Durable goods pricing with reference price effects

A price benchmark shaped by consumers on the basis of their perception of past prices is known as a reference price. Behavioral decision research suggests that consumers are likely to be backward-looking in that they make purchase decisions based not only on the current price but also on the reference price. It is evident that the reference price effect, which has significant impact on consumer demand, exists for both consumables and durables. Yet, how this effect works has only been investigated in relation to the pricing of consumables, and thus the corresponding results are unable to yield normative implications for durable goods pricing where the saturation effect must enter the picture. This study aims to provide marketers of durables with relevant insights that can be practically used to guide their design of pricing strategies in the presence of the reference price effect. Specifically, we develop a dynamic pricing model which incorporates both the reference price effect and the saturation effect into a framework to broaden our understanding on the durable goods pricing problem. As the internet technology and social media have enhanced consumers’ ability to recall and compare past prices, the need for such a pricing model with backward-looking consumer behavior is increasingly compelling. Our results indicate that while it is optimal for a myopic seller to adopt the skimming pricing strategy, either the price skimming strategy or the penetration strategy is optimal for a forward-looking seller, contingent on the potential market and consumers’ reference price effects.     

Strategic Management of Distressed Inventory

It is well known that maximizing revenue from a fixed stock of perishable goods may require discounting prices rather than allowing unsold inventory to perish. This behavior is seen in industries ranging from fashion retail to tour packages and baked goods. A number of authors have addressed the markdown management problem in which a seller seeks to determine the optimal sequence of discounts to maximize the revenue from a fixed stock of perishable goods. However, merchants who consistently use markdown policies risk training customers to “wait for the sale.” We investigate models in which the decision to sell inventory at a discount will change the future expectations of customers and hence their buying behavior. We show that, in equilibrium, a single‐price policy is optimal if all consumers are strategic and demand is known to the seller. Relaxing any of these conditions can lead to a situation in which a two‐price markdown policy is optimal. We show using numerical simulation that if customers update their expectations of availability over time, then optimal sales limit policies can evolve in a complex fashion.     

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.     

竞争环境下基于顾客策略行为的易逝品动态定价研究

在两个提供相同易逝品的零售商折线竞争下,从顾客策略行为出发,研究竞争环境下两零售商的动态定价策略。首先建立供大于求的情况下两零售商动态定价模型,给出了均衡价格满足的条件,并探讨了在一些特殊情况下均衡价格的特性。然后将这一模型扩展到供小于求的情形,探讨模型的求解方法。算例分析了在折线竞争模式下零售商在面对顾客策略行为时,如何动态的决定价格。同时发现,在供大于求的情况下,顾客策略行为导致零售商的收益降低;在供小于求的情况下,一定程度的顾客策略行为可以使零售商获得更高的期望收益。     

Managing Risks in Multiple Online Auctions: An Options Approach*

The scenario of established business sellers utilizing online auction markets to reach consumers and sell new products is becoming increasingly common. We propose a class of risk management tools, loosely based on the concept of financial options that can be employed by such sellers. While conceptually similar to options in financial markets, we empirically demonstrate that option instruments within auction markets cannot be developed employing similar methodologies, because the fundamental tenets of extant option pricing models do not hold within online auction markets. We provide a framework to analyze the value proposition of options to potential sellers, option‐holder behavior implications on auction processes, and seller strategies to write and price options that maximize potential revenues. We then develop an approach that enables a seller to assess the demand for options under different option price and volume scenarios. We compare option prices derived from our approach with those derived from the Black‐Scholes model ( Black & Scholes, 1973 ) and discuss the implications of the price differences. Experiments based on actual auction data suggest that options can provide significant benefits under a variety of option‐holder behavioral patterns.     

Group Selling,Product Durability,and Consumer Behavior

Firms producing complementary goods often strategically form groups and jointly sell their products to better coordinate their decisions. For consumer durables, decisions about such collaboration might be complicated due to two factors. Because of their durability and presence of used goods markets, such products engender “future” price competition between new and used goods. On the other hand, consumers of such products might be forward‐looking and patient, both of which affect their purchasing behavior. In this study, we study how the above product and consumer characteristics interact to affect the group selling decisions of complementary firms. We do so through a two‐period model consisting of a value chain with two upstream manufacturers and a downstream retailer. When consumers are relatively impatient and reluctant to wait to buy later, group selling by manufacturers will take place only when the end product is relatively perishable, that is, product durability is low. However, if consumers are patient, that is, willing to wait, collaboration happens only when the end product is quite durable; for relatively perishable products the manufacturers sell their products separately. We also comment on how our results are affected by factors like manufacturers directly selling to end consumers or there being multiple opportunities to decide whether or not to use group selling strategy.     

“双积分”政策下汽车制造商竞争定价与减排策略研究

"双积分"政策的实施对汽车制造商的定价决策产生了重要影响。考虑卖方由同时生产燃油车和新能源汽车的制造商1和仅生产新能源汽车的制造商2组成,在消费者低碳偏好和价格竞争影响下分别针对制造商1对燃油车采取和不采取节能减排措施的情况,研究"双积分"政策下汽车制造商的定价策略和减排决策,探讨新能源汽车积分值和积分比例要求对政府和企业决策的作用效果。进一步,通过对不同情形的结果进行分析,得到"双积分"政策的出台、消费者低碳偏好及制造商采取节能减排措施对制造商定价和减排决策带来的变化,并通过算例分析验证了结论。研究结果表明:(1)"双积分"政策可以降低新能源汽车的价格,提高新能源汽车制造商的利润,促进燃油车主动减排。(2)当新能源汽车的需求价格弹性系数和需求交叉价格弹性系数处于较高水平时,政府要制定较高的每台新能源汽车积分值。(3)燃油车的油耗水平存在一个环境属性标准,当油耗水平低于一定值时,随着新能源汽车积分比例要求的不断增大,制造商1选择提高燃油车价格。(4)消费者低碳偏好是提高燃油车减排水平的重要因素,政府可以对减排技术先进的燃油车制造商进行低油耗认证,提高消费者低油耗燃油车需求,激励燃油车制...     

An Experimental Investigation of Procurement Auctions with Asymmetric Sellers

Electronic reverse auctions are a commonly used procurement mechanism. Research to date has focused on suppliers who are ex ante symmetric in that their costs are drawn from a common distribution. However, in many cases, a seller's range of potential costs depends on their own operations, location, or economies of scale and scope. Thus, understanding how different bidder types impact auction outcomes is key when designing an auction. This study reports the results of the first controlled laboratory experiment designed to compare prices between first‐price and second‐price procurement auctions for homogeneous goods when seller cost types are asymmetric and the number of bidders varies. The results indicate that first‐price auctions generate lower prices regardless of market composition. The results also reveal that first‐price auctions are at least weakly more efficient than second‐price auctions despite the theoretical prediction that the reverse should hold in asymmetric auctions. Post hoc analysis of individual bidders' behavior in first‐price auctions revealed evidence that bidders systematically underbid when their cost realizations were close to the lower bound. Furthermore, bidders adjust their behavior based on the type of the other bidders in the market in a manner inconsistent with theory. Consequently, adding a third bidder to a two‐bidder market is not advantageous to the buyer unless that third bidder is a low‐cost type.     

Stimulating Early Adoption of New Products through Channel Disintegration

Conventional wisdom holds that adding layers to a distribution channel is detrimental to the interests of consumers and the channel that serves them. In contrast, our study indicates that a disintegrated channel structure can be desirable in some instances. When consumers have valuation uncertainty prior to consuming a product, having an independent retailer may boost both channel profits and consumer surplus relative to direct selling by an integrated firm. The quandary in selling such products is that after early adopters make their purchase decisions, the seller may alter prices in such a way that makes early adopters' decisions appear suboptimal in hindsight. Since the seller cannot credibly commit to future prices, customers are reluctant to adopt early, choosing instead to delay their purchase decisions. This delay is certainly detrimental to the interest of the distribution channel, but the rejection of the early adoption discount can equally reduce consumer surplus. This problem can be mitigated by introducing an independent retailer. The familiar double marginalization “problem” from channel disintegration can credibly assure customers of unfavorable future prices for late adoption. This assurance attracts more customers to seek early adoption, leading to lower overall retail prices, increased supply, and higher consumer and producer surpluses.     

Channel Strategies for Durable Goods: Coexistence of Selling and Leasing to Individual and Corporate Consumers

In durable goods markets, such as those for automobiles or computers, the coexistence of selling and leasing is common as is the existence of both corporate and individual consumers. Leases to corporate consumers affect the price of used goods on the second‐hand market which in turn affect the buying and leasing behavior of individual consumers. The setting of prices (or volumes) for sale and lease to individual and corporate consumers is a complicated problem for manufacturers. We consider a manufacturer who concurrently sells and leases a finitely durable good to both individual and corporate consumers. The interaction between the manufacturer and consumers is modeled as a dynamic sequential game, where each player seeks to maximize its own payoff over an infinite horizon. We study how the corporate channel substitutability of new goods and used goods and transaction costs in the second‐hand market affect the manufacturer's pricing decisions, consumer behavior, and social welfare in the retail market. Making a number of simplifying assumptions, including two‐period lifetime for the finitely durable goods, we consider Markov Perfect Equilibrium as the solution concept. We show that the manufacturer can maximize her profit by segmenting consumers according to their willingness to pay. Selling and leasing are the mechanisms used for price discrimination in the retail market. We show that as she leases a larger share of her production to the corporate consumer, (1) the manufacturer does not necessarily have to adjust the optimal selling price of new goods to individual consumers, and the volume of sales of new goods to individual consumers can stay the same; (2) the manufacturer does increase the retail lease price, and the number of individual leases decreases; (3) the net supply of used goods on the market increases, leading to a lower market price for used goods; and (4) more individual consumers are able to participate in the market, and their collective welfare or net utility improves. We also show that as production costs increase the manufacturer increases prices, reducing volumes across all channels. When transaction costs increase, the manufacturer reduces leasing in both corporate and retail channels.     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

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.     

不确定需求下考虑资金约束的生鲜农产品政府补贴策略

针对需求不确定环境下政府如何对生鲜农产品供应链进行补贴的问题,在考虑财政资金的约束下,分别构建了无政府补贴、采购补贴和销售补贴三种情形下的博弈模型。通过对比分析得出了政府的最优补贴策略,并分析了补贴策略对生鲜供应链最优决策的影响,最后用数值算例进一步说明了不同补贴策略对不同类型生鲜农产品的影响。研究发现,补贴策略的选择与财政预算密切相关。在财政预算充裕时,两种补贴策略都有效且可行,都能平抑物价、增加供给、拉动需求;从改善社会整体福利的角度,采购补贴为最优策略;从补贴资金效率的角度,销售补贴为最优策略。在销售补贴预算充裕而采购补贴预算存在缺口时,销售补贴为最优策略。在财政预算不足时,政府的最优策略就是不干涉市场的运营。     

投资者结构、交易失衡与商品期货市场的价格发现效率

基于上海期货交易所铝、铜、橡胶和燃料油期货合约两种投资者结构的分账户数据,分析不同类型投资者交易失衡对我国商品期货市场收益、价格发现与波动的影响。结果表明:(1)个人投资者和投机者的交易失衡暗示其寻找最佳买多或卖空时点的能力不足,存在明显的过度自信、过度投机和羊群行为,加剧商品期货价格波动;(2)机构投资者和套期保值者常常表现出与个人投资者和投机者相反的交易意愿,他们能够较好地把握买入与卖出时机,且更愿意冒险持有头寸,有助于缓解商品期货价格波动;(3)商品期货价格的变动趋势表明机构投资者和套期保值者具有一定的信息优势,能够在一定程度上预测商品期货价格的未来走势,他们极其乐观或悲观的交易失衡可以向商品期货市场传递有效的信息和时间信号。因此,提高机构投资者和套期保值者的成交量(持仓量)比例,优化投资者结构,可以有效促进我国商品期货市场的价格发现,降低期货价波动风险。此外,大型投机者的交易活动也可以在一定程度上缓解商品期货价格波动。     

Advance selling with freebies and limited production capacity

We consider a two-period pricing model in which a seller offers freebies along with the product when making advance sales, and production is constrained by capacity. The seller can offer freebies to increase both market base and customer׳s valuation toward the product in advance. The customers strategically determine whether to purchase the product in advance and gain freebies when their valuation on the product is uncertain, or delay their purchase decision until the regular selling period. We characterize the optimal pricing, quality level of the freebie and production quantity decisions that maximize the expected profits of the seller over the two periods.     

P2P Marketplaces and Retailing in the Presence of Consumers' Valuation Uncertainty

Can peer‐to‐peer (P2P) marketplaces benefit traditional supply chains when consumers may experience valuation risk? P2P marketplaces can mitigate consumers' risk by allowing them to trade mismatched goods; yet, they also impose a threat to retailers and their suppliers as they compete over consumers. Further, do profit‐maximizing marketplaces always extract the entire consumer surplus from the online trades? Our two‐period model highlights the effects introduced by P2P marketplaces while accounting for the platform's pricing decisions. We prove that with low product unit cost, the P2P marketplace sets its transaction fee to the market clearing price, thereby extracting all of the seller surplus. In this range of product unit cost, the supply chain partners are worse off due to the emergence of a P2P marketplace. However, when the unit cost is high, the platform sets its transaction fee to be less than the market clearing price, intentionally leaving money on the table, as a mechanism to stimulate first period demand for new goods in expectation for some of them to be traded later, in the second period, via the marketplace. It is not until the surplus left with the sellers is sufficiently high that the supply chain partners manage to extract some of this surplus, ultimately making them better off due to a P2P marketplace. We further analyze the impact of a P2P marketplace on consumer surplus and social welfare. In addition, we consider model variants accounting for a frictionless platform and consumer strategic waiting.     

不同市场能力下的“电商—平台—物流”在线销售系统的决策研究

近年来,随着互联网的快速发展,市场上衍生出了一些在线销售网站。考虑了一个包含电商卖家、电商平台和物流公司的在线销售系统模型,其中需求依赖于产品价格、平台和物流服务水平。研究了当物流、平台同时决策时,在线销售系统中电商卖家和平台、物流之间的不同市场能力结构问题。考虑了3种不同市场能力的分散决策模型:(1)物流-平台Stackelberg模型;(2)电商Stackelberg模型;(3)Nash模型。相关的均衡解和最优利润被得到。研究结果表明,在不同的市场能力结构下,当物流公司和平台同时决策时,即使他们的服务投入不相同,但最优收费相同。市场能力结构对在线销售成员和消费者有重要的影响。对电商而言,当市场能力较高时,会制定较低的零售价格,并获得最多的利润,同时能够提升消费者购买的积极性;当市场能力较低时,电商会制定较高的零售价格,并获得最少的利润。对平台和物流公司而言,当市场能力较高时,会制定比较高的收费,同时付出较少的努力,但并不能获得最高利润,同时会打击消费者的积极性;但是,当市场能力较低时,他们一定获得最少的利润。在Nash模型中,平台和物流公司会付出最大的努力,同时获得最大的利润,而整个在线销售系统的总利润也是最多。在物流-平台Stackelberg模型中,平台和物流公司付出的努力最少,而整个在线销售系统的总利润也最少。     

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.     

考虑消费者有限理性的体验式商品订购与库存配给策略

退货遗忘与缺货后悔是消费者在现实中普遍存在的有限理性行为。在考虑这两种有限理性行为以及销售商提供无理由退款承诺的基础上,构建了一个两期模型对体验式商品的订购与库存配给策略进行了分析。研究得到如下结论：首先,只有当产品价值的上界大于某个临界值时,消费者才会在两个销售期内购买产品,销售商应该采取库存配给策略以应对消费者的策略行为;其次,销售商的收益随着消费者满意概率、退货遗忘率和缺货后悔程度的增大而增大。数值分析表明：当消费者满意概率或产品满足率感知偏差较大时,消费者策略行为的负面影响在一定程度上得到减轻;虽然有限理性总是可以提高销售商的收益,但是退货遗忘与缺货后悔对销售商收益增长的影响作用是不同的。