Signaling Quality: Dynamic Price-Advertising Model

This paper extends the existing quality-signaling literature by investigating the roles of price and advertising levels as quality indicators in a dynamic framework. Considering perceived quality as a form of goodwill, we modify the well-known Nerlove-Arrow dynamic model to include price effects. In our model, price is used both as a monetary constraint and as a signal of quality, while advertising spending is used only as a signaling device, and thus purely as a dissipative expense. Utilizing optimal control, we determine optimal decision rules for a firm regarding both price and advertising over time as functions of perceived quality. The results indicate that, when prices act as monetary constraints and are reduced to increase demand, the firm should use the signaling role of advertising by increasing spending to accelerate perceived quality increases. In cases when the value of the perceived quality goes up together with the increase in the perceived quality by more than the demand, in percentage terms, the firm should increase the price (use its signaling role). At steady-state, we find that the level of optimal profit margin relative to price decreases with the elasticity of demand with respect to the brand price. However, higher elasticity of demand with respect to the firm’s perceived quality and/or a higher impact of price (advertising) lead/leads to a higher optimal profit margin (advertising spending) relative to price (revenue).     

Dual role of price and myopia in a marketing channel

In this paper we study a dynamic two-player channel where the manufacturer controls the wholesale price and the investment in quality and the retailer chooses the retail price. We consider that the retail price affects both the demand and the perceived quality of the brand and that its variations contribute to the building of an internal reference price. One of the model’s distinctive features is that it accounts for the two meanings of price, i.e., its classical objective measure of the cost of acquiring a particular quantity of the product, and its subjective roles as an assessment of the quality of the product and an evaluation of gains or losses (deal vs. sacrifice) resulting from buying a “cheap” or an “expensive” product. This dual computation is done with respect to the internal reference price.     

Consumer price sensitivity in the retail industry: Latitude of acceptance with heterogeneous demand

Estimating the effect of price changes on demand is an essential task for retailers. This study proposes a methodology based on consumer utility for modeling the price thresholds phenomenon that allows for threshold asymmetry, incorporates consumer heterogeneity and uses weekly aggregated brand-level data. Unlike other studies based on consumer utility models, which generate results only for the price elasticity of market share, a methodology for estimating price elasticity of demand is also included. Data on fast-moving goods (detergents, toilet paper, soft drinks, meats, liquid juices and yogurts) supplied by a major retail chain are used to demonstrate the existence of price thresholds and their effects on price elasticity. In every case it was found that within the thresholds or latitude of acceptance, consumers are relatively less sensitive to price variations while beyond them a higher sensitivity was observed. In some cases a product brand was classified as inelastic within the latitude of acceptance and elastic outside of it.     

Advertising Strategies in a Differential Game with Negative Competitor’s Interference

We consider a duopolistic industry where the current sales of each firm is proportional to its goodwill stock. The evolution of the latter depends positively on own advertising effort and negatively on competitor’s advertising. A standard assumption in the literature in differential games of advertising is that the players remain active throughout the whole (infinite) duration of the game. We relax this assumption and characterize the circumstances under which a firm finds it optimal to remain or exit the industry. Among other things, it is shown that, if both players are “strong”, then the unique Nash equilibrium is the same that one would obtain in the absence of interference from competitor’s advertising. Research supported by Ministry of University and Research of Italy, University of Padua and NSERC, Canada.     

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.     

Customization competition between branded firms: Continuous extension of product line from core product

We study a competition of product customization between two branded firms by a game-theoretic approach. Firms produce products with two attributes: one attribute indicates a characteristic with regard to “function” or “design” of a product and the other indicates “taste” or “flavor” of the product, which reflects consumers’ brand/taste preferences. Two branded firms have their own specific core products and our customization is defined as a continuous extension of their product line from the core product only along the “function” attribute. In particular, we allow asymmetric positions of core products, which may create the position advantage/disadvantage between firms. We suppose that consumers incur their selection costs with regard to finding their most favorable item among a rich variety of products and firms incur their customizing costs with regard to extending their product lines. We first show that in the equilibrium, branded firms should fundamentally adopt their customizations to cover the center space in the market as far as possible, regardless of the position of the competitor’s core product. Therefore, the position of the core product contributes to the creation of a competitive advantage: when one firm’s core product is located more closely to the center of the market than the competitor’s, its customization can always cover more range of the center space in the market, while keeping its degree of customization smaller than the competitor’s. Furthermore, we show some implications of unit-cost improvement: in a short run, a firm is better off concentrating on the improvement of the unit selection cost rather than the unit customizing cost. In contrast, in a long run, both firms can benefit from the improvement of the unit customizing cost.     

A study on the demand and response correspondences in the presence of indivisibilities

This paper attempts to study market and noncooperative game models in the presence of indivisibilities from a unified point of view. For market models we examine the sum of consumers’ demand correspondences mapping an integral price space to an integral commodity space, whereas for noncooperative game models we investigate the product of players’ response correspondences mapping a discrete strategy profile space to itself. We show that, in several typical models, the sum and the product correspondences share an important property that they are ‘locally gross direction preserving’, on the standard triangulation of the convex hull of the domain. Moreover, we prove the existence of a Walrasian equilibrium and a Nash equilibrium in respective models through a discrete multivariate mean value theorem.     

On the uniqueness of Bertrand equilibrium

We introduce product differentiation in the model of price competition with strictly convex costs in which firms have to supply all of the forthcoming demand. We find that although a continuum of equilibria exists in a homogeneous product market, the competitive price equilibrium is the only robust one. Specifically, as long as the equilibrium correspondence is nonempty, the equilibrium price converges to the competitive price when the degree of product differentiation shrinks to zero.     

Feedback Stackelberg equilibrium strategies when the private label competes with the national brand

We consider a noncooperative differential game where a retailer sells her own private label in addition to the manufacturer’s brand. We assume that each brand’s goodwill evolves according to a modified Nerlove-Arrow dynamics, in such a way that the advertising effort of one brand hurts the competitor’s goodwill stock. We characterize Feedback-Stackelberg pricing and advertising strategies and employ simulations to analyze their sensitivity to the main model parameters. We thank an anonymous Reviewer for very helpful comments. Research supported by NSERC, Canada, and FQRSC, Quebec. Research completed when the second author was a visiting professor at GERAD, HEC Montréal. The second author’s research was partially supported by MEC and JCYL under projects SEJ2005-03858/ECON and VA045A06, co-financed by FEDER funds.     

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.     

The dynamics of price, quality and productivity improvement decisions

Although quality has received significant attention during the last decades and its economic benefits are beyond any doubt, lots of questions have remained unanswered as to how much, when, and in what to invest to maintain sustainable competitive advantage. A model is introduced here to guide a firm in addressing these questions. The firm produces a single product and operates in a market where monopolistic competition is effective. Demand for the product in the industry depends on both price and performance quality. Increasing productivity knowledge decreases unit production cost, but demand for the company’s product decreases over time, as competitors will be able to offer products with similar performance. Productivity and quality knowledge can be developed through induced and autonomous learning in order to strengthen company position. The paper provides an optimal control formulation of the problem and develops necessary conditions for optimality and characterizes the dynamics of optimal price, quality and investment decisions.     

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.     

A two stage stochastic equilibrium model for electricity markets with two way contracts

This paper investigates generators’ strategic behaviors in contract signing in the forward market and power transaction in the electricity spot market. A stochastic equilibrium program with equilibrium constraints (SEPEC) model is proposed to characterize the interaction of generators’ competition in the two markets. The model is an extension of a similar model proposed by Gans et al. (Aust J Manage 23:83–96, 1998) for a duopoly market to an oligopoly market. The main results of the paper concern the structure of a Nash–Cournot equilibrium in the forward-spot market: first, we develop a result on the existence and uniqueness of the equilibrium in the spot market for every demand scenario. Then, we show the monotonicity and convexity of each generator’s dispatch quantity in the spot equilibrium by taking it as a function of the forward contracts. Finally, we establish some sufficient conditions for the existence of a local and global Nash equilibrium in the forward-spot markets. Numerical experiments are carried out to illustrate how the proposed SEPEC model can be used to analyze interactions of the markets.     

基于“进场费+收益共享”契约的供应链协调策略研究

在超市等自助零售环境下,影响产品需求的往往是产品的感知质量,而产品感知质量不仅取决于产品质量水平,还受货架空间展示量的影响。本文基于价格和感知质量依赖的需求函数,分别建立了一体化供应链集中决策模型以及考虑是否存在进场费的寄售契约下零售商主导的Stackelberg博弈模型,研究了制造商和零售商的产品定价和货架空间展示策略,并给出了进场费+收益共享的供应链协调策略。研究结果表明分散供应链环境下产品的最优零售价格并不总高于集中决策下产品的最优定价,也就是说提升感知质量在一定程度上可以缓解双重边际效应。另外,收取进场费的收益共享模式可以实现供应链的完美协调,这在理论上说明了进场费模式在一定的市场环境下是合理的。     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

Competitive Price Equilibrium with Consumer Reservation Utility

This paper studies a competitive price equilibrium in the market of a product category where consumers are homogeneous with a reservation utility below which they will not purchase the product. The impact of the reservation utility on the price equilibrium is of particular interest, because the reservation utility may change according to the business cycle and economic environments. Using multinomial logit model to describe market response, we study the comparative statics of the prices, profits and market shares of firms, each of which produces one brand in the product category, with respect to the reservation utility in the Nash equilibrium. It is shown that, as the reservation utility increases, the prices as well as the profits at Nash equilibrium decrease. Also, in the case of duopoly market, the firm with lower cost structure will increase its market share as the reservation utility increases.     

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.     

Joint pricing-servicing decision and channel strategies in the supply chain

This paper investigates the equilibrium behavior of a two-echelon supply chain in four channel strategies: (i) vertical integration, (ii) vertical Nash (iii) manufacturer’s Stackelberg and (vi) retailer’s Stackelberg. We examine the price and service level decision for each of the above four channel strategies in two cases: (i) Simultaneous service-level decision: Here, the manufacturer and retailer simultaneously choose a service level. (ii) Sequentially service-level decision: Here, the manufacturer and retailer sequentially choose a service level. We model the demand as a deterministic linear function of retailer’s price and both manufacturer’s and retailer’s service levels. We discuss the optimal configuration from each individual’s perspective for each of the above channel strategies. We show that vertical integration dominates other strategies and leads to the highest service level but lowest retail price among various channel coordination policies considered here. We yield several conclusions about the provision of service level by each supply chain individual to coordinate the channel.     

Pricing and Advertising of Private and National Brands in a Dynamic Marketing Channel

We consider a marketing channel where a retailer sells, along the manufacturer’s brand, its own store brand. We assume that each player invests in advertising in order to build the brand’s goodwill. One distinctive feature of this paper is the introduction of the negative effect of own advertising on other player’s goodwill stock evolution. We characterize feedback-Nash pricing and advertising strategies and assess the impact of the store brand and national brand’s goodwill stocks on these strategies in different settings. The main findings suggest first that investing in building up some equity for each brand reduces the price competition between them and propels the market power for both. Second, the retailer will pass to consumer an increase in its purchasing cost of the national brand in all situations as no coordination is taken into account to counter the double marginalization problem. Finally, the higher the brand equity of the store brand, the more the retailer invests in advertising.     

On price competition in location-price models with spatially separated markets

In this paper we study price competition for two types of location-price models in which facility locations are set up and price decisions have to be made in order to maximise profit. We discuss the existence and determination of equilibrium prices in a general location space when facilities have different production costs. It is assumed that each price is bounded from below and demand for a single homogeneous product is price-inelastic. When facilities set mill prices, a price equilibrium rarely exists and necessary conditions for existence are obtained. In particular, when the location space is a tree network, we give a characterisation of the locations for which a unique equilibrium exists for two competitors. With spatial price discrimination, though equilibrium prices might not exist, it is shown that ε-equilibrium prices always exist for any locations of the facilities. A characterisation of ε-equilibrium is also given. Then the location-price problem is reduced to a location problem. A comparison of results with the two types of price determination is also presented. This work has been supported by the Ministry of Science and Technology of Spain under the research project BEC2002-01026, in part financed by the European Regional Development Fund (ERDF).