optimal promotion planning depth and frequency for a two stage supply chain under markov switching demand abstract in considering the retailer supplier supply chain this paper analyzes how a retailer reasonably decides both the depth and frequency of the price discount promotion including or excluding a supplier s inventory decision assuming that the promotion frequency used by the retailer is probabilistic we model a promotion inventory decision under an ar 1 demand with a markov switching promotion regime after obtaining the optimal promotion plan our analysis also considers the behavior of the optimal promotion decision the retailer s price format selection either an every day low price policy edlp or a promotion policy hilo and the impact of information sharing of promotion status on the system s performance our results suggest that a retailer tends to overpromote if inventory cost is excluded in its promotion decision that increasing the market share is a preferable action for both the retailer and the supplier that total margin and price elasticity play an important role in selecting the price format and that the profitability for a supplier of sharing promotion information depends on the transition probabilities of the markov switching regime

optimal dynamic pricing of inventories with stochastic demand over finite horizons in many industries managers face the problem of selling a given stock of items by a deadline we investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm s objective is to maximize expected revenues examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry which markets space such as seats on airline flights cabins on vacation cruises and rooms in hotels that become worthless if not sold by a specific time we formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp price as a function of the stock level and the length of the horizon for a particular exponential family of demand functions we find the optimal pricing policy in closed form for general demand functions we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity finally we extend our results to the case where demand is compound poisson only a finite number of prices is allowed the demand rate is time varying holding costs are incurred and cash flows are discounted the initial stock is a decision variable and reordering overbooking and random cancellations are allowed

evaluating greening farm policies a structural model for assessing agri environmental subsidies this study uses a structural econometric model to evaluate the impacts of support from a european union agri environmental program designed to reduce nutrient pollution from agricultural land drawing on a representative sample of individual grain farms we first quantify the effects of agri environmental payments on farms decisions on land allocation and on fertilizer use we then combine the predicted land allocation and fertilizer use with environmental production functions to quantify the impact on nutrient loading finally we assess the monetary value of reduced nutrient pollution drawing on a recent valuation study

on monoculture and the structure of crop rotations an issue when seeking to identify rotation choice is persistence in yield enhancement and input saving carry over effects focusing on carry over length and the monoculture decision we use quasi convexity of choice functions to develop price independent and price dependent principles concerning rotation structure iowa corn soybean rotation data suggest corn has one year memory for corn soybeans in the prior year is yield increasing 16 5 bu ac and nitrogen saving 51 lb ac the hypothesis that soybean has two year memory cannot be rejected corn in the prior year two years increases yield by 7 bu ac 11 6 bu ac we simulate to find price and practice subsidy levels that support different rotations

a multivariate sample selection model estimating cigarette and alcohol demands with zero observations heckman s sample selection model is generalized to the multivariate case and used to estimate demands for cigarettes beer and wine by individuals in the united states the specification allows correlations between the error terms of multiple selection and level equations and nests the popular bivariate sample selection model and two part model empirical results suggest that the proposed model performs better than the restricted specifications differentiated effects of variables on probabilities and levels of consumption also suggest rejection of the tobit system gender differences are present and demographic variables are more important than income in determining consumption of cigarettes beer and wine

optimal dynamic pricing for perishable assets with nonhomogeneous demand we consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon customers whose reservation price distribution changes over time arrive according to a nonhomogeneous poisson process we show that at any given time the optimal price decreases with inventory we also identify a sufficient condition under which the optimal price decreases over time for a given inventory level this sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time in addition to shedding managerial insight these structural properties enable efficient computation of the optimal policy numerical studies are conducted to show the revenue impact of dynamic price policies price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price for the former our examples show that using optimal dynamic optimal policies achieves 2 4 7 3 revenue improvement over the optimal single price policy for the latter the revenue increase can be as high as 100 these results explain why yield management has become so essential to fashion retailing and travel service industries

will dynamic pricing outperform theoretical analysis and empirical evidence from o2o on demand food service market abstract this study attempts to identify the pricing strategy of three most commonly used on demand food service platforms in china based on detailed information of more than 240 000 orders and further evaluates the impact of pricing strategy on platform performance we find that some platforms adopt dynamic pricing strategies while other platforms adopt static pricing strategies considering the unique structure of the o2o on demand food service market in china we develop a dyadic two sided market theory and demonstrate that compared with static pricing strategies dynamic pricing strategies perform better consistent with our theory our empirical analysis also suggests that platforms adopting dynamic pricing strategies have a significantly higher level of demand compared with platforms adopting static strategies in addition our results indicate the importance of delivery speed red envelopes and ratings in promoting demand

optimal monopolist pricing under demand uncertainty in dynamic markets we examine pricing policy for a monopolist facing uncertain demand in a market characterized by dynamics on the demand side such as diffusion or saturation effects and or on the cost side experience curve effects our model explicitly incorporates the impact of demand uncertainty and thus allows us to analyze the implications of uncertainty on the optimal price path by contrasting the stochastic policy with the corresponding deterministic policy we begin with an analysis of the general model and then focus on several special cases based on well known demand specifications to gain more specific insights and to suggest directional guidelines for dynamic pricing decisions in an uncertain environment in general the interaction among uncertainty demand and or cost dynamics and firm s discount rate thus farsighted firms operating under dynamic market conditions with high demand uncertainty such as high tech companies with innovative products for consumer or industrial markets should attach partic

quasi and simulated likelihood approaches to censored demand systems food consumption by food stamp recipients in the united states a quasi maximum likelihood estimator is proposed and applied to a censored translog demand system for foods using a sample of food stamp recipients in the united states the procedure produces remarkably close parameter and elasticity estimates to those of the simulated maximum likelihood procedure a two step procedure is also considered but it produces different elasticities demands are found to be price elastic for pork and fish but price inelastic for all other food products gross complementarity and net substitutability are obvious but these cross price effects are much less pronounced than own price and total food expenditure effects copyright 2003 oxford university press

retail pricing and clearance sales sellers of new products are faced with having to guess demand conditions to set price appropriately but sellers are able to adjustprice over time and to learn from past mistakes additionally it is not necessary that all goods be sold with certainty it is sometimes better to set a high price and to risk no sale this process is modeledto explain retail pricing behavior and the time distribution of transactions prices start high and fall as a function of time on theshelf the initial price and rate of decline can be predicted and depends on thinness of the market the proportion of customers who are window shoppers and other observable characteristics copyright 1986 by american economic association

simultaneously learning and optimizing using controlled variance pricing price experimentation is an important tool for firms to find the optimal selling price of their products it should be conducted properly since experimenting with selling prices can be costly a firm therefore needs to find a pricing policy that optimally balances between learning the optimal price and gaining revenue in this paper we propose such a pricing policy called controlled variance pricing cvp the key idea of the policy is to enhance the certainty equivalent pricing policy with a taboo interval around the average of previously chosen prices the width of the taboo interval shrinks at an appropriate rate as the amount of data gathered gets large this guarantees sufficient price dispersion for a large class of demand models we show that this procedure is strongly consistent which means that eventually the value of the optimal price will be learned and derive upper bounds on the regret which is the expected amount of money lost due to not using the optimal price numerical tests indicate that cvp performs well on different demand models and time scales this paper was accepted by assaf zeevi stochastic models and simulation

the timing and magnitude of retail store markdowns evidence from weekends and holidays we examine daily prices of eight goods at seventeen retail stores collected in ann arbor michigan over a four month period from november 1 to february 28 we focus on weekly and seasonal price patterns and on the frequency of price markdowns or sales there were frequent markdowns in the intensive shopping period prior to christmas and a tendency for such sales to occur on weekends we interpret these findings as evidence that a significant number of markdowns are timed to occur when shopping intensity is exogenously high we complement the imperfect information based motives for sales in the literature by contributing an additional element based on the role of bulk shopping and increasing returns in the shopping technology

the impact of customer returns on pricing and order decisions abstract in this paper we address the simultaneous determination of price and inventory replenishment when customers return product to the firm we examine cases when the quantity of returned product is a function of both the quantity sold and the price in single and multi period problems with and without uncertainty in demand we derive results for optimal prices and order quantities and discuss how the firm should change price and inventory quantities in order to mitigate the negative effects of returns from customers

optimal discounting and replenishment policies for perishable products abstract we consider a retailer selling a perishable product with short shelf life and uncertain demand facing these key decisions a whether to discount old er items b how much discount to offer and c what should be the replenishment policy in order to better understand the impact of consumer behavior and shelf life on these decisions we consider four models in model a the product has a shelf life of two periods and the retailer decides whether or not to offer a discount the amount of discount is exogenous and assumed to be large enough so that all the customers prefer the old product to the new one when a discount is offered based on several numerical examples we find that a threshold discounting policy in which a discount is offered if and only if the inventory of old product is below a threshold is optimal in model b the retailer also decides how much discount to offer model c extends model b and considers a new pool of customers who are willing to purchase from the retailer when a discount is offered in both models b and c the product has a shelf life of two periods while model d explores what happens with longer shelf life we analyze and compare these models to present different managerial insights

optimal dynamic pricing for expanding networks this paper analyzes the dynamic pricing decision of a monopolist marketing a new product or service whose consumption value increases with the expansion of the network of adopters we characterize an optimal pricing strategy which maximizes the present value of the monopolist s profits subject to the dynamics of the demand for network access these dynamics depend among other factors on the current price and consumer anticipations about future network growth we examine the effects of changes in the growth anticipations and the discount rate on the optimal equilibrium access price and network size it is shown that higher growth anticipations and a lower discount rate result in a lower equilibrium price and a larger network

pricing competition with inventory considerations in a hazard rate prone market of durables abstract this paper addresses bertrand type pricing competition between two firms producing partially differentiated durables over a finite planning horizon the demand for durables characterized by increasing returns of scale to a price reduction is led by the hazard rate while the effect of inventories on pricing of non durables is widely recognized the management and marketing literature typically overlooks this effect in regard to horizontally competing firms for durables in this paper we show that the pricing trajectory of durables may significantly alter when inventory dynamics are accounted for in particular the price may hike upwards before dropping gradually grow or even stay at the same level over the entire product life while it would only decline if inventories and related costs are disregarded furthermore the well known optimal pricing strategy of following the pattern of sales does not necessarily confirm even for symmetric equilibria when the competing firms have either an inventory surplus or shortage

estimation of censored demand equations from large cross section data the article develops an alternative econometric methodology to estimate a system of censored demand equations using a large cross section data from colombian urban households the approach preserves the behavioralinformation expressed by zero expenditures and conforms with the requirements imposed by consumer theory in a way consistent with the random utility hypothesis we motivate the choice of the tobit modelas a statistical representation of consumer behavior and introduce the methodology by specifying the aids model modified according to both a translating and scaling demographic transformation we propose to estimate each demand equation in unrestricted form using the jackknife technique we then recover the demand parameters imposing the cross equations restrictions by using minimum distance estimation the empirical results of the censored demand system for specific households of policy relevance are reported copyright 2000 oxford university press

dynamic pricing of inventory capacity with infrequent price changes we consider a problem of dynamically pricing a single product sold by a monopolist over a short time period if demand characteristics change throughout the period it becomes attractive for the company to adjust price continuously to respond to such changes i e price discriminate intertemporally however in practice there is typically a limit on the number of times the price can be adjusted due to the high costs associated with frequent price changes if that is the case instead of a continuous pricing rule the company might want to establish a piece wise constant pricing policy in order to limit the number of price adjustments such a pricing policy which involves optimal choice of prices and timing of price changes is the focus of this paper we analyze the pricing problem with a limited number of price changes in a dynamic deterministic environment in which demand depends on the current price and time and there is a capacity inventory constraint that may be set optimally ahead of the selling season the arrival rate can evolve in time arbitrarily allowing us to model situations in which prices decrease increase or neither we consider several plausible scenarios where pricing and or timing of price changes are endogenized various notions of complementarity single crossing property supermodularity and total positivity are explored to derive structural results conditions sufficient for the uniqueness of the solution and the monotonicity of prices throughout the sales period furthermore we characterize the impact of the capacity constraint on the optimal prices and the timing of price changes and provide several other comparative statics results additional insights are obtained directly from the solutions of various special cases

a new product growth for model consumer durables this article originally appeared in management science january 1969 volume 15 number 5 pp 215 227 published by the institute of management sciences a growth model for the timing of initial purchase of new products is developed and tested empirically against data for eleven consumer durables the basic assumption of the model is that the timing of a consumer s initial purchase is related to the number of previous buyers a behavioral rationale for the model is offered in terms of innovative and imitative behavior the model yields good predictions of the sales peak and the timing of the peak when applied to historical data a long range forecast is developed for the sales of color television sets

cyclic pricing by a durable goods monopolist in the model of this paper a monopoly seller of a durable good holds periodic sales as a means of price discrimination a new cohort of consumers enters the market in each period interested in purchasing the good either immediately or after a delay within each cohort consumers vary in their tastes for the good under broad conditions the seller will vary the price over time in most periods he will charge a price just low enough to sell immediately to consumers with a high willingness to pay periodically however he will drop the price far enough to sell to an accumulated group of consumers with a low willingness to pay

optimal policies of yield management with multiple predetermined prices it is a common practice for industries to price the same products at different levels for example airlines charge various fares for a common pool of seats seasonal products are sold at full or discount prices during different phases of the season this article presents a model that reflects this yield management problem the model assumes that 1 products are offered at multiple predetermined prices over time 2 demand is price sensitive and obeys the poisson process and 3 price is allowed to change monotonically i e either the markup or markdown policy is implemented to maximize the expected revenue management needs to determine the optimal times to switch between prices based on the remaining season and inventory major results in this research include 1 an exact solution for the continuous time model 2 piecewise concavity of the value function with respect to time and inventory and 3 monotonicity of the optimal policy the implementation of optimal policies is fairly facile because of the existence of threshold points embedded in the value function the value function and time thresholds can be solved with a reasonable computation effort numerical examples are provided

dynamic pricing models for used products in remanufacturing with lost sales and uncertain quality in this paper we investigate the remanufacturing problem of pricing single class used products cores in the face of random price dependent returns and random demand specifically we propose a dynamic pricing policy for the cores and then model the problem as a continuous time markov decision process we first design a basic model that does not consider the quality uncertainty of cores and then extend our model to incorporate this factor besides proving optimal policy uniqueness and establishing monotonicity results for the optimal policy we also characterize the impact of system parameters on the optimal policies which can provide simple managerial insights finally we use computational experiments to assess the benefits of dynamic pricing compared to static pricing and identify the impacts of specific parameters on the relative merits of dynamic pricing policy

optimal price markup policy for an inventory model with random price fluctuations and option for additional purchase abstract in this paper based on the analysis of empirical data of dealer and retailer prices and sales of cement as a prototype of functional products we develop a probabilistic inventory model for the situation when dealer s selling price fluctuates and affects the retailer s selling price demand is a function of price markup and retailer s purchase price dynamic price markup policy is proposed and optimal length of replenishment cycle and order quantity is obtained concavity of the profit function with respect to price markup is discussed a procurement policy which considers opportunity of purchase at a low price before the end of the optimal replenishment cycle is proposed and compared with other policies algorithm numerical examples sensitivity analysis and managerial insights are presented

modeling heterogeneous farm responses to european union biofuel support with a random parameter multicrop model although there is now widespread evidence of substantial variability in economic agents responses to economic drivers in many applied economics fields this variability has been largely overlooked by econometric agricultural production models this article sets out to fill this gap by providing methodological contributions and empirical results first we consider panel data multicrop models featuring random intercept and slope parameters to account for the heterogeneous responses of crop producers to economic drivers second we show that monte carlo expectation maximization algorithms are particularly well suited to estimating this type of model third based on an application of our empirical modeling framework with a sample of french grain crop producers we demonstrate substantial variability in farmers responses to economic incentives fourth we use the estimated model and a simple statistical calibration procedure to build farm specific simulation models which are then used to evaluate the effects of the rapeseed price increase induced by european union eu biofuel support our simulation results demonstrate that ignoring the variability in the considered farmers responses to the economic incentives results in significant overestimation of the increases in rapeseed yield levels and variable input use levels induced by eu biofuel support as well as significant underestimation of the variability in the congruent increases in rapeseed acreages

demand uncertainty and sales a study of fashion and markdown pricing the theory of clearance sales is expanded and applied to explain why markups markdowns and the frequency of sales of merchandise sold by department stores have increased dramatically in recent years and why they differ across merchandise groups tha major theme of the paper is that the growing role of fashion and product variety is an important reason for these increases and for the differences between merchandise groups the growing importance of fashion is illustrated by documenting the declining use of whites and the increasing use of colors and prints estimates of the effects of imports and technological and demographic changes on markups and markdowns are presented copyright 1988 by american economic association

estimating the environmental impact of land and production decisions with multivariate selection rules and panel data we propose an estimation procedure dealing with multivariate selection and dynamics in land choice and unobserved heterogeneity in structural and crop selection equations the method is applied to a multi output profit function with multiple corner solutions and farm level panel data estimation results reveal that the single selection rule associated with the tobit procedure is rejected in favor of our multivariate selection treatment inconsistent estimates are expected with the tobit procedure or if farmer fixed effects are omitted which can have important consequences for policy recommendations as illustrated in an evaluation of nitrogen runoff elasticities with respect to economic variables copyright 2011 oxford university press

dynamic monopoly pricing under a poisson type uncertain demand this article explores dynamic pricing strategies in the presence of uncertainty diffusion dynamics experience curve effects and a poisson type of uncertainty in the demand are incorporated in a model using the framework of a stochastic control problem the results indicate that the movement of the expected price depends on the relative strength of the contingent effects and the effects of the experience if the direction of the former is opposite to the latter and is substantial enough to dominate it the expected price path will show a pattern different from the one predicted by a deterministic model copyright 1992 by university of chicago press

an approach for developing an optimal discount pricing policy this paper addresses the problem of why and how a seller should develop a discount pricing structure even if such a pricing structure does not alter ultimate demand the situation modeled is most appropriate where the seller s product does not represent a major component of the buyer s final product where the demand for the product is derived or where the price is only one of many factors considered in making a purchase decision a model of buyer reaction to any given pricing scheme is developed to show that there exists a unified pricing policy which motivates the buyer to increase its ordering quantity per order thereby reducing the joint buyer and seller ordering and holding costs as a result the seller is able to reduce its costs while leaving the buyer no worse off and often better off the model is extended to handle variable ordering and shipping costs and situations where the seller faces numerous groups of buyers each having different ordering policies finally a case study is presented explicitly showing how the proposed pricing policy can be applied to the situation of a large seller selling to a number of different buyer groups

structural agricultural land use modeling for spatial agro environmental policy analysis this paper develops a spatially disaggregated structural econometric model of agricultural land use and production based on the joint multi output technology representation introduced by chambers and just 1989 starting from a flexible specification of the farm profit function we derive land use allocation input application crop yield and livestock intensity equations in a joint and theoretically consistent framework to account for the presence of censored observations in micro level data the model is estimated as a system of two limit tobit equations via quasi maximum likelihood we present an empirical application using fine scale spatial data covering the entirety of england and wales and including the main economic policy and environmental drivers of land use change in the past forty years a simulation of the effects of diffuse pollution reduction measures illustrates how our approach can be applied for agro environmental policy appraisal

the rational effect of price promotions on sales and consumption we explore the rational effect of price variation on sales and consumption in markets where consumers are uncertain about the future price of goods we first derive an optimal ordering policy which expresses the amount a consumer should purchase and consume in a given period as a function of the observed price of the good the distribution of future prices and the nature of his or her inventory this policy extends previous normative models of inventory control such as those by golabi 1985 and kalymon 1970 to the case where the amount to consume in a given period is an explicit decision variable and prices follow a first order stochastic process we then use this model to explore how changes in the long run frequency and temporal correlations of price promotions should normatively affect the contemporaneous relationship between purchase consumption and price among the predictions which follow from the model are that consumption should rationally increase with the size of existing inventories the short term sensitivity of sales to prices should be greater than that of consumption to price and this discrepancy increases with decreases in the temporal correlation of price deals and the long term relative frequency of price deals

dynamic pricing and ordering decisions by a monopolist this paper considers the relationship between pricing and ordering decisions for a monopolistic retailer facing a known demand function where over the inventory cycle the product may exhibit i physical decay or deterioration of inventory called wastage and ii decrease in market value called value drop associated with each unit of inventory on hand the retailer is allowed to continuously vary the selling price of the product over the cycle we introduce a notion of instantaneous margin and use it to derive profit maximizing conditions for the retailer the model explains the markdown of retail goods subject to decay it also provides guidance in determining when price changes during the cycle are worthwhile due to product aging how often such changes should be made and how such changes affect ordering intervals and quantities

dynamic pricing when consumers are strategic analysis of posted and contingent pricing schemes abstract we study dynamic pricing policies for a monopolist selling perishable products over a finite time horizon to strategic buyers buyers are strategic in the sense that they anticipate the firm s price policies it is expensive and administratively difficult for most brick and mortar retailers to change prices placing limits on the number of price changes and the types of pricing policies they can adopt the simplest policy is to commit to a set of price changes a more complex alternative is to let the price depend on sales history we investigate two pricing schemes that we call posted and contingent pricing using the posted pricing scheme the firm announces a set of prices at the beginning of the horizon in the contingent pricing scheme price evolution depends upon demand realization our focus is on the posted pricing scheme because of its ease of implementation counter to intuition we find that neither a posted pricing scheme nor a contingent pricing scheme is dominant and the difference in expected revenues of these two schemes is small limiting the number of price changes will result in a decrease in expected revenues we show that a multi unit auction with a reservation price provides an upper bound for expected revenues for both pricing schemes numerical examples suggest that a posted pricing scheme with two or three price changes is enough to achieve revenues that are close to the upper bound dynamic pricing is only useful when strategic buyers perceive scarcity we study the impact of scarcity and derive the optimal stocking levels for large markets finally we investigate whether or not it is optimal for the seller to conceal inventory or sales information from buyers a firm benefits if it does not reveal the number of units it has available for sale at the beginning of the season or subsequently withholds information about the number of units sold

a dynamic model of acreage allocation with general and crop specific soil capital we develop an empirically tractable model of acreage allocation decisions in which farmers consider impacts of current crop production 00 future soil productivity because of the soil productivity effects future crop prices are shown to affect current acreage allocations government programs which alter farmers expectations of future crop prices relative to current prices also alter farmers consideration of soil productivity effects of current acreage allocations reduced form and structural versions of our model are shown to yield reasonable parameter estimates

optimal pricing and inventory control policy with quantity based price differentiation a firm facing price dependent stochastic demand aims to maximize its total expected profit over a planning horizon in addition to the regular unit selling price the firm can utilize quantity discounts to increase sales we refer to this dual pricing strategy as quantity based price differentiation at the beginning of each period the firm needs to make three decisions replenish the inventory set the unit selling price if the unit sales mode is deployed and set the quantity discount price if the quantity sales mode is deployed or the combination of the two modes of sales we identify conditions under which the optimal inventory control policy and selling pricing strategy is well structured remarkably under a utility based demand framework these conditions can be unified by a simple regularity assumption that has long been used in the auction and mechanism design literature moreover sharper structural results are yielded for the optimal selling strategy we also examine the comparative advantag

the effect of agricultural policies on land use and environmental quality in this paper i consider the environmental quality gains that may be achieved by reducing agricultural income supports a new methodology is developed to estimate land use shares in an application to wisconsin milk price support reductions result in shifts of marginal agricultural land to forest reducing soil erosion and providing off site water quality improvements the environmental benefits are estimated to be at least as large as the decreased welfare burden on consumers and taxpayers indicating a central role for environmental quality considerations in motivating policy reforms and a more efficient means of achieving the environmental quality goals of land retirement programs

information distortion in a supply chain the bullwhip effect this article originally appeared in management science april 1997 volume 43 number 4 pp 546 558 published by the institute of management sciences consider a series of companies in a supply chain each of whom orders from its immediate upstream member in this setting inbound orders from a downstream member serve as a valuable informational input to upstream production and inventory decisions this paper claims that the information transferred in the form of orders tends to be distorted and can misguide upstream members in their inventory and production decisions in particular the variance of orders may be larger than that of sales and distortion tends to increase as one moves upstream a phenomenon termed bullwhip effect this paper analyzes four sources of the bullwhip effect demand signal processing rationing game order batching and price variations actions that can be taken to mitigate the detrimental impact of this distortion are also discussed

a periodic review inventory model with demand influenced by promotion decisions in this paper we use a markov decision process mdp to model the joint inventorypromotion decision problem the state variable of the mdp represents the demand state brought about by changing environmental factors as well as promotion decisions the demand state in a period determines the distribution of the random demand in that period optimal inventory and promotion decision policies in the finite horizon problem are obtained via dynamic programming under certain conditions we show that there is a threshold inventory level p for each demand state such that if the threshold is exceeded then it is desirable to promote the product for the proportional ordering cost case the optimal inventory replenishment policy is a base stock type policy with the optimal base stock level dependent on the promotion decision

clearance pricing and inventory policies for retail chains clearance pricing and end of season inventory management are challenging and important problems in retailing sales rates depend upon price seasonal effects and the remaining assortment of items available to customers there is little time to react to observed sales and pricing errors result in either loss of potential revenue or excess inventory to be liquidated this paper develops optimal clearance prices and inventory management policies that take into account the impact of reduced assortment and seasonal changes on sales rates versions of these policies have been tested and implemented at three major retail chains and these applications are summarized and discussed

optimal starting times for end of season sales and optimal stopping times for promotional fares many industries face the problem of selling a fixed stock of items over a finite horizon these industries include airlines selling seats before planes depart hotels renting rooms before midnight theaters selling seats before curtain time and retailers selling seasonal goods such as air conditioners or winter coats before the end of the season given a fixed number of seats rooms or coats the objective for these industries is to maximize revenues in excess of salvage value when demand is price sensitive and stochastic pricing is an effective tool to maximize revenues in this paper we address the problem of deciding the optimal timing of a single price change from a given initial price to either a given lower or higher second price under mild conditions we show that it is optimal to decrease resp to increase the initial price as soon as the time to go falls below resp above a time threshold that depends on the number of yet unsold items

price endings when prices signal quality this paper provides a theoretical explanation for why firms behave as though they use round prices to signal quality by replacing the linear demand curve in bagwell and riordan s 1991 price as a signal of quality model with a kinked demand curve and analyzing what price endings firms are most likely to use the following observations can be made 1 firms that are using high prices to signal quality are more likely to set those prices at round numbers and 2 price endings themselves are not necessarily signals of quality a simulation was conducted to demonstrate that these findings generally hold true even in the presence of demand spikes at 9 ending prices e g schindler and kibarian 1996 finally empirical evidence is provided to demonstrate that firms tend to use more round prices for higherquality products and that this relationship is even stronger for product categories where consumers are less able to detect the true level of quality prior to purchase

dynamic pricing of multiple home delivery options abstract online grocers accept delivery bookings and have to deliver groceries to consumers residences grocery stores operate on very thin margins therefore a critical question that an online grocery store needs to address is the cost of home delivery operations in this paper we develop a markov decision process based pricing model that recognizes the need to balance utilization of delivery capacity by the grocer and the need to have the goods delivered at the most convenient time for the customer the model dynamically adjusts delivery prices as customers arrive and make choices the optimal prices have the following properties first the optimal prices are such that the online grocer gains the same expected payoff in the remaining booking horizon regardless of the delivery option independently chosen by a consumer second with unit order sizes delivery prices can increase due to dynamic substitution effects as there is less time left in the booking horizon

from microlevel decisions to landscape changes an assessment of agricultural conservation policies the growth in conservation programs has created a need for modeling frameworks capable of measuring microlevel behavioral responses and macrolevel landscape changes this paper presents an empirical model that predicts farmers production practices and the resulting levels of agricultural runoffs at more than 42 000 agricultural sites in the upper mississippi river basin under alternative conservation policies results suggest that payments for conservation tillage and crop rotations increase the use of these conservation practices however the acreage response is inelastic and the programs are not likely to be cost effective on their own for addressing hypoxia problem in the gulf of mexico

the impact of information enrichment on the bullwhip effect in supply chains a control engineering perspective this paper examines the beneficial impact of information sharing in multi echelon supply chains we compare a traditional supply chain in which only the first stage in the chain observes end consumer demand and upstream stages have to base their forecasts on incoming orders with an information enriched supply chain where customer demand data e g epos data is shared throughout the chain two types of replenishment rules are analysed order up to out policies and smoothing policies policies used to reduce or dampen variability in the demand for the class of out policies we will show that information sharing helps to reduce the bullwhipeffect variance amplification of ordering quantities in supply chains significantly especially at higher levels in the chain however the bullwhip problem is not completely eliminated and it still increases as one moves up the chain for the smoothing policies we show that information sharing is necessary to reduce order variance at higher levels of the chain the methodology is based on control systems engineering and allows us to gain valuable insights into the dynamic behaviour of supply chain replenishment rules we also introduce acontrolengineering based measure to quantify the variance amplification bullwhip or variance reduction

coordinating clearance markdown sales of seasonal products in retail chains in this paper we propose a methodology to set prices of perishable items in the context of a retail chain with coordinated prices among its stores and compare its performance with actual practice in a real case study we formulate a stochastic dynamic programming problem and develop heuristic solutions that approximate optimal solutions satisfactorily to compare this methodology with current practices in the industry we conducted two sets of experiments using the expertise of a product manager of a large retail company in chile in the first case we contrast the performance of the proposed methodology with the revenues obtained during the 1995 autumn winter season in the second case we compare it with the performance of the experienced product manager in a simulation game setting in both cases our methodology provides significantly better results than those obtained by current practices

combined pricing and inventory control under uncertainty this paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty more specifically we analyze the following single item periodic review model demands in consecutive periods are independent but their distributions depend on the item s price in accordance with general stochastic demand functions the price charged in any given period can be specified dynamically as a function of the state of the system a replenishment order may be placed at the beginning of some or all of the periods stockouts are fully backlogged we address both finite and infinite horizon models with the objective of maximizing total expected discounted profit or its time average value assuming that prices can either be adjusted arbitrarily upward or downward or that they can only be decreased we characterize the structure of an optimal combined pricing and inventory strategy for all of the above types of models we also develop an efficient value iteration method to compute these optimal strategies finally we report on an extensive numerical study that characterizes various qualitative properties of the optimal strategies and corresponding optimal profit values

managing product variety with advance selling and capacity restrictions abstract in this research we analyze the impact of advance selling with price discount on a firms ability to maximize the expected profit the production environment of the firm is characterized by short selling cycle multiple products demand variability and capacity restrictions the advance orders are randomly distributed with the parameters dependent on the discount levels under advance selling the advance orders are used to update the demand forecast of selling season and are delivered at the start of the selling season the problem is modeled as a three stage stochastic non linear programming problem we derive the concavity of the problem under customers willingness to buy in advance our solution methodology comprises the variance reduction technique of antithetic variates that gives credible value of price discount levels for different sets of demand values we also provide sensitivity analysis of the problem parameters to derive insights into the behavior of the expected profit and the benefits due to advance selling under capacity restrictions

marketing driven channel coordination with revenue sharing contracts under price promotion to end customers this paper explores the equilibrium behavior of a basic supplier retailer distribution channel with and without revenue sharing contracts under price promotion to end customers three types of promotional demand patterns characterized by different features of dynamic price sensitivity are considered to rationalize price promotional effects on end customer demands under such a retail price promotion scheme this work develops a basic model to investigate decentralized channel members equilibrium decisions in pricing and logistics operations using a two stage stackelberg game approach extending from the basic model this work further derives the equilibrium solutions of the dyadic members under channel coordination with revenue sharing contracts analytical results show that under certain conditions both the supplier and retailer can gain more profits through revenue sharing contracts by means of appropriate promotional pricing strategies moreover the supplier should provide additional economic incentives to the retailer furthermore a counter profit revenue sharing chain effect is found in the illustrative examples such a phenomenon infers that the more the retailer requests to share from a unit of sale the more it may lose under the revenue sharing supply chain coordination scheme

optimal product line pricing the influence of elasticities and cross elasticities the authors focus on the determination of optimal prices for products in a product line most firms offer more than a single brand and ultimately are concerned with the overall results of the enti

the semiflexible almost ideal demand system abstract the concept of a semiflexible functional form is applied to the almost ideal ai demand system this yields a demand model that is more parsimonious than standard ones while preserving a degree of flexibility that satisfies the curvature property of concavity of the underlying expenditure function at least locally and that preserves the desirable properties of the ai model aggregation across consumers and nonlinearity of the engel curves the model is illustrated with an application to a relatively large demand system emphasizing food consumption

rental price and rental duration under retail competition consider a retailer that rents products to customers for a pre specified rental duration by considering the dynamics of uncertain rental demand and return processes we first present a base model that is intended to analyze the impact of rental duration on the stocking level the rental price and the retailer s profit due to the complexity of the base model we develop an approximation scheme to obtain tractable results also we apply the base model to analyze a situation in which a retailer enters a revenue sharing agreement with a distributor moreover we expand our base model to address the issue of competition in rental duration and rental price the analysis of our competitive model in a duopolistic environment suggests that the market equilibrium depends on the market potential and the rental duration sensitivity furthermore we establish conditions under which one firm will charge a lower rental price while the other firm will offer a longer rental duration in equilibrium

demand fluctuation and chaotic behaviour by interaction between customers and suppliers this paper presents an investigation on simulation of interaction between customers and suppliers in a three tier supply chain system in the simulation customers respond to the price discount offer made by the supplier and the supplier makes adjusts the price according to stock held the simulation shows that the behaviour of such interaction exhibits deterministic chaos it is found that the attractors of the model move with the environment and the initial states thus the bifurcating points in such a system are unable to provide a guideline in system design to avoid chaos

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

why are products sold on sale explanations of pricing regularities this paper reports on interesting changes in markdown pricing practices over time and differences in the pricing within a product line the price discrimination and the uncertainty hypotheses appear to better explain the data than the peak load hypothesis fashion has become more important over time and appears to explain the greater seasonal variation in retail apparel prices in recent years differences in uncertainty also explains differences in the pricing of different types of men s dress shirts

periodic pricing of seasonal products in retailing this paper studies intertemporal pricing policies when selling seasonal products in retail stores we first present a continuous time model where a seller faces a stochastic arrival of customers with different valuations of the product for this model we characterize the optimal pricing policies as functions of time and inventory we use this model as a benchmark against which we compare more realistic models that consider periodic pricing reviews we show that the structure of the optimal pricing policies in this case is consistent with the procedures observed in practice retail stores successively discount the product during the season and promote a liquidation sale at the end of the planning horizon we also show that the loss experienced when implementing periodic pricing reviews instead of continuous policies is small when the appropriate number of reviews is chosen several interesting economic insights emerge from our analysis for example uncertainty in the demand for new products leads to higher prices larger discounts and more unsold inventory finally we study the effect of announced discount policies on prices and profits we show that stores that have adopted this type of strategy usually set prices such that with high probability the merchandise is sold during the first periods and the largest discounts rarely take place

dynamic advertising and pricing with constant demand elasticities in this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand the state space is discrete time is continuous and the planing horizon is allowed to be finite or infinite a dynamic version of the dorfman steiner identity will be derived explicit expressions of the optimal advertising and pricing policies of the value function and of the optimal advertising expenditures will be given the general results will be used to analyze the case of impatient customers furthermore particular time inhomogeneous models and homogeneous ones with and without discounting will be examined we will study the social efficiency of a monopolist s optimal policies and the consequences of specific subsidies from a buyer s perspective our analysis reveals that waiting when looking at immediate expected prices is never profitable should two or more units be available but we will also prove that the sequence of average sales prices is monotone decreasing moreover the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space

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

a two echelon allocation model and the value of information under correlated forecasts and demands abstract in this article we explore the effects of incorporating forecasts explicitly in a two echelon allocation model which consists of a central depot and several retailers in particular we investigate the possible benefits on the system costs and inventory levels the depot does not hold any inventory and the demand is observed only at the retailers under a general correlated demand forecast structure we obtain the approximate system wide order up to level and the expected system cost in order to assess the value of information provided by keeping track of the forecasts we construct a comparable inventory system operating under a standard demand model we demonstrate that the standard demand model results in higher order up to levels and higher system costs

intertemporal price discrimination and sales strategy under incomplete information this article examines intertemporal price variations to provide a theoretical explanation for them when firms have only incomplete information about consumers reservation prices for the commodity we contend that some intertemporal price variations can result from attempts by firms to discriminate among consumers we demonstrate that such price discrimination is the optimal policy for a seller if consumers have a higher time discount rate than producers

product servicing for lifespan extension and sustainable consumption an optimization approach abstract sustainable consumption has been defined as the consumption of goods and services that meet basic needs and quality of life without jeopardizing the needs of future generations oecd 2002 lifespan extension of durable products underpins sustainable consumption this paper describes a novel approach to extend product lifespans by using product servicing that conceptualizes the interactions of a producer a policy maker and multiple consumer segments having different price demand relationships we propose a multi period mathematical optimization model that maximizes the producer s profit while optimizing the prices of different servicing options production quantities and inventory levels a computational study elicits several insights about how the optimal production or alternatively consumption quantities are affected by the introduction of product servicing and the effects of various product characteristics and government incentive or penalty levels on producer s profitability and on product servicing decisions we conclude that quantitative optimization models are useful for evaluating the impacts of different regulatory policies assessing the benefits of offering product servicing options and investing in design for durability and serviceability

a taxonomy and research overview of perishable asset revenue management yield management overbooking and pricing this paper proposes the term perishable asset revenue management to denote the field that combines the areas of yield management overbooking and pricing for perishable assets after summarizing the characteristics common to problems in this field the paper discusses the objectives and constraints faced by decision makers then it offers a comprehensive taxonomy with 14 different elements and reviews the research that has been done related to each element finally it suggests some important areas of future research that can help bridge the gap between theory and application

a sample selection approach to censored demand systems the multivariate sample selection model is extended to a nonlinear equation system with partial selection and applied to household meat consumption in china elasticity estimates differ from those obtained from conventional maximum likelihood and tobit estimates chinese meat products are gross complements while net substitution also exists in some cases the use of micro survey data has been popular in estimating consumer demand equations important features of microdata include censored dependent variables estimation procedures for censored consumer demand systems include the primal kuhn tucker approach of wales and woodland 1983 dual virtualprice approach of lee and pitt 1986 and the tobit system amemiya 1974 estimated by generalized maximum entropy golan perloff and shen 2001 and maximum simulated likelihood dong gould and kaiser 2004 yen lin and smallwood 2003 procedures less efficient alternatives include the quasi maximum likelihood estimator yen lin and smallwood 2003 the generalized method of moments estimator meyerhoefer ranney and sahn 2005 and a number of two step estimators heien and wessells 1990 perali and chavas 2000 shonkwiler and yen 1999 yen 2005 recently proposed a maximum likelihood ml procedure for the multivariate sample selection model mssm an extension of the bivariate sample selection model heckman 1979 which had motivated the procedures of heien and wessells 1990 and shonkwiler and yen 1999 the mssm was developed in the context of linear equations and in addition is not strictly applicable for a partially selective equation system viz

chapter 11 pricing models in marketing publisher summary this chapter brings together a set of diverse efforts in the recent literature on the modeling of price decisions and related questions in marketing there has been an impressive growth in the array of topics investigated in the literature various trends in the development of pricing models are evident from the foregoing review first one trend has been to develop theoretical models to describe observed pricing strategies in the marketplace and to derive conditions under which certain strategies are optimal this trend is clearly evident when one considers the area of dynamic pricing models another trend is an attempt to develop pricing models in which certain aspects of consumer behavior e g asymmetric response to price increases versus price decreases are incorporated this development is quite recent and does offer a large potential a third dominant direction is the use of game theoretic models for developing equilibrium pricing strategies

using imperfect advance demand information in ordering and rationing decisions in this paper we consider an inventory problem with two demand classes having different priorities the appropriate policy of rationing the available stock i e reserving some stock for meeting prospective future demand of preferred customers at the expense of deliberately losing some of the currently materialized demand of lower demand class es relies on the estimation of the future demand utilizing current signals on future demand which we refer to as imperfect advance demand information adi decreases uncertainty on future demand and may help to make better decisions on when to start rejecting lower class demand we develop a model that incorporates imperfect adi with inventory ordering replenishment decision and rationing available stock in a two period setting we show some structural properties solve the rationing problem and propose solution methods based on monte carlo simulation for the ordering problem we conduct numerical tests to measure the impact of system parameters on the expected value of imperfect adi and provide useful managerial insights

implementing supplier codes of conduct in global supply chains process explanations from theoretic and empirical perspectives western buying companies impose supplier codes of conduct scc on their suppliers in developing countries however many suppliers cannot fully comply with scc and some of them even cheat in scc in this research we link contract characteristics price pressure production complexity contract duration to the likelihood of supplier s commitment to scc through a mediating process how the buying companies govern their suppliers our structural equation model analysis shows that the hierarchy relational norms governance is a perfect mediator of contract characteristics effects on the likelihood of supplier s commitment the market governance an insignificant one the managerial implications are provided for successfully implementing scc in global supply chains

optimal price skimming by a monopolist facing rational consumers this paper considers the intertemporal pricing problem for a monopolist marketing a new product the key feature differentiating this paper from the extant management science literature on intertemporal pricing is the assumption that consumers are intertemporal utility maximizers a subgame perfect nash equilibrium pricing policy is characterized and shown to involve intertemporal price discrimination we compare this policy to the optimal policy for a monopolist facing myopic consumers and find that for any given state prices are always lower with rational consumers than with myopic consumers for plausible parameter values the assumption of consumer rationality can be shown to lead to large differences in optimal prices moreover if a monopolist facing rational consumers implements the optimal myopic consumer pricing policy profits can be significantly less than if the monopolist follows the equilibrium pricing policy for rational consumers

food vs fiber an analysis of agricultural support policy in turkey the present study evaluates the effects of agricultural policies on farm land allocation the analysis is applied to turkey a country where a persistent gap between rural income and urban income has motivated governments to enact policies that support farm income this paper evaluates two sets of policy instruments output support which increases farm revenue from specific crops and input support which subsidizes particular farm inputs it also investigates the effects of agricultural policy on farmers incentive to produce fiber cotton versus food corn and other foods using farm level data from two regions of turkey the analysis finds that input supports have had stronger effects on land allocation than output supports it also shows the presence of significant substitution effects across crops with the subsidizing of cotton having a significant negative effect on the incentive to grow food crops this provides useful insights into the economic tradeoff between food and fiber in the design of agricultural policy and its effects on a country s food security

the profit maximizing capacitated lot size pclsp problem this paper extends the results for capacitated lot sizing research to include pricing based on a few examples the new version appears to by much easier to solve computationally the paper by including price can modify demand as well as production schedule due to model assumptions form of demand a feasible solution can be found easily unlike clsp

a multiproduct dynamic pricing problem and its applications to network yield management a firm has inventories of a set of components that are used to produce a set of products there is a finite horizon over which the firm can sell its products demand for each product is a stochastic point process with an intensity that is a function of the vector of prices for the products and the time at which these prices are offered the problem is to price the finished products so as to maximize total expected revenue over the finite sales horizon an upper bound on the optimal expected revenue is established by analyzing a deterministic version of the problem the solution to the deterministic problem suggests two heuristics for the stochastic problem that are shown to be asymptotically optimal as the expected sales volume tends to infinity several applications of the model to network yield management are given numerical examples illustrate both the range of problems that can be modeled under this framework and the effectiveness of the proposed heuristics the results provide several fundamental insights into the performance of yield management systems

technical note a note on the structure of joint inventory pricing control with leadtimes we consider a joint inventory pricing control problem for a periodic review single stage inventory system with a positive order leadtime and a linear order cost demands in consecutive periods are independent but their distributions depend on the price in accordance with a stochastic demand function of additive form pricing and ordering decisions are made simultaneously at the beginning of each period the objective is to maximize the total expected discounted profit over a finite horizon we partially characterize the structure of the optimal joint ordering and pricing policies we also show that our structural analysis can be extended to a multistage or serial inventory system with constant or stochastic leadtimes and an assemble to order system with price sensitive demand

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

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

theoretical models of sales promotions contributions limitations and a future research agenda our objective in this paper is to review theoretical models of sales promotions we highlight the key contributions of these models discuss their limitations and outline an agenda for future research managerial questions examined in these models include some very fundamental issues such as why firms resort to the use of sales promotions in mature markets and why the use of sales promotions has increased dramatically during the last two decades also included in this review are models that address firm level strategic issues such as the allocation of dollars between advertising and sales promotions and the relative emphasis on trade promotions vis a vis consumer promotions we also review theoretical models that explain how consumers respond to price promotions and what type of sales promotion tools may be superior to others in a particular market the review concludes with a possible agenda for future research

optimal ordering and pricing strategies in the presence of a b2b spot market abstract in the current paper we examine the effect of a b2b spot market on the strategic behavior and the performance of a reseller who continues to use the traditional channel while participating in a b2b spot market we analyze the case in which a risk neutral reseller faces an additive or multiplicative demand function and identify sufficient conditions under which the optimal order quantity and retail price exist and are unique we then analytically examine the case in which a risk averse reseller participates in a fully liquid spot market we also study numerically how varying liquidity spot price volatility demand variability and correlation coefficient affect a firm s strategies and performance we find that demand variability significantly affects both pricing and ordering strategies whereas the spot price volatility has less influence on pricing decisions our results also show that for a risk averse reseller to charge a lower retail price when the spot market liquidity increases is desirable we further show that a b2b spot market cannot always improve a reseller s utility these findings shed light on how resellers can adjust their procurement and pricing strategies to align with the new business environment created by the emergence of b2b spot markets as well as have obvious implications for the development of a b2b spot market

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

effects of price promotions on variety seeking and reinforcement behavior a stochastic model is proposed to examine how changes in frequency of price discounts affect brand choice decisions of consumers who exhibit variety seeking and reinforcement behavior it is shown that the effect on choice depends on whether the brand offering discounts is a major or minor brand in the product category this model extends the existing literature on stochastic models of variety seeking behavior by explicitly incorporating switching due to promotions along with intrinsic switching due to variety seeking the model yields testable hypotheses which are supported in a laboratory experiment and on analyses of the iri cracker data

monopolist pricing with dynamic demand and production cost this paper deals with pricing of a new product over time by a monopolist who maximizes the discounted profit stream the interdependency of cost and demand on cumulative production makes the problem inherently dynamic cost is assumed to be declining with cumulative production learning curve effect while demand is a function of price and cumulative sales representing word of mouth and saturation effects the paper addresses this problem in a general framework that includes several previous results as special cases and provides new insights in other situations while the learning curve and word of mouth effect cause prices to be lower than the price that maximizes immediate revenues the saturation factor has the opposite effect the price path over time is affected by these factors and the interest rate we characterize the price path under several different situations and interpret the results for policy guidelines