a multiobjective approach to vendor selection abstract purchases from vendors involve significant costs for many firms decisions related to these purchases include the selection of vendors and the determination of order quantities to be placed with the selected vendors such decisions are frequently multiobjective in nature that is they are evaluated by more than one criterion at least 23 criteria for various vendor selection problems have been identified in this article we present a multiobjective approach to systematically analyze the inherent tradeoffs involved in multicriteria vendor selection problems the approach is motivated by and demonstrated with an actual purchasing problem facing a division of a fortune 500 company

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

the analysis of optimal control model in matching problem between manufacturing and marketing abstract a mathematical model is developed and presented to solve the optimal control problem in matching between manufacturing and marketing when the market demand possesses the property of linearity the main purpose of this paper is to investigate the optimal choice between production rate which may affect the inventory level and the optimal sales rate at each time through different pricing strategies so as to achieve the maximum profit for a given planning horizon the results demonstrated that the relative size of the output yielded by minimizing average cost and yielded by maximizing profit at constant zero inventory can determine the optimal production rate and sales rate furthermore the optimal inventory policy can be determined to be a constant zero inventory policy or constant positive inventory policy or mixed inventory policy according to the value of optimal production rate

pricing and scheduling decisions with leadtime flexibility this paper studies a problem faced by a manufacturer who has the ability to set prices to influence demand reject orders and set leadtimes or due dates for accepted orders we present decision models that integrate pricing and production decisions for the cases where the manufacturer charges the same price or different prices to different customers through numerical analyses we present insights regarding the benefits of price customization leadtime and inventory flexibilities in various demand environments

optimal joint pricing and lot sizing with fixed and variable capacity this paper examines previously unexplored fixed and variable capacity problems of jointly determining an item s price and lot size for a profit maximizing firm facing constant but price dependent demands over a planning horizon we apply geometric programming to these constrained nonlinear maximization problems with nonconcave objective functions and obtain global optimal solutions using kuhn tucker condition marginal and sensitivity analyses we investigate model interactions provide managerial implications on the optimal capacity decisions and explore the postoptimal behavior of the price lot size and capacity expansion and reduction size some findings cast interesting insights different from previous just in time management studies without pricing consideration

effects of a hybrid price stock dependent demand on the optimal solutions of a deteriorating inventory system and trade credit policy on re manufactured product abstract this study contributes to formulate a deteriorating inventory model with a hybrid price stock dependent demand with credit for units in stock period in the presence of trade credit policy by using the discounted cash flow approach on re manufactured products in real life the demand function is not always constant or linear or nonlinear the demand rate of any items goes up and down in the real market due to the sum of two different types of demand this study observes that the demand is depending on price and stock of the product time value of money and trade credit policy the objective of this study is to find optimum cycle time optimum selling price and present profit of all future cash flows the model starts with mathematical formulating and thereafter studies the necessary and sufficient conditions for obtaining the unique optimal solution the theoretical solution procedure and case examples have studied for validation of this model moreover the sensitivity analysis is expressed out with respect to main parameters and managerial application is obtained this study uses the different demand functions of a simple pricing inventory system to find out the maximum profit on re manufactured products

coordination of pricing and multiple period production across multiple constant priced goods this paper addresses the problem of jointly determining prices and production schedules for a set of items that are produced on the same production equipment under the assumptions that the production setup costs are negligible and that demand is seasonal but price dependent we exploit the special structure of the problem to develop a solution procedure through a set of numerical examples we demonstrate how a product s contribution to aggregate seasonality can increase its optimal price our examples also demonstrate that among products that experience demand peaks during the firm s busy season those that peak early in the busy season should be priced more aggressively than those that peak later

coordination of pricing and multi period production for constant priced goods this paper addresses the problem of jointly determining a single price and production schedule for a product with seasonal demand under the assumption that the ratio of the demands in any two periods does not depend upon the price at which the product is offered we develop a procedure that guarantees an optimal solution perhaps more importantly however our model provides insight into the manner in which the firm s production cost increases with the intensity of total demand

strong planning and forecast horizons for a model with simultaneous price and production decisions abstract in this paper we have solved a general inventory model with simultaneous price and production decisions both linear and non linear strictly convex production cost cases are treated upper and lower bounds are imposed on state as well as control variables the problem is solved by using the lagrangian form of the maximum principle strong planning and strong forecast horizons are obtained these arise when the state variable reaches its upper or lower bound the existence of these horizons permits the decomposition of the whole problem into a set of smaller problems which can be solved separately and their solutions put together to form a complete solution to the problem finally we derive a forward branch and bound algorithm to solve the problem the algorithm is illustrated with a simple example

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

financial technology shocks and the case of the missing m2 m2 growth was unusually weak in the early 1990s when its velocity soared although m2 growth subsequently recovered its velocity plateaued at a high level giving rise to a case of missing money these swings in m2 growth have accompanied opposite swings in bond mutual fund inflows m2 growth is better tracked and the missing m2 problem is resolved when money models are modified to account for shifts in bond mutual fund costs this approach avoids the capital gains and portfolio substitution problems posed by adding bond or equity funds to m2 while capturing the substitution effects relevant to money demand

pricing and the news vendor problem a review with extensions in the newsvendor problem a decision maker facing random demand for a perishable product decides how much of it to stock for a single selling period this simple problem with its intuitively appealing solution is a crucial building block of stochastic inventory theory which comprises a vast literature focusing on operational efficiency typically in this literature market parameters such as demand and selling price are exogenous however incorporating these factors into the mode l can provide an excellent vehicle for examining how operational problems interact with marketing issues to influence decision making at the firm level in this paper we examine an extension of the newsvendor problem in which stocking quantity and selling price are set simultaneously we provide a comprehensive review that synthesizes existing results for the single period problem and develop additional results to enrich the existing knowledge base we also review and develop insight into a dynamic inventory extension of this problem and motivate the applicability of such models

modelling imperfect advance demand information and analysis of optimal inventory policies we consider an inventory control problem where it is possible to collect some imperfect information on future demand we refer to such information as imperfect advance demand information adi which may occur in different forms of applications a simple example is a company that uses sales representatives to market its products in which case the collection of sales representatives information as to the number of customers interested in a product can generate an indication about the future sales of that product hence it constitutes imperfect adi other applications include internet retailing vendor managed inventory vmi applications and collaborative planning forecasting and replenishment cpfr environments we develop a model that incorporates imperfect adi with ordering decisions under our system settings we show that the optimal policy is of order up to type where the order level is a function of imperfect adi we also provide some characterizations of the optimal solution we develop an expression for the expected cost benefits of imperfect adi for the myopic problem our analytical and empirical findings reveal the conditions under which imperfect adi is more valuable

optimal inventory policies for profit maximizing eoq models under various cost functions in this paper we establish and analyze three eoq based inventory models under profit maximization via geometric programming gp techniques through gp we find optimal order quantity and price for each of these models considering production lot sizing as well as marketing pricing decisions we also investigate the effects on the changes in the optimal solutions when different parameters are changed in addition a comparative analysis between the profit maximization models is conducted by investigating the error in the optimal price order quantity and profit of these models several interesting economic implications and insights can be observed

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

modeling credit card borrowing a comparison of type i and type ii tobit approaches this study focuses on credit cards as a borrowing medium using 1998 survey of consumer finance data the type ii tobit approach used here overcomes a shortcoming of the conventional type i tobit model which restricts the coefficients of the binary borrowing decision the first step and balance level decision the second step to have the same sign by separately estimating the first and second steps as reduced form functions in which the overall effects of supply and demand are incorporated the type ii tobit procedure yields more consistent results with other studies and quantifies the marginal effect elasticity of a particular determinant for practical uses more than 11 000 bank and nonbank holding companies issued credit cards in 1997 among these firms the top 50 issuers market share is 90 4 and the 10 largest credit card issuers hold 57 3 of total outstanding balances bank holding company revenue from interest on outstanding balances is 57 5 billion which is 77 8 of the total revenue of 73 9 billion moreover about 80 of 102 million u s households own at least one credit card demand for credit cards consists of two components one being the demand as a transaction medium and the other being the demand as a borrowing medium over 68 of bank type credit card holders use their credit cards only as a transaction medium 1 which means that they pay off their balances in full each month cargill and wendel 1996 however other credit card holders use their cards as a source of short term lowamount borrowing or as an instrument for consumption smoothing this study focuses on credit cards as a borrowing medium total household debts have been investigated in other studies relating household debt levels to credit or liquidity constraints using a two step selection approach duca and rosenthal 1993 examine the extent to which borrowing constraints restrict household access to debt and the manner in which lenders vary debt limits across borrowers crook 2001 investigates the determinants of credit constraints and the factors in the amount of household debt with a multistage model however it is necessary to separate the credit card debt from other household debts in the sense that every credit card user could borrow without incurring a transaction cost brito and hartley 1995 provide a theoretical model in which the equilibrium interest rate can be very high and inflexible under the

integrating marketing and production planning in make to order companies abstract make to order companies are in the business of supplying products only in response to a customer s order they may supply unique products made to a customer s specification and or a limited range of products they range from the traditional job shop e g cutting pieces of metal to a specific shape to producers of machine tools e g a vulcanising line a major problem is the divide between sales marketing and production the production function is often faced with unrealistic delivery dates for incoming orders this arises when the sales force quote delivery dates and prices which will maximise the chance of the company winning the order the lack of coordination with production often leads to confirmed orders being delivered later than promised by sales and or being produced at a loss or alternatively production has to delay other orders with consequent extra costs the need to integrate sales and production planning considerations at the customer enquiry stage in deciding how to respond has been pointed out by several authors yet little research has been carried out the paper will discuss some possible approaches to the problem these essentially depend on estimating routinely the probability of winning an enquiry order dependent on many factors including price and lead time etc companies do not traditionally keep records of this data particularly records of unsuccessful bids and on competitors in addition the paper describes the experience of setting up a system to collect such data in a major uk company and the potential uses of such a database

land leasing and local government behaviour in china evidence from beijing since 2004 two auction mechanisms listing auctions and tender auctions have played a dominant role in land lease arrangements for real estate development in beijing listing auctions in land markets are similar to general english auctions where bidders offer the highest price to win however in tender auctions winners are determined by the bidding price and the bidder s financial capability and reputation based on granted land parcels from 2006 to 2012 in beijing this paper attempts to examine the price differences between the two auctions and the role of land auction in urban development and price stabilisation we find that land policy in beijing which aims to stabilise land prices and to provide low price residences has been integrated with urban development planning in terms of spatial and density pattern land leasing in beijing is not only a land policy but also a part of the strategy framework of local development

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

integrated pricing and lot sizing decision in a two echelon supply chain with a finite production rate abstract in this paper we consider a supply chain consisting of a supplier and a retailer selling the product manufactured by the supplier in a market in which the demand for the product is decreasing in the price set by the retailer previous research on coordinating the supply chain with price sensitive demand often assumes that either the supplier purchases the product or the supplier has an infinitely large production rate we consider explicitly the supplier s finite production rate in the pricing and lot sizing decision which causes the problem much more challenging we first investigate the optimization problem in the decentralized scenario to find the optimal order quantity and selling price for the retailer as well as the optimal wholesale price and lot size multiplier for the supplier we then solve the joint optimization problem in the centralized supply chain to find the optimal order quantity the selling price and the optimal lot size multiplier we provide two sequential algorithms to solve the joint optimization problem computational experiments show that the algorithms are effective all 448 tested problems are solved optimally and efficient it only takes a few iterations to converge for each tested problem the supply chain coordination mechanism is then designed through an all unit quantity discount policy and a franchise fee

optimal production purchasing and pricing a differential game approach abstract this paper deals with a problem of determining optimal production and pricing policies of a manufacturing firm which is supplying a retailer the latter faces a price dependent demand function towards the final consumers and wishes to determine optimal purchasing and pricing policies both firms carry inventories and backlogging is permitted the problem is modelled as a two player nonzero sum differential game with the inventory levels as the state variables the controls are the rates of production and purchasing as well as the prices assuming linear production costs but convex ordering and holding costs open loop nash controls are characterized by using switching point analysis as well as phase diagrams

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

technological change and the households demand for currency abstract it is shown that accounting for technology variations across households and periods is important to obtain theoretically consistent estimates of the demand for currency an inventory model is presented where the withdrawal technology is explicitly modeled both the level and the interest rate elasticity of cash holdings depend on the withdrawal technology available to households empirical proxies for the household withdrawal technology based on the diffusion of cash withdrawal points measured at city level are used to test the model predictions on a panel of italian household data over the 1993 2004 period

due date dd quotation and capacity planning in make to order companies results from an empirical analysis the current competitive context puts manufacturers under increasing pressure to provide products and services that meet the particular requirements of individual customers calling for high flexibility in business processes the complexity and the uncertainty of demand are particularly high in customized contexts such as the make to order mto and engineer to order eto sectors where the ability to deal with more and more differentiated requirements in terms of product features delivery lead time and cost is crucial in order to be competitive in such a context due date dd quotation and capacity evaluation at the customer enquiry stage are of strategic importance having a large impact on the company performance despite the large impact on company performance the importance of dd setting and order acceptance processes and related decisions is often underestimated in practice and the issue is underexposed in the literature as the applicability of most of the proposed models is limited and there are too few empirical studies describing the practices adopted for capacity and delivery lead time management in industrial contexts this study is aimed at developing an understanding of these practices based on a sample of 15 italian capital goods manufacturers an interpretative framework is proposed in order to identify the main contextual factors impacting company choices a model that formalizes the decision process for setting dds in the analyzed cases is then proposed suggesting different procedures depending on the type of enquiry submission dd set by companies or customers and customer order fast or slow

marketing production decisions in an industrial channel of distribution this paper presents a model that considers the interface between marketing and production decisions in a channel of distribution of industrial goods comprised of a manufacturer and a distributor the key issue investigated is the nature of the coordination within the channel in light of an unstable pattern of seasonal demand the investigation which focuses on dynamic issues considers production activities such as product delivery and inventory policy and their link to marketing strategies such as pricing policies the focus here is on the dynamic nature of the coordinational aspects of the various policies for example the following questions are addressed what is the distributor s pricing strategy throughout the season what is the nature of the contractual price in the channel under what conditions should the distributor carry no inventory throughout the seasonal period under what conditions should the manufacturer carry no inventory what is the impact of the seasonal parameters and differing h

pricing and lead time decisions for make to order firms with contingent orders abstract make to order mto firms have few standard products and volatile difficult to predict demand a production order usually stems from a successful bid which presents the mto firm s terms including price and lead time to satisfy a prospective customer s stated requirements the customer may decide to accept reject or modify these terms until the customer decides the tendered bid is a contingent demand on the mto firm s future production capacity in the short run this capacity may be relatively fixed and if the customer awards the contract to another bidder it may simply go to waste to hedge against this possibility the mto firm can bid on other projects that require the same capacity however this strategy introduces a new source of lead time uncertainty if two or more booked orders must contend for the same resources some work will inevitably be bumped to later time periods thus a hedging strategy carries the risk of penalties for late deliveries in this paper we model this little discussed source of lead time uncertainty and introduce a technique that simultaneously optimizes pricing and lead time decisions for mto firms with contingent orders we illustrate the procedure with a simple numerical example

a joint optimal pricing rebate value and lot sizing model delayed incentives in the form of mail in cash rebates are very popular among manufacturers and more recently among retailers one of the main advantages of rebates is that while they increase demand a small proportion of consumers redeem them in this paper we formulate and solve models for jointly determining the optimal price rebate face value and the optimal order quantity for a price and rebate sensitive deterministic demand the models show that under realistic conditions offering rebates can have significant pricing and inventory policy implications and can lead to a significant increase in profit

joint dynamic pricing and lot sizing under competition abstract we study the joint dynamic pricing and lot sizing problem when firms operate in a competitive environment bearing in mind that a dynamic pricing strategy is successful when customers understand it we assume each firm selects prices from a discrete set the problem corresponds to a bertrand model so the pricing strategies of the firms should constitute a nash equilibrium given the combinatorial nature of the decisions computing the equilibrium in a tractable time may not be feasible for larger instances in order to compute the equilibrium efficiently we propose a framework consisting of solving iteratively mixed integer programming formulations the framework reduces the complexity of the problem by using the fact that pricing and inventory planning remain stable to marginal variations in competitors prices

a model to evaluate acquisition price and quantity of used products for remanufacturing abstract in this paper an analytical model is proposed to evaluate optimal acquisition price and quantity policy based on the quality of returned used products that are subsequently used for remanufacturing the model is developed from the perspective of a consolidation center which facilitates the collection of used products in various collection centers by offering an acquisition price based on the quality of used products receive all of the collected used products and consolidate them with replacement parts before sending the consignment to the remanufacturer it is assumed that the consolidation center receives an order from the remanufacturer for a set quantity and an associated price for used products in a quality level the consolidation center then evaluates optimal acquisition price and quantity policy for used products based on the available information on stochastic return quantity and quality and the cost of predefined set of replacement parts the policy so obtained is offered to the collection centers to initiate the collection of used products in their respective area of operation the impact of the model is studied through a numerical study the authors believe that the model developed here is the first such pricing model in a reverse logistics setting

joint production and pricing decisions with setup costs and capacity constraints we consider the problem of setting prices and choosing production quantities for a single product over a finite horizon for a capacity constrained manufacturer facing price sensitive demands there is a fixed cost per production run and a variable cost per unit produced both of which may vary by period we characterize properties of the optimal solution considering cases with constant and time varying capacity and with and without speculative motive for holding inventory we show that counter to intuition optimal prices may increase as the capacity increases even when capacity is constant over the horizon we also show that increases in capacity do not always exhibit diminishing marginal returns our procedure produces solutions with much higher profits than can be obtained from a sophisticated sequential procedure in which a well informed and optimum seeking marketing department makes pricing decisions and the manufacturing department seeks to satisfy the resulting demands at minimum cost our results also suggest that firms with seasonal demand and tight capacity constraints should be more aggressive in setting prices to manage their demands than what is typically done in practice finally we discuss how a decision maker can use our procedure as an aid in solving multiproduct versions of the problem

empirical evidence on payment media costs and switch points abstract this paper recovers micro cost schedules of consumers payment instruments from aggregate transaction costs we assume that only two moments of the size distribution of payments matter the number and volume of transactions these variables explain the transaction costs of currency and debit card payments with much precision for a representative 1998 sample of dutch retailers the results imply that low fixed transaction costs favor currency for small transactions while low variable transaction costs favor debit card payments for large transactions the switch point is 30 euros but including the hidden costs of currency would lower it to 13 euros

marriage markets and money a coasian theory of household formation this article integrates search based models of marriage and money we think about households as organizations the way coase thinks about firms as alternatives to markets that become more attractive when transactions costs increase in the model individuals consume market and home produced goods and home production is facilitated by marriage market frictions including taxes search and bargaining problems increase the marriage propensity the inflation tax encourages marriage because being single is cash intensive microdata confirm singles use cash more than married people we use macrodata over many countries to investigate how marriage responds to inflation taxation and other variables

microfoundations and the demand for money the reader should note that i write this piece in a style that aims to be accessible to that much neglected representative agent the woman on the eurostar train hence unlike the man on the clapham omnibus i assume my intrepid traveller has reasonable knowledge of monetary economics and econometrics but not of the details of the demand for money space constraints force me to indulge in a certain amount of poetic licence but i hope this results in poetic justice there have been many wars fought on this particular battlefield some with almost religious zeal on the theoretical side of the debate we sometimes have the equivalent of religious fundamentalists be they muslims jews christians etc who would dismiss almost any evidence unless it were associated with a strong microtheoretic basis as laid down in the koran talmud or bible the empirical side encompasses agnostics atheists as well as born again econometricians pure theorists inhabit the sunlit uplands while applied economists and policymakers flounder in the muddy plain below occasionally gaining solace from their copy of zen and the art of motorcycle maintenance in general in economics we do not have the luxury of controlled experiments as is the case in the natural sciences what distinguishes good microfoundations from bad and how to weight priors and statistical evidence is subject to much dispute leamer i983 hendry et al i990 as in religion sometimes there is the occasional miracle proclaimed after a suitable interval a new saint may be declared and disciples flock to the new shrine later doubts may arise as to whether a miracle really did occur human behaviour is difficult to explain let alone predict so the search for the equivalent of the holy grail ark of the covenant etc is bound to be arduous in scholarly journals we generally read of the success of the demand for money like diplomats who are sent abroad to lie for the good of their country publication may require applied economists to be somewhat economical with the actualite lovell i983 leamer i983 in this article i want to be as honest as possible about our success and failures in this area the prior information an armchair economist would consider when thinking about the demand for money over the past 40 years in western industrialised countries which have experienced moderate inflation might

does the market pay off earnings returns to education in urban china previous work on the market transition in reform era china has missed the direct link between individuals labour market history and individuals labour market outcome a typology of workers is developed based on individuals labour market histories and a model of selective mobility of workers from the state sector to the market sector is offered as an explanation for higher earnings returns to education in the market sector analysis of data from an urban survey in china reveals that commonly observed higher earnings returns to education in the market sector are limited only to recent market entrants and that early market entrants resemble state workers in both their level of earnings and returns to education these results challenge the prevailing wisdom that education is necessarily more highly rewarded in the market sector thus it is concluded that higher returns to education in the market sector should not be construed as being caused by marketization per se and instead that the sorting process of workers in labour markets helps explain the sectoral differentials

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

optimal pricing and production in an inventory model abstract this paper deals with the problem of simultaneously determining the optimal price policy and production rate over a given planning horizon for nonlinear demand functions and convex inventory and shortage cost functions the optimal solution paths are derived by using optimal control theory the treatment of linear nonsmooth cost functions requires the use of a generalized maximum principle the solution method is a phase portrait analysis providing insight into the optimal pricing and production policies as well as the resulting inventory paths moreover it is shown that in the case of nonsmooth piecewise linear cost functions the equilibrium is approached within finite time although the model is nonlinear in the control variables finally it is illustrated that exogenous fluctuations in the demand rate seasonal demand pattern amount to cyclical optimal solutions

simultaneous price and due date settings for multiple customer classes extending the model of eur j oper res 116 2 1999 305 that under contingent capacity simultaneously optimizes the bidding price and due date for each incoming order we propose a bidding model with multiple customer segments classified based on parameters of willingness to pay sensitivity to short delivery time quality level requirement and intensity of competition the winning probability function was also modified to be of more practical and robust model in reflecting stochastic nature of customer s decision two sequencing rules namely the early due date edd for time critical orders and first come first serve fcfs for regular orders were applied to determine the sequencing position of each incoming order and a simplified pattern search algorithm was used to improve the efficiency in searching for optimal price and due date the simulation results show that in general our proposed model and method can significantly increase the marginal revenue to the firm

a profit maximizing economic lot scheduling problem with price optimization the economic lot scheduling problem elsp is a well known problem that focuses on scheduling the production of multiple items on a single machine such that inventory and setup costs are minimized in this paper we extend the elsp to include price optimization with the objective to maximize profits a solution approach based on column generation is provided and shown to produce very close to optimal results with short solution times on a set of test problems the results are discussed and recommendations for further research are provided

the demand for credit cards evidence from the survey of consumer finances i introduction the credit card market has expanded rapidly over the past 20 years in 1983 65 of households held at least one card by 1998 about 74 did so the size of real balances on these cards more than tripled in this period analysts have proposed a number of explanations for the increase but untangling the main causes is complicated by the unique nature of the credit card financial product an individual who obtains a credit card has obtained the right to borrow a certain amount called the limit with no questions asked under predetermined payback rules thus credit cards involve both assets and liabilities the available limits are best thought of as assets which can be used by a consumer to hedge against future income shortfalls or just to facilitate paying for goods and thereby reducing the need to carry cash the asset and limit components of credit cards makes them similar to financial instruments for example the asset component is essentially an option a subject that has been studied extensively in the corporate finance literature the seminal work is black and scholes 1973 who developed a method for valuing an option washam and davis 1998 extend this method to the problem of valuing the liquidity of credit resources this body of literature suggests that for some people a credit card can be viewed as a source of liquid funds for business purposes moreover once a credit card is used it becomes a debt liability in effect these are loans that the user has taken on to cover an income shortfall or simply to make a purchase for which borrowing makes sense again a corporate equivalent would be line of credit borrowing see myers 1989 or miller et al 1998 for an introduction these similarities raise the question of what sort of sample one should analyze for a study of consumer use of credit cards in all likelihood many average consumers who use credit cards are actually business entrepreneurs who use the cards to finance small business considering that wealth is an important element of any study of credit cards one faces the further problem that small business wealth is hard to measure accurately some research lindh and ohlsson 1998 suggests that access to liquid credit such as credit cards can make the difference between becoming self employed or not dunn and holtz eakin 2000 argue that family financial capital can ease the transition to self employment although they do not discuss credit availability in their study their results are strong evidence that credit cards would also ease that transition other studies that focus on the role of liquid credit and entrepreneurial activity include meyer 1990 blanchflower and oswald 1998 cox and japelli 1990 and evans and jovanovich 1989 our focus here is not on the use of credit cards as a business financing tool however it is apparent from this literature that business finance certainly plays a powerful role in determining the use of credit cards by some owners the research suggests that entrepreneurs would be more likely to be using credit cards for financing business rather than for consumer purposes for this reason it is important to separate the self employed from the non self employed in our sample looking specifically at consumers the unusual nature of the credit card financial product raises interesting questions for empirical researchers who hope as we do to provide some estimates of the responsiveness of the credit card demand to standard price and income effects the object of this article is to raise these questions and then answer some of them estimating regression models using data from the survey of consumer finances scf specifically we make two empirical approaches first we model credit card demand as a two stage process with a consumer obtaining limits in the first stage and then borrowing some fraction of those limits in the second

reverse auction with buyer supplier negotiation using bi level distributed programming this study presents a framework for solving a sealed bid multi issue and multi sourcing reverse auction problem in which negotiation takes place between the buyer and the suppliers during the bidding process the problem is formulated as a bi level distributed programming model in which the buyer is the upper level decision maker while suppliers at the lower level make decisions independent of each other the negotiation process between the buyer and the suppliers is facilitated via the iterative exchange of decision information between the upper and lower levels of the model the outcome of the sealed bid auction is determined using an algorithm designed to establish the optimum quantity allocation and delivery time at the upper level and the corresponding optimized production plans at the lower level the feasibility of the proposed approach is demonstrated via an illustrative example

on manufacturing marketing incentives stereotypically marketing is mainly concerned about satisfying customers and manufacturing is mainly interested in factory efficiency using the principal agent agency paradigm which assumes that the marketing and manufacturing managers of the firm will act in their self interest we seek incentive plans that will induce those managers to act so that the owner of the firm can attain as much as possible of the residual returns one optimal incentive plan can be interpreted as follows the owner subcontracts to pay the manufacturing manager a fixed rate for all capacity he delivers each marketing manager receives all of the returns from his product in turn all managers pay a fixed fee to the owner under this plan the marketing managers will often complain about the stock level decisions even though these levels are announced in advance under a revised plan the owner can eliminate such complaints by delegating the stocking decisions to the respective marketing managers without any loss this plan is interpreted as requiring the owner to make a futures market for manufacturing capacity paying the manufacturing manager the expected marginal value for each unit of capacity delivered receiving the realized marginal value from the marketing managers and losing money on average in the process

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

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

price and lead time quotation for contract and spot customers we study price and lead time quotation decisions in a make to order system with two customer classes 1 contract customers whose orders are practically always accepted and fulfilled based on a contract price and lead time agreed on at the beginning of the time horizon and 2 spot purchasers who arrive over time and are quoted a price and lead time pair dynamically the objective is to maximize the long run expected average profit per unit time where profit from a customer is defined as revenues minus lateness penalties incurred because of lead time violations we model the dynamic quotation problem of the spot purchasers as an infinite horizon markov decision process given a fixed price and lead time for contract customers we analyze the impact of customer preferences e g price and lead time sensitivity on the optimal price and lead time decisions for spot purchasers and characterize the optimal policy we explore the benefits of dynamic quotation compared to the use of fixed price and lead tim

the welfare effect of access to credit i present a model in which credit and outside money can be used as means of payment in order to analyze how access to credit aects welfare when credit markets feature limited participation allowing more agents to use credit has an ambiguous eect on welfare because it may make consumption risk sharing more ine cient i calibrate the model using u s data on credit card transactions and show that the increase in access to credit from 1990 to the near present has had a slightly negative impact on welfare

inventory policies under various optimizing criteria and variable markup rates this paper extends the deterministic eoq model to reflect various optimizing criteria and alternative demand and price structures its primary purpose is to develop decision rules for the management of finished goods inventories especially in retailing where inventories are evaluated in the same way as any other investment namely on their ability to generate profits rather than on the traditional least cost basis to that effect the models developed here consider demand to be a function of price with price defined as a markup of unit cost the decision variables are the order quantity and the markup rate possible optimizing objectives include profits return on investment or residual income the three most widely used evaluators of short term investment performance optimal solutions for each case are obtained and the resulting inventory policies evaluated

credit cards and money demand a cross sectional study this study investigates credit card holding and the household demands for several monetary assets in a simultaneous equations framework it exploits the detailed data on household assets as well as demographic and preference characteristics in the 1983 survey of consumer finances a key finding is that consistent with theory a higher probability of credit card ownership implies lower demand for transaction balances with no effect on small time deposit balances copyright 1995 by ohio state university press

reinforcement learning for joint pricing lead time and scheduling decisions in make to order systems the paper investigates a problem faced by a make to order mto firm that has the ability to reject or accept orders and set prices and lead times to influence demands inventory holding costs for early completed orders tardiness costs for late delivery orders order rejection costs manufacturing variable costs and fixed costs are considered in order to maximize the expected profits in an infinite planning horizon with stochastic demands the firm needs to make decisions from the following aspects which orders to accept or reject the trade off between price and lead time and the potential for increased demand against capacity constraints we model the problem as a semi markov decision problem smdp and develop a reinforcement learning rl based q learning algorithm qla for the problem in addition we build a discrete event simulation model to validate the performance of the qla and compare the experimental results with two benchmark policies the first come first serve fcfs policy and a threshold heuristic policy it is shown that the qla outperforms the existing policies

investing in reduced setups in the eoq model this paper is motivated by the observation that the japanese have devoted much time and energy to decreasing setup costs in their manufacturing processes and that there has been little in the way of a formal framework available to use to think about such efforts the object of this paper is to begin to provide such a framework the framework developed identifies only one aspect of the advantages of reducing setups namely reduced inventory related operating costs the other advantages such as improved quality control flexibility and increased effective capacity are not accounted for in this paper nevertheless substantial reductions in setups may be warranted based solely on the benefits identified in this paper the approach taken here introduces an investment cost associated with changing the current setup level and adds a per unit time amortization of this cost to the other costs identified in the standard eoq model the general problem becomes that of minimizing the sum of a convex and a concave function in two special cases the minimization can be carried out explicitly in one of these cases numerous interpretations of the results are made including comparisons of japanese and american practices for example holding other parameters constant there is a critical sales level such that investment is made in reducing setups if and only if the sales rate is above that level when such investment is made the optimal lot size is independent of the sales rate the paper also addresses the joint selection of the setup cost and the sales rate selection of the sales rate is seen as incorporating explicit production and holding costs into the classical monopolist s pricing problem an explicit solution is obtained for the model postulated

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

durable goods monopoly with entry of new consumers this paper analyzes a model of a dynamic monopolist who produces at constant unit cost each period a new cohort of consumers enters the market each entering cohort is identical consumers within a cohort have different tastes for the good my main results are if players are sufficiently patient any positive average profit less than the maximum feasible level can be attained in a subgame perfect equilibrium in the subset of subgame perfect equilibria in which players use stationary strategies the seller cannot make sales at prices significantly greater than the lowest willingness to pay when period length goes to zero and the seller attains the maximum profit when commitment is feasible by charging the same static monopoly price in every period this paper analyzes a model of a dynamic monopolist who operates in a market in which there is a regular flow of new consumers the seller produces a durable good at constant unit cost each period a new cohort of consumers enters the market consumers wish to buy exactly one unit of the item but are willing to wait resales are not allowed each entering cohort is identical

coordinating inventory control and pricing strategies with random demand and fixed ordering cost the finite horizon case we analyze a finite horizon single product periodic review model in which pricing and production inventory decisions are made simultaneously demands in different periods are random variables that are independent of each other and their distributions depend on the product price pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered the objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon we show that when the demand model is additive the profit to go functions arek concave and hence an s s p policy is optimal in such a policy the period inventory is managed based on the classical s s policy and price is determined based on the inventory position at the beginning of each period for more general demand functions i e multiplicative plus additive functions we demonstrate that the profit to go function is not necessarilyk concave and an s s p policy is not necessarily optimal we introduce a new concept the symmetrick concave functions and apply it to provide a characterization of the optimal policy

market premium social process and statisticism statistics is a powerful yet potentially dangerous tool more than two decades ago the late otis dudley duncan 1984 226 warned us concerning the danger of statisticism the notion that computing is synonymous with doing research the naive faith that statistics is a complete or sufficient basis for scientific methodology the superstition that statistical formulas exist for evaluating such things as the relative merits of different substantive theo

a game theory approach in seller buyer supply chain in this paper several seller buyer supply chain models are proposed which incorporate both cost factors as well as elements of competition and cooperation between seller and buyer we assume that unit marketing expenditure and unit price charged by the buyer influence the demand of the product being sold the relationships between seller and buyer will be modeled by non cooperative and cooperative games respectively the non cooperative game is based on the stackelberg strategy solution concept where we consider separately the case when the seller is the leader seller stackelberg and also when the buyer is the leader buyer stackelberg pareto efficient solutions will be provided for the cooperative game model numerical examples presented in this paper including sensitivity analysis of some key parameters will compare the results between different models considered

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

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

the impact of dynamic pricing on the economic order decision this paper analyzes the impact of dynamic pricing on the single product economic order decision of a monopolist retailer items are procured from an external supplier according to the economic order quantity eoq model and are sold to customers on a single market without competition following the simple monopolist pricing problem coordinated decision making of optimal pricing and ordering is influenced by operating costs including ordering and inventory holding costs and the demand rate obtained from a price response function the retailer is allowed to vary the selling price either in a fixed number of discrete points in time or continuously while constant and continuous pricing have received much attention in the literature problems with a limited number of price changes are rather rare this paper illustrates the benefit of dynamically changing prices to achieve operational efficiency in the eoq model that is to trigger high demand rates when inventories are high we provide structural properties of the optimal time instants when the price should be changed taking into account costs for changes in price it provides numerical guidance on number timing and size of price changes during an order cycle numerical examples show that the benefits of dynamic pricing in an eoq framework can be achieved with only a few price changes and that products being unprofitable under static pricing may become profitable under dynamic pricing

dynamic version of the economic lot size model this article originally appeared in management science october 1958 volume 5 number 1 pp 89 96 published by the institute of management sciences a forward algorithm for a solution to the following dynamic version of the economic lot size model is given allowing the possibility of demands for a single item inventory holding charges and setup costs to vary over n periods we desire a minimum total cost inventory management scheme which satisfies known demand in every period disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full n periods

simultaneous and dynamic price production inventory and capacity decisions abstract this paper concerns a profit maximizing firm that derives the optimal price for its output level of output level of inventory and composition of productive capacity over time first it is assumed that capacity may be acquired to either increase or replace the firm s existing productive capacity second it is assumed that the acquisition of new capacity causes a reduction in the firm s production cost lastly it is assumed that demand which is expressed as a function of time and price must be met either from current production or from inventory clearly the level of production cannot exceed the productive capacity at any time the optimal control model formulated requires the solution of a two point boundary value problem so that a discrete approximation numerical procedure is presented numerical results indicate that due to anticipated technological improvement the acquisition of new capacity is postponed and occurs in greater magnitude later in the planning horizon in addition as a result of upgrading productive capacity through the acquisition of new technology numerical results show that a firm lowers its per unit production cost and thereby reduces the optimal price charged for output which increases demand furthermore since the level of capacity is increased due to the purchase of new technology less reliance on inventory is necessary to meet peak demand lastly it is shown that a larger firm optimally acquires a greater level of new capacity over the planning horizon to reduce its operating costs and thereby further its competitive advantage

effects of credit and debit cards on the currency demand we analyze the effects of credit and debit cards on the currency in circulation by using gmm estimation instead of using the data obtained by surveys we use monthly data obtained by an interbank institution that keeps the statistics of all credit and debit cards usage of a small open economy turkey for the period over 2002m1 2006m10 as expected from the theory we find that an increase in the usage of credit and debit cards leads to a decrease in the currency demand moreover the usage of the debit cards has a bigger effect on the money demand compared to the usage of the credit cards we also find that the effect of credit cards is mostly through purchases and the effect of debit cards is mostly through withdrawals

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

price delivery time guarantees and capacity selection this paper studies the impact of using delivery time guarantees as a competitive strategy in service industries where demands are sensitive to both price and delivery time we assume that delivery reliability is crucial and investment in capacity expansion is plausible in order to maintain a high probability of delivering the time guarantee a mathematical framework is proposed to understand the interrelations among pricing delivery time guarantee and capacity expansion decisions specifically an optimization model is developed to determine the joint optimal selection of these three important decision variables with an objective of maximizing the average net profit we characterize the optimal decisions and study their qualitative behaviors as various parameters change we further present a numerical example to illustrate how the results of our model can be used to provide useful managerial insights for selecting the best competing strategies for firms with different operating characteristics our model and results are also applicable to a make to order manufacturing environment

optimal pricing and lot sizing under conditions of perishability and partial backordering we formulate a generalized model of dynamic pricing and lot sizing by a reseller who sells a perishable good we assume that when it is economic to backlog demand the reseller can plan for periods of shortage during which demand can be partially backordered when the good is highly perishable the reseller may need to backlog demand in order to market the good at a reasonable price we present a simple solution procedure for solving the optimization problem the procedure entails solving first a single nonlinear equation and then if required two nonlinear equations

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