Pricing Policy in a Supply Chain: Negotiation or Posted Pricing

This article examines the choice of pricing policy (posted pricing or negotiation) toward end customers in a supply chain. Many retailers actively decide whether or not to encourage negotiation on the shop floor. Of course, the retailer's pricing policy influences not only the retailer's profit, but also the profits of the manufacturers who sell through the retailer. However, little is known about the forces that shape the pricing policy when two self‐interested parties interact in a supply chain. We consider two alternative models depending on who has the power to decide the pricing policy: the manufacturer or the retailer. We find that an increase in the wholesale price weakens the retailer's ability to price discriminate through negotiation. Therefore, the retailer prefers negotiation at lower wholesale prices and posted pricing at higher wholesale prices. We also find that whenever the retailer prefers negotiation, the manufacturer does too. Therefore, the retailer's discretion over the pricing policy causes friction only when the retailer wants to use posted pricing, while the manufacturer wishes the retailer to use negotiation. We show that such friction arises only when product availability or the cost of negotiation is moderate. In this case, we show that the manufacturer may offer a substantial discount to persuade the retailer to negotiate. Surprisingly, in this region of friction, a decrease in the supply chain's capacity or an increase in negotiation costs (both of which are typically considered as worsening the retailer's business environment) translates into higher profit for the retailer.     

独立定价还是共同定价:新支付工具的定价策略

基于新支付工具发展初期市场特征构建双边市场定价模型，分析共同定价和独立定价策略下企业利润和社会福利最大化新支付工具定价。研究显示：政府较企业对新支付工具制定更低价格水平促使用户支付选择转移，特别是在共同定价策略下会有效提升市场效率，达到社会福利最大；但若政府无法做到共同定价，特别在新支付工具成本优势不明显时，会使支付工具间存在过度补贴而降低社会福利，这时企业利润最大化定价为次优选择。     

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.     

不同价格模式下的双渠道供应链决策研究

针对由直销渠道和传统零售渠道组成的供应链,考虑需求同时受价格和广告投入影响的情况下供应链的最优决策问题。分别讨论由零售商决定渠道价格的价格一致模式和制造商与零售商分别决定渠道价格的价格非一致模式下的Stackelberg博弈模型,并研究在价格非一致模式下合作广告对决策的影响。最后算例分析将两种价格模式与集中决策模式下的最优决策值及供应链总收益进行比较。分析结果表明,对于制造商和整个双渠道供应链而言,采用价格非一致模式优于价格一致的模式。对于零售商而言,在一定条件下价格一致模式对自己有利。     

基于资本监管要求和还款意愿的贷款定价研究

在借款人有道德风险的情况下,如何合理地确定贷款价格是一个理论界及实务界面临的共同难题。本文分析了企业的还款意愿对商业银行贷款定价的影响,并将还款意愿融入到信用风险定价的结构化模型中,建立了资本监管下商业银行贷款定价模型。研究表明,贷款占用银行的监管资本越多或银行吸收存款的利率越高,贷款价格也越高;企业的还款意愿越弱,则银行给企业的贷款价格越高;反之,企业的还款意愿越强,则银行给企业的贷款价格越低。     

Pareto‐Improving Contracts for Express Package Delivery Services

We address the problem of an express package delivery company in structuring a long‐term customer contract whose terms may include prices that differ by day‐of‐week and by speed‐of‐service. The company traditionally offered speed‐of‐service pricing to its customers, but without day‐of‐week differentiation, resulting in customer demands with considerable day‐of‐week seasonality. The package delivery company hoped that using day‐of‐week and speed‐of‐service price differentiation for contract customers would induce these customers to adjust their demands to become counter‐cyclical to the non‐contract demand. Although this usually cannot be achieved by pricing alone, we devise an approach that utilizes day‐of‐week and speed‐of‐service pricing as an element of a Pareto‐improving contract. The contract provides the lowest‐cost arrangement for the package delivery company while ensuring that the customer is at least as well off as he would have been under the existing pricing structure. The contract pricing smoothes the package delivery company's demand and reduces peak requirements for transport capacity. The latter helps to decrease capital costs, which may allow a further price reduction for the customer. We formulate the pricing problem as a biconvex optimization model, and present a methodology for designing the contract and numerical examples that illustrate the achievable savings.     

双边市场中用户满意度与平台战略的选择

目前,有关双边市场理论的研究多在单期博弈模型中展开,并未在多期的情况下考虑平台的动态定价问题.显然,这与两边用户总是在平台中展开多次交易,平台总是面临动态定价的客观现实相违背.基于此,本文构建了一个双寡头两期动态博弈模型,通过引入用户满意度,研究了双边平台在不同定价策略(统一定价策略和歧视定价策略)和不同战略(短期战略和长期战略)情形下的最优定价,比较了策略间和战略间的差异性和有效性.研究发现: 第一期获得较大市场份额并不能保证平台在第二期竞争中占据优势地位,也不能保证获得较高重复购买率;歧视定价策略比统一定价策略更有利于平台获得较高利润,而不利于两边用户效用和社会福利水平的提升;(歧视定价策略,歧视定价策略)是帕累托上策均衡解;两期社会福利总水平仅仅与平台的定价策略有关,而与平台的战略无关.     

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.     

定价核之谜与概率权重函数

采用期权及标的资产价格数据, 基于离散时间EGARCH模型和连续时间GARCH扩散模型分别估计了客观与风险中性密度, 进而推导了经验定价核. 在此基础上, 基于等级依赖期望效用模型, 在标准的效应函数形式下构建了相应的概率权重函数. 采用香港恒生指数及其指数权证价格数据进行实证研究, 结果表明: (1) 经验定价核不是单调递减的, 而是展现出驼峰(非单调性), 即“定价核之谜”;(2) 经验概率权重函数展现S型, 表明市场投资者低估尾部概率事件, 高估中、高概率事件;(3) “定价核之谜”可以由具有标准效用函数与S型概率权重函数的等级依赖期望效用模型解释。     

上海期铜定价的实证检验

在考虑交易费用、存贮费用、交割费用和保证金的情况下,研究了上海期铜市场的定价问题.根据期货与现货的关系,运用无套利基本原理,给出了期货资产的定价公式.这个公式与使用经典无套利定价方法确定的无摩擦市场期货价格本质上不同的是:这个价格不是一个确定的值,而是一个区间.最后,运用这个公式对上海期铜9601至0206共78个合约进行了实证检验,检验结果表明上海期铜的实际价格落在定价区间的频率约为7.83%,而且随着时间的推移,价格落在定价区间内的频率越来越高,这标志着上海期铜市场在逐步走向成熟,市场的交易效率在不断提高.     

An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

We consider a pricing and short‐term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time‐dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time‐dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non‐decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.     

时变风险厌恶下的期权定价——基于上证50ETF期权的实证研究

传统的随机波动率（SV）期权定价是在投资者具有常数风险偏好假设下进行的.但近年来越来越多的研究表明，市场参与者具有时变风险厌恶特征.基于此，本文对时变风险厌恶条件下的期权定价问题进行深入研究.首先，对传统的（非仿射）常数风险厌恶SV（CRA-SV）期权定价模型进行扩展，构建时变风险厌恶SV（TVRA-SV）期权定价模型对期权进行定价，并分析时变风险厌恶对期权价格的影响；其次，采用标的资产与期权数据信息，建立基于连续粒子滤波的极大似然估计方法，对定价模型的客观与风险中性参数进行联合估计；最后，采用我国期权市场上的上证50ETF期权数据，对构建的定价模型进行实证检验.结果表明：TVRA-SV期权定价模型相比传统的CRA-SV期权定价模型具有更好的数据拟合效果，能够更充分地刻画标的上证50ETF收益率在客观与风险中性测度下的波动性；TVRA-SV期权定价模型相比传统的Black-Scholes（B-S）期权定价模型和CRA-SV期权定价模型都具有明显更高的定价精确性。     

基于用户电器分类的智能电网实时定价研究

目前，电力运行环境日趋复杂，电力体制改革也在不断进行。针对电力行业逐渐向信息化转变、能源利用率较低以及用户与电力公司交互性不高的现状，提出了一种电器分类实时定价模型。该模型根据不同类型用户的用电器进行分类，电力公司根据不同类型电器的用电情况实时制定出不同种类电器的用电价格，以便引导用户在不同时段根据不同类型电器的电价来使用电器，控制居民的用电行为。智能电表的使用，可使用户了解到不同电器的实时电价，并以此调整使用电器，电力公司也随时得到用户的用电量来调整电价和供电量，达到削峰填谷的作用。此模型既有时效性也能使供需双方用电效用最大化。最后通过数值实验对比分析，结果验证了所提出的模型的有效性。     

中国铁矿石期货市场的定价影响力研究——基于VEC-SVAR模型的实证分析

为探究中国铁矿石期货这一新兴市场的定价影响力状况以评价其对于中国铁矿石国际定价权的提升所起到的作用，本文从期货市场功能的视角，采用以VEC-SVAR模型为核心的研究方法，选取2013年10月至2016年3月的相关日度历史数据，对中国铁矿石期货价格与国内外现货价格间的动态联动及引导关系进行实证分析。结果表明：中国铁矿石期货价格与国内外现货价格之间存在高度关联性和长期均衡关系，已具备风险规避功能，可用于套期保值转移市场风险，但尚不具备有效的价格发现功能，无法对国内外现货价格的形成起决定和引导作用，定价影响力较弱，并未实质性地促进中国铁矿石国际定价权的提升；以TSI为代表的国际铁矿石现货价格指数占据绝对的定价权主导地位，但其高度的价格独立性和不透明的编制过程隐藏有价格操纵的可能性。     

顾客策略行为下差异产品两阶段定价模型研究

互联网和信息技术的发展,为零售商收集顾客信息带来方便的同时,也使得消费者变得越来越具有策略性和选择性。首先,构建零售商只销售一种高质量产品的情形,研究其两阶段的定价策略,并分析产品的跨期折扣因子对产品的零售价格、销售量和零售商利润的影响。然后,考虑零售商可提供高质量和低质量两种产品的情形,顾客在第一销售期、第二销售期都可以选择两种产品。构建两阶段的定价决策模型,并分析产品的跨期折扣因子、顾客对低质量产品的接受度等参数对产品两阶段的零售价格、销售量的影响。最后,用数值算例分析了第二种模型下顾客对低质量产品的接受度等模型参数对零售商两阶段总利润的影响,然后比较了第一种和第二种模型下高质量产品的零售价格和销售量。研究结论较全面的分析了顾客策略行为对差异产品两阶段销售期的定价决策的影响,为零售商进行定价优化决策提供了十分重要的参考。     

Managing Clearance Sales in the Presence of Strategic Customers

We study the effect of strategic customer behavior on pricing and rationing decisions of a firm selling a single product over two periods. The seller may limit the availability of the product (that is, ration) in the second (clearance) period. Some customers are strategic and respond to the firm's decisions by timing their purchases. When capacity is nonconstraining and the seller has pricing flexibility, we show that rationing in the clearance period cannot improve revenue. However, when prices are fixed in advance, rationing can improve revenue. In the latter case, we conduct a detailed analysis for linear and exponential demand curves and derive explicit expressions for optimal rationing levels. We find that the policy of doing the better of not restricting availability at the clearance price or not offering the product at the clearance price is typically near optimal. Our analysis also suggests that rationing—although sometimes offering considerable benefit over allowing unrestricted availability in the clearance period—may allow the seller to obtain only a small fraction of the optimal revenue when the prices are chosen optimally without rationing. We extend the analysis to cases where the capacity is constraining and obtain similar results.     

A Choice‐Based Dynamic Programming Approach for Setting Opaque Prices

Opaque pricing is a form of pricing where certain characteristics of the product or service are hidden from the consumer until after purchase. In essence, opaque selling transforms a differentiated good into a commodity. Opaque pricing has become popular in service pricing as it allows firms to sell their differentiated product at higher prices to regular brand loyal customers while simultaneously selling to non‐brand loyal customers at discounted prices. We use a nested logit model in combination with logistic regression and dynamic programming to illustrate how a service firm can optimally set prices on an opaque sales channel. The choice model allows the characterization of consumer trade‐offs when purchasing opaque products while the dynamic programming approach allows the characterization of the optimal pricing policy as a function of inventory and time remaining. We compare optimal prices and expected revenues when dynamic pricing is restricted to daily price changes. We provide an illustrative example using data from an opaque selling mechanism ( Hotwire.com ) and a Washington DC‐based hotel.     

Pricing Decisions During Inter‐Generational Product Transition

How should companies price products during an inter‐generational transition? High uncertainty in a new product introduction often leads to extreme cases of demand and supply mismatches. Pricing is an effective tool to either prevent or alleviate these problems. We study the optimal pricing decisions in the context of a product transition in which a new‐generation product replaces an old one. We formulate the dynamic pricing problem and derive the optimal prices for both the old and new products. Our analysis sheds light on the pattern of the optimal prices for the two products during the transition and on how product replacement, along with several other dynamics including substitution, external competition, scarcity, and inventory, affect the optimal prices. We also determine the optimal initial inventory for each product and discuss a heuristic method.     

Optimal Uniform Pricing Strategy of a Service Firm When Facing Two Classes of Customers

When facing heterogeneous customers, how should a service firm make its pricing decision to maximize revenue? If discrimination is allowed, then priority schemes and differentiated pricing are often used to achieve that. In many applications, however, the firm cannot or is not allowed to set discriminatory prices, for example, list price in retail stores, online shopping, and gas stations; thus a uniform price must be applied to all customers. This study addresses the optimal uniform pricing problem of a service firm using a queueing system with two classes of customers. Our result shows that the potential pool of customers plays a central role in the firm's optimal decision. Depending on the range of system parameters, which are determined explicitly by the primitive data, the firm's optimal strategy may choose to serve only one class of customers, a subset of a class of customers, or a combination of different classes of customers. In addition, the optimal price is in general not monotonic with respect to the potential market sizes because their changes may lead to a major shift in the firm's decision on which customer class to serve. However, unless such a shift occurs, the optimal price is weakly decreasing in the potential market sizes.