Dual-Role Based Pricing in a Dynamic and Competitive Environment

The dual role of price, as a product attribute signaling quality and as a measure of sacrifice, serving as a benchmark for comparing the utility gains from superior product quality, is now well established in the marketing and economic literature. However, knowledge about their long-run impact and the influence of competition on these effects still remains very sparse. In the current paper, with reference to a dynamic and competitive framework, an analytical model is proposed to help determining optimal decision rules for price incorporating both roles. The main results are as follows: (i) The optimal pricing policy is determined as a Nash equilibrium strategy. (ii) The resulting equilibrium price is higher than an equilibrium that disregards the carryover price effects. (iii) For a symmetric competition, we provide normative rules on how firms should set prices as a function of the perceived quality; particularly, how the price should be set initially, when there is little product familiarity and the perceived quality is low, and how this price should vary as the perceived quality increases. (iv) At steady state, we find that the level of equilibrium margin, in percentage terms, decreases with the elasticity of demand with respect to the brand price, but this decrease is moderated by the elasticity of demand with respect to the brand perceived quality, the cross elasticity of demand with respect to the competitor’s perceived quality and the effect of the competitor’s current price on the firm’s perceived quality deterioration. The author thanks Konstantin Kogan for helpful discussions and comments.     

Coordinating ordering and pricing decisions in a two-stage distribution system with price-sensitive demand through short-term discounting

We consider a short-term discounting model in which the distributor offers a discounted price for the retailers’ orders placed at the beginning of its replenishment cycle, in a non-cooperative distribution system with one distributor and multiple retailers, each facing price-sensitive demand. We examine the value of the price discount strategy as a mechanism for the distributor to coordinate the retailers’ ordering and pricing decisions under two common types of demand, linear demand in price and constant elasticity demand in price. Our numerical study reveals that, in the presence of homogeneous retailers (namely, retailers with identical demand rates), the distributor’s profit improvement due to coordination generally decreases as the number of retailers or the inventory holding cost rate increases, but increases as price elasticity increases. Although an increase in the inventory holding cost rate has a negative effect on the distributor’s profit, it may have a positive effect on the retailers’ profits. We further find that with heterogeneous retailers (namely, retailers with different demand rates), offering a discounted price under linear demand benefits the distributor when both the inventory holding cost rate and the variation in demand are either small or large. This cross effect, however, is absent under constant elasticity demand.     

Pricing policy in dynamic markets and a generalization of the Ramsey rule

Pricing policy in a regulated monopoly industry is usually based on maximizing welfare or some other measure of utility level of return on investment. Previously, the Ramsey pricing policy which states that the percentage deviation of quasi-optimal price from marginal cost for each product must be inversely proportional to its price elasticity of demand, has been developed for a static market. The Ramsey framework assumes instantaneous demand response to price changes; empirical evidence suggests demand changes occur dynamically through time.In this paper an optimum pricing rule for a profit maximizing firm based on a general time varying demand model in a dynamic market is obtained assuming a single price change at the beginning of the planning period. A dynamic market equivalent of the well known inverse elasticity law of the static market is developed. Defining the concept of average price elasticity for dynamic markets we show that the inverse elasticity law of static markets takes an inequality form in dynamic markets. For demand functions which decrease, increase or are constant with time the optimum price markups are greater than, less than, or equal to the inverse of the average price elasticity, respectively.The results are then generalized to the case of a constrained welfare maximizing firm. This leads to the development of a dynamic market generalization of the well known Ramsey pricing rule. A simple rule for making quantitative arguments about the relative size of the optimum price in static and dynamic markets is also derived.This work was completed when the author was with Bell Laboratories, USA.     

基于消费者效用模型的贵重首饰经销商决策行为研究

以异质性消费者为对象,研究关税税率调整对贵重首饰经销商决策行为的影响。在个人理性与激励相容的约束条件下,构建基于异质性消费者效用模型的需求函数,分析不同市场类型下经销商的最优决策选择。考虑消费者价格敏感度对社会福利的影响,并在此基础上分析了最优关税税率水平。研究发现:(1)贵重首饰经销商决策行为不仅受政府关税税率的影响,还受消费者价格敏感度的影响;(2)在消费者价格敏感度一定的前提下,若想通过关税来调控贵重首饰市场,关税税率应该控制在一定的区间范围;(3)在关税税率一定的条件下,贵重首饰市场的类型主要受消费者价格敏感度的影响。     

物价、利率与收入对居民消费需求影响研究——基于时变参数状态空间模型

运用时变参数状态空间模型对我国改革开放三十年来物价、利率与收入对农村和城镇居民消费需求影响的动态特征进行了研究。发现物价、收入对农村和城镇居民的消费需求弹性不同,农村消费需求受收入影响较大,而城市居民消费需求受物价影响较大;利率对农村和城镇居民消费需求影响不显著,利率机制目前还不是调解中国消费需求的理想工具。在此基础上给出了相应的政策建议。     

需求弹性与垄断企业的价格歧视

本给出了垄断企业实行价格歧视的价格比较模型．在垄断企业获取最大利润的前提下，利用需求弹性分析了垄断企业价格歧视的成因，探讨了它们的数量特征，并进一步利用该模型描述了市场需求对垄断企业实行价格歧视的影响。     

Bidding under price uncertainty in multi-unit pay-as-bid procurement auctions for power systems reserve

In this paper a methodology for profit maximized bidding under price uncertainty in a day-ahead, multi-unit and pay-as-bid procurement auction for power systems reserve is proposed. Within this novel methodology a bidder is considered to follow a Bayes-strategy. Thereby, one bidder is assumed to behave strategically and the behavior of the remaining is summarized in a probability distribution of the market price and a reaction function to price dumping by the strategic bidder. With this approach two problems arise: First, as a pay-as-bid auction is considered, no uniform price and therefore no single probability distribution of the market price is readily available. Second, if historic bidding data of all participants are used to estimate such a distribution and market power is a relevant factor, the bid of the strategically behaving bidder is likely to influence the distribution. Within this paper for both of the problems solutions are presented. It is shown that by estimating a probability of acceptance the optimal bidding price with respect to a given capacity can be calculated by maximizing a stochastic non-linear objective function of expected profit. Taking the characteristics of recently established markets in Germany into account, the methodology is applied using exemplary data. It is shown that the methodology helps to manage existing price uncertainties and hence supports the trading decisions of a bidder. It is inferred that the developed methodology may also be used for bidding on other auction markets with a similar market design.     

Estimating consumers' willingness to pay for individual quality attributes with DEA

In a highly competitive environment, a product's commercial success depends increasingly more upon the ability to satisfy consumers' preferences that are highly diversified. Since a product typically comprises a host of technological attributes, its market value incorporates all of the individual values of technological attributes. If the willingness-to-pay (WTP) for individual quality attributes of a product is known, one can conjecture the overall WTP or the imputed market price for the product. The market price listed by the producer has to be equal to or lower than this WTP for the commercial survival of the product. In this paper, we propose a methodology for estimating the value of individual product characteristics and thus the overall WTP of the product with DEA. Our methodology is based on a model derived from consumer demand theory on the one hand, and the recent developments in DEA on the other hand. The paper also presents a real case study for the mobile phone market, which is characterized by its high speed of innovation. On the theoretical side, we expect our framework to provide a possibility of combining DEA and consumer demand theory. We also expect that the empirical application will shed some light on the nature of the process of product differentiation based on consumers' valuation.     

可再生能源配额制下异质权力发电商的绿色生产决策研究

基于可再生能源配额的政策背景,本文构造了发电商三种不同市场权力结构下的绿色生产决策模型。讨论了敏感参数对异质权力发电商最优决策结果的影响,基于参数范围分析了不同权力结构下的最优决策效果。通过消费者效用、发电成本、环境保护的社会福利函数,识别出了参数最优取值范围内的最优决策效果的市场结构。结果显示:当绿证交易价格、最低配额比例超过最低临界值时,绿色发电商能够实现最优决策效果,但对传统发电商的最大利润产生了显著的“挤出”效应。若绿证交易价格和电力需求价格弹性系数在最佳区间内,则传统和绿色发电商既能够达到最优决策效果,又可以最大限度促进社会福利效用的单调增加,即存在绿色发电商主导的最优市场决策结构,但不存在最优纳什决策结构。     

关于需求价格弹性的探讨

需求价格弹性是管理经济学中的一个重要概念,是指导市场行为的重要指标,如何理解需求价格弹性概念,掌握弹性的计算方法就显得格外重要.本文探讨需求价格弹性的概念及计算方法.     

面向战略型消费者的产品创新与定价策略

考虑垄断制造商面向战略型消费者时的产品创新与定价问题。运用消费者效用理论和博弈论等方法,构建静态和动态定价下制造商和消费者两期决策模型并求解分析。结果表明,消费者是否购买以及何时购买产品取决于升级换代产品的价格阈值。与静态定价相比较,动态定价能使制造商获得更多期望收益,但会降低消费者剩余、弱化制造商的产品创新积极性,并且这种弱化现象在产品价值折扣系数较高的情况下尤为明显。战略消费者购买行为对制造商的产品创新、期望收益和消费者剩余的影响,不仅依赖于制造商选择何种定价策略,还取决于产品价值折扣系数的大小。研究结论为消费者的产品购买和升级换代提供了理论建议,为企业的产品创新和定价提供了决策参考。     

Dynamic Pricing via Dynamic Programming<Superscript>1</Superscript>

This article specifies an efficient numerical scheme for computing optimal dynamic prices in a setting where the demand in a given period depends on the price in that period, cumulative sales up to the current period, and remaining market potential. The problem is studied in a deterministic and monopolistic context with a general form of the demand function. While traditional approaches produce closed-form equations that are difficult to solve due to the boundary conditions, we specify a computationally tractable numerical procedure by converting the problem to an initial-value problem based on a dynamic programming formulation. We find also that the optimal price dynamics preserves certain properties over the planning horizon: the unit revenue is linearly proportional to the demand elasticity of price; the unit revenue is constant over time when the demand elasticity is constant; and the sales rate is constant over time when the demand elasticity is linear in the price. ¹We acknowledge professor robert e. kalaba for initiating this work and suggesting solution methods.     

展厅现象下电子零售商与传统零售商的价格竞争

针对双渠道中存在消费者先通过实体店体验产品,而转移电子渠道购买的展厅现象,运用消费者效用理论,建立不同购买方式下电子零售商和传统零售商的定价决策模型,通过对不同情形下最优决策的比较分析,进一步研究展厅现象如何影响电子零售商和传统零售商的定价和利润。研究表明:三种购买方式同时存在时,展厅现象将加剧传统零售商与电子零售商的价格竞争,导致双方利润受损,但当电子渠道接受度较高或是较低且实体店体验对电子渠道接受度的影响较大时,电子零售商可以利用展厅现象提高其销售价格并获利。     

竞争型“以旧换再”闭环供应链策略选择及生产决策研究

针对两阶段闭环供应链系统,研究了古诺竞争型闭环供应链中的“以旧换再”策略选择问题。研究发现:(1)企业如何及何时实施“以旧换再”策略取决于自身及竞争企业的再制造水平。再制造水平不仅影响了企业的“以旧换再”数量,同时还会影响产品市场份额及利润。(2)“以旧换再”策略可以提高企业竞争力,增加企业产品市场份额和提高收益;(3)提高 “以旧换再”补贴及再制造产品接受度, 降低“二手市场”价格,均可以降低企业实施“以旧换再”策略和提高企业的“以旧换再”数量。     

Endogenous Fluctuations in Two-Sector Models: Role of Preferences

We consider a discrete-time two-sector CES (constant elasticity of substitution) economy with sector specific external effects and nonlinear preferences. Our goal is to examine carefully the influence of the utility curvature on the occurrence of multiple equilibria. We show that local indeterminacy depends on an interplay between factor substitutability and the elasticity of intertemporal substitution in consumption. Moreover, considering that, when the external effects are set equal to zero, we get a two-sector optimal growth model, we study also the role of the utility curvature on the occurrence of competitive equilibrium cycles. We show that persistent endogenous fluctuations and macroeconomic volatility require a strong enough elasticity of intertemporal substitution in consumption. We thank two anonymous referees for helpful comments and suggestions. External effects are feedbacks from the other agents in the economy who face also identical maximizing problems. See Benhabib and Farmer (Ref. 1) for a survey. Global indeterminacy based on a finite number of equilibria is associated with the existence of thresholds and multiple steady states. See Deissenberg, Feichtinger, Semmler, and Wirl (Ref. 2).     

面向电子商务的应用——基于多Agen t的消费者需求代理系统

首先根据电子商务环境下消费者需求的特点,在对多A gen t技术论述的基础上,建立了基于多A gen t的消费者需求代理系统.接着对系统具体工作流程进行了深入分析:先针对不同消费者建立相应的用户模型,以便为不同消费者提供效用最大化的产品或产品服务的组合,然后采用协商型A gen t,完成网上产品或服务的交易.最后提出了基于遗传算法的协商谈判策略,以提高消费者需求代理系统的协商能力.     

平台型企业定价影响因素研究:以银行卡为例

本文运用双边市场理论,构建了平台型企业的定价模型及回归方程,并运用国内14家商业银行2001~2017年的实际运营数据,对构建的模型和方程进行了实证检验。研究结论表明,平台对买方价格决定的主要影响因素有:平台向消费者(买方)提供产品或服务的成本、买方边的需求价格弹性,产品(服务)差异化程度,以及相对方(商户)接入平台的数量;而平台对卖方价格决定的主要影响因素有:卖方给买方产生的网络外部性强度,卖方边的需求价格弹性,以及市场份额。     

The value of information for price dependent demand

Predicting demand and determining optimal pricing are essential components of operations management. It is often useful to think in terms of the price elasticity of demand when reasoning about the demand curve. Firms wishing to invest in demand prediction and information gathering should reason about the relationship between the expected value of perfect information (EVPI) on demand and demand elasticity. Should firms pay more/less for information on demand if elasticity is high/low? Furthermore, when considering different product prices, correlation may exist between demand at different prices. Should firms pay more/less for information if the correlation between demand at different prices is high or low? This paper derives analytic and numeric results to answer these questions. We start with the assumption that demand is uncertain and follows a uniformly distributed band around a deterministic demand curve where the upper and lower bounds of the demand distribution vary with price. This formulation enables a closed form expression for EVPI that provides a useful benchmark. We find nuanced behavior of EVPI that depends on both the elasticity and the initial price preference. The EVPI approaches zero as elasticity increases (decreases) for a firm that initially prefers the low (high) price. Numerical results using the truncated normal and beta distributions relax assumptions about the uniform distribution and show EVPI is similar when the distribution variances are similar. Finally, we relax the assumption of perfect information and show the expected value of imperfect information (EVOI) follows similar patterns as EVPI with respect to demand elasticity.     

需求弹性、抗衡势力与价格歧视

构建完全信息动态博弈模型,考察下游市场需求弹性、零售商抗衡势力对中间产品价格歧视的影响问题。结果表明,低弹性市场中零售商抗衡势力会削弱价格歧视,且改善低弹性市场消费者福利,而高弹性市场中零售商抗衡势力会增强价格歧视,且损害低弹性市场消费者福利。而高弹性市场消费者福利的变化则依赖于零售商的抗衡势力强度,只有当抗衡势力较强时,高弹性市场消费者福利才能够得到改善。     

Optimal dynamic marketing-mix policies for frequently purchased products and services versus consumer durable goods: A generalized analytic approach

This paper deals with the qualitative characterization of optimal pricing and advertising policies together with the optimal ratio of the advertising elasticity of demand to its price elasticity over time. The problem is studied for frequently purchased products and services (FPS) as well as consumer durable goods (CDG) in both monopolistic and duopolistic markets. Demand dynamics, cost learning and discounting of future profits are taken into consideration. In addition, both the open-loop and feedback methodologies are pursued to characterize and compare the derived optimal policies.The paper uses an analytical approach to characterize the optimal dynamic policies in a general setting as is mathematically tractable, followed by the analysis of more specific models to gain additional managerial insights while maintaining a certain degree of generality. Optimal FPS marketing-mix policies are shown to be different from their CDG counterparts for both monopolistic and duopolistic markets. While the ratio of advertising elasticity to price elasticity appears to have been governed by similar set of rules for FPS and CDG, the direction of change of such ratio over time looks different from each other. Managerial implications and directions for future research are also discussed.