strategic capacity rationing to induce early purchases dynamic pricing offers the potential to increase revenues at the same time it creates an incentive for customers to strategize over the timing of their purchases a firm should ideally account for this behavior when making its pricing and stocking decisions in particular we investigate whether it is optimal for a firm to create rationing risk by deliberately understocking products then the resulting threat of shortages creates an incentive for customers to purchase early at higher prices but when does such a strategy make sense if it is profitable to create shortages what is the optimal amount of rationing risk to create we develop a stylized model to study this problem in our model customers have heterogeneous valuations for the firm s product and face declining prices over two periods customers are assumed to have identical risk preferences and know the price path and fill rate in each period via its capacity choice the firm is able to control the fill rate and hence the rationing risk faced by customers customers behave strategically and weigh the payoff of immediate purchases against the expected payoff of delaying their purchases we analyze the capacity choice that maximizes the firm s profits first we consider a monopoly market and characterize conditions under which rationing is optimal we examine how the optimal amount of rationing is affected by the magnitude of price changes over time and the degree of risk aversion among customers we then analyze an oligopoly version of the model and show that competition reduces the firms ability to profit from rationing indeed there exists a critical number of firms beyond which a rationing equilibrium cannot be supported

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

the environmental kuznets curve and flow versus stock pollution the neglect of future damages in this paper we offer a possible explanation for the empirical finding that the pollution income relationship pir for flow pollutants is an environmental kuznets curve ekc i e inverted u shaped but that the pir for stock pollutants is monotonically rising we analyse an overlapping generations model with two pollutants the flow pollutant causes immediate damages but the stock pollutant harms the environment only in the future hence a succession of myopic governments lets stock pollution grow with income in contrast the flow pollutant follows an ekc whose downturn might be caused by the neglect of future damages and by ever rising stock pollution without the stock pollutant the pir for the flow pollutant can increase monotonically we also show that the turning point of the ekc for the flow pollutant lies at lower levels of income and of flow pollution if stock pollution is high and harmful this casts doubts on most empirical ekc studies because they assume that the turning point occurs at the same income level in all countries however it is consistent with recent empirical findings that the income level at the turning point of the ekc varies across countries

using asset prices to measure the cost of business cycles we measure the cost of consumption fluctuations using an approach that does not require the specification of preferences and instead uses asset prices we measure the marginal cost of consumption fluctuations the per unit benefit of a marginal reduction in consumption fluctuations expressed as a percentage of lifetime consumption we find that the gains from eliminating all consumption uncertainty are very large however for consumption fluctuations corresponding to business cycle frequencies we estimate the marginal cost to be between 0 08 percent and 0 49 percent of lifetime consumption

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

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

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

dynamic control of a monopolist s product and process innovation with reference quality our main purpose is to investigate the dynamic control problem of a monopolist s product and process innovation under reference quality the main features of this article are i a monopolist deal

behavioral anomalies in consumer wait or buy decisions and their implications for markdown management the decision to buy an item at a regular price or wait for a possible markdown involves a multidimensional trade off between the value of the item the delay in getting it the likelihood of getting it and the magnitude of the price discount such trade offs are prone to behavioral anomalies by which human decision makers deviate from the discounted expected utility model we build an axiomatic preference model that accounts for three well known anomalies and produces a parsimonious generalization of discounted expected utility we then plug this behavioral model into a stackelberg nash game between a firm that decides the price discount and a continuum of consumers who decide to wait or buy anticipating other consumers decisions and the resultant likelihood of product availability we solve the markdown management problem and contrast the results of our model with those under discounted expected utility we analytically show that accounting for the behavioral anomalies can result in larger markdowns a

costs of business cycles for unskilled workers abstract unskilled workers are subject to a much larger risk of unemployment during recessions than are skilled workers moreover unskilled workers earn less income which limits their ability to self insure we examine how this heterogeneity in unemployment risk and income across different skill groups translates into heterogeneity in the cost of business cycles we find that the welfare cost of business cycles for unskilled workers is substantially higher than the welfare cost for skilled workers

economic development and co2 emissions a nonparametric panel approach we examine the empirical relation between co2 emissions per capita and gdp per capita during the period 1960 1996 using a panel of 100 countries relying on the nonparametric poolability test of baltagi et al baltagi b h hidalgo j li q 1996 a nonparametric test for poolability using panel data journal of econometrics 75 345 367 we find evidence of structural stability of the relationship we then specify a nonparametric panel data model with country specific effects estimation results show that this relationship is upward sloping nonparametric specification tests do not reject monotonicity but do reject the polynomial functional form which leads to the environmental kuznets curve in several studies

product and price competition with satiation effects consumers become satiated with a product when purchasing too much too quickly how much is too much and how quickly is too quickly depends on the characteristics of the product relative to the time interval between consumption periods knowing that consumers allocate their budget to products that generate less satiation effects retailers should then choose to sell products that induce minimal satiation but usually this is operationally more costly to study this trade off we provide an analytical model based on utility theory that relates customer consumption to price and satiation in the context of multiple competing retailers we determine the purchasing pattern over time and provide an explicit expression to determine the consumption level in steady state we derive market shares and show that they take the form of an attraction model in which the attractiveness depends on price and product satiation we use this to analyze the competition between firms that maximize long term average profit we characterize the equilibrium under three scenarios i price only competition ii product only competition and iii price and product competition the results reveal the interplay between a key marketing lever price and the firm s ability to offer products that generate less satiation in particular we show that when a firm becomes more efficient at reducing satiation its competitor may benefit if competition is on product only but not if it is on price and product we also find that when satiation effects are not managed a firm s profit may be significantly reduced while a strategic competitor can largely benefit this paper was accepted by yossi aviv operations management

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

dynamic pricing strategies with reference effects we consider the dynamic pricing problem of a monopolist firm in a market with repeated interactions where demand is sensitive to the firm s pricing history consumers have memory and are prone to human decision making biases and cognitive limitations as the firm manipulates prices consumers form a reference price that adjusts as an anchoring standard based on price perceptions purchase decisions are made by assessing prices as discounts or surcharges relative to the reference price in the spirit of prospect theory we prove that optimal pricing policies induce a perception of monotonic prices whereby consumers always perceive a discount respectively surcharge relative to their expectations the effect is that of a skimming or penetration strategy the firm s optimal pricing path is monotonic on the long run but not necessarily at the introductory stage if consumers are loss averse we show that optimal prices converge to a constant steady state price characterized by a simple implicit equation otherwise the optimal policy cycles the range of steady states is wider the more loss averse consumers are steady state prices decrease with the strength of the reference effect and with customers memory all else equal offering lower prices to frequent customers may be suboptimal however if these are less sensitive to price changes than occasional buyers if managers ignore such long term implications of their pricing strategy the model indicates that they will systematically price too low and lose revenue our results hold under very general reference dependent demand models

confronting the environmental kuznets curve t he environmental kuznets curve posits an inverted u relationship between pollution and economic development kuznets s name was apparently attached to the curve by grossman and krueger 1993 who noted its resemblance to kuznets s inverted u relationship between income inequality and development in the first stage of industrialization pollution in the environmental kuznets curve world grows rapidly because people are more interested in jobs and income than clean air and water communities are too poor to pay for abatement and environmental regulation is correspondingly weak the balance shifts as income rises leading industrial sectors become cleaner people value the environment more highly and regulatory institutions become more effective along the curve pollution levels off in the middle income range and then falls toward pre industrial levels in wealthy societies the environmental kuznets curve model has elicited conflicting reactions from researchers and policymakers applied econometricians have generally accepted the basic tenets of the model and focused on measuring its parameters their regressions typically fitted to cross sectional observations across countries or regions suggest that air and water pollution increase with development until per capita income reaches a range of 5000 to 8000 when income rises beyond that level pollution starts to decline as shown in the conventional ekc line in figure 1 in developing countries some policymakers have interpreted such results as conveying a message about priorities grow first then clean up numerous critics have challenged the conventional environmental kuznets curve both as a representation of what actually happens in the development process and as a policy prescription some pessimistic critics argue that crosssectional evidence for the environmental kuznets curve is nothing more than a

dynamic quality policies with reference quality effects abstractdynamic pricing policies with reference price demand have been intensely analysed less studied are dynamic quality policies with reference quality demand this article studies the dynamic quality policy of a firm whose consumers use a reference point in their decision making in line with the principles of behavioural economics more specifically i consider reference quality formation in an optimal control setting by solving on the basis of pontryagin s maximum principle i obtain analytical solutions to the optimal quality policy the managerial implications of quality reference for dynamic quality policy are discussed

uncertainty shocks asset supply and pricing over the business cycle this article estimates a business cycle model with endogenous financial asset supply and ambiguity averse investors firms shareholders choose not only production and investment but also capital structure and payout policy subject to financial frictions an increase in uncertainty about profits lowers stock prices and leads firms to substitute away from debt as well as reduce shareholder payout this mechanism parsimoniously accounts for the postwar comovement in investment stock prices leverage and payout at both business cycle and medium term cycle frequencies ambiguity aversion permits a markov switching var representation of the model while preserving the effect of uncertainty shocks on the time variation in the equity premium

are markets with loss averse consumers more sensitive to losses behavioral pricing and revenue management aim to incorporate realistic consumer behavior into firms pricing and inventory models the key input to these models is market demand which is often assumed to inherit the characteristics of consumer behavior as when for example one assumes that a market consisting of loss averse consumers is more responsive to losses than to gains yet market demand and consumer behavior need not be related and so we argue that approach to modeling market demand is misguided this paper proposes an approach that accounts for the heterogeneity in consumer valuation we aggregate the demand of individual loss averse consumers to obtain market demand and show that market demand may be more responsive to gains or losses or it may be equally responsive our results have profound implications not only for how best to characterize the market demand of behaviorally biased consumers but also for determining the firm s optimal pricing policy this paper was accepted by serguei net

nonparametric panel data model for crude oil and stock market prices in net oil importing countries abstract this paper introduces an innovative nonparametric panel data approach to model the long run relationship between the monthly oil price index and stock market price indices of ten large net oil importing countries namely the united states japan china south korea india germany france singapore italy and spain in the proposed model we allow the coefficient on the oil price index to be a time varying function which evolves over time in a way that is assumed to be unknown we also allow the common trend function to evolve over time as well as extending the model further to incorporate country specific trend functions we employ a data driven local linear method to estimate these time varying trend and coefficient functions the results show that despite being largely positive there are several downward trends reflecting the aftermath of the iraq war and the recent unprecedented drop in the oil price overall we find that the nonparametric panel data model better captures the way in which the underlying stock oil price relationship has evolved over time in comparison to the point estimates of the parametric counterpart moreover we find that stock market fundamentals play a significant role in determining the oil stock price relationship our findings have important implication for policymakers and financial speculators

globalization and its challenges rudi was born and grew up in krefeld germany he was an undergraduate at the university of geneva and completed his ph d at the university of chicago in 1971 which is where we met he was a student of robert mundell and both the subject matter the development of the mundell fleming model and the elegance and insights of his early work reflected mundell s influence he taught at the university of rochester and at the university of chicago before accepting an offer from mit in 1975

the welfare cost of business cycles revisited finite lives and cyclical variation in idiosyncratic risk abstract this paper investigates the welfare costs of business cycles in a heterogeneous agent overlapping generations economy which is distinguished by idiosyncratic labor market risk aggregate variation arises both in terms of aggregate productivity shocks and countercyclical variation in the volatility of idiosyncratic shocks based on both aggregate data and microeconomic data from the panel study on income dynamics we find the welfare benefits of eliminating aggregate variation to be large an order of magnitude larger than those originally documented by lucas 1987 the key difference is countercyclical variation in idiosycratic risk which both amplifies the welfare cost of aggregate productivity shocks and imposes a cost of its own the magnitude of these effects increases non linearly in risk aversion our results therefore are consistent with the increasingly popular notion that distributional effects are an important aspect of understanding the welfare cost of business cycles

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

optimal design of social comparison effects setting reference groups and reference points in this paper we study how social planners should exploit social comparisons to pursue their objectives we consider two modes of social comparison referred to as behind averse and ahead seeking behaviors depending on whether individuals experience a utility loss from underperforming or a utility gain from overperforming relative to their peers modeling social comparison as a game between players we find that ahead seeking behavior leads to output polarization whereas behind averse behavior leads to output clustering a social planner can mitigate these effects in two ways i by providing the full reference distribution of outputs instead of an aggregate reference point based on the average output and ii by assigning players into uniform rather than diverse reference groups social planners may thus need to tailor the reference structure to the predominant mode of social comparison and their objective a performance focused social planner may set the reference structure so as to maximize the output of either the top or the bottom player depending on whether she puts greater marginal weight to larger or smaller outputs when the social planner also cares about utility she faces a dilemma because performance optimization may not be aligned with utility maximization inevitably the social planner will have to confront equity issues because better performance may not reflect greater effort or greater ability this paper was accepted by serguei netessine operations management

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

turnpike properties in a finite horizon differential game dynamic duopoly with sticky prices the authors study the equilibrium price paths of a finite horizon dynamic duopoly model in which the market price does not have to adjust instantaneously in response to changes in the quantity supplied a complete analysis of the feedback nash equilibrium of a finite horizon linear quadratic differential game with a control constraint is presented two equilibrium price paths are identified and it is shown that they both remain close to the infinite horizon globally asymptotically stable stationary equilibrium except for some initial and final time copyright 1990 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

the reference effects on a retailer s dynamic pricing and inventory strategies with strategic consumers we consider a retailer that sells the same or different versions of the product season after season at the beginning of each season stage 1 the retailer places an order and sells the product at the full price as the sales unfold the retailer has an opportunity to mark down the price stage 2 which creates an incentive for strategic consumers to delay their purchases for price discount however consumers do not know the markdown price exactly when they time their purchases instead they learn from the retailer s past prices and form their estimate of the markdown price called the reference price to decide if they purchase at the full price or wait for the markdown in the current selling season we characterize the properties of the optimal ordering and markdown decisions and show that markdowns if adopted appropriately do not necessarily destroy the stability of a business even in the presence of strategic consumers furthermore the consumers reference exhibits a mean reverting pattern under certain conditions that is the reference fluctuates around a mean value reflecting the practice of most stable businesses we conduct numerical studies to investigate the impact of consumer learning about the reference price and various system parameters on the retailer s optimal strategies and profitability in the presence of strategic consumers

multiattribute loss aversion and reference dependence evidence from the performing arts industry we study the prevalence of multiattribute loss aversion and reference effects in a revenue management setting based on data of individual level purchases over a series of concert performances the reference dependence that drives consumer choice is not only based on the price but also on observed sales as a fraction of the seating capacity during their past visits we find that consumers suffer from loss aversion on both prices and seats sold consumers incur significant utility loss when prices are above their references or when the actual seat sales are lower than their references we suggest pricing policies that can address consumer decisions driven by such reference dependence and loss aversion this paper was accepted by vishal gaur operations management

price coordination in distribution channels a dynamic perspective abstract in this study we investigate two important questions related to dynamic pricing in distribution channels i are coordinated pricing decisions efficient in a context where prices have carry over effects on demand ii should firms practice a skimming or a penetration strategy if they choose to coordinate or to decentralize their activities to answer these questions we consider a differential game that takes place in a bilateral monopoly where the past retail prices paid by consumers contribute to the building of a reference price the latter is used by consumers as a benchmark to evaluate the value of the product and by firms to decide whether to adopt a skimming or a penetration strategy we then compute and compare strategies total channel profits and individual profits under vertical integration and decentralization at steady state and along the optimal time paths one of our main findings states that for some values of the initial reference price there is a time interval where channel decentralization performs better than coordination during this transition period at least one of the channel members could be tempted to end his cooperation especially if he is not farsighted and if there are no binding agreements with the other channel partners

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

selecting optimal selling format of a product in b2c online auctions with boundedly rational customers abstract the advancement of internet technology has enabled new formats for selling products in the b2c online auctions at present on the major online auction sites there exist three popular selling formats namely the posted price pure auction and buy price auction formats it is an important decision problem for a firm to select the most profitable format to sell its products through the internet the customer behavior is of course a crucial element of the decision process to the best of our knowledge most models available today assume that customers are perfectly rational to better understand the decision process in this paper we incorporate the concept of bounded rationality into consideration we first present a behavior choice function to characterize the behavior of the customers with bounded rationality then corresponding to each selling format we construct a revenue model based on the bounded rationality for analysis finally we conduct some elaborate computational experiments to investigate the performance of each revenue model for developing new managerial insights our computational results clearly demonstrate how the bounded rationality of customer behavior affects the choice of a preferable selling format for a b2c firm in an online auction

dynamic duopolistic competition with sticky prices the authors study duopolistic competition in a homogeneous good through time under the assumption that its current desirability is an exponentially weighted function of accumulated past consumption this implies that the current price of the good does not decline by as much to accommodate any given level of current consumption our an alysis is conducted in terms of a differential game it is found that the equilibrium price corresponding to the open loop nash equilibriu m strategies approaches the static cournot equilibrium price while th e equilibrium price corresponding to the closed loop nash equilibrium strategies which are subgame perfect approaches a price below it copyright 1987 by the econometric society

high price or low price an experimental study on a markdown pricing policy abstract this study examines whether strategic customers behavioral patterns remain consistent in different pricing scenarios under a markdown pricing policy these customers decision patterns have been widely discussed because they significantly influence the expected monetary output contrary to rational assumptions the behavioral research literature indicates that customers behavioral biases manifest in their reference dependency risk and loss attitudes and fill rate misperceptions however the relationship between behavioral biases and various pricing scenarios has not been carefully examined accordingly we conducted laboratory experiments to observe customers behavioral performance in a series of pricing scenarios to provide pricing suggestions for sellers our experimental results demonstrate that behavioral factors reflecting risk and loss attitudes as well as reference dependency can clearly describe customers behavioral biases meanwhile our estimation shows that the degrees of risk and loss attitude are not constant but depend on price settings the lower the full price in the initial period the higher the degrees of aversion to both risk and loss given such behavioral patterns we suggest that sellers should set their full prices lower than the normative value when the fill rate in period two is low and set them higher than the normative value when the fill rate in period two is high

revenue management with partially refundable fares we introduce and analyze an intertemporal choice model where customer valuations are uncertain and evolve over time the model leads directly to the study of call options on capacity that are similar to partially refundable fares we show that the capacity provider earns significantly higher revenues by selling real options on capacity than on low to high pricing we also investigate the social implications and show that the use of options is both socially optimal and socially efficient

stability and chaos in demand based pricing under social interactions abstract demand based pricing is often used to moderate demand fluctuations so as to level resource utilization and increase profitability however such pricing policies may not be effective when customers purchase decisions are influenced by social interactions this paper investigates the demand dynamics under a demand based pricing policy of a frequently purchased service when social interactions are at work customers are heterogeneous and adaptively forward looking existing customers re purchase decisions are based on adaptively formed price expectations and reservation prices potential customers are attracted through social interactions with existing customers the demand process is characterized by a two dimensional dynamical system it is shown that the equilibrium demand can be unstable for a given reservation price distribution we first analyze the stability of the equilibrium demand under various scenarios of social interactions and customers adaptively forward looking behavior and then characterize their dynamics using the bifurcation plots lyapunov exponents and return maps the results indicate that the demand process can be stable periodic or chaotic the study shows that the intended effect of a demand based pricing policy may be offset by customers adaptively forward looking behavior under the influence of social interactions in fact the interplay of these factors may even lead to chaotic demand dynamics the result highlights the complex dynamics produced by a simple demand price mechanism under social interactions for a demand based pricing strategy to be effective companies must take social interactions into account

a comparative analysis of reference price models the effect of reference price on brand choice decisions has been well documented in the literature researchers however have differed in their conceptualizations and therefore in their modeling of reference price in this article we evaluate five alternative models of reference price of which two are stimulus based i e based on information available at the point of purchase and three that are memory based i e based on price history and or other contextual factors we calibrate the models using scanner panel data for peanut butter liquid detergent ground coffee and tissue to account for heterogeneity in model parameters we employ a latent class approach and select the best segmentation scheme for each model the best model of reference price is then selected on the basis of fit and prediction as well as on the basis of parsimony in cases where the fits of the models are not very different in all four categories we find that the best reference price model is a memory based model namely one that is based on the brand s own price history in the liquid detergent category however we find that one of the stimulus based models namely the current price of a previously chosen brand also performs fairly well we discuss the implications of these findings

ambiguity aversion asset prices and the welfare costs of aggregate fluctuations under the hypothesis that aggregate u s consumption is random and more importantly viewed as ambiguous by consumers we examine the implications for asset prices and for how consumption uctuations in uence consumer welfare first considering a simple mehra prescott style endowment economy with a representative agent facing consumption uctuations calibrated to match u s data we study to what extent ambiguity aversion can deliver asset prices that are consistent with data a high return on equity and a low return on riskfree bonds for some conflgurations of preference parameters a discount factor a degree of relative risk aversion and a measure of ambiguity aversion we flnd that it can we then use these parameter conflgurations to investigate how much consumers would be willing to pay to reduce endowment uctuations to zero thus delivering a lucas style welfare cost of uctuations these costs turn out to be very large consumers can be willing to pay over 10 of consumption in permanent terms

the time series properties of aggregate consumption implications for the costs of fluctuations the properties of the stochastic process followed by aggregate consumption affect the estimates of the costs of fluctuations this paper pursues two approaches to modeling consumption dynamics and measuring how much society dislikes fluctuations one statistical and one economic the statistical approach estimates the properties of consumption and calculates the costs of having consumption fluctuating around its mean growth the paper finds that persistence is a crucial determinant of the costs and that the high persistence in the data severely distorts conventional measures it shows how to compute valid estimates and confidence intervals the economic approach uses a calibrated model of optimal consumption and measures the costs of eliminating income shocks this uncovers a further cost of uncertainty through its impact on precautionary savings and investment the two approaches lead to costs of fluctuations that are higher than the common wisdom between 0 5 and 5 of per capita consumption jel e32 e21 e60

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

the informational aspect of the group buying mechanism abstract this paper studies the group buying mechanism from a dynamic perspective we consider a seller that offers a product in the form of group buying priced low but uncertain and spot purchasing priced high but guaranteed in the case of group buying the information associated with the number of participating customers is updated in the middle of the sale customers are assumed to be strategic with a time dependent utility in addition to choosing between spot purchasing and group buying customers could choose to delay their decisions until the information update we characterize the customer behavior within a rational expectations framework we then consider the effect of information and demand dynamics our results show that whereas an improvement in information quality has a positive effect on customer surplus and the group buying success rate the effect of inter temporal demand correlation is mixed we also discuss the seller s profit maximization problem and derive the condition to be satisfied at the optimal group size

explicit solutions of optimization models and differential games with nonsmooth asymmetric reference price effects models in marketing with asymmetric reference effects lead to nonsmooth optimization problems and differential games which cannot be solved using standard methods in this study we introduce a new method for calculating explicitly optimal strategies open loop equilibria and closed loop equilibria of such nonsmooth problems application of this method to the case of asymmetric reference price effects with loss aversive consumers leads to the following conclusions 1 when the planning horizon is infinite after an introductory stage the optimal price stabilizes at a steady state price which is slightly below the optimal price in the absence of reference price effects 2 the optimal strategy is the same as in the symmetric case but with the loss parameter determined by the initial reference price 3 competition does not change the qualitative behavior of the optimal strategy 4 adopting an appropriate constant price strategy results in a minute decline in profits

efficient algorithms for the dynamic pricing problem with reference price effect we analyze a finite horizon dynamic pricing model in which demand at each period depends on not only the current price but also past prices through reference prices a unique feature but also a significant challenge in this model is the asymmetry in reference price effect which implies that the underlying optimization problem is nonsmooth and no standard optimization methods can be applied we identify a few key structural properties of the problem which enable us to develop strongly polynomial time algorithms to compute the optimal prices for several plausible scenarios we complement our exact algorithms by proposing an approximation heuristic and provide an upper bound on the optimal objective value finally we conduct numerical experiments to study the optimal price path and demonstrate the value of dynamic pricing when demands are seasonal we further compare numerically one of the exact algorithms with the heuristic and offer managerial suggestions this paper was accepted by yinyu ye optimization

an exploration of the effects of pessimism and doubt on asset returns the subjective distribution of growth rates of aggregate consumption is characterized by pessimism if it is first order stochastically dominated by the objective distribution uniform pessimism is a leftward translation of the objective distribution of the logarithm of the growth rate the subjective distribution is characterized by doubt if it is mean preserving spread of the objective distribution pessimism and doubt both reduce the riskfree rate and thus can help resolve the riskfree rate puzzle uniform pessimism and doubt both increase the average equity premium and thus can help resolve the equity premium puzzle

multi period pricing in the presence of competition and social influence abstract this paper examines single and dynamic pricing policies of two competing firms over two periods in the presence of social influence assuming two firms adopt the same pricing policy we find that under either pricing policy firm profits always decrease with the degree of social influence firms prefer dynamic pricing policy when social influence is either relatively weak or sufficiently strong for firms under dynamic pricing policy to set zero prices in the first period otherwise single pricing policy is more preferable the conclusions are similar when the market size varies over periods except that dynamic pricing policy is always more profitable if the market size in period 2 is sufficiently large we have further compared the two pricing policies with posted pricing policy the results show that dynamic pricing policy dominates when social influence is relatively weak while posted pricing policy dominates when social influence is sufficiently strong because of the synergy between social influence and the reference price effect finally when each firm freely chooses either single or dynamic pricing policy we find that if the degree of social influence is relatively small two asymmetric equilibria exist where two firms adopt different pricing policies if the degree of social influence is very large however the unique equilibrium is both firms adopting dynamic pricing policy these findings provide important implications for firms to make more informed pricing decisions in an increasingly competitive environment with strong social influence

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

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

searching for a kuznets curve in environmental efficiency using kernel estimation abstract the paper constructs environmental efficiency indexes for a sample consisting of high and low income countries using nonparametric production frontier techniques and then establishes an environmental kuznets relationship for environmental efficiency by nadaraya watson kernel estimation methodology

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

dynamic pricing in the presence of inventory considerations research overview current practices and future directions the benefits of dynamic pricing methods have long been known in industries such as airlines hotels and electric utilities where the capacity is fixed in the short term and perishable in recent years there has been an increasing adoption of dynamic pricing policies in retail and other industries where the sellers have the ability to store inventory three factors contributed to this phenomenon 1 the increased availability of demand data 2 the ease of changing prices due to new technologies and 3 the availability of decision support tools for analyzing demand data and for dynamic pricing this paper constitutes a review of the literature and current practices in dynamic pricing given its applicability in most markets and its increasing adoption in practice our focus is on dynamic intertemporal pricing in the presence of inventory considerations

an investigation of reference price segments abstract empirical research on reference price has typically assumed that consumers use either an internal reference price irp or an external reference price erp but not both in brand choice decisions in this article the authors assume that consumers use both irp and erp but may consider one of them more salient than the other the authors develop a model that segments consumers on the basis of the differences in the importance they assign to each type of reference price as well as in their brand preferences and responses to marketing mix variables the authors calibrate the model on data for four categories liquid detergents ketchup tissue and yogurt in all four categories the proposed model performs significantly better than the one that assumes that consumers use either irp or erp exclusively the authors discuss the managerial implications of this finding

an index of loss aversion to a considerable extent risk aversion as it is commonly observed is caused by loss aversion several indexes of loss aversion have been proposed in the literature the one proposed in this paper leads to a clear decomposition of risk attitude into three distinct components basic utility probability weighting and loss aversion the index is independent of the unit of payment the main theorem shows how the indexes of different decision makers can be compared through observed choices

pricing and manufacturing decisions when demand is a function of prices in multiple periods in most deterministic manufacturing decision models demand is either known or induced by pricing decisions in the period that the demand is experienced however in more realistic market scenarios consumers make purchase decisions with respect to price not only in the current period but also in past and future periods we model a joint manufacturing pricing decision problem accounting for that portion of demand realized in each period that is induced by the interaction of pricing decisions in the current period and in previous periods we formulate a mathematical programming model and develop solution techniques we identify structural properties of our models and develop closed form solutions and effective heuristics for various special cases of our models finally we conduct extensive computational experiments to quantify the effectiveness of our heuristics and to develop managerial insights

markdown or everyday low price the role of behavioral motives we study a seller s optimal pricing and inventory strategies when behavioral nonpecuniary motives affect consumers purchase decisions in particular the seller chooses between two pricing strategies markdown or everyday low price and determines the optimal prices and inventory level two salient behavioral motives that impact consumers purchase decisions and the seller s optimal strategies are anticipated regret and misperception of product availability regret arises when a consumer initially chooses to wait but encounters stockout later or when the consumer buys the product at the high price but realizes that the product is still available at the markdown price in addition consumers often perceive the product s future availability to be different than its actual availability we determine and quantify that both regret and availability misperception have significant operational and profit implications for the seller for example ignoring these behavioral factors can result in up to 10 profit

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

manufacturer retailer contracting with asymmetric information on retailer s degree of loss aversion abstract in a recent paper wang c webster s 2007 channel coordination for a supply chain with a risk neutral manufacturer and a loss averse retailer decision sciences 38 3 361 389 the authors study a supply chain consisting of a risk neutral manufacturer and a loss averse retailer and show that the supply chain can be coordinated by three contracts buy back bb gain loss sharing gl and gain loss sharing and buy back glb they assume that the retailer s degree of loss aversion is common knowledge however this assumption cannot reflect real situations since in the real industry one party s degree of loss aversion is usually unknown by other parties in the present paper we propose a principal agent model assuming the retailer s degree of loss aversion to be asymmetric information within the principal agent framework we obtain the following results 1 an optimal mgl modified gl contract menu which is based on the gl contract studied in wang and webster 2007 is derived for the manufacturer the principal by mechanism design theory 2 under the mgl contract menu information asymmetry lowers the production quantity decreases the manufacturer s profit and deteriorates supply chain performance while increasing the retailer s utility 3 the mgl contract menu can coordinate the supply chain with asymmetric information in an implementable way if the wholesale price is endogenously determined by the manufacturer and its lower bound is 0

a differential game design of watershed pollution management under ecological compensation criterion abstract the watershed ecological compensation is used as a policy instrument in china in order to reduce water pollution and attain watershed sustainability in this paper we construct a differential game between a local government and a profit maximizing local firm with one competitor in a watershed ecological compensation system then the optimal dynamic strategy is obtained by applying maximum principle finally we investigate the influence of shadow prices on control variables and firm s output in three different cases this study focuses on how to reach a balance between the sustainable development of local economy and the effective protection of water resources from an ecological perspective for the local government as well as on how to maximize the profit of the local firm in an ecological compensation system

technical note personalized dynamic pricing of limited inventories prior work has investigated time and inventory level dependent pricing of limited inventories with finite selling horizons we consider a third dimension in addition to time and inventory level that the firms can use in setting their prices the information that the firm has at the individual customer level an arriving customer provides a signal to the firm which is an imperfect indicator of the customer s willingness to pay and the firm makes a personalized price offer depending on the signal inventory level and time we consider two different models full personalization and partial personalization in the full personalization model the firm charges any price it wishes given the customer signal while in the partial personalization model the firm can charge one of two prices we find that a mere correlation between the signals and customers willingness to pay is not sufficient to ensure intuitive relationships between the signal and the optimal prices we determine a stronger condition which leads to several structural properties including the monotonicity of the optimal price with respect to the signal in the full personalization model for the partial personalization model we show that the optimal pricing policy is of threshold type and that the threshold is monotonic in the inventory level and time