Static and Dynamic Pricing of Excess Capacity in a Make‐to‐Order Environment

We consider a make‐to‐order manufacturer that serves two customer classes: core customers who pay a fixed negotiated price, and “fill‐in” customers who make submittal decisions based on the current price set by the firm. Using a Markovian queueing model, we determine how much the firm can gain by explicitly accounting for the status of its production facility in making pricing decisions. Specifically, we examine three pricing policies: (1) static, state‐independent pricing, (2) constant pricing up to a cutoff state, and (3) general state‐dependent pricing. We determine properties of each policy, and illustrate numerically the financial gains that the firm can achieve by following each policy as compared with simpler policies. Our main result is that constant pricing up to a cutoff state can dramatically outperform a state‐independent policy, while at the same time achieving most of the increase in revenue achievable from general state‐dependent pricing. Thus, we find that constant pricing up to a cutoff state presents an attractive tradeoff between ease of implementation and revenue gain. When the costs of policy design and implementation are taken into account, this simple heuristic may actually out‐perform general state‐dependent pricing in some settings.     

Committed Versus Contingent Pricing Under Competition

Should capacitated firms set prices responsively to uncertain market conditions in a competitive environment? We study a duopoly selling differentiated substitutable products with fixed capacities under demand uncertainty, where firms can either commit to a fixed price ex ante, or elect to price contingently ex post, e.g., to charge high prices in booming markets, and low prices in slack markets. Interestingly, we analytically show that even for completely symmetric model primitives, asymmetric equilibria of strategic pricing decisions may arise, in which one firm commits statically and the other firm prices contingently; in this case, there also exists a unique mixed strategy equilibrium. Such equilibrium behavior tends to emerge, when capacity is ampler, and products are less differentiated or demand uncertainty is lower. With asymmetric fixed capacities, if demand uncertainty is low, a unique asymmetric equilibrium emerges, in which the firm with more capacity chooses committed pricing and the firm with less capacity chooses contingent pricing. We identify two countervailing profit effects of contingent pricing under competition: gains from responsively charging high price under high demand, and losses from intensified price competition under low demand. It is the latter detrimental effect that may prevent both firms from choosing a contingent pricing strategy in equilibrium. We show that the insights remain valid when capacity decisions are endogenized. We caution that responsive price changes under aggressive competition of less differentiated products can result in profit‐killing discounting.     

引入策略型消费者遗憾心理的时尚产品定价策略

通过对时尚策略型消费行为的研究,把消费者心理动机归结为两种,其一是因冲动购买而错过降价产生的“高价遗憾”;其二是因等待降价并延迟购买而遭遇缺货产生的“缺货遗憾”,并在此基础上,在一个两周期销售中分析其对企业的降低标价(Markdown, MD)与抬高标价(Markup, MU)两种定价模式的影响机理。首先把两种遗憾心理因素纳入消费者的效用函数,建模分析了需求随机下降低标价(抬高标价)两阶段销售模式中供应商如何通过考虑消费者行为设置不同阶段价格和限量配给水平的决策。并在此基础上通过不同定价模式下供应商收益参数的对比,重点分析了两种遗憾心理因素效应对销售阶段分割的综合影响。研究发现：有遗憾心理的消费者将削弱延迟购买倾向,供应商可通过制造适当的配给风险诱导顾客高价期购买;其次两种定价类型下,当满足一定条件时,面对遗憾心理的消费群体,企业均能实现比统一定价更高的最优收益,并且抬高标价比降低标价的优化效果更明显。     

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.     

Measuring Market Power in the Ready‐to‐Eat Cereal Industry

The ready‐to‐eat cereal industry is characterized by high concentration, high price‐cost margins, large advertising‐to‐sales ratios, and numerous introductions of new products. Previous researchers have concluded that the ready‐to‐eat cereal industry is a classic example of an industry with nearly collusive pricing behavior and intense nonprice competition. This paper empirically examines this conclusion. In particular, I estimate price‐cost margins, but more importantly I am able empirically to separate these margins into three sources: (i) that which is due to product differentiation; (ii) that which is due to multi‐product firm pricing; and (iii) that due to potential price collusion. The results suggest that given the demand for different brands of cereal, the first two effects explain most of the observed price‐cost margins. I conclude that prices in the industry are consistent with noncollusive pricing behavior, despite the high price‐cost margins. Leading firms are able to maintain a portfolio of differentiated products and influence the perceived product quality. It is these two factors that lead to high price‐cost margins.     

Browse‐and‐Switch: Retail‐Online Competition under Value Uncertainty

Although online shopping is becoming popular, consumers who are unsure about whether to buy a product may find it advantageous to visit a brick‐and‐mortar retail store to first examine the product before purchasing it. But, after browsing at the store, consumers have the option of switching to an e‐tailer to purchase the item at a cheaper price rather than buying at the store. Recent business press refers to this browse‐and‐switch behavior as “showrooming,” and attributes to it the declining profits of brick‐and‐mortar retailers. To study the effect of the browse‐and‐switch option on retail and online pricing strategies and profits, we analyze a stylized economic model that incorporates uncertainty in consumers' valuation of the product, captures the heterogeneity among consumers in their inclination to purchase online, and permits product returns. We consider various equilibrium scenarios for different combinations of consumer shopping behaviors, characterize the parameter ranges for each scenario, and demonstrate that browse‐and‐switch behavior can indeed occur under equilibrium. Our analysis further shows that the option for consumers to browse‐and‐switch intensifies competition, reducing the profits for both firms.     

A WTP‐Choice Model: Empirical Validation,Competitive and Centralized Pricing

Willingness To Pay (WTP) of customers plays an anchoring role in pricing. This study proposes a new choice model based on WTP, incorporating sequential decision making, where the products with positive utility of purchase are considered in the order of customer preference. We compare WTP‐choice model with the commonly used (multinomial) Logit model with respect to the underlying choice process, information requirement, and independence of irrelevant alternatives. Using WTP‐choice model, we find and compare equilibrium and centrally optimal prices and profits without considering inventory availability. In addition, we compare equilibrium prices and profits in two contexts: without considering inventory availability and under lost sales. One of the interesting results with WTP‐choice model is the “loose coupling” of retailers in competition; prices are not coupled but profits are. That is, each retailer should charge the monopoly price as the collection of these prices constitute an equilibrium but each retailer's profit depends on other retailers' prices. Loose coupling fails with dependence of WTPs or dependence of preference on prices. Also, we show that competition among retailers facing dependent WTPs can cause price cycles under some conditions. We consider real‐life data on sales of yogurt, ketchup, candy melt, and tuna, and check if a version of WTP‐choice model (with uniform, triangle, or shifted exponential WTP distribution), standard or mixed Logit model fits better and predicts the sales better. These empirical tests establish that WTP‐choice model compares well and should be considered as a legitimate alternative to Logit models for studying pricing for products with low price and high frequency of purchase.     

Mass Customization and Guardrails: “You Can Not Be All Things to All People”

A mass customization strategy enables a firm to match its product designs to unique consumer tastes. In a classic horizontal product‐differentiation framework, a consumer's utility is a decreasing function of the distance between their ideal taste and the taste defined by the most closely aligned product the firm offers. A consumer thus considers the taste mismatch associated with their purchased product, but otherwise the positioning of the firm's product portfolio (or, “brand image”) is immaterial. In contrast, self‐congruency theory suggests that consumers assess how well both the purchased product and its overall brand image match with their ideal taste. Therefore, we incorporate within the consumer utility function both product‐specific and brand‐level components. Mass customization has the potential to improve taste alignment with regard to a specific purchased product, but at the risk of increasing brand dilution. Absent brand dilution concerns, a firm will optimally serve all consumers’ ideal tastes at a single price. In contrast, by endogenizing dilution costs within the consumer utility model, we prove that a mass‐customizing firm optimally uses differential pricing. Moreover, we show that the firm offers reduced prices to consumers with extreme tastes (to stimulate consumer “travel”), with a higher and fixed price being offered to those consumers having more central (mainstream) tastes. Given that a continuous spectrum of prices will likely not be practical in application, we also consider the more pragmatic approach of augmenting the uniformly priced mass customization range with preset (non‐customized) outlying designs, which serve customers at the taste extremes. We prove this practical approach performs close to optimal.     

Entry Deterrence of Capacitated Competition Using Price and Non‐Price Strategies

We analyze the role of pricing and branding in an incumbent firm's decision when facing competition from an entrant firm with limited capacity. We do so by studying two price competition models (Stackelberg and Nash), where we consider the incumbent's entry‐deterrence pricing strategy based on a potential entrant's capacity size. In an extension, we also study a branding model, where the incumbent firm, in addition to pricing, can also invest in influencing market preference for its product. With these models, we study conditions under which the incumbent firm may block the entrant (i.e., prevent entry without any market actions), deter the entrant (i.e., stop entry with suitable market actions) or accommodate the entrant (i.e., allow entry and compete), and how the entrant will allocate its limited capacity across its own and the new market, if entry occurs. We also study the timing difference between the two different dynamics of the price competition models and find that the incumbent's first‐mover advantage benefits both the incumbent and the entrant. Interestingly, the entrant firm's profits are not monotonically increasing in its capacity even when it is costless to build capacity. In the branding model, we show that in some cases, the incumbent may even increase its price and successfully deter entry by investing in consumer's preference for its product. Finally, we incorporate demand uncertainty into our model and show that the incumbent benefits from demand uncertainty while the entrant may be worse off depending on the magnitude of demand uncertainty and its capacity.     

How Costs and Heterogeneous Consumer Price Sensitivity Interact with Add‐On Pricing

Firms often cite cost savings as a reason why they charge separately for add‐ons. Firms also often face situations where consumers' price sensitivity is correlated with their valuation of add‐ons. While cost savings may directly translate into profit gains in some scenarios, this study examines the strategic implications of add‐on pricing and is the first to suggest that cost savings from add‐on pricing may in fact result in profit loss for firms when consumers are heterogeneous in price sensitivity. This is because add‐on pricing can trigger a revenue loss that exceeds any cost savings, thus leading to a negative net profit change for competing firms. Even if firms have the capability to pre‐commit to not adopting add‐on pricing, we show that competing firms can be locked in a prisoner's dilemma where all choose to adopt add‐on pricing and lose profits (as compared to none adopting add‐on pricing). We further show the possibility that the greater the cost of providing the add‐on (and the greater the cost savings generated from add‐on pricing), the worse this profit loss gets.     

消费者寻求多样化与厂商折扣定价竞争

在很多市场环境中，消费者喜欢尝试不同产品的特性，重复消费同一商品会产生滞留成本。本文通过构建两期动态博弈模型，研究了滞留成本对企业折扣券定价行为的影响，并与其他定价策略的市场绩效进行了比较。本文研究结果表明：（1）企业会通过折扣券奖励忠诚的消费者，即企业会对重复购买自己产品的消费者给予价格优惠，而对新消费者制定高价格；（2）在均衡中，随着滞留成本的提升，消费者剩余和社会总福利降低，企业利润上升；（3）与其他定价机制相比较，折扣券定价策略下的社会总福利较低，政策制定者应当限制此类策略的应用。     

Optimal Pricing Strategies for Capacity Leasing Based on Time and Volume Usage in Telecommunication Networks

In this study, we examined optimal pricing strategies for “pay‐per‐time,” “pay‐per‐volume,” and “pay‐per‐both‐time‐and‐volume” based leasing of data networks in a monopoly environment. Conventionally, network capacity distribution includes short‐/long‐term bandwidth and/or usage time leasing. When customers choose connection‐time–based pricing, their rational behavior is to fully utilize the bandwidth capacity within a fixed time period, which may cause the network to burst (or overload). Conversely, when customers choose volume‐based strategies their rational behavior is to send only the minimum bytes necessary (even for time‐fixed tasks for real time applications), causing the quality of the task to decrease, which in turn creates an opportunity cost for the provider. Choosing a pay‐per time and volume hybridized pricing scheme allows customers to take advantage of both pricing strategies while lessening the disadvantages of each, because consumers generally have both time‐ and size‐fixed tasks such as batch data transactions. One of the key contributions of this study is to show that pay‐per both time and volume pricing is a viable and often preferable alternative to the offerings based on only time or volume, and that judicious use of such a pricing policy is profitable to the network provider.     

Inventory‐Based Dynamic Pricing with Costly Price Adjustment

We study an average‐cost stochastic inventory control problem in which the firm can replenish inventory and adjust the price at anytime. We establish the optimality to change the price from low to high in each replenishment cycle as inventory is depleted. With costly price adjustment, scale economies of inventory replenishment are reflected in the cycle time instead of lot size—An increased fixed ordering cost leads to an extended replenishment cycle but does not necessarily increase the order quantity. A reduced marginal cost of ordering calls for an increased order quantity, as well as speeding up product selling within a cycle. We derive useful properties of the profit function that allows for reducing computational complexity of the problem. For systems requiring short replenishment cycles, the optimal solution can be easily computed by applying these properties. For systems requiring long replenishment cycles, we further consider a relaxed problem that is computational tractable. Under this relaxation, the sum of fixed ordering cost and price adjustment cost is equal to (greater than, less than) the total inventory holding cost within a replenishment cycle when the inventory holding cost is linear (convex, concave) in the stock level. Moreover, under the optimal solution, the time‐average profit is the same across all price segments when the inventory holding cost is accounted properly. Through a numerical study, we demonstrate that inventory‐based dynamic pricing can lead to significant profit improvement compared with static pricing and limited price adjustment can yield a benefit that is close to unlimited price adjustment. To be able to enjoy the benefit of dynamic pricing, however, it is important to appropriately choose inventory levels at which the price is revised.     

Profitability of Service‐Level‐Based Price Differentiation with Inventory Rationing

In this paper, we study the profitability of service‐level‐based price differentiation (SLBPD) in an inventory‐rationing context. SLBPD implies that a company offers several combinations of prices and guaranteed service levels, from which customers self‐select; different customers choose different offerings because they incur different shortage costs if an order is not fulfilled immediately. We develop an analytical model for SLBPD and explore if and when such a service differentiation strategy yields higher profits than a single undifferentiated offering. The results of our analyses suggest that SLBPD is profitable only if a company faces pricing restrictions, e.g., because of competitive pressure or regulatory restrictions. We develop necessary and sufficient conditions under which a specific and relevant form of SLBPD (called “service‐level‐based upselling”) is profitable, and provide an algorithm to compute the optimal parameters of such a policy. Based on this algorithm we carry out numerical analyses that allow us to characterize the profit increment of service‐level‐based upselling. We derive managerial insights into the attractiveness of SLBPD and explain how our basic analytical framework can be extended to account for more complex practical features.     

信息不对称条件下的企业集团转移定价研究

本文研究了信息不对称条件下企业集团的转移定价决策问题,提出了歧视转移定价法。即在信息不对称条件下,当上游子企业对中间产品具有完全垄断能力时,企业集团将转移定价决策权下放给上游子企业,上游子企业根据内外部市场需求的差异,采用差别定价策略。通过与市场基础转移定价和边际成本转移定价相比较,得出歧视转移定价可以增加企业集团的整体利润。     

Pricing Software Upgrades: The Role of Product Improvement and User Costs

The computer software industry is an extreme example of rapid new product introduction. However, many consumers are sophisticated enough to anticipate the availability of upgrades in the future. This creates the possibility that consumers might either postpone purchase or buy early on and never upgrade. In response, many software producers offer special upgrade pricing to old customers in order to mitigate the effects of strategic consumer behavior. We analyze the optimality of upgrade pricing by characterizing the relationship between magnitude of product improvement and the equilibrium pricing structure, particularly in the context of user upgrade costs. This upgrade cost (such as the cost of upgrading complementary hardware or drivers) is incurred by the user when she buys the new version but is not captured by the upgrade price for the software. Our approach is to formulate a game theoretic model where consumers can look ahead and anticipate prices and product qualities while the firm can offer special upgrade pricing. We classify upgrades as minor, moderate or large based on the primitive parameters. We find that at sufficiently large user costs, upgrade pricing is an effective tool for minor and large upgrades but not moderate upgrades. Thus, upgrade pricing is suboptimal for the firm for a middle range of product improvement. User upgrade costs have both direct and indirect effects on the pricing decision. The indirect effect arises because the upgrade cost is a critical factor in determining whether all old consumers would upgrade to a new product or not, and this further alters the product improvement threshold at which special upgrade pricing becomes optimal. Finally, we also analyze the impact of upgrade pricing on the total coverage of the market.     

上下游市场存在竞争的企业集团转移定价研究

基于不对称的竞争环境,研究了企业集团的中间产品的转移定价问题,研究结果表明,中间产品的转移定价策略取决于上游子公司和上游竞争公司之间的不对称程度:当不对称程度较大时,企业集团应采取Hirshleifer的边际成本转移定价策略;当不对称程度较小时,企业集团应采取部分非中心化结构的转移定价策略。     

Optimal Pricing of Two Successive‐Generation Products with Trade‐in Options under Uncertainty

To entice consumers to purchase both current and next generation products, many manufacturers and retailers offer trade‐in programs that allow buyers of the first generation product to trade‐in the product and purchase the new generation product at a lower price. By considering the interactions between “forward‐looking” consumers and a firm when a trade‐in program is offered, we analyze a two‐period dynamic game to determine the optimal prices of two successive‐generation products in equilibrium, and examine the conditions under which trade‐in programs are beneficial to the firm. Our model incorporates market heterogeneity (valuation of the first generation product varies among the consumer population), product uncertainty (the incremental value of the new product is uncertain before its introduction), and consumers' forward‐looking behavior (consumers take future product valuation and prices into consideration when making purchasing decisions). With the trade‐in option, we show that consumers are willing to pay a price that is higher than their valuations of the current product. Furthermore, trade‐in programs are more beneficial to the firm when: (i) the durability of the current product is high; (ii) the market heterogeneity is low; or (iii) the uncertainty level (or the expected incremental value) of the new product is high. Finally, when the incremental value of the new product is more uncertain, consumers are more willing to purchase the current product because of the “option” value of the trade‐in programs and thus trade‐in programs can be more beneficial to the firm in this case.     

Transfer Pricing and Sourcing Strategies for Multinational Firms

Taking advantage of low tax rates using transfer pricing and taking advantage of low production costs using offshoring are two strategies multinational firms (MNFs) use to increase profits. We identify an important trade‐off that MNFs face in setting their transfer prices: the conflict between (i) the incentive role and (ii) the tax role of the transfer price. For MNFs, we find the profit‐maximizing transfer‐pricing strategies that motivate divisional management to (i) make good sourcing decisions and (ii) take advantage of favorable tax rates. We quantify the absolute and relative maximum inefficiency in terms of the after‐tax MNF's profit change from using a single transfer‐pricing system as compared to the dual transfer‐pricing system. We show that the highest relative loss is attained when the average sourcing cost and the tax differential are high. We demonstrate that the highest absolute loss is attained when the average outsourcing cost is approximately equal to the offshoring cost. We extend our results to two practical variations in MNF structures: an MNF that faces operational constraints on its offshoring capacity and an MNF that uses compensation contracts linked to after‐tax firm‐wide profits. Our insights help MNFs' managers identify when to use single and dual transfer‐pricing systems.