stochastic dea with ordinal data applied to a multi attribute pricing problem multiple attribute pricing problems are highly challenging due to the dynamic and uncertain features in the associated market in this paper we address the condominium multiple attribute pricing problem using data envelopment analysis dea in this study we simultaneously consider stochastic variables non discretionary variables and ordinal data and present a new type of dea model based on our proposed dea an effective performance measurement tool is developed to provide a basis for understanding the condominium pricing problem to direct and monitor the implementation of pricing strategy and to provide information regarding the results of pricing efforts for units sold as well as insights for future building design a case study is executed on a leading canadian condominium developer

please or squeeze brand performance implications of constrained and unconstrained multi item promotions existing research on price promotions typically investigates the effects of single product promotions however brand managers often promote multiple items simultaneously to bolster the performance of a complete brand line this paper investigates the brand performance implications of such multi item promotions we distinguish between two types of multi item promotions traditional unconstrained multi item promotions that grant a discount irrespective of the size or composition of the purchase set and constrained multi item promotions that require consumers to purchase specific quantities self bundling or even predetermined combinations fixed bundling of promoted items using a normative consumer decision model the authors analyze the relative effectiveness of these promotions in terms of unit sales and revenue impact and show that promotion performance is moderated by consumers preference for variety the authors find that unconstrained multi item promotions outperform single item promotions especially in markets without variety seeking in markets with variety seeking unconstrained multi item promotions are not as effective in stealing extra sales from competition because consumers prefer to spread their purchases across all items including competitive ones however in those markets self bundling promotions are particularly effective because they force consumers to adopt larger amounts of the promoted items at the expense of competitors finally in neither type of market does fixed bundling substantially improve promotion performance

measuring heterogeneous reservation prices for product bundles this paper develops a model for capturing continuous heterogeneity in the joint distribution of reservation prices for products and bundles our model is derived from utility theory and captures both within and among subject variability furthermore it provides dollarmetric reservation prices and individual level estimates that allow the firm to target customers and develop customized and nonlinear pricing policies our experiments show that regardless of whether the products are durables or nondurables the model captures heterogeneity and predicts well models that assume homogeneity perform poorly especially in predicting choice of the bundle furthermore the methodology is robust even when respondents evaluate few profiles self stated reservation prices do not have any informational content beyond that contained in the basic model the direct elicitation method appears to understate overstate the variation in reservation prices across consumers for low priced high priced products and bundles hence this method yields biased demand estimates and leads to suboptimal product line pricing policy the optimization results show that the product line pricing policy depends on the degree of heterogeneity in the reservation prices of the individual products and the bundle a uniformly high price strategy for all products and bundles is optimal when heterogeneity is high otherwise a hybrid strategy is optimal

compatibility and bundling of complementary goods in a duopoly this paper presents a simple model of compatibility and bundling in industries where consumers assemble several necessary components into a system that is close to their ideal the authors show that for a wide range of parameters firms will choose to produce compatible components but will offer discounts to consumers who purchase all components from the same firm however firms would be better off if they could commit not to provide such discounts furthermore the equilibrium tends to involve socially excessive bundling finally mixed bundling strategies tend to increase the range of parameters over which socially excessive standardization occurs copyright 1992 by blackwell publishing ltd

software piracy an analysis of protection strategies software piracy by users is generally believed to harm both software firms through lower profits and buying customers through higher prices thus it is thought that perfect and costless technological protection would benefit both firms and consumers the model developed here suggests that in some circumstances even with significant piracy not protecting can be the best policy both raising firm profits and lowering selling prices key to the analysis is joining the presence of a positive network externality with the fact that piracy increases the total number of program users the network externality exists because consumers have an incentive to economize on post purchase learning and customization costs

optimal bundling of technological products with network externality for many high tech and internet related products utility to consumers depends in part on the size of the user base a phenomenon called network externality a firm with a portfolio of these and other products that are often asymmetric in their degree of network externality or marginal cost may have to look beyond the traditional strategies of pure components pure bundling and mixed bundling one such strategic alternative in a two product case would be a so called mixed bundling 1 under which the bundle and product 1 are offered but the other product can only be purchased in a bundled form the purpose of this study is to compare and contrast the impact of such asymmetry or symmetry in direct network externality and cost on the choice of bundling strategies we model a monopolist firm that has a product in each of two categories and faces heterogeneous consumers results suggest that pure bundling is more profitable when both products have low marginal costs or high network externality whereas pure components or mixed bundling 1 is more profitable when the products diverge in their costs and network externality e g only one product has network externality traditional mixed bundling is optimal in other instances

economic and policy implications of restricted patch distribution in this paper we study how restricting the availability of patches to legal users impacts the vendor s profits market share software maintenance decisions and welfare outcomes prior work on this topic assumes that the hacker s effort is independent of the vendor s decision to release the patch freely or not clearly if the patch is not available to everyone the hacker finds it easier to exploit the vulnerability in the product and as a result is likely to alter his effort to understand the role of a strategic hacker we build a game theoretic model where the hacker s decision is endogenous with this model we find that the hacker s effort may on the one hand decrease the utility that the vendor can extract from the consumers but on the other hand may help differentiate the legal version of the product from the pirated version a vendor can strategically exploit the hacker s behavior in its pricing and software maintenance decisions the endogeneity of the hacker s actions drives several of

an analysis of bundle pricing the case of biotech seeds biotechnology has provided opportunities for strategic management and pricing of patented products this article analyzes the economics and strategy of bundling and bundle pricing of biotech traits in seeds when the bundling of genes traits is decided by biotech firms firms may choose among subadditive pricing component pricing or superadditive pricing strategies we argue that complementarity among component genes contributes to subadditive pricing while substitution among components contributes to superadditive pricing the nature of bundle pricing is explored empirically using u s seed corn data from 2000 to 2007 we document that subadditive bundle pricing of traits is commonly found in the seed corn market however we also present evidence of superadditive pricing and component pricing the presence of different pricing and bundling strategies suggests a rapidly advancing and complex market the preponderance of subadditive pricing suggests that trait bundling offers benefits to farmers exhibiting strong demand for multiple complementary genetic traits jel classifications l4 l13 l65

a simulation based approach to price optimisation of the mixed bundling problem with capacity constraints abstract in this paper we analyse a service provider s mixed bundling problem for services such as sporting events or holiday packages pursuing the objective of maximising total revenue the service provider has to determine static prices for each single product at the beginning of the selling period additionally an optimal package price has to be chosen for the bundle that comprises one unit of each single product because of capacity constraints the availability of products can change over time such that consumers are forced to switch from their preferred subset of products to an alternative following dynamic substitution we propose two mixed integer linear programmes based on reservation prices that appropriately model the consumer choice process to address the bundling problem it becomes evident that the determination of the optimal prices is computationally expensive even for small problem classes therefore we develop metaheuristics using variable neighbourhoods to evaluate their performance we propose the following new approach our extensive computational study is performed using especially generated scenarios for which the optimal product prices are known for this purpose we present a set of conditions for the generation of reservation prices that guarantee the optimality of the predefined prices based on our computational results managerial insights are derived

bundle pricing of inventories with stochastic demand we consider a retailer selling a fixed inventory of two perishable products over a finite horizon assuming poisson arrivals and a bivariate reservation price distribution we determine the optimal product and bundle prices that maximize the expected revenue our results indicate that the performances of mixed bundling pure bundling and unbundled sales strategies heavily depend on the parameters of the demand process and the initial inventory levels bundling appears to be most effective with negatively correlated reservation prices and high starting inventory levels when the starting inventory levels are equal and in excess of average demand most of the benefits of bundling can be achieved through pure bundling however the mixed bundling strategy dominates the other two when the starting inventory levels are not equal we also observe that an incorrect modeling of the reservation prices may lead to significant losses the model is extended to allow for price changes during the selling horizon it is shown that offering price bundles mid season may be more effective than changing individual product prices

bundling as a facilitating device a reinterpretation of leverage theory tying good monopolists that extract full consumer surplus from independent sales of their tying good may nevertheless choose to bundle in order to induce a favorable response by their tied market rivals in particular bundling may facilitate supracompetitive prices for the tied good copyright 1991 by the london school of economics and political science

bundling of substitutes or complements abstract the adams yellen two good bundling framework is generalized to allow the goods to be substitutes or complements general theorems on price change effects are given a monopolist may find it most profitable to offer the goods only as a bundle even if they are imperfect substitutes or to not bundle the goods even if they are complements if one good is competitively sold a monopoly producer of the other good can never increase profits by offering his good only as part of a bundle however such a monopolist might profitably offer his good in both bundled and unbundled form to price discriminate even if the two goods are substitutes

intertemporal price discrimination with two products we study the two product monopoly profit maximization problem for a seller who can commit to a dynamic pricing strategy we show that if consumers valuations are not strongly ordered then optimality for the seller can require intertemporal price discrimination the seller offers a choice between supplying a complete bundle now or delaying the supply of a component of that bundle until a later date for general valuations we establish a sufficient condition for such dynamic pricing to be more profitable than mixed bundling so we show that the established no discrimination across time result does not extend to two product sellers under standard taste distributions

complementary goods creating capturing and competing for value this paper studies the strategic interaction between firms producing strictly complementary products with strict complements a consumer derives positive utility only when both products are used together we show that value capture and value creation problems arise when such products are developed and sold by separate firms nonintegrated producers although the firms tend to price higher for given quality levels their provision of quality is so low that in equilibrium prices are set well below what an integrated monopolist would choose when one firm can mandate a royalty fee from the complementor producer as often occurs in arrangements between hardware and software makers we find that the value capture problem is mitigated to some extent and consumer surplus rises however because royalty fees greatly reduce the incentives of the firm paying them to invest in quality the arrangement exacerbates the value creation problem and leads to even lower total quality surprisingly this result can reverse with competition specifically when the firm charging the royalty fee faces a vertically differentiated competitor the value creation problem is greatly reduced opening the door for the possibility of a pareto improving outcome in which all firms and consumers benefit it is worth noting that this outcome cannot be achieved by giving firms the option of introducing a line of product variants competition serves as a necessary commitment ingredient

information and strategic political polarisation we develop a model of electoral competition in which two opportunistic candidates select their policy position and invest in quality policy positions are observed and during the campaign the press reveals some information about quality we demonstrate that when information is imperfect the blackdowns median voter theorem fails to hold for intermediate information levels the unique equilibrium is such that candidates propose policies different from the median voter s bliss point by contrast convergence to the median occurs when quality is almost always or almost never revealed we also show that a profit maximising press may collect more information than socially optimal during the 1995 electoral campaign in belgium the vld a traditionally right wing

a more general theory of commodity bundling this paper extends the standard model of bundling as a price discrimination device to allow products to be substitutes and for products to be supplied by separate sellers whether integrated or separate firms have an incentive to introduce a bundling discount when demand for the bundle is elastic relative to demand for stand alone products product substitutability typically gives an integrated firm a greater incentive to offer a bundle discount relative to the model with additive preferences while substitutability is often the sole reason why separate sellers wish to offer inter firm discounts when separate sellers coordinate on an inter firm discount they can use the discount to overturn product substitutability and relax competition

a probabilistic approach to pricing a bundle of products or services the authors propose a probabilistic approach to optimally price a bundle of products or services that maximizes seller s profits their focus is on situations in which consumer decision making is o

mixed bundling in two sided markets in the presence of installed base effects we analyze mixed bundling in two sided markets where installed base effects are present and find that the pricing structure deviates from traditional bundling as well as the standard two sided markets literature we determine prices on both sides fall with bundling mixed bundling acts as a price discrimination tool segmenting the market more efficiently consequently as a by product of this price discrimination the two sides are better coordinated and social welfare is enhanced we show unambiguously that platform participations increase on both sides of the market after theoretically evaluating the impact mixed bundling has on prices and welfare we take the model predictions to data from the portable video game console market we find empirical support for all theoretical predictions this paper was accepted by j miguel villas boas marketing

how buyers evaluate product bundles a model of anchoring and adjustment how do buyers evaluate a bundle of items the most common approach in earlier economic analyses see e g adams and yellen 1976 schmalensee 1984 was to start with the additivity assumption the overall utility of a bundle equals the sum of the bundle items individual utilities the restrictiveness of this additivity assumption was later recognized and removes dansby and conrad 1984 guiltinan 1987 hanson and martin 1990 however the question of how buyers evaluation processes may account for additivity or a lack thereof has remained largely unexplored

research note competitive bundling and counterbundling with generalist and specialist firms bundling which is the practice of selling two or more products or services in a package is a pervasive marketing practice and is often used as a strategic competitive tool however there has not been enough consideration of competitive bundling situations in which exit of a competitor is not a concern in this paper we address this issue by identifying conditions under which strategic competitors may or may not resort to bundling when competitor exit considerations are absent we study competition between a multiproduct generalist firm and two single product specialist firms in two product categories one of which has undifferentiated products and the other has differentiated products in our model the specialist firms can form an alliance to bundle their products in competing with the generalist firm in contrast to the previous literature we find that concurrent bundling by competitors if it occurs in equilibrium is profitable we also find that when one competitor bundles and the other does not the bundling firm gains a greater share of customers and makes a higher profit however when conditions favor counterbundling by a competitor such counterbundling helps the competitor retain its customers finally we note that under other market conditions concurrent bundling by competitors escalates price competition to the extent that retaining customers through bundling is not profitable in such a case we show that strategic competitors are better off having asymmetric product lines with one competitor bundling and the other selling unbundled

buying sharing and renting information goods information goods such as books journals computer software music and videos can be copied shared resold or rented when such opportunities for sharing are present the content producer will generally sell a smaller amount at a higher price which may increase or decrease profits i identify three circumstances where profits increase 1 when the transactions cost of sharing is less than the marginal cost of production 2 when content is viewed only a few times and transactions costs of sharing are low and 3 when a sharing market provides a way to segment high value and low value users

customized bundle pricing for information goods a nonlinear mixed integer programming approach this paper proposes using nonlinear mixed integer programming to solve the customized bundle pricing problem in which consumers are allowed to choose up to n goods out of a larger pool of j goods prior work has suggested that this mechanism has attractive features for the pricing of information and other low marginal cost goods although closed form solutions exist for this problem for certain cases of consumer preferences many interesting scenarios cannot be easily handled without a numerical solution procedure in this paper we investigate the efficiency gains created by customized bundling over the alternatives of pure bundling or individual sale under different assumptions about customer preferences and firm cost structure as well as the potential loss of efficiency caused by pricing with incomplete information about consumer reservation values our analysis suggests that customized bundling enhances sellers profits and enhances welfare when consumers do not place positive values on all goods and that this consumer characteristic is much more important than the shape of the valuation distribution in determining the optimal pricing scheme we also find that customized bundling outperforms both pure bundling and individual sale in the presence of incomplete information and that customized bundling still outperforms other simpler pricing schemes even when exact consumer valuations are not known ex ante

pricing of demand related products can ignoring cross category effect be a smart choice abstract this paper studies pricing strategies of competing retailers offering substitutable products in multiple product categories for such retailers in addition to accounting for within category pricing effects cross category effects can also influence consumers purchase decisions and thereby impact the retailers optimal pricing strategies we model consumers utility for purchasing substitutable products from the same category and from other categories as well we then solve a game theoretic model to identify the retailers optimal prices and profits our results show that accounting for cross category effects largely influences the retailers pricing and profitability in particular cross category effects influence the sensitivity of prices to within category substitution levels while cross category effects have an impact on retailers equilibrium strategies this effect is only relevant when within category substitution effects are present we also find that intentionally ignoring cross category effects leads to lower prices for categories that are either substitutable or highly complementary and to higher prices otherwise when not accounting for the fact that the two categories are demand related implies lower prices than when this information is accounted for then at least one retailer chooses to disregard the cross category effect at equilibrium finally we find evidence for prisoner s dilemma situations where both retailers ignore cross category effect at equilibrium while accounting for it would yield them higher profits

optimal bundling and pricing under a monopoly contrasting complements and substitutes from independently valued products we develop an analytical model of contingent valuations and address two questions of import to a monopolist i should a given pair of complements or substitutes be sold separately pure components together pure bundling or both mixed bundling and at what prices ii how do optimal bundling and pricing strategies for complements and substitutes differ from those for independently valued products we find that the combination of marginal cost levels and the degree of complementarity or substitutability determines which of the three bundling strategies is optimal complements and substitutes should typically be priced higher than independently valued products

cross market discounts firms in several markets attract consumers by offering discounts in other unrelated markets this promotion strategy which we call cross market discounts has been successfully adopted in the last few years by many grocery retailers in partnership with gasoline retailers across north america europe and australia in this paper we use an analytical model to investigate the major forces driving the profitability of this novel promotion strategy we consider a generalized scenario in which purchases in a source market lead to price discounts redeemable in a target market our analysis shows that this strategy can be a revenue driver by simultaneously increasing prices as well as sales in the source market even though we assume the demand curve to be downward sloping in price moreover it distributes additional consumption motivated by the discount in two markets and under diminishing marginal returns from consumption this can simultaneously increase firm profits and consumer welfare more effectively than traditional nonlinear pricing strategies our study provides many other interesting insights as well and our key results are in accordance with anecdotal evidence obtained from managers and industry publications

mixed bundling of two independently valued goods this paper develops analytical results and insights for the mixed bundling problem of pricing a product line consisting of two component goods with valuations distributed uniformly and independently in 0 a1 and 0 a2 respectively with a1 a2 and a bundle of the two goods this setting has previously been considered analytically intractable by deriving component good prices as exact algebraic functions of the optimal bundle price i reduce the multiproduct pricing problem to a univariate nonlinear optimization problem in the bundle price when the two component goods are sufficiently asymmetric in valuations the optimal solution is partial mixed bundling one component good is not sold separately for which i derive exact conditions and optimal prices an exact analytical solution is also given for mixed bundling of two information goods component goods with zero marginal costs for the general case i derive a closed form approximation of the optimal bundle price pb 0 5724w1 0 5695w2

gaussian demand and commodity bundling in an important and widely cited essay adams and yellen 1976 examine the use of package selling as a price discrimination device they consider a monopolist producing two goods with constant unit costs and facing buyers with diverse tastes the marginal utility of a second unit of either good is assumed to be zero for all buyers the two goods are independent in demand for all buyers so that any buyer s reservation price for the first unit of either good is independent of the market price of the other thus the maximum amount any buyer would pay for a bundle consisting of one unit of each good is the sum of the two reservation prices and buyers are completely described by the values of those two prices 2 resale markets are assumed away in order to obtain comparative results for alternative pricing strategies the distribution of reservation prices in the adams yellen framework is assumed to be bivariate normal implications of gaussian demand are explored pure bundling is shown to operate by reducing buyer diversity thus facilitating the capture of consumers surplus it generally makes buyers worse off than unbundled sales it is more profitable if average reservation prices are high enough mixed bundling combines advantages of both pure bundling and unbundled sales and it is generally strictly more profitable than either bundling which treats goods symmetrically seems most attractive under symmetric reservation price distributions i am indebted to severin borenstein for superb research assistance to the ford motor company for research support through a grant to m i t and to the harvard economics department for housing me as a visiting scholar while most of this research was performed of course only i can be held responsible for this essay s shortcomings 1 the first clear recognition of this possibility seems to have been by stigler 1968 but also see burstein 1960 2 paroush and peles 1981 relax the assumption that consumers purchase at most one unit of each good but they consider only two types of buyers both with linear demand functions they retain the assumption that demands are independent for all buyers telser 1979 and phillips 1981 use different frameworks to analyze bundling policies spence 1980 explores the relation between bundling across commodities as here and bundling multiple units of the same

optimal bundling strategies under heavy tailed valuations we develop a framework for the optimal bundling problem of a multiproduct monopolist who provides goods to consumers with private valuations that are random draws from a distribution with heavy tails we show that in the vickrey auction setting the buyers prefer separate provision of the goods to any bundles we also provide a complete characterization of the optimal bundling strategies for a monopolist producer who provides goods for profit maximizing prices for products with low marginal costs the seller s optimal strategy is to provide goods separately when consumers valuations are heavy tailed and in a single bundle when valuations are thin tailed these conclusions are reversed for goods with high marginal costs for simplicity we use a specific class of independent and identically distributed random variables but our results can be generalized to include dependence skewness and the case of nonidentical one dimensional distributions

an industry equilibrium analysis of downstream vertical integration this paper investigates the effect of product substitutability on nash equilibrium distribution structures in a duopoly where each manufacturer distributes its goods through a single exclusive retailer which may be either a franchised outlet or a factory store static linear demand and cost functions are assumed and a number of rules about players expectations of competitors behavior are examined it is found that for most specifications product substitutability does influence the equilibrium distribution structure for low degrees of substitutability each manufacturer will distribute its product through a company store for more highly competitive goods manufacturers will be more likely to use a decentralized distribution system this article was originally published in marketing science volume 2 issue 2 pages 161 191 in 1983

software copyright infringement among college students in recent years the issue of infringement in the software industry has gained international attention as the demand for software continues to grow the growing presence of unauthorized reproduction of copyrighted products inhibits full potential growth and discourages creative activity this study analyses the extent of software copyright infringement among college students and attitudes of these students with regard to risk of apprehension and conviction this study finds a significantly higher likelihood of infringement for computer majors and male students and a decrease in the likelihood of infringement for older students this study also uncovers differences in attitudes toward risk of apprehension and conviction between majors in scientific fields and those in business and economics whereas the first group of majors appears to exhibit risky behaviour the latter tends to be more risk averse

trading higher software piracy for higher profits the case of phantom piracy faced with the sustained problem of piracy that costs nearly 40 billion in annual revenue losses the software industry has adopted a number of technical legal and economic strategies to curb piracy and stem the resulting losses our work complements and contributes to the existing literature by exploring the possible effect of another economic lever product bundling on the relationship governing piracy and seller profits the traditional economic rationale of demand pooling from bundling that enables sellers to extract higher surplus and its particular attractiveness for information goods with negligible marginal and bundling costs carry over to our analysis however the presence of piracy injects several new facets to our analysis bundling creates a shared level of piracy of disparate products and under certain conditions to the detriment of one of the products we argue that by construction of the copyright laws the act of bundling itself can have a deterrence effect this deterrence effect alo

the welfare implications of unauthorized reproduction of intellectual property in the presence of demand network externalities this paper finds that unauthorized reproduction of intellectual property in the presence of demand network externalities can not only induce greater firm profits relative to the case where there is no copying it can lead to a pareto improvement in social welfare ceteris paribus when network externalities are present firms have a greater incentive to expand output because marginal revenue is higher and or they may wish to create preemptive installed bases this paper suggests that unauthorized copying can be a relatively efficient means of achieving this by allowing the firm in effect to price discriminate among different classes of consumers copyright 1994 by blackwell publishing ltd

optimal bundling strategies in multiobject auctions of complements or substitutes we consider a problem at the interface of auctions and bundling our revenue maximizing seller seeking to auction one unit each of two complements or substitutes in the best of three formats the auction of the bundle separate auctions of the individual items and a combinatorial auction we draw on an analytical model to address the following questions i which of the auctioning strategies is optimal under the second price sealed bid format ii what is the optimal strategy for the bidders iii when the objects are asymmetrically valued e g super bowl ticket versus souvenir what is the optimal auctioning sequence under the pure components strategy our results suggest that separate auctions of the two objects are superior to the auction of the bundle for most substitutes and even moderate complements when there are at least four bidders the auction of the pure bundle is better suited for strong complements or with too few bidders when the combinatorial auction is an available option it weakly dominates the auction of the pure bundle but has domains of inferiority relative to the separate auctions when the objects are asymmetric in value it is optimal to auction the higher valued object first

a strategic motivation for commodity bundling the analytical literature on commodity bundling explains the practice of selling two or more differentiated products in a single package as a surrogate for direct price discrimination in contrast this paper shows that imperfect competition creates a strategic incentive to bundle the profitability of bundling whether it adversely affects rival producers and whether it yields an overall efficiency gain depends inter alia on the nature of product market competition the role of complementarity in explaining why firms bundle is also explored copyright 1990 by blackwell publishing ltd

multiproduct pricing in oligopoly abstract this paper proposes a two good model of price competition where some consumers visit all shops and others visit only one we find that information frictions lead to price dispersion when the two goods are complements their prices will tend to be negatively correlated so if one is priced high the other will be discounted this finding is supported by some empirical evidence which suggests that simultaneous price discounts of complements are infrequent if the goods are substitutes their prices will be uncorrelated potentially rationalizing the lack of evidence on their co pricing when selling complements retailers earn higher profits than in the one good model through taxing captive consumers with a high overall price tag and attracting shoppers by pricing one of the goods aggressively bundling practices are thus shown to be detrimental to retailers profits

product bundling impacts of product heterogeneity and risk considerations abstract bundling has been extensively studied in the literature and its benefits have been manifested through three perspectives of achieving better price discrimination helping to save costs and preserving the power for deterring a potential entrant in this study we examine two aspects of bundling which have not been studied before we examine the impact of product heterogeneity on bundling decisions we also address risk considerations in a bundling problem specifically we consider a retailer who has the option of selling a bundle of two products pure bundling policy or selling the products separately no bundling policy the retailer could also face a product selection problem for which we consider three scenarios of choosing two products with perfectly positively correlated perfectly negatively correlated or independent reservation prices we use a mean variance approach to include retailer s risk through her profit variability when maximizing the expected value of profit we characterize the conditions under which a policy or scenario performs better than the others under the influence of product heterogeneity and or retailer s risk aversion among other findings we show that optimal bundling price chosen by a risk averse decision maker cannot be larger than the one chosen by a risk neutral decision maker

products with branded components an approach for premium pricing and partner selection an increasing number of products are being sold with components that themselves are brand names examples are personal computers with intel microprocessors and diet soft drinks that use the nutrasweet formulation branded components may alter consumers valuation of the bundle necessitating changes in the ways firms identify and price such bundled products surprisingly the existing marketing literature is silent on this issue the purpose of our paper is to propose an analytical approach that helps marketers of products with branded components make optimal pricing and partner selection decisions our managerial objectives are twofold a to the seller of the bundled product we suggest the optimal bundled product offering optimal selling prices of alternative products revenues and profits and b to the branded component manufacturers we indicate the most favorable alliance partners and payoff gains losses of aligning with other branded components instead of unbranded alternatives our analytical approach is also likely to be helpful to academics researching bundling and ingredient branding issues the specific problem modeled assumes the bundled product has two components that are consumed jointly furthermore each component can be either a brand name or unbranded in this model the consumer has no control over the choice of the components in the bundle the seller decides what form of bundle components i e branded or unbranded to offer we assume that the product that is marketed eventually enjoys a monopoly drawing from research in signaling and brand alliance we posit each branded component may either enrich or suppress the value of the partnering component in the bundle as perceived by the consumers our approach has three methodological stages first we build an individual level model to assess the valuation of alternative products and their principal components at the level of a randomly drawn consumer to do so we rely primarily on the theory of reservation prices and weber s theory on price value changes second we aggregate such valuation across consumers to assess the market s overall valuation for this purpose we invoke parametric distributions based on integral transform theory third we develop payoff functions based on market valuation of alternative products and supply side costs the managerial objectives are met based on results from this stage our approach was successfully applied to the context of a university bookstore that intends to sell windows based laptop computers the two principal components of the laptop computer bundle are the microprocessor chip and the personal computer platform on which the chip is implanted the seller may choose either compaq with intel inside or a simpler bundle featuring one of these with an unbranded complementary component or an entirely unbranded bundle we used data collected from 192 potential consumers via a survey included in the survey were measures of consumers perceptions of functional aspects of the components and their reservation prices for alternative bundled products the approach identified the most profitable bundle for the seller and its optimal price it also provided estimates of the revenue impact of the gain or loss for each branded component by partnering the other branded component instead of the unbranded alternative as such the model facilitates the determination of the optimal price price premium and profits for products with branded components as well as the identification of the ideal partner for each branded component manufacturer it is apt to caution that products with branded components need not always lead to price premiums or lead to win win outcomes reasons such as incongruity between the branded components or domination of one of the components over the other may drive potential consumers away thus hurting profits implications of the results to negotiate component prices are discussed in the paper the study limitations and directions for future research are also presented

optimal bundle formation and pricing of two products with limited stock abstract in this study we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm one of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit product demands follow a poisson process with a price dependent rate customer reservation prices are assumed to have a joint distribution we study the impact of reservation price distributions initial inventory levels product prices demand arrival rates and cost of bundling we observe that the expected profit decreases as the correlation between the reservation prices of two products increases with negative correlation bundling cost has a significant impact on the number of bundles formed when the product prices are low the retailer sells individual products as well as the bundle mixed bundling when they are high the retailer sells only bundles pure bundling the expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases for high starting inventory levels the retailer reduces bundle price and offers more bundles the number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases impacts of substitutability and complementarity of products are also investigated the retailer forms more bundles or charges higher prices for the bundle or both as the products become more complementary and less substitutable

why firms may prefer not to price discriminate via mixed bundling abstract we analyze a simple model of joint purchase discounts using a discrete choice framework to characterize consumer choices the model suggests that mixed bundling is more likely to be associated with monopoly this is due to the benefits reaped via price discrimination in a duopoly environment however only pure components pricing may be offered in equilibrium since firms fear the extra degree of competition inherent in mixed bundling

bundling with customer self selection a simple approach to bundling low marginal cost goods with declining costs of distributing digital products comes renewed interest in strategies for pricing goods with low marginal costs in this paper we evaluate customized bundling a pricing strategy that gives consumers the right to choose up to a quantity m of goods drawn from a larger pool of n different goods for a fixed price we show that the complex mixed bundle problem can be reduced to the customized bundle problem under some commonly used assumptions we also show that for a monopoly seller of low marginal cost goods this strategy outperforms individual selling m 1 and pure bundling m n when goods have a positive marginal cost or when customers have heterogeneous preferences over goods comparative statics results also show that the optimal bundle size for customized bundling decreases in both heterogeneity of consumer preferences over different goods and marginal costs of production we further explore how the customized bundle solution is affected by factors such as the nature of distribution functions in which valuations are drawn the correlations of values across goods and the complementarity or substitutability among products altogether our results suggest that customized bundling has a number of advantages both in theory and practice over other bundling strategies in many relevant settings

multiproduct monopoly commodity bundling and correlation of values through what selling strategy can a multiproduct monopolist maximize his profits when his knowledge about individual consumers preferences is limited one possibility extensively studied in the context of a single good monopoly is to use quantity dependent pricing as a means of discriminating among customers with differing tastes see for example oi 1971 and maskin and riley 1984 an alternative technique for price discrimination first suggested by stigler 1968 and analyzed further by adams and yellen 1976 is for the monopolist to package two or more products in bundles rather than selling them separately through a series of examples adams and yellen illustrate that bundling can serve as a useful price discrimination device even when all consumers willingnesses to pay for each of the goods individually are unaffected by whether they are also consuming the other product a typical example is illustrated in figure i adapted from figure iv in adams and yellen where there are two goods three consumers ab c who consume at most one unit of each good with reservation values for each good that are independent of whether the other good is consumed and zero costs of production there a bundle offered at a price of 100 fully extracts all potential surplus which would be impossible pricing the goods independently unfortunately though these authors do not provide any general characterization of the circumstances in which bundling is actually a multiproduct monopolist s optimal strategy their examples however such as figure i create the impression that the profitable use of bundling

practice prize winner pricing digital content product lines a model and application for the national academies press we examine the problem of how a content provider specifically the national academies press nap can optimally price the different forms of its product print and pdf that it sells online whereas products in the traditional product line generally tend to be substitutes the different content product forms could range from being substitutes to being complements across customers thus the content provider can possibly sell bundles of the product forms leading to additional revenue we first discuss nap s decision context and describe the model we proposed for developing nap s optimal pricing policies for its different forms we describe the choice experiment we conducted on the publisher s website that maximally uses the online interface to collect relevant data needed to estimate our model we show how nap embraced the results from the model for developing a new business model and how it used the insights derived from the study to set pricing policies and monitor sales performance as a function of pricing finally we perform validation of the model and the implemented policies using dynamic modeling of sales data from nap s website the paper illustrates how e commerce technologies can lead to the development of optimal policies using marketing models

a general choice model for bundles with multiple category products application to market segmentation and optimal pricing for bundles abstract the attribute based approach to study customer choices cannot deal with bundles of heterogeneous components which are usually drawn from different product categories the authors develop the comparability based balance model which is a unified framework for modeling bundle choices the model can be employed for any bundle regardless of the heterogeneity of bundle components under a pure bundling strategy the conjoint model and balance model are special cases of the general model the authors use mixture distributions in a hierarchical bayesian framework to incorporate consumer heterogeneity in a more flexible manner than the extant approaches such as latent class and random coefficient models the empirical tests of the model show that most attribute effects are significant and consistent with the model s predictions the model is superior to those that do not consider the issues of comparability of attributes latent class structure and heterogeneity among respondents the authors show how