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.     

面向价值共创的服务衍生供需决策优化研究

针对制造企业服务衍生时，制造企业与客户间可能存在的"双重边际效应"问题，以制造企业服务衍生特征刻画为基础，构建了服务衍生供需价值创造模型，比较分析了分散和集中两种决策情形下的价值创造，发现集中决策下供需双方能够创造整体更高的价值，但制造企业存在陷入"服务悖论"的风险，由此，设计了有助于协调供需价值分配的收益共享契约。研究表明，收益共享契约能够缓解制造企业与客户间的"双重边际效应"，契约能够激发制造企业以更为积极主动的态度改进服务衍生方案，提升方案的性价比，并由此促进市场需求，实现供需双方的价值共创。     

Optimal Retail Return Policies with Wardrobing

Many retailers offer refunds to consumers who, after a trial period, return a product that they find does not fit their needs. Some consumers are willing to use this return option opportunistically for short‐term consumption rather than its intended purpose of resolving fit uncertainty. Such behavior has been termed “wardrobing.” Restocking fees (partial refunds) can be used to combat wardrobing. However, there is a trade‐off involved, since partial refunds will be viewed negatively by consumers who return an item due to a true lack of fit. In this study, we consider how the extent of wardrobing (how many consumers consider such behavior) and the benefit of wardrobing (how much value can be extracted during the trial) impact firm pricing decisions and profits in this retail context. Our results imply that an increase in the extent of wardrobing is most detrimental to profits when the current extent of wardrobing is low. On the contrary, if the extent of wardrobing is already very high, and the benefit of wardrobing to consumers is also high, the retailer can set prices and refunds such that additional wardrobing actually increases firm profits. In a model extension, we show how a retailer can effectively screen wardrobers from ordinary consumers by offering a menu of price/refund pairs, and that such an approach can lead to increased profits if the extent of wardrobing is sufficiently high. Overall, our findings provide new insights into how retailers can set prices and refund policies to effectively manage opportunistic behavior by consumers.     

存在战略购买需求的定价、供给、机制选择和配给研究

本文研究存在战略购买需求的易逝资产销售策略问题。垄断厂商基于利润最大化目标确定易逝资产定价、供给、机制选择和配给策略,战略消费者通过锚定预期价格安排战略购买时机。不同于通常基于效用理论研究定价的思路,本文首先基于锚定效应和跨期价格均衡思想探寻不同战略等待购买规模的市场预期需求曲线和动静态定价区域;其次在众多预期需求曲线中寻找市场有效定价前沿（即有效预期需求曲线）;再次在利润曲面上找出与有效定价前沿对应的容量扩展线（即最大利润曲线）;最后沿容量扩展线和有效定价前沿搜寻最大期望利润及相应策略。研究表明,消费者保留价异质和需求不确定性是动态定价和战略购买存在的根本原因;市场在不同战略等待购买规模状态拥有不同预期需求曲线,最大战略等待购买规模状态预期需求曲线是市场有效定价前沿。动静态定价机制各有其所适用的容量和价格空间,消费者保留价水平和战略消费者规模决定动态定价空间大小,随机需求分布差异只影响动态定价空间形状（即影响需求弹性）。在跨期价格均衡区域内,提价和扩容都会加剧消费者战略购买程度,供给越大定价往往越低。战略购买不仅会降低厂商供给、定价和利润水平,改变不同类型消费者之间高低价购买机会,甚至还可能影响定价机制选择和配给策略。压缩过度供给和虚高价格空间可降低战略购买导致的利润损失。本文研究结果可为考虑消费者行为的需求价格理论研究和运营管理实践提供参考。     

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.     

Financial Hedging and Optimal Procurement Policies under Correlated Price and Demand

We consider a firm that procures an input commodity to produce an output commodity to sell to the end retailer. The retailer's demand for the output commodity is negatively correlated with the price of the output commodity. The firm can sell the output commodity to the retailer through a spot, forward or an index‐based contract. Input and output commodity prices are also correlated and follow a joint stochastic price process. The firm maximizes shareholder value by jointly determining optimal procurement and hedging policies. We show that partial hedging dominates both perfect hedging and no‐hedging when input price, output price, and demand are correlated. We characterize the optimal financial hedging and procurement policies as a function of the term structure of the commodity prices, the correlation between the input and output prices, and the firm's operating characteristics. In addition, our analysis illustrates that hedging is most beneficial when output price volatility is high and input price volatility is low. Our model is tested on futures price data for corn and ethanol from the Chicago Mercantile Exchange.     

Combined Pricing and Portfolio Option Procurement

In this paper, we study a single‐product periodic‐review inventory system that faces random and price‐dependent demand. The firm can purchase the product either from option contracts or from the spot market. Different option contracts are offered by a set of suppliers with a two‐part fee structure: a unit reservation cost and a unit exercising cost. The spot market price is random and its realization may affect the subsequent option contract prices. The firm decides the reservation quantity from each supplier and the product selling price at the beginning of each period and the number of options to exercise (inventory replenishment) at the end of the period to maximize the total expected profit over its planning horizon. We show that the optimal inventory replenishment policy is order‐up‐to type with a sequence of decreasing thresholds. We also investigate the optimal option‐reservation policy and the optimal pricing strategy. The optimal reservation quantities and selling price are shown to be both decreasing in the starting inventory level when demand function is additive. Building upon the analytical results, we conduct a numerical study to unveil additional managerial insights. Among other things, we quantify the values of the option contracts and dynamic pricing to the firm and show that they are more significant when the market demand becomes more volatile.     

Improving Profits by Bundling Vertically Differentiated Products

We consider a firm managing a category of vertically differentiated goods, that is, products which differ with respect to an attribute for which all consumers prefer more to less. The goods can be sold individually, in which case they are referred to as components, or in bundles. The firm chooses the assortment of components and bundles and their selling prices to maximize profit. We show that each bundling strategy (pure components, pure bundling or mixed bundling) can be optimal and obtain closed‐form expressions for the optimal selling prices. We provide insights on the structure of the optimal assortment and prices. In particular, we show that, when consumers benefit from consuming the components jointly, the products in the optimal assortment form nested sets. When consumers do not benefit from the joint consumption of components, the bundles should be offered at a positive discount. We find that bundling vertically differentiated products can significantly improve profits, even if consumers do not benefit from consuming the components jointly. The value of bundling comes from increased sales: a firm, which understands that its customers may buy multiple types of components, offers bundles of components, incentivizing customers to buy more.     

Understanding the Price Effects of the MillerCoors Joint Venture

We document abrupt increases in retail beer prices just after the consummation of the MillerCoors joint venture, both for MillerCoors and its major competitor, Anheuser‐Busch. Within the context of a differentiated‐products pricing model, we test and reject the hypothesis that the price increases can be explained by movement from one Nash–Bertrand equilibrium to another. Counterfactual simulations imply that prices after the joint venture are 6%–8% higher than they would have been with Nash–Bertrand competition, and that markups are 17%–18% higher. We relate the results to documentary evidence that the joint venture may have facilitated price coordination.     

Sales Force and Competition in Financial Product Markets: The Case of Mexico's Social Security Privatization

This paper examines how sales force impacts competition and equilibrium prices in the context of a privatized pension market. We use detailed administrative data on fund manager choices and worker characteristics at the inception of Mexico's privatized social security system, where fund managers had to set prices (management fees) at the national level, but could select sales force levels by local geographic areas. We develop and estimate a model of fund manager choice where sales force can increase or decrease customer price sensitivity. We find exposure to sales force lowered price sensitivity, leading to inelastic demand and high equilibrium fees. We simulate oft proposed policy solutions: a supply‐side policy with a competitive government player and a demand‐side policy that increases price elasticity. We find that demand‐side policies are necessary to foster competition in social safety net markets with large segments of inelastic consumers.     

EQUIVALENCE RESULTS FOR OPTIMAL PASS‐THROUGH,OPTIMAL INDEXING TO EXCHANGE RATES,AND OPTIMAL CHOICE OF CURRENCY FOR EXPORT PRICING

Firms sometimes write price lists or catalogs for their exports, so they set prices for a period of time and do not adjust prices during that interval in response to changes in their environment. The firm sets the price either in its own currency or the importer's currency. This paper draws a simple link between the choice of currency and the pricing decision of a firm that changes prices in response to all shocks. Specifically, if the latter firm's price has a lower variance in terms of its own currency than the importer's currency, then the firm with a price list will set the price in its own currency (and otherwise it will set price in the foreign currency). This relationship is established by consideration of the firm with a price list as a special case of a firm that indexes its export price to the exchange rate. (JEL: F4, F1)     

Optimal Per‐Use Rentals and Sales of Durable Products and Their Distinct Roles in Price Discrimination

We consider a setting in which consumers experience distinct instances of need for a durable product at random intervals. Each instance of need is associated with a random utility and the consumers are differentiated according to the frequency with which they experience such instances of need. We use our model of consumer utility to characterize the firm's optimal strategy of whether to sell, rent, or do a combination of both in terms of the transaction costs and consumers' usage characteristics. We find that the two modes of operation serve different roles in allowing the firm to price discriminate. While sales allow the firm to discriminate among consumers of different usage frequencies, rentals allow it to discriminate according to consumers' realized valuations. Consequently, even when transaction costs are negligible, it is often optimal for the firm to simultaneously rent and sell its product. In addition, we find that although sales and rentals are substitutes and that the offering of sales weakly increases rental prices, it is possible that the introduction of rentals to a pure selling operation can either increase or decrease the optimal sales prices.     

Divide and Conquer: Competing with Free Technology Under Network Effects

We study how a commercial firm competes with a free open source product. The market consists of two customer segments with different preferences and is characterized by positive network effects. The commercial firm makes product and pricing decisions to maximize its profit. The open source developers make product decisions to maximize the weighted sum of the segments' consumer surplus, in addition to their intrinsic motivation. The more importance open source developers attach to consumer surplus, the more effort they put into developing software features. Even if consumers do not end up adopting the open source product, it can act as a credible threat to the commercial firm, forcing the firm to lower its prices. If the open source developers' intrinsic motivation is high enough, they will develop software regardless of eventual market dynamics. If the open source product is available first, all participants are better off when the commercial and open source products are compatible. However, if the commercial firm can enter the market first, it can increase its profits and gain market share by being incompatible with its open source competitor, even if customers can later switch at zero cost. This first‐mover advantage does not arise because users are “locked in,” but because the commercial firm deploys a “divide and conquer” strategy to attract early adopters and exploit late adopters. To capitalize on its first‐mover advantage, the commercial firm must increase its development investment to improve its product features.     

The Retail Space‐Exchange Problem with Pricing and Space Allocation Decisions

We consider retail space‐exchange problems where two retailers exchange shelf space to increase accessibility to more of their consumers in more locations without opening new stores. Using the Hotelling model, we find two retailers’ optimal prices, given their host and guest space in two stores under the space‐exchange strategy. Next, using the optimal space‐dependent prices, we analyze a non‐cooperative game, where each retailer makes a space allocation decision for the retailer's own store. We show that the two retailers will implement such a strategy in the game, if and only if their stores are large enough to serve more than one‐half of their consumers. Nash equilibrium for the game exists, and its value depends on consumers’ utilities and trip costs as well as the total available space in each retailer's store. Moreover, as a result of the space‐exchange strategy, each retailer's prices in two stores are both higher than the retailer's price before the space exchange, but they may or may not be identical.     

MATERIALS PRICES AND PRODUCTIVITY

There is substantial within‐industry variation in the prices that plants pay for their material inputs. Using plant‐level data from the US Census Bureau, I explore the consequences and sources of this variation in materials prices. For a sample of industries with relatively homogeneous products, the standard deviation of plant‐level productivity would be 7% smaller if all plants faced the same materials prices. Moreover, plant‐level materials prices are persistent, spatially correlated, and positively associated with the probability of exit. The contribution of entry and exit to aggregate productivity growth is smaller for productivity measures that are purged of materials price variation. After documenting these patterns, I discuss three potential sources of materials price variation: geography, differences in suppliers' marginal costs, and within‐supplier markup differences. Together, these variables explain 15% of the variation of materials prices.     

Firm Size and Employment Dynamics: Estimations of Labor Demand Elasticities Using a Fractional Panel Probit Model

This paper examines the comprehensive discussion on the relationship between job creation, or destruction and firm size. More specifically, the study will determine whether the argument about small‐ and medium‐sized enterprises (SMEs) showing higher employment dynamics is confirmed or not. As such, the following work applies elasticities from a standard labor demand model derived from the estimations of fractional probit models for panel data, as process recommended in Papke and Wooldridge [2008; Journal of Econometrics 145(1–2): 121–133]. Elasticities are a useful measure of employment dynamics, if it is assumed that SMEs act on the same markets. The elasticity results from German establishment data illustrate that firm size does matter for the increase or decrease of employment. SMEs with less than 10 workers exhibit a higher employment dynamic, compared with other entities, at each respective percentile in the distribution of the wage share. Additionally, the outcome of the analysis weakly confirms the hypothesis that smaller firms are more restricted to capital markets, compared with large entities. The results also illustrate that firm size only explains one aspect of job creation and destruction. As stated in the well‐known Hicks–Marshall rules for elasticities of factor demand, the results illustrate that the reaction of labor demand on economic changes increases with the share of labor. Firms with a high share of labor also have larger elasticities, compared with firms with a strong use of capital. Both effects, the size effect and the effect of the proportion of labor, would blend in reality, and therefore, possibly lead to controversial results for the relationship between firm size and employment dynamics. In addition, a model with a negative relationship among both variables is too simple to explain the behavior of firms.     

考虑消费者预期的电动汽车分时租赁市场价格竞争模型

分时租赁平台作为电动汽车推广的主要方式，其特征与打车软件类似，在风险资本的推动下极易引发价格战。各租车公司的市场需求量不仅与自己的定价有关，也与竞争对手的定价策略相关，目标都是各自利润的最大化。本文在考虑消费者预期的基础上，研究了需求函数为线性情形下的多人博弈，证明了此博弈是超模博弈以及Nash均衡的存在性和唯一性。并进一步揭示了降价幅度、交叉价格和价格敏感消费群体占比对均衡价格、均衡需求量和利润的影响关系，讨论了价格竞争过程中各租车公司的决策过程与利弊关系。结果表明：任意租车公司的降价行为都会引发整个市场的降价反应，且降价幅度随着博弈阶段的推进逐渐减小，最终收敛于均衡价格；动态定价博弈存在最优组合策略，市场竞争时应当把握好降价幅度，避免过度的价格竞争；均衡价格是关于消费者预期的单调减函数，价格敏感的消费群体占比越大，租车公司间价格竞争越激烈，降价幅度会越大，均衡价格越低；对于市场份额大的租车公司利润是关于价格敏感型消费者占比的单调增函数，但对中小租车公司而言则是单调减函数，价格敏感的消费者越多，对大公司有利，对中小公司不利。     

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.     

基于混合定向方式的移动定向广告投放策略研究

以移动广告为研究背景,研究地理定向和消费者产品偏好定向相结合的混合定向方式下企业的定向广告投放策略,同时通过对比企业投放定向广告与大众广告,研究企业的广告策略选择问题。研究发现,企业运用定向广告策略应针对不同的消费者群体提供差异化较大的营销策略:对属于企业近距离范围且偏好企业产品的优势市场,企业应加大广告投放力度并实行高价;为了争取部分远端劣势市场的收益,企业应向其投放一定力度的广告并实行低价;对属于双方的竞争市场,企业应选择中等程度的广告和价格。同时,通过与企业投放大众广告相比较,发现竞争企业使用定向广告策略反而不如使用大众广告策略。     

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。