The effects of sensitization and habituation in durable goods markets

We develop a model to study the impact of changes in price sensitivity on the firm as it introduces multiple generations of a durable product where unit costs are a convex function of quality. We incorporate the psychological processes of sensitization and habituation into a model of discretionary purchasing of replacement products motivated by past experience. When price sensitivity decreases with each purchase (sensitization), the myopic firm offers a higher quality product at a much higher price with each generation. When price sensitivity increases with each purchase (habituation), the myopic firm engages in price skimming. When sensitization is followed by habituation, the myopic firm eventually provides higher quality than the market is willing to pay for, leading to a steep drop-off in sales and profits. The actions of the forward-looking firm depend on the discount rate. A firm with a low discount rate builds its customer base before offering a higher quality and higher priced product. In contrast, a firm with a high discount rate quickly increases price and quality following the same path to falling profits of the myopic firm. These results provide insight into the firm and consumer behaviors underlying the phenomenon of “performance oversupply” identified in the innovation literature.     

Selling multiple units to strategic consumers

We consider a monopolist firm selling to strategic customers who may purchase more than one unit of a product in a two-period model. We provide closed-form solutions for the firm’s optimal prices and show that they are non-monotonic in both the value of the second unit and the strategic level of customers. Particularly, the first-period price can increase as customers become more strategic, in contrast to the single-unit setting where it always decreases in the strategic level of customers.     

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。     

Pricing and market segmentation using opaque selling mechanisms

In opaque selling certain characteristics of the product or service are hidden from the consumer until after purchase, transforming a differentiated good into somewhat of a commodity. Opaque selling has become popular in service pricing as it allows firms to sell their differentiated products at higher prices to regular brand loyal customers while simultaneously selling to non-loyal customers at discounted prices. We develop a stylized model of consumer choice that illustrates the role of opaque selling in market segmentation. We model a firm selling a product via three selling channels: a regular full information channel, an opaque posted price channel and an opaque bidding channel where consumers specify the price they are willing to pay. We illustrate the segmentation created by opaque selling as well as compare optimal revenues and prices for sellers using regular full information channels with those using opaque selling mechanisms in conjunction with regular channels. We also study the segmentation and policy changes induced by capacity constraints.     

SAA-regularized methods for multiproduct price optimization under the pure characteristics demand model

Utility-based choice models are often used to determine a consumer’s purchase decision among a list of available products; to provide an estimate of product demands; and, when data on purchase decisions or market shares are available, to infer consumers’ preferences over observed product characteristics. These models also serve as a building block in modeling firms’ pricing and assortment optimization problems. We consider a firm’s multiproduct pricing problem, in which product demands are determined by a pure characteristics model. A sample average approximation (SAA) method is used to approximate the expected market share of products and the firm profit. We propose an SAA-regularized method for the multiproduct price optimization problem. We present convergence analysis and numerical examples to show the efficiency and the effectiveness of the proposed method.     

Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly

This paper analyzes the impact of dynamic and fixed-ratio pricing policies on firm profits and equilibrium prices under competition. Firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times. In each period, customers first purchase from the low price firm and then from the high price firm up to their inventories, provided the prices are lower than the maximum they are willing to pay. The main conclusions of this paper are as follows: although dynamic pricing is a more sophisticated policy than fixed-ratio pricing, it may lead to decreased equilibrium profits; under both pricing policies, one firm assumes the role of a low-cost high-output firm while the other assumes the role of a high-cost low-output firm; and, the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices.     

Price and quality competition: The effect of differentiation and vertical integration

This paper studies an instance of price and quality competition between firms as seen in the recent Internet market. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. Characterizing this competition from a microeconomic viewpoint, we consider two possible business strategies that firms can utilize to overcome the competition—the differentiation and the vertical integration with another complementary firm. We show an interesting result not seen in the well-known Bertrand price competition: not only does the differentiation always increase the firms’ profits, but also it can increase the consumer’s welfare in a quality-sensitive market. We further derive that under some mild conditions the monopolistic vertical integration that excludes the combination-purchase with a competitor’s product is beneficial for both the integrated firm and its consumers.     

An integrated product returns model with logistics and marketing coordination

We develop an integrated approach for analyzing logistics and marketing decisions within the context of designing an optimal returns system for a retailer servicing two distinct market segments. At the operational level, we show that the optimal refund price is not unique. Moreover, it is such that if both market segments return a purchased product, then neither segment will receive a full money-back refund; and it is such that if one or both segments do not return a purchased product, then a refund premium over the purchase price is possible, but the refund premium will not be enough to offset a customer's total net cost of purchase and return. We also show that any improvement to the returns system that results in increased logistical efficiency or marketing effectiveness will be accompanied by an increase in the selling price of the product. At the strategic level, we show that if the retailer does not coordinate its logistics and marketing efforts to improve the overall returns system, then it will tend to over-invest in one of the functions and under-invest in the other. Finally, we illustrate how our model can be generalized to the case in which a customer's ex post valuation of the product falls along a continuum.     

Strategic upfront marketing channel integration as an entry barrier

This paper investigates an organizational design problem concerning whether duopolistic firms competing in a product market should vertically integrate or separate their marketing channels in a dynamic noncooperative game setting. Previous operational research models have shown that the separation of the marketing channel with the adoption of a two-part tariff contract is the dominant strategy compared with integration for each firm if the two firms face retail price competition, and thereby constitutes the subgame perfect Nash equilibrium (SPNE). Contrary to this previous insight, this paper demonstrates that if exogenous parameters that characterize fixed costs, product substitutability, and a demand function fall into a specific region, marketing channel integration dominates the separation strategy when one of the two firms is the incumbent firm while the other is a potential entrant. In other words, the well-known result in the price-setting game can be reversed when we take entry threats into consideration. Specifically, we show that upfront vertical integration of the marketing channel enables the incumbent to deter the entry of the potential competitor and to monopolize the market in the SPNE. This result has operational implications for a firm confronting the threat of potential rivals entering the market, in that the firm can use this apparently inferior strategy as a commitment device, which creates a virtual entry barrier.     

Optimal purchasing policy in a two-component assembly system with different purchasing contracts for each component

This paper considers an assembly system where a firm produces a single product which is assembled using two types of components (component 1 and component 2). The components are provided by individual suppliers (supplier 1 and supplier 2). We assume that the firm makes different procurement contracts with supplier 1 and supplier 2. To supplier 1, the firm specifies the maximum inventory level of component 1 and makes a commitment to purchase the component as long as its inventory level is below this target level. To supplier 2, the firm has the option of purchasing or rejecting component 2 at each instant supplier 2 provides it. Formulating our model as a Markov decision problem, we identify a component 2 purchasing policy which maximizes the firm’s profits subject to the costs of rejecting component 1, holding component 2, and purchasing component 2. We also investigate how the changes in the sales price and cost parameters affect the optimal purchasing policy. Finally, we present numerical study for the optimal performance evaluation.This material is based upon work supported by the Korea Science and Engineering Foundation (KOSEF) through the Northeast Asia e-Logistics Research Center at University of Incheon.     

考虑消费者行为转化的零售商两阶段动态定价研究

考虑消费者呈现的不同行为特征,将其划分为两类:策略型和短视型。不同类型的消费者对同一产品会给出差别估价,假设这一估价呈随机分布,研究存在消费者行为转化的产品两阶段动态定价问题。引入消费者剩余对策略型和短视型消费者的市场响应特征进行描述,考虑贴现率,建立两阶段动态定价模型,分析不同类型消费者的差别决策过程,并且采用逆推法求解动态定价模型,得到最优价格策略。研究表明消费者期望购买数量与降价幅度都和转化率成负相关,此外,通过对比考虑转化和不考虑转化的两种情形下零售商总的期望利润,发现如果零售商没有考虑转化率而仅根据市场初期调查的消费者构成来进行产品定价将会给零售商带来损失,并且两种情形的利润差值随转化率的升高呈先上升后下降的变化趋势。     

Dynamic Network-Based Discriminatory Pricing

We study the dynamic pricing decisions for competitive network service providers. We assume that each competing firm follows a three-part pricing scheme, which consists of an ongoing membership fee, a usage fee for communications within the networks, and another usage fee for communications across the networks. The difference between the two usage fees is the network-based price discount that allows price discrimination. We study the firms problems as a differential game and establish the optimal pricing policy as a Nash equilibrium feedback strategy depending on only the network sizes (i.e., the number of subscribers). We compare the dynamic network-based discount with the static discount. In the special case of a uniform calling pattern, we find that the firm network-based dynamic discount is always lower than the static discount; we find also that the firm that has a larger network can offer a bigger discount. These results are useful particularly for managers. To get further insights into the dynamic pricing policies, we explore the case of symmetric competition using numerical simulation.Communicated by G. Leitmann     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

Brand positioning under lexicographic choice rules

This paper discusses a brand positioning model in which two brands of a product are to be positioned in a price-quality space under a new behavioral assumption. This assumption asserts that customers determine the highest-quality product within their reservation price and purchase it, provided its quality does not fall short of a minimum standard. The model also includes producers' costs that are incurred for delivering a certain quality. We first delineate reaction functions for the optimal location of one brand, give a location of its competitor. We then show that Nash equilibria do not exist as long as price and quality are both variable. Finally, we consider a two phase model: in the first phase, the duopolists sequentially choose their quality levels under the assumption that both competitors know that in the second phase, a Nash equilibrium in prices follows. Single-variable mathematical programming formulations are presented to solve the problem. A numerical example is also given to illustrate the working of the model.     

Optimal ordering policies in inventory systems with random demand and random deal offerings

In this paper, we determine the optimal order policies for a firm facing random demand and random deal offerings. In a periodic review setting, a firm may first place an order at the regular price. Later in the period, if a price promotion is offered by the supplier (with a certain probability), the firm may decide to place another order. We consider two models in the paper. In the first model, the firm does not share the cost savings (due to the promotion offered by the supplier) with its own customers, i.e. its demand distribution remains fixed. In the second model, the cost savings are shared with the final customers. As a result, the demand distribution shifts to the right. For both the models, in a dynamic finite-horizon problem, the order policy structure is divided into three regions and is as follows. If the initial inventory level for the firm exceeds a certain threshold level, it is optimal not to order anything. If it is in the medium range, it is optimal to wait for the promotion and order only if it is offered. The order quantity when the promotion is offered has an ‘order up to’ policy structure. Finally, if the inventory level is below another threshold, it is optimal to place an order at the regular price, and to place a second order if the promotion is offered. The low initial inventory level makes it risky to just wait for the promotion to be offered. The sum of the order quantities in this case has an ‘order up to’ structure. Finally, we model the supplier's problem as a Stackelberg game and discuss the motivation for the supplier to offer a promotion for the case of uniform demand distribution for the firm. In the first model (when the firm does not share the cost savings with its customers), we show that it is rarely optimal for the supplier to offer a promotion. In the second model, the supplier may offer a promotion depending on the price elasticity of the product.     

Contract and product quality in platform selling

More and more e-tailers (platforms) are allowing manufacturers direct access to customers. Two common contracts are offered by platforms to manufacturers: the revenue sharing contract where a platform appropriates a portion of the manufacturer’s revenue, and the fixed fee contract where a platform charges a fixed rent for each sale. Using an analytical model, this paper studies the interrelationship between a platform’s contract choice and a manufacturer’s product quality decision. We find that if product quality is exogenously given, the platform will always adopt the revenue sharing contract. If the manufacturer endogenously decides the quality, however, the platform’s contract choice may be changed. This is because the revenue sharing contract, compared to fixed fee, leads to a lower selling price of the manufacturer, whereas the fixed fee contract can motivate a higher quality than does revenue sharing. As a result, a large (small) market heterogeneity induces the platform to adopt the revenue sharing (fixed fee) contract. We also extend the model to several directions, finding that longer product line, manufacturer competition, lower marginal production cost, and higher platform cost all tend to induce the platform to put forward a fixed fee contract; while if quality decision is less flexible than contract decision, the platform is more ready to embrace revenue sharing. Besides, when there are two platforms competing for the same market, they should differentiate their contract choices so as to mitigate competition.     

Optimal strategies for general price-quality decision models of new products with learning production costs

The question of product quality permeates every level of business and is becoming crucial for the survival of modern manufacturing firms in automotive and high-tech industries. In this paper, we deal with the optimal price and quality policies for the introduction of a new product. On the supply side, the firm wants to determine the unit price and quality level over time given that unit cost declines along a learning curve, and increases if quality is made greater. On the demand side, dynamic demand is related to price and quality, as well as to cumulative sales (which represent diffusion and saturation effects). We will model this problem in a general framework that includes several previous results as special cases.By applying the maximum principle, we will derive the optimal price and quality policies and discover the interactions between these two major strategic marketing instruments, and the diffusion process. Several fundamental theoretical results will be established for the model. Under certain specified conditions higher prices do imply higher quality, and under other conditions the optimal price declines over time while the product quality improves. To illustrate these results, the theoretical results are applied to two specific-cases: the first one is a simple nonseparable demand growth function in price and quality, the other is a separable demand function of price and quality.     

考虑海外代购的品牌商定价模型研究

随着海外代购体量的日趋增大,代购带来的低价威胁对于在不同国家不同市场销售产品的公司来说已经成为一个日益严重的问题。同时,代购渠道中假货的问题也愈发严重。因此,在海外代购背景下探究产品定价模型具有必要性。以往研究普遍认为这种未经授权的销售会削减品牌方的利润,但实则不然。基于这一发现,本研究为在两个不同市场销售相同产品但面临代购低价威胁的公司制定考虑代购的市场定价模型。由公司制定两个市场的价格,消费者选择是否从包括代购在内的三个渠道购买产品。推出两个授权市场的最优价格,分析各参数变化对最优价格的影响,并校验最优价格对消费者需求和总利润的影响。模型分析表明,高价市场中有部分消费者需求转向海外代购,同时低价市场的消费者需求也受到了影响,且在一定条件下,提高高价市场的产品定价能够扩大低价市场的需求,从代购的角度解释了现实中需求曲线向上倾斜的现象。此外,两个独立市场之间的价格差距对代购市场的销售也产生了积极影响,并且在某些条件下,增大价格差距可以提高公司的收益水平。随后讨论了一种极端模型和三种扩展模型,通过模型分析表示,扩展后的定价模型也显示出与基础市场模型相似的灵敏度分析结果,同样得到两个市场的价差扩大会导致代购市场的销售额增加的结论,并且在一定条件下,公司的利润更高,增加了结论的可信度。     

A note on price and quality competition between asymmetric firms

This paper analyzes the impact of asymmetry between firms on the outcome of price and quality competition from a microeconomic viewpoint. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. The asymmetry arises from the difference in consumers’ loyalty to each firm; that asymmetry then determines a character of differentiation between firms. Our purpose is to show how asymmetry influences competition under varying consumers’ price- and quality-sensitivity. In doing so, we extend earlier work in the area of price and quality competition. We show that in both the moderately quality-sensitive and price-sensitive markets, higher consumers’ sensitivity as well as lower consumers’ loyalty to any firm leads to intense competition, resulting in a decrease of both firms’ equilibrium profits. On the other hand, in highly quality-sensitive market, asymmetry compels the smaller firm to change its competitive strategy. In general, this is more beneficial to the larger firm, as the smaller firm’s profit tends to decline. In the worst case, the smaller firm is driven out of business under equilibrium.     

Stochastic modelling of household behaviour before,during and after a consumer price promotion

A stochastic model is developed to study household behaviour with regard to purchase quantity, brand choice and purchase timing before, during and after a price change and a price promotion such as price-offs and price-cuts. The basic assumption of the model is that price promotion and levels of consumer inventory influence a household's purchase-timing and brand-switching decisions. The model incorporates market segments and brand switching on aggregated demand for the brands by the use of multivariate Markov processes. A transient stochastic model is employed to analyse the dynamic process of household behaviour before, during, and after a price promotion. The interpurchase time that is derived from the model does not require any assumptions and is not independently, identically distributed. An empirical analysis using the Information Resources Incorporated cracker data indicated that (1) price promotion does affect household purchase of the brand and (2) households with larger family size tend to purchase promoted items. We conjecture that households with larger family size take advantage of the lower price of the promoted brands while smaller households tend to remain loyal to one brand.