)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e7.80 (3.83)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBlade Quantity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1 blade\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e11.57 (5.09)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2 blades\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e13.45 (4.61)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3 blades\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e28.96 (0.03)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4 blades\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e23.90 (8.57)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5 blades\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e25.08 (6.50)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u0026ndash;9 blades\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e30.08 (10.02)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10 blades\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e30.08 (9.81)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u0026thinsp;+\u0026thinsp;blades\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e36.35 (11.85)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cem\u003eNotes\u003c/em\u003e: Standard deviations are in parentheses. Average prices are presented for US data only, except for the data by country.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eExamples of market data and price indices\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003eMarket Data\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003ePrice Indices\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePrice\u003c/p\u003e\u003cp\u003e[1]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBlade quantity\u003c/p\u003e\u003cp\u003e[2]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eBase price\u003c/p\u003e\u003cp\u003e[3]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eStandardized price\u003c/p\u003e\u003cp\u003e[4] = [3]/ [1]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003ePrice per blade\u003c/p\u003e\u003cp\u003e[5] = ([4]\u0026ndash;1)/ ([2]\u0026ndash;1)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan\u003e$\u003c/span\u003e10.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e10.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan\u003e$\u003c/span\u003e10.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e10.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.09\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan\u003e$\u003c/span\u003e13.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e10.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan\u003e$\u003c/span\u003e15.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e10.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDescriptive statistics of shaving cream bundles\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCategory\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAverage Price\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eAverage Unit Quantity\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCountry\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUSA (USD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e168\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e29.27 (28.14)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e6.80 (10.76)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKorea (KRW)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e273\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e22,421.25 (23,533.24)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.82 (8.47)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBrand\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGillette\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e228\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e31.78 (31.54)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e8.29 (12.40)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchick\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e16.77 (6.08)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.57 (1.40)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNivea\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e126\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e25.75 (18.01)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.40 (2.68)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUnit Quantity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1 unit\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e9.63 (4.12)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2 units\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e16.15 (4.41)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3 units\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e19.47 (1.81)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4 units\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e43\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e24.36 (10.10)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5 units\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e39.21 (10.81)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u0026ndash;9 units\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e33.36 (10.57)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10 units\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e56.80 (0.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u0026thinsp;+\u0026thinsp;units\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e71.13 (38.71)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cem\u003eNotes\u003c/em\u003e: Standard deviations are in parentheses. Average prices are presented for US data only, except for the data by country.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eInfluence of quantities on standardized selling price A. Razir bundle\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAll Data\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSouth Korea\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBlade-quantity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.292 (0.014)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.325 (0.024)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.277 (0.016)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBlade-quantity\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.003 (0.002)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.002 (0.003)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.005 (0.002)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eConstant\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2.072 (0.245)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.150 (0.280)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.673 (0.095)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e.868\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e.860\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e.895\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e176\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eB. Shaving cream\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAll Data\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSouth Korea\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUnit-quantity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.508 (0.028)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.438 (0.023)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.609 (0.038)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUnit-quantity\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.003 (0.001)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.005 (0.001)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.003 (0.001)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eConstant\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.869 (1.497)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.976 (0.905)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3.262 (0.364)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e.773\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e.861\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e.836\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e441\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e168\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e273\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cem\u003eNotes\u003c/em\u003e: Dummy coefficients are not presented. \u003csup\u003e*\u003c/sup\u003e\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.05.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eInfluence of quantities on price per unit A. Razor\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAll Data\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSouth Korea\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBlade quantity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.003 (0.006)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.006 (0.009)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.008 (0.009)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBlade quantity\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.002 (0.001)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.002 (0.001)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.002 (0.001)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eConstant\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.285 (0.134)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.212 (0.144)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.123 (0.062)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e.460\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e.372\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e.478\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e136\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e76\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eB. Shaving cream\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAll Data\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSouth Korea\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUnit quantity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.021 (0.005)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.019 (0.005)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.023 (0.009)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUnit quantity\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.000 (0.000)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.000 (0.000)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.000 (0.000)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eConstant\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.323 (0.387)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.314 (0.276)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.265 (0.088)\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e.539\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e.542\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e.508\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e345\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e132\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e213\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cem\u003eNotes\u003c/em\u003e: Dummy coefficients are not presented. \u003csup\u003e*\u003c/sup\u003e\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.05.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eEthical approval\u003c/h2\u003e\u003cp\u003eNot applicable.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eConflicts of interest\u003c/strong\u003e\u003cp\u003eThe author declares no conflicts of interest.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eThis work received no external funding.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAuthor A has colleced and analyzed data, and wrote the whole manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data will be posted on public data repository.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAdams, W. J., and J. L. Yellen. 1976. \u0026ldquo;Commodity Bundling and the Burden of Monopoly.\u0026rdquo; \u003cem\u003eQuarterly Journal of Economics\u003c/em\u003e 90 (3): 475\u0026ndash;98.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBakos, Y., and E. Brynjolfsson. 1999. \u0026ldquo;Bundling Information Goods: Pricing, Profits, and Efficiency.\u0026rdquo; \u003cem\u003eManagement Science\u003c/em\u003e 45 (12): 1613\u0026ndash;30.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChintagunta, P. K., S. Gopinath, and S. Venkataraman. 2018. \u0026ldquo;The Empirical Implications of Bundling in Consumer Goods Markets.\u0026rdquo; \u003cem\u003eMarketing Science\u003c/em\u003e 37 (6): 970\u0026ndash;93.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eClerides, S., and P. Courty. 2017. \u0026ldquo;Sales, Quantity Surcharges and Consumer Inattention.\u0026rdquo; \u003cem\u003eReview of Economic Studies\u003c/em\u003e84 (2): 960\u0026ndash;86.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGerstner, E., and J. D. Hess. 1987. \u0026ldquo;Why Do Hot Dogs Come in Packs of 10 and Buns in 8s? A Demand for Coordination.\u0026rdquo; \u003cem\u003eJournal of Business\u003c/em\u003e 60 (4): 491\u0026ndash;517.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGupta, S. 1988. \u0026ldquo;Impact of Sales Promotions on When, What, and How Much to Buy.\u0026rdquo; \u003cem\u003eJournal of Marketing Research\u003c/em\u003e25 (4): 342\u0026ndash;55.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHartmann, W. R., and H. S. Nair. 2010. \u0026ldquo;Retail Competition and the Dynamics of Consumer Demand for Tied Goods.\u0026rdquo; \u003cem\u003eMarketing Science\u003c/em\u003e 29 (2): 366\u0026ndash;86.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIyengar, R., and K. Jedidi. 2012. \u0026ldquo;A Conjoint Approach to Multi-part Pricing.\u0026rdquo; \u003cem\u003eMarketing Science\u003c/em\u003e 31 (6): 1018\u0026ndash;38.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eManning, K. C., D. E. Sprott, and A. D. Miyazaki. 1998. \u0026ldquo;Consumer Response to Quantity Surcharges: Implications for Retail Price Setting.\u0026rdquo; \u003cem\u003eJournal of Retailing\u003c/em\u003e 74 (3): 373\u0026ndash;99.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMaxwell, S. 1995. \u0026ldquo;What Makes a Sale \u0026lsquo;a Sale\u0026rsquo;? The Influence of Internal Reference Prices and Sale Signs on Choice Certainty.\u0026rdquo; \u003cem\u003eJournal of Retailing\u003c/em\u003e 71 (3): 245\u0026ndash;62.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNagle, T. T., and G. M\u0026uuml;ller. 2018. \u003cem\u003eThe Strategy and Tactics of Pricing: A Guide to Growing More Profitably\u003c/em\u003e. London: Routledge.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNalebuff, B. 2004. \u0026ldquo;Bundling as an Entry Barrier.\u0026rdquo; \u003cem\u003eQuarterly Journal of Economics\u003c/em\u003e 119 (1): 159\u0026ndash;87.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNeslin, S. A., and R. W. Shoemaker. 1989. \u0026ldquo;An Alternative Explanation for Lower Repeat Rates after Promotion Purchases.\u0026rdquo; \u003cem\u003eJournal of Marketing Research\u003c/em\u003e 26 (2): 205\u0026ndash;13.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSchmalensee, R. 1984. \u0026ldquo;Gaussian Demand and Commodity Bundling.\u0026rdquo; \u003cem\u003eJournal of Business\u003c/em\u003e 57 (S2): S211\u0026ndash;30.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eShapiro, C. 1995. \u0026ldquo;Aftermarkets and Consumer Welfare: Making Sense of Kodak.\u0026rdquo; \u003cem\u003eAntitrust Law Journal\u003c/em\u003e 63 (2): 483\u0026ndash;511.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eStremersch, S., and G. J. Tellis. 2002. \u0026ldquo;Strategic Bundling of Products and Prices: A New Synthesis for Marketing.\u0026rdquo; \u003cem\u003eJournal of Marketing\u003c/em\u003e 66 (1): 55\u0026ndash;72.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWansink, B., and R. Deshpand\u0026eacute;. 1994. \u0026ldquo;Out of Sight, Out of Mind: The Impact of Household Stockpiling on Usage Rates.\u0026rdquo; \u003cem\u003eMarketing Letters\u003c/em\u003e 5 (1): 91\u0026ndash;100.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e Combining razor and shaving cream bundle data and analyzing interaction was not appropriate because of the differing nature of bundling between the two products and the disparity in the average price per quantity.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-revenue-and-pricing-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Journal of Revenue and Pricing Management](https://www.palgrave.com/gp/journal/41272)","snPcode":"41272","submissionUrl":"https://submission.springernature.com/new-submission/41272/3","title":"Journal of Revenue and Pricing Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer SNAPPs","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"tied goods, bundling, quantity discount, captive pricing","lastPublishedDoi":"10.21203/rs.3.rs-7625937/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7625937/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research examines how firms apply quantity discounts to tied versus untied goods in volume bundles, focusing on shaving razors and shaving cream. Tied goods require joint use (e.g., razors and blades), while untied goods are consumed independently (e.g., shaving cream). We test whether bundling discounts differ across these categories. Market data from major online retailers show consistent discounts for shaving cream bundles but not for razor bundles. Findings indicate quantity discounts are less common for tied goods, highlighting product interdependence as a key factor shaping firms\u0026rsquo; pricing strategies.\u003c/p\u003e","manuscriptTitle":"Volume bundle pricing for tied goods and untied goods in the marketplace","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-16 20:36:11","doi":"10.21203/rs.3.rs-7625937/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-05T11:39:37+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-30T07:27:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-14T01:22:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"191367266914449462010858088352117910227","date":"2025-10-03T21:45:16+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"210006405488638039273394489972885119750","date":"2025-10-03T08:20:26+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-03T07:47:19+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-25T17:01:59+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-25T17:00:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Revenue and Pricing Management","date":"2025-09-16T04:55:32+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-revenue-and-pricing-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Journal of Revenue and Pricing Management](https://www.palgrave.com/gp/journal/41272)","snPcode":"41272","submissionUrl":"https://submission.springernature.com/new-submission/41272/3","title":"Journal of Revenue and Pricing Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer SNAPPs","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"89e4c441-5570-4ea5-8b5d-cdeaec09cd5a","owner":[],"postedDate":"October 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-01-29T15:35:54+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-16 20:36:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7625937","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7625937","identity":"rs-7625937","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}