Optimal Two‐Part Pricing under Demand Uncertainty

This paper examines the pricing behavior of a risk‐averse monopolistic firm under demand uncertainty. The firm produces a single good at a constant marginal cost. To facilitate sales, the firm uses a two‐part pricing contract that includes a membership fee and a selling price per unit. The good is sold to a continuum of heterogeneous consumers who are subject to a common demand shock. We show that the global and marginal effects of risk aversion are to push the unit price closer to the constant marginal cost and to shrink the market coverage so as to limit the firm’s risk exposure to the demand uncertainty. The more risk‐averse firm as such charges a higher membership fee to consumers. We further show that an increase in the fixed cost of production induces the firm to lower (raise) the unit price, to raise (lower) the membership fee, and to shrink (enlarge) the market coverage under decreasing (increasing) absolute risk aversion. The firm’s optimal two‐part pricing contract, however, is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving‐spread increase in the demand uncertainty induces the firm to lower the unit price, to raise the membership fee, and to shrink the market coverage under either decreasing or constant absolute risk aversion. The firm’s risk preferences as such play a pivotal role in determining the optimal two‐part pricing under demand uncertainty. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal Two‐part Pricing under Cost Uncertainty

This paper examines the optimal two‐part pricing under cost uncertainty. We consider a risk‐averse monopolistic firm that is subject to a cost shock to its constant marginal cost of production. The firm uses two‐part pricing to sell its output to a continuum of heterogeneous consumers. We show that the global and marginal effects of risk aversion on the firm's optimal two‐part pricing are to raise the unit price and lower the fixed payment. We further show that an increase in the fixed cost of production induces the firm to raise (lower) the unit price and lower (raise) the fixed payment under decreasing (increasing) absolute risk aversion. The firm's optimal two‐part pricing is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving spread increase in cost uncertainty induces the firm to raise the unit price and lower the fixed payment under either decreasing or constant absolute risk aversion. Copyright © 2011 John Wiley & Sons, Ltd.     

Personalized Pricing and Quality Customization

We embed the principal–agent model in a model of spatial differentiation with correlated consumer preferences to investigate the competitive implications of personalized pricing and quality allocation (PPQ), whereby duopoly firms charge different prices and offer different qualities to different consumers, based on their willingness to pay. Our model sheds light on the equilibrium product-line pricing and quality schedules offered by firms, given that none, one, or both firms implement PPQ. The adoption of PPQ has three effects in our model: it enables firms to extract higher rents from loyal customers, intensifies price competition for nonloyal customers, and eliminates cannibalization from customer self-selection. Contrary to prior literature on one-to-one marketing and price discrimination, we show that even symmetric firms can avoid the well-known Prisoner's Dilemma problem when they engage in personalized pricing and quality customization. When both firms have PPQ, consumer surplus is nonmonotonic in valuations such that some low-valuation consumers get higher surplus than high-valuation consumers. The adoption of PPQ can reduce information asymmetry, and therefore sellers offer higher-quality products after the adoption of PPQ. Overall, we find that while the simultaneous adoption of PPQ generally improves total social welfare and firm profits, it decreases total consumer surplus.     

Bundling and joint marketing by rival firms

We study joint marketing by firms who price discriminate between consumers who patronize only one firm (single purchasers) and those who purchase from both (bundle purchasers). Firms either set the price of the bundle and then compete along side the bundle; or they determine a rebate that is applied to joint purchasers and then set prices. Even though the pricing structure in the joint marketing scheme is determined noncooperatively, the commitment to the joint marketing agreement allows firms to leverage their stand‐alone prices—leading to higher profits and lower consumer surplus in either case, compared to both uniform pricing and independent price discrimination without a joint marketing agreement. Nevertheless the two schemes differ dramatically, in that rebates increase joint purchasing, whereas bundle pricing diminishes bundle purchases.     

Pricing Experience Goods: The Effects of Customer Recognition and Commitment

In a two‐period model of nondurable experience goods, we compare the profit and social welfare effects of behavior‐based price discrimination (BBPD) and price commitment (PC) (relative to time‐consistent pricing) in a monopoly. We find that when the static, full‐information monopoly price is higher (lower) than the mean consumer valuation, PC yields higher (lower) profits and social welfare than BBPD. We also identify the market conditions under which BBPD does not increase firm profits and provide an explanation as to when the firm should discriminate against its first‐time and repeat customers, respectively.     

Price dispersion and optimal price categories with limited memory consumers

In this paper, we study consumers with limited memory and examine the effects of their price categorization on the pricing strategies of competing firms. The valuations of consumers are assumed to be heterogeneous. We find that it is possible to observe price dispersion even when each firm charges a single price if the consumers categorize prices non‐optimally. Moreover, we demonstrate that the likelihood of a price dispersion outcome is reduced when consumers with limited memory set up the price categories optimally. These findings suggest that the consumers' limited memory and their sub‐optimal behavior, that is, their inability to choose price categories optimally can be a reason for observed price dispersion.     

Imperfect Behavior‐Based Price Discrimination

In this article, we develop a model encompassing behavior‐based discriminatory pricing as a limit case of a more general framework where firms have incomplete information about consumers’ purchase histories. We show that information accuracy has a nonmonotonic impact on profits and the worst situation for firms is when information accuracy is intermediate. We also discuss welfare and consumer surplus implications of information accuracy. Although welfare monotonically decreases with the level of information accuracy, there is an inverse U‐shape relationship between consumers surplus and information accuracy.     

Learning quality through prices and word‐of‐mouth communication

This paper studies the effect of word‐of‐mouth communication on the optimal pricing strategy for new experience goods. I consider a dynamic monopoly model with asymmetric information about product quality, in which consumers learn in equilibrium from both prices and other consumers. The main result is that word‐of‐mouth communication is essential for the existence of separating equilibria, wherein the high‐quality monopolist signals high quality through a low introductory price (lower than the monopoly price), and the low‐quality one charges the monopoly price. The intuition is simple: low prices are costly, and will only be used by firms confident enough that increased experimentation (and therefore communication among consumers) will yield good news about quality and increased future profits. Additional results are the following: for the high‐quality seller, the expected price (quantity) is increasing (decreasing) over time; whereas for the low‐quality one, the opposite is true. Moreover, signaling becomes more difficult when consumers pay less attention to their peers' reports and more attention to past prices. Finally, word‐of‐mouth communication improves consumer welfare.     

A Model of Direct and Intermediated Sales

We examine a model in which an upstream firm can sell directly online and through heterogeneous intermediaries to heterogeneous consumers engaging in time-consuming search. Direct online sales may be more or less convenient and involve costly returns if the good fits consumers poorly. Direct selling appeals to higher-value consumers and increases the upstream firm's profits by allowing price discrimination. Competition and segmentation due to direct sales results in lower intermediary prices, making all consumers better off. Thus, entry by an upstream firm increases consumer surplus at the expense of intermediaries with the net result being an increase in social welfare.     

Customization with Vertically Differentiated Products

We consider a duopoly market with heterogeneous consumers. The firms initially produce vertically differentiated standard products located at the end points of the variety interval. Customization provides ideal varieties for consumers but has no effect on quality. The firms first choose whether to customize their products, then engage in price competition. We show that the low‐quality firm never customizes alone; customization becomes more likely as the difference between the firms’ qualities increases; and less likely as the fixed cost of customization increases. We extend the base model by relaxing two important assumptions—uniform pricing and exogenous quality. The main conclusions with uniform pricing continue to hold when price customization is allowed. In the second extension the firms’ qualities are endogenously determined. We show that the firms choose to be either substantially differentiated in quality or nondifferentiated.     

Competition with Aftermarket Power When Consumers Are Heterogeneous

We study a model of competitive foremarkets and partly monopolized aftermarkets. We show that high aftermarket power prompts firms to engage in inefficiently aggressive below‐cost pricing in the foremarket. This inefficiency is driven by the presence of consumers with valuations below marginal cost. While for intermediate aftermarket power their presence leads to a competition‐softening effect, for high aftermarket power firms attract increasing numbers of unprofitable consumers by aggressively pricing below cost. For high aftermarket power, firms' equilibrium profits can therefore be decreasing in aftermarket power but are always higher than for low aftermarket power. If firms engage in price discrimination by bundling the foremarket and aftermarket goods or by reducing their aftermarket power, they avoid selling to unprofitable consumers but also reduce the competition‐softening effect. This decreases firms' equilibrium profits but increases consumer and social welfare.     

Strategic Invasion in Markets with Switching Costs

We investigate the role of consumer switching costs in a three-stage model in which the entrant and the incumbent firm set prices sequentially and then the consumers decide from which firm to buy. We characterize the unique subgame perfect equilibrium and find that even an entrant with a higher marginal cost may profitably invade part of the market due to the existence of switching costs. Switching costs benefit both firms but harm consumers. This model is used to understand pricing behavior in the US telecommunications industry.     

Revealing Incentives for Compatibility Provision in Vertically Differentiated Network Industries

We determine the incentives for compatibility provision of firms that produce network goods with different intrinsic qualities when firms do not have veto power over compatibility. When network effects are strong, there are multiple equilibria in pricing and consumer decisions. We show that in some equilibria, it is the high‐quality firm that invests in compatibility, whereas in others, the low‐quality firm triggers compatibility. The socially optimal compatibility degree is zero, except under very strong network effects, where one of the equilibria has all consumers buying the low‐quality good. In this case, a partial degree of compatibility is optimal.     

Information Gathering and Marketing

Consumers have only partial knowledge before making a purchase decision, but can acquire more‐detailed information. Marketing makes it easier or harder for these consumers to do so. When consumers are ex ante heterogeneous, the firm might choose an intermediate marketing strategy for two quite different reasons. First, as a nonprice means of discrimination—it can make information only partially available, in a way that induces some, but not all, consumers to acquire the information. Second, when the firm cannot commit to a given investment in ensuring quality, the marketing and pricing strategy can act as a commitment device.     

Randal Heeb Innovation and Vertical Integration in Complementary Markets

This paper studies vertical integration by an essential-good monopolist into complementary markets. Unlike previous studies of complementary products, consumers are allowed to purchase some components of a complementary basket, but not others. Two different pricing strategies by the integrated firm may emerge. In mass-market equilibria, the price of the complement under integration is zero and it is given away with the essential good. Niche-market equilibria have more conventional pricing. This dichotomy is consistent with consumer software pricing. Integration enhances consumer and total surplus, unless it leads to exit by the higher-quality rival, in which case welfare is reduced. Exit is most likely when it is least damaging to consumer welfare. Integration reduces innovation by the rival firm. The effect on innovation by the integrated firm is ambiguous, but numerical computation of an extended model indicates that integration increases the innovation of the integrated firm and enhances welfare.     

Price Dynamics and Consumer Learning

This paper studies the price dynamics induced by strategic firm behavior in the presence of consumer learning about the uncertain quality differential of the products offered by a duopoly. It is found that consumers learn slowly and that prices converge also slowly to full-information levels. A consequence is that the incentives affirms to manipulate consumers' beliefs are persistent. Although pricing tends to be aggressive at the early stages, and average prices eventually increase over time, price wars may occur at intermediate stages of the product life cycle.     

Coupons and price discrimination in vertically‐correlated markets

This research analyzes the non‐cooperative and cooperative strategies with respect to manufacturer and retailer coupons. In a model with one manufacturer selling its product to one retailer, it is found that the retailer can achieve third‐degree price discrimination equilibrium in retail markets by issuing coupons to demanders with higher elasticity. Although facing only one retailer, the manufacturer can also achieve the same third‐degree price discrimination equilibrium by issuing coupons directly to demanders of higher elasticity. However, when only one firm issues the coupon, both manufacturer and retailer coupons can help alleviate the channel profit loss due to double marginalization. If the manufacturer and the retailer non‐cooperatively issue coupons, then the subgame‐perfect Nash equilibrium outcomes are equivalent to those under the successive third‐degree price discrimination. Moreover, cooperative strategies between the manufacturer and the retailer can eliminate double marginalization, achieve the vertical integration effect, and lead to higher profits, consumer surpluses, and social surpluses than non‐cooperative coupon strategies. Copyright © 2004 John Wiley & Sons, Ltd.     

Firm entry,product repositioning and welfare

We show that the entry of a second firm in a horizontally differentiated market (ala Hotelling) may harm consumers as prices increase and consumer’s surplus possibly decrease. We first derive the price and the consumer’s surplus of a monopoly which is located at the center of the market. When a second firm enters the market the first firm repositions and the two firms locate at their equilibrium points. Although competition adds to variety and increases consumer’s surplus, the post entry increase in price may outweight the gains from extra variety and make consumers worse off.     

Price‐matching policy with imperfect information

The model of price‐matching policy emphasizes on the importance of information imperfection. The demand is derived based on the assumptions that consumers have different reservation prices and different preferences over location. When a firm undercuts its competitor's price, it changes the demand structure of the market. The result shows that price‐matching policies are anticompetitive, but they do not facilitate monopoly price. Copyright © 2005 John Wiley & Sons, Ltd.     

SMOOTH QUANTILE‐BASED MODELING OF BRAND SALES,PRICE AND PROMOTIONAL EFFECTS FROM RETAIL SCANNER PANELS

Semiparametric quantile regression is employed to flexibly estimate sales response for frequently purchased consumer goods. Using retail store‐level data, we compare the performance of models with and without monotonic smoothing for fit and prediction accuracy. We find that (a) flexible models with monotonicity constraints imposed on price effects dominate both in‐sample and out‐of‐sample comparisons while being robust even at the boundaries of the price distribution when data is sparse; (b) quantile‐based confidence intervals are much more accurate compared to least‐squares‐based intervals; (c) specifications reflecting that managers may not have exact knowledge about future competitive pricing perform extremely well. Copyright © 2013 John Wiley & Sons, Ltd.