pricing and lot sizing decisions for perishable goods when demand depends on selling price reference price product freshness and displayed stocks abstract price is an important factor affecting demand rate based on economic and marketing theory in addition today s health conscious consumers prefer a product further from its expiration date because it is fresher and can be stored longer furthermore a large display of goods in a supermarket induces customers to buy more due to its visibility variety and seasonality as a result we develop a joint pricing and lot sizing model for retailers selling perishable products in which the demand depends on not only the selling price and reference price but also the product freshness linked to expiration date and displayed stock level we then formulate the problem as a deterministic model in which the retailer determines the optimal selling prices and ending inventory levels to maximize the discounted total profit furthermore we discuss the retailer s optimal decisions under two scenarios of demand behavior loss neutrality and loss aversion our theoretical analysis shows that the optimal pricing and ending inventory level strategies are both monotonic in time and the equilibrium of the system is unique for these two scenarios of demand behavior finally a set of structural properties and sensitivity analysis is also developed to characterize the impacts of model parameters on the optimal decisions

optimal dynamic pricing for deteriorating items with reference price effects when inventories stimulate demand abstract in this paper we incorporate reference price effects into a deteriorating inventory problem when the demand rate depends on displayed stock level and selling price simultaneously reference price effects are formed empirically by customers to adjust current price perception on the basis of past purchases the market demand is assumed to be responsive to the difference between the current selling price and the reference price which is perceived as a loss or a gain we consider three scenarios of market demand loss neutrality loss aversion and loss seeking an optimal dynamic pricing model is established to determine a pricing strategy maximizing the discounted total profit over an infinite time horizon theoretical results are derived to demonstrate the existence of the optimal solutions and to explore the relationships between optimal pricing decisions and an initial reference price based on mild assumptions numerical example and sensitivity analysis are presented to illustrate the theoretical results and managerial insights finally concluding remarks are offered

technical note intertemporal price discrimination via reference price effects we consider the dynamic pricing problem a monopolistic seller faces when customers arrive in heterogeneous time periods and their purchase decisions are affected by reference prices formed from their past observations of prices we illustrate that a new form of price discrimination opportunity exists in such situations where the seller s optimal pricing strategy is a cyclic one even when the customers are loss neutral and their demand functions are identical this result differs from those of prior studies where the optimal price paths are shown to be asymptotically constant and thus is unique due to the interaction between the heterogeneous arrivals and the reference price effects we also provide the cycle length of the optimal pricing policy when the demand function is linear and when customers are loss neutral in this era when customer information is easier accessible our results suggest the sellers consider this new dimension of price discrimination in conjunction with the old ones to take advan

optimal retailer investments in green operations and preservation technology for deteriorating items abstract this paper examines the impact of dynamic retailer investments in green operations while considering the reference price effect a replenishment problem based on joint pricing dynamic investment in green operations preservation technology and optimal replenishment times for deteriorating items is considered as a way to maximize retailer profit in this problem the demand rate depends on the sales and reference prices as well as green concern level optimal control theory is employed to obtain a dynamic investment rate and a simulated annealing algorithm is used to find the solution of the nonlinear constraint optimization problem which determines the price preservation technology investment and replenishment cycle time in addition computational simulations and sensitivity analyses are carried out to offer managerial insights the findings suggest that continuous investment in green operations and preservation technology can significantly improve the retailer s financial performance the consumer reference price is an important influence on the retailer s decision to invest in green operations furthermore results show that the higher price sensitivity of the market always discourages the retailer from investing in green operations the retailer needs to invest more in green operations for products with relatively high unit value

practice prize report an assortmentwide decision support system for dynamic pricing and promotion planning in diy retailing the main objective of this report is to describe a decision support system for dynamic retail pricing and promotion planning our weekly demand model incorporates price reference price effects seasonality article availability information features and discounts building on previous research we quantify demand interdependencies and integrate the resulting profit lifting effects into the optimal pricing model the methodology was developed and implemented at baumax an austrian do it yourself retailer along with the practical requirements an objective function was employed that can be used as a vehicle for implementing a retailer s strategy eight pricing rounds with thousands of different stock keeping units have each served as a testing ground for our approach based on various benchmarking methods a positive impact on profit was reported the currently implemented marketing decision support system increased gross profit on average by 8 1 and sales by 2 1

consumer normal price estimation market versus personal standards in reference price models internal reference price is typically estimated from actual market prices given the generally poor price knowledge consumers have exhibited in prior research the question is whether it is reasonable to use actual market prices to estimate consumers internal reference price standards the initial answer provided in this research surprisingly is yes although internal reference prices are measurable and do affect consumer price perception the gains in measuring and using those standards in predicting brand choice for frequently purchased products may not be worth the costs reasons why the surrogate price measure may work and implications for the measurement of internal reference price standards are considered

variable pricing in oligopoly markets behavioral research has found that consumers respond to variability in prices in addition to price levels we show that this finding can explain why some firms vary their prices more frequently than others we examine pricing strategies composed of an average price and price variability and employ logit market share models to analyze equilibrium pricing strategies in an oligopoly two competing logit specifications termed price sensitivity and payoff sensitivity are considered and are shown to yield contradictory implications for pricing policy from three empirical studies on restaurant choice we find that the price sensitivity model is the better model

technical note a price vector model of demand for consumer durables preliminary developments although considerable research has been conducted on optimal pricing policies for manufacturers relatively little work has been done on how price enters the consumer choice process in this paper a model is developed for durables purchasing which integrates both economic and behavioral research by specifying a vector of five price concepts which affect purchasing behavior of particular interest are variables relating to future price expectations due to data limitations a revised model is estimated and the results provide preliminary support for the general model

the impact of heterogeneity in purchase timing and price responsiveness on estimates of sticker shock effects the notion that individuals have an internal reference price against which they compare observed prices is well supported by several psychological theories empirically several papers in the marketing literature employing scanner panel data have modeled the impact of reference prices on brand choice via the sticker shock formulation in which consumers evaluate choice alternatives using differences between shelf prices and reference prices most of the studies reported thus far have not accounted for heterogeneity in price response among consumers and have typically imputed reference prices from the shelf prices of brands that a consumer is supposed to have observed on previous purchases in the category since category marketing activity can differentially affect the purchase timing of households we argue that this measure of reference price may follow certain systematic patterns across consumers and when combined with unaccounted for price response heterogeneity may result in a spurious sticker shock effect specifically we show that estimates of sticker shock are biased upward if households that are price sensitive in the brand choice decision are also more responsive to category promotion activity in their purchase timing decision we discuss some general conditions under which the bias occurs and conduct a simulation experiment to confirm our specific hypotheses our simulation results show that changes in purchase timing are a critical determinant of the bias in the sticker shock effect we also show that unaccounted for price response heterogeneity can in itself result in a biased sticker shock parameter however this requires very large differences in price sensitivities across consumers far greater than what is normally observed we develop a hierarchical bayes version of the nested logit model which models heterogeneity via individual level parameters in a continuous random effects framework we estimate the model on scanner panel data from the yogurt and ketchup categories we find in both categories that the 95 probability interval of the posterior distribution of the mean sticker shock coefficient contains the value zero therefore at least for the data used in this study there is no evidence for the sticker shock effect at the aggregate level in contrast the corresponding coefficient from a standard model which ignores this heterogeneity is highly significant and supports the existence of a possibly spurious sticker shock effect consistent with our explanation of the underlying cause of the bias households that are more price sensitive in the choice decision are also found to be more responsive to category promotion activity in their decision to purchase in the category the results highlight the measurement problems associated with imputing reference prices from past prices since the frequency duration and price level of a retailer s promotional program depend on its size and prevalence accurate estimates of the sticker shock effect are essential for formulating optimal promotion strategies an adequate accounting of consumer heterogeneity is critical to this effort

riding the waves revealing the impact of intrayear category demand cycles on advertising and pricing effectiveness abstractgoing beyond traditional seasonality this research introduces the concept of the intrayear category demand cycle this phenomenon reflects demand cycles most consumer packaged goods categories experience throughout the year with periods of higher demand following periods of lower demand the author argues that acknowledging the existence of these cycles and understanding their impact on both advertising and pricing effectiveness and practice is critical for marketers specifically the author demonstrates how both advertising and price elasticities and observed advertising and prices evolve along these cycles for a unique set of 252 brands ranging from high advertising high priced premium mass brands to low advertising low priced value niche brands in 61 consumer packaged goods categories overall both advertising efectiveness and observed advertising are found to be stronger at demand peaks surprisingly consumer reactions to price decreases are weaker at demand peaks whereas reactions

incorporating reference price effects into a theory of consumer choice although there has been a good deal of research on incorporating the effects of reference price formation into empirical models of consumer buying behavior little formal theoretical work had been undertaken to date this paper incorporates reference price effects into the traditional economic theory of consumer choice and examines the effects of reference price formation on the results of the traditional theory its marketing implications and the implications for empirical models which examine the effects of reference price formation on actual consumer behavior several implications of the theoretical model are empirically tested using weekly retail egg sales data from southern california this analysis indicates that reference price formation does have significant effects on consumer behavior furthermore these effects are asymmetric with consumers two and a half times more responsive to egg price increases that are in excess of the reference price than they are to comparable egg price decreases

modeling loss aversion and reference dependence effects on brand choice based upon a recently developed multiattribute generalization of prospect theory s value function tversky and kahneman 1991 we argue that consumer choice is influenced by the position of brands relative to multiattribute reference points and that consumers weigh losses from a reference point more than equivalent sized gains loss aversion we sketch implications of this model for understanding brand choice we develop a multinomial logit formulation of a reference dependent choice model calibrating it using scanner data in addition to providing better fit in both estimation and forecast periods than a standard multinomial logit model the model s coefficients demonstrate significant loss aversion as hypothesized we also discuss the implications of a reference dependent view of consumer choice for modeling brand choice demonstrate that loss aversion can account for asymmetric responses to changes in product characteristics and examine other implications for competitive strategy

dynamic stochastic inventory management with reference price effects we analyze the joint inventory and pricing decisions of a firm when demand depends on not only the current selling price but also a memory based reference price and customers are loss averse the presence of reference price effect leads to a nonconcave one period expected revenue in price and reference price we introduce a transformation technique that allows us to prove under some mild assumptions the optimality of a reference price dependent base stock list price policy which is characterized by a base stock level and a target reference price in addition we show that the target reference price is increasing in the reference price but except in the loss neutral case the base stock level is not monotone in the reference price we also show that in the steady state of the model with the reference price effect the optimal price is lower while the optimal base stock level is higher than their counterparts in the model without the reference price effect

price promotions limiting competitive encroachment in this paper we explore equilibrium pricing strategies in an infinite horizon repeated game for an oligopoly we model the interactions between three firms in a market of switchers and loyals our analysis shows that if there are sufficiently large number of switchers in the market the demand parameter is within an acceptable range and the firms have a sufficiently low discount rate alternating promotions between national firms can be an outcome of a perfect nash equilibrium between competing firms this equilibrium results in an implicit collusion between national firms and therefore suggests that price promotions can be interpreted as a long run strategy pursued by national firms to defend their market shares from possible encroachments of a third firm in this way we attempt to provide an explanation for the patterns of promotion observed in some industries and in particular the beverage industry

a competitive dynamic pricing model when demand is interdependent over time abstract in this study we contribute to the dynamic pricing literature by developing a finite horizon model for two firms offering substitutable and nonperishable products with different quality levels customers can purchase and store the products even if they do not need them at the time in order to use them in future the stockpile of the products generated by customers affects the demand in future periods therefore the demand for each product not only is a function of prices and quality levels but also of the products stockpile levels in addition the stockpile levels change the customers consumption behavior more product in a stockpile leads to more consumption therefore we address not only the price and demand relationship but also the stockpiling and consumption relationship in a competitive environment the decision variable of each firm at the beginning of each period is its unit sale price we use a deterministic dynamic program to calculate the equilibrium prices at the beginning of each period by assuming that the market stockpile is public information we show the existence of a unique nash equilibrium we next consider the case when the firms do not know the market stockpile we then develop appropriate heuristics to calculate the optimal prices in each case a numerical study is also provided to calculate the price levels in different scenarios and compare their performances

empirical generalizations from reference price research considerable theoretical justification for consumers use of psychological reference points exists from the research literature from a managerial perspective one of the most important applications of this concept is reference price an internal standard against which observed prices are compared in this paper we propose three empirical generalizations that are well supported in the marketing literature first there is ample evidence that consumers use reference prices in making brand choices second the empirical results on reference pricing also support the generalization that consumers rely on past prices as part of the reference price formation process third consistent with other research on loss aversion consumers have been found to be more sensitive to losses i e observed prices higher than reference prices than gains we also propose topics for further research on reference prices

the bright side of loss aversion in dynamic and competitive markets a well established phenomenon of consumer buying behavior is that consumers evaluate prices relative to a reference point and exhibit loss aversion i e their propensity to buy is more negatively affected by prices above the reference point than it is positively affected by prices below the reference point the objective of this paper is to analytically examine how the competitive strategy and profitability of firms are affected by the presence of consumer loss aversion in the price dimension although we assume that consumer loss aversion increases consumer propensity to search for lower prices we find that it does not necessarily lead to lower prices or profits when firms compete over multiple periods and when the consumer reference price in subsequent periods is affected by current prices specifically consumer loss aversion could lead to higher prices and profits when consumer valuation is sufficiently high relative to search costs and the proportion of consumers with positive search costs is in an intermediate range we also show that when forward looking firms incorporate the negative effect of price promotions on future profits the equilibrium range of price promotions may actually increase

an empirical analysis of latitude of price acceptance in consumer package goods scanner panel data analyses for sweetened and unsweetened drink categories with four brands in each support the presence of a region of price insensitivity around a reference price the analyses also suggest that consumers with higher average reference price have a wider latitude of price acceptance consumers with a higher frequency of purchase i e shorter average interpurchase time interval are found to have a narrower latitude of price acceptance because they are more aware of the range of price distributions finally consumers with a higher average brand loyalty have a wider latitude of price acceptance demonstrating greater tolerance of price fluctuations

has children s poverty become more persistent iffood stamp benefits are counted as income there is little change in estimates ofpersistent povertyfor children between the late 1960s and early 1980s however the absence of change in persistent poverty masks a number of important changes in the demographic and statistical structure ofpersistent poverty these changes include increasing inequality in the distribution of permanent socioeconomic position greater dependence on social assistance and the more familiar demographic changes such as increased numbers of single parent families higher educational attainments of parents and decline in family size

competitive promotional strategies this article analyzes the equilibrium pricing strategies of brands engaged in a pricing game each brand has a monopoly market loyal consumers and competes with others in a common market called brand switchers in the case of a duopoly it is shown that the behavior of the brand switchers characterizes the equilibrium behavior of the duopolists this article focuses on two key comparative statics namely the depth of discounts away from a regular high price and the probability of giving a deal or the frequency of deals how these properties vary with the size of the loyal markets and the behavior of the brand switching population is discussed copyright 1988 by the university of chicago

modeling the psychology of consumer and firm behavior with behavioral economics abstract marketing is an applied science that tries to explain and influence how firms and consumers behave in markets marketing models are usually applications of standard economic theories which rely on strong assumptions of rationality of consumers and firms behavioral economics explores the implications of the limits of rationality with the goal of making economic theories more plausible by explaining and predicting behavior more accurately while maintaining formal power this article reviews six behavioral economics models that are useful to marketing three models generalize standard preference structures to allow for sensitivity to reference points and loss aversion social preferences toward outcomes of others and preference for instant gratification the other three models generalize the concept of game theoretic equilibrium allowing decision makers to make mistakes encounter limits on the depth of strategic thinking and equilibrate by learning from feedback the authors also discuss a sp

anchoring effects evidence from art auctions in order to separate anchoring where an irrelevant message has an effect on the outcome from rational learning where past prices are not irrelevant because they may be used to estimate unobservable quality we use the following strategy we first develop a hedonic prediction of price for both the current sale e g the 2006 sale and the previous sale these hedonic predic tions are based on observable characteristics of each painting and an index of overall prices we then regress actual sale price on our hedonic prediction on the difference between the actual price in the previous sale and our hedonic prediction this expression tests for anchoring and on the difference between the actual price in the previous sale and our hedonic prediction of price in the previous sale this expression controls for unobservable characteristics the test for anchor ing is the extent to which the actual price in the previous sale affects the current sale price we can identify anchoring from other effects because the demand for art which is captured by the average overall price index changes over time whereas the unobservable component of qual ity is assumed to remain constant between auctions this allows us to control for unobserved quality characteristics as long as something drastic has not happened between sales such as a painting has been deemed a fake which is a very rare occurrence the assumption of constant quality is a realistic one

dual role of price and myopia in a marketing channel abstract 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 our objective is to investigate the impact of retailer s myopia on the pricing strategies and payoffs of channel members in this context a myopic retailer is an agent that disregards the effects of its pricing strategy on the evolution of the perceived brand quality and the reference price

consumer price and promotion expectations an experimental study the authors report results from a controlled experiment designed to investigate the impact of a brand s price promotion frequency and the depth of promotional price discounts on the price consumers

an alternative explanation for lower repeat rates after promotion purchases several authors have observed that average repeat rates are lower after a promotion purchase one interpretation of this result is that a media coupon or cents off promotion undermines the consumer

the equity estimator for marketing research we introduce a new biased estimator called the equity estimator to estimate parameters of linear models in the presence of multicollinearity we then employ a comprehensive simulation methodology to evaluate ols the equity estimator and a particular form of the ridge estimator which has received some attention in the statistical literature we show that both equity and ridge perform significantly better than ols on a variety of performance measures over most of the parameter space the equity estimator does much better than the ridge estimator on the squared error criterion on other criteria the equity estimator performs marginally better than ridge in particular equity does well when the degree of multicollinearity among the explanatory variables is high and or the r2 of ols for the sample is less than 0 7 conditions frequently encountered in marketing research we discuss how the results of this study can be used by marketing researchers in choosing an appropriate estimator for their particular application

an empirical analysis of internal and external reference prices using scanner data single source yogurt data are used to examine whether both internal and external reference prices affect purchase decisions internal reference prices are memory resident prices based on actual fair or other price concepts external reference prices are observed stimuli such as regular prices that stores may display along with a sale price for comparability discrete choice models with variables representing the two types of reference prices are estimated and both types of variables are found to have significant effects on purchase probabilities this suggests that consumers may use multiple reference points in evaluating price in purchase decisions in addition a model using an indicator of a sale price discount explains purchase probabilities as well as one that models the actual discount which suggests that consumers may be reacting to the indication of savings rather than to the amount of the discount

the impact of reference price effects on the profitability of price promotions this paper investigates the impact of reference price effects on retailer price promotions and describes why these effects can make promoting profitable first we analyze the profit impact of reference price effects generated by a single period of promotion the promotion can increase profit if the gain that these effects create in the promotion period outweighs the loss they create in future periods we then describe how retailers can estimate the optimal strategy of recurring promotions that maximizes profits from reference price effects over a time horizon examples of such strategies are presented for a retailer selling a national brand of peanut butter we obtain insights into how promotion prices timing and profits are affected by changes in costs interest rates consumers reactions to reference price effects and error in estimates used in the model the retailer s optimal reaction to a trade deal is also examined this strategy involves a phase of increased promotion activity sandwiched between phases of decreased activity we explain these results using the effects described in the single period model

the timing of sales this paper presents a model of intertemporal price discrimination a fixed number of sellers produce a homogeneous good consumers with different preferences enter the market in each period and leave when they make a purchase the sellers typically vary their prices over time charging a high price in most periods but occasionally cutting the price to sell to a large group of customers with a low reservation price in some equilibria all stores lower their price at the same time and to the same level

reference effects of price and promotion on brand choice behavior when consumers are exposed to pricing and promotional activity by frequently purchased packaged goods they may develop expectations that are used as points of reference in evaluating future activi

technical note dynamic pricing with gain seeking reference price effects we study a dynamic pricing problem of a firm facing reference price effects at an aggregate demand level where demand is more sensitive to gains than losses we find that even the myopic pricing strategy belongs to one type of discontinuous maps which can exhibit complex dynamics over time our numerical examples show that in general the optimal pricing strategies may not admit any simple characterizations and the resulting reference price price dynamics can be very complicated we then show for a special case that a cyclic skimming pricing strategy is optimal and we provide conditions to guarantee the optimality of high low pricing strategies

anchoring on credit spreads this paper documents that the path of credit spreads since a firm s last loan influences the level at which it can currently borrow if spreads have moved in the firm s favor i e declined it is charged a higher interest rate than is justified by current fundamentals whereas if spreads have moved to the firm s detriment it is charged a lower rate we evaluate several possible explanations for this finding and conclude that anchoring to past deal terms is most plausible

the effects of consumers price expectations on sellers dynamic pricing strategies abstract the authors propose a dynamic market equilibrium model to investigate how consumers form price expectations and how these expectations influence their sequential search behavior and prices in the market they derive a perfect bayesian nash equilibrium and show that whereas higher current period prices induce search consumers who observe higher historical prices form higher price expectations become more pessimistic and search less furthermore the authors show that when prices increase as a result of an increase in marginal costs consumers respond by searching more which then leads to higher prices and instant price adjustment in contrast because consumer search activities decline when prices fall sellers may respond by lowering their prices just enough to dampen consumers search tendencies when costs decrease the authors test their theoretical model and its implications and find support for it in a series of simulated market experiments

returns to human capital under uncertain reform good guys finish last abstract this paper models the career decisions of agents heterogeneous in their ability facing the possibility of future drastic changes e g reforms affecting the demand for different professions supposing that the uncertainty arises after educational choices have been made by the cohort of agents we analyze their response to it depending on ability and educational attainment we show that the more able individuals tend to stay in their original profession while their less able counterparts are more likely to switch to an alternative occupation if reform does take place the more able agents will be forced to change careers since they switch late they miss the benefits of learning by doing this adverse selection has important implications for the analysis of labor allocation during transition from central planning to markets in particular it lowers productivity in the emerging market occupations reducing the benefits of reforms

pricing and promotions in asymmetric duopolies this paper develops a modeling framework for making promotions decisions in contrast to some of the prior research the framework explicitly models promotions its central feature is the view of promotions competition as a multistage game in which regular prices are chosen first followed by the choice of promotion depths and frequencies it is used to illustrate the nature of competition between a national brand and private label in equilibrium the national brand promotes to ensure that the private label does not try to attract consumers away from the national brand moreover the private label does not promote this equilibrium is also contrasted with varian s framework used by other researchers in which mixed strategy equilibrium prices are interpreted as promotions

asymmetric reference price effects and dynamic pricing policies we consider a group of frequently purchased consumer brands which are partial substitutes and examine two situations the first where the group of brands is managed by a retailer and second where the brands compete in an oligopoly we assume that demand is a function of actual prices and reference prices and develop optimal dynamic pricing policies for each situation in addition to researchers studying pricing strategy our results may interest retailers choosing between hi lo pricing and an everyday low price and manufacturers assessing whether to follow procter gamble s lead and replace a policy of funding consumer price reductions through trade deals with a constant wholesale price a reference price is an anchoring level formed by customers based on the pricing environment the literature suggests that demand for a brand depends not only on the brand price but also whether the brand price is greater than the reference price a perceived loss or is less than it a perceived gain the responses to gains and losses are asymmetric broadly speaking we find that when enough consumers weigh gains more than losses the optimal pricing policy is cyclical likewise when they weigh losses more than gains a constant price is optimal thus we provide a rationale for dynamic pricing which is quite distinct from the three explanations previously offered 1 decreasing unit variable costs due to learning effects 2 the transfer of inventory to consumers who face lower inventory holding costs than do retailers and 3 competitive effects our explanations apply even when the other explanations do not i e in mature product categories where learning effects are minimal when retailer inventories are minimized through the use of just in time policies and when competitive effects do not exist as in a monopoly greenleaf 1995 has shown numerically that in the presence of reference price effects the optimal pricing policy for a monopolist can be cyclical we first analytically extend greenleaf s result to a monopolist with a constant cost of goods facing a homogeneous market where all customers either weigh gains more than losses or vice versa using this building block we examine a monopolist retailer managing multiple brands we assume that demand is a linear function of prices of multiple brands and together with an expression which reflects the reference price effect further we assume that the retailer maximizes average profit per period next we analyze a duopoly and extend the results to an oligopoly we assume that the manufacturers are able to set the retail prices as in an integrated channel here we retain the same demand function as for the retailer and derive markov perfect nash equilibria we use two alternative processes of reference price formation the exponential smoothed es past price process which is frequently used in the literature and for the multi brand situations the recently proposed reference brand rb process hardie johnson and fader 1993 in the latter the reference price is the current price of the last brand bought the reference brand we adapt the individual level rb formulation in hardie et al to an aggregate demand specification for the es process we obtain most results analytically for the rb process we use simulation finally we extend our results to a population with two customer segments segment 1 which weighs gains more than losses and segment 2 which does the opposite i e is loss averse when the market consists exclusively of segment 1 customers and es is the reference price process we find that prices are cyclical in all cases analyzed i e for a monopoly a monopolist retailer managing multiple brands a duopoly and an oligopoly if the rb formulation is the underlying process a monopolist retailer managing two brands uses cyclical prices but in a duopoly the equilibrium solution is for the brands to maintain constant prices when all customers belong to segment 2 i e they are loss averse constant prices are optimal in all cases for both reference price formulations when the population consists of both segment 1 and segment 2 and the es process applies we develop a sufficient condition for cyclical pricing policies to be optimal the condition is expressed in terms of the proportion of the two segment sizes the absolute difference between the gain and loss parameters of each segment and their respective exponential smoothing constants interestingly for reasonable values of the latter two factors cyclical policies are optimal even when the proportion of segment 1 is quite small similar magnitudes are obtained numerically for the rb case

dynamic pricing with loss averse consumers and peak end anchoring we study the dynamic pricing implications of a new behaviorally motivated reference price mechanism based on the peak end memory mode this model suggests that consumers anchor on a reference price that is a weighted average of the lowest and most recent prices loss averse consumers are more sensitive to perceived losses than gains relative to this reference price we find that a range of constant pricing policies is optimal for the corresponding dynamic pricing problem this range is wider the more consumers anchor on lowest prices and it persists when buyers are loss neutral in contrast with previous literature in a transient regime the optimal pricing policy is monotone and converges to a steady state price which is lower the more extreme and salient the low price anchor is our results suggest that behavioral regularities such as peak end anchoring and loss aversion limit the benefits of varying prices and caution that the adverse effects of deep discounts on the firm s optimal prices and profits might be more enduring than previous models predict