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

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

price dispersion price flexibility and repeated purchasing this paper presents a search model in which consumers repeatedly purchase a commodity the repetition of purchases leads to the formation of implicit contracts with sellers which generate a kink in the demand curve facing each seller these kinks can generate equilibrium price dispersion under conditions where single purchase search models predict no price dispersion despite the kinks prices are at least partially flexible in that some and possibly all sellers change their prices in response to changes in production costs or demand dispersion de prix flexibilite des prix et achats repetes ce memoire presente un modele de recherche dans lequel les consommateurs font des achats repete s d un bien la repetition de l achat entraine la formation de contrats implicites avec les vendeurs ceci cree un pli dans la cedule de demande a laquelle chaque vendeur fait face ces plis peuvent engendrer une dispersion des prix d equilibre alors que le meme modele ne predirait aucune dispersion de prix en l absence d achats repet s malgre les plis les prix sont au moins partiellement flexibles puisque certains vendeurs tous peut re peuvent changer leurs prix en reponse a des changements dans les cofuts de production ou dans la demande

inventories rational expectations and the business cycle abstract the simplest macroeconomic models in which markets clear instantaneously and expectations are rational preclude the existence of business cycles that is of serially correlated deviations of output from trend this paper studies one of several mechanisms that can be used to make these so called new classical models produce business cycles the mechanism is the gradual adjustment of inventory stocks two macroeconomic models of inventory holdings are formulated both imply first that current output should be a decreasing function of the stock of inventories and second that inventories once perturbed from equilibrium levels should adjust only gradually these two features are then embedded into an otherwise standard macroeconomic model in which markets clear instantaneously and expectations are rational two principal conclusions are reached first disturbances such as unanticipated changes in money will set in motion serially correlated deviations of output from trend second if desired inventories are sensitive to the real interest rate then even fully anticipated changes in money can affect real variables

fiscal policy and business cycle characteristics in a heterogeneous agent macro model abstract this paper explores the macroeconomic implications of changing fiscal policy in a heterogeneous interacting agent hia model the key contributions to the existing hia complex adaptive trivial system cats literature include the addition of a progressive income tax structure an expanded role for redistribution and a stylized reactive government sector in certain specifications deficit financed tax cuts are shown to effectively shorten recessions while deficit financed spending stimulus is able to lengthen recoveries alternative specifications provide ambiguous support for generalizing the effectiveness of these policy treatments robustness checks support the general findings that increased redistribution towards the unemployed results in higher unemployment rates greater inequality and shorter contractions

dynamic capacity management with substitution we examine a multiperiod capacity allocation model with upgrading there are multiple product types corresponding to multiple classes of demand and the firm purchases capacity of each product before the first period within each period after demand arrives products are allocated to customers customers who arrive to find that their product has been depleted can be upgraded by at most one level we show that the optimal allocation policy is a simple two step algorithm first use any available capacity to satisfy same class demand and then upgrade customers until capacity reaches a protection limit so that in the second step the higher level capacity is rationed we show that these results hold both when all capacity is salvaged at the end of the last demand period as well as when capacity can be replenished in the latter case an order up to policy is optimal for replenishment although finding the optimal protection limits is computationally intensive we describe bounds for the optimal protection limits that take little effort to compute and can be used to effectively solve large problems using these heuristics we examine numerically the relative value of strictly optimal capacity and dynamic rationing the value of perfect demand information and the impact of demand and economic parameters on the value of optimal substitution

lowest unique bid auctions with population uncertainty abstract we characterize the unique poisson nash equilibrium of the l owest u nique b id a uction luba when the number of bidders is uncertain and follows a poisson distribution

inventories and price inflexibility a firm maximizing expected discounted profits taking account of the actions of its competitors choosing price and output before stochastic demand is known and holding inventories or unfilled orders to accommodate discrepancies between output and demand is shown to respond to a change in demand by changing its output whether the demand change is transitory or permanent but by changing the price it charges only if the demand change is permanent this proposition is shown to be consistent with german data the data are qualitative the empirical analysis uses the multivariate conditional logit model the empirical results are summarized by gamma coefficients

gambling by auctions abstract we provide theoretical and empirical analysis of a selling mechanism used by an internet web site that combines important features of auctions and gambling this is the first analysis of such a selling mechanism which provides insights into how the two kinds of behavior might be related in real life the winner of the object is the bidder with the highest bid not submitted by any other bidder in the equilibrium of our game theoretical model each bid made with positive probability yields the same probability of winning bidders are more likely to submit higher bids and the bid distribution does not depend on the value of the object or the highest bid allowed if one controls for the number of bidders most of these key theoretical predictions are confirmed by the data

a note on poisson contests we apply the environmental equivalence property of poisson games myerson in int j game theory 27 375 392 1998b to show that in contests in which the number of contestants is a poisson random variable with at least two expected contestants and a non increasing return to effort ex ante aggregate effort is less than in a corresponding contest wherein the number of participants is equal to the expected number of contestants under uncertainty uncertainty about the number of participants in a rent seeking contest seems natural with rent seeking contests attracting socially wasteful investments of effort or scarce resources uncertainty generates a social benefit

an empirical analysis of scarcity strategies in the automobile industry recent product introductions such as the xbox 360 sony playstation 2 and pt cruiser have been characterized by shortage of these products some experts have suggested that such scarcity can be a deliberate strategy for making the product more desirable in this paper we empirically examine the relationship between introductory inventory levels and consumer preference in the u s automobile industry and show that relative scarcity of a car at the time of introduction is associated with higher consumer preference for the product furthermore we perform an empirical test of alternative theories about the rationale for introductory product scarcity specifically we consider two theories of supplier induced scarcity namely the buying frenzy theory and the signaling theory and an alternative theory that suggests that demand uncertainty causes introductory product scarcity we find more support for the signaling theory of supplier induced scarcity than the buying frenzy theory or the demand uncertainty theory in our analysis of the automobile market

social learning and dynamic pricing of durable goods we analyze the impacts of social learning sl on the dynamic pricing and consumer adoption of durable goods in a two period monopoly consumers can make either early uninformed purchases or late but potentially informed purchases as a result of social learning several results are derived first we identify the market conditions under which ex ante homogeneous consumers may choose to purchase at different times second equilibrium adoption may demonstrate inertia where all adopt late or frenzy where all adopt early in particular adoption inertia appears when sl intensity is reasonably high but may vanish when sl intensity exceeds a certain threshold third firm profits and social welfare first weakly decrease in sl intensity and may then jump up by a lump sum amount at the threshold sl intensity level mentioned above last we show that the firm potentially benefits from informative advertising or investing to cultivate more social learning

monetary disturbances inventory fluctations and the level of sales a theoretical and empirical analysis there has in the past several years been a revival of interest in the topic of inventory fluctuation and its relationship to the short run dynamics of output one important reason for this interest can be traced to the pioneering work on aggregate supply begun by lucas 11 12 and extended among many others by barro 3 4 in their models the behavior of output is driven by intertemporal considerations it is a natural extension of such models if output is storable to consider the implication of producers whose current output can either be sold immediately or held in stock for future sales current sales by the same token may be either current production or goods from inventory in a recent paper blinder and fischet 6 develop such a model using it they demonstrate that inventory dynamics can be an explanation for an empirical weakness of simple versions of the lucas type models real world business cycles are characterized by considerable persistence simple equilibrium business cycle models do not exhibit such persistence or in some cases it is present only through the ad hoc presence of a lagged output term in the aggregate supply function except for the influence of inventories producers in the blinder fischer analysis behave as do producers in most new classical macro models they are price takers and quantity setters in a model where inventories exert an influence on output decisions such neoclassical behavior cannot be ascribed to perfectly competitive conditions if firms are perfect competitors output decisions will not reflect the state of current inventories

revenue management under a general discrete choice model of consumer behavior customer choice behavior such as buy up and buy down is an important phenomenon in a wide range of revenue management contexts yet most revenue management methodologies ignore this phenomenon or at best approximate it in a heuristic way in this paper we provide an exact and quite general analysis of this problem specifically we analyze a single leg reserve management problem in which the buyers choice behavior is modeled explicitly the choice model is very general simply specifying the probability of purchase for each fare product as a function of the set of fare products offered the control problem is to decide which subset of fare products to offer at each point in time we show that the optimal policy for this problem has a quite simple form namely it consists of identifying an ordered family of efficient subsets s 1 s m and at each point in time opening one of these sets s k where the optimal index k is increasing in the remaining capacity x and decreasing in the remaining time that is the more capacity or less time available the further the optimal set is along this sequence we also show that the optimal policy is a nested allocation policy if and only if the sequence of efficient sets is nested that is s 1 s 2 s m moreover we give a characterization of when nesting by fare order is optimal we also develop an estimation procedure for this setting based on the expectation maximization em method that jointly estimates arrival rates and choice model parameters when no purchase outcomes are unobservable numerical results are given to illustrate both the model and estimation procedure

recent advances in modelling seasonality abstract in this paper we review recent developments in econometric modelling of economic time series with seasonality the prime focus is on econometric models which incorporate explicit descriptions of seasonal variation instead of removing this variation using a seasonal adjustment method this review centres around developments in seasonal unit root models and in periodic parameter models both in the univariate and multivariate context several empirical examples are used for illustration we also discuss several areas for further research

dynamic capacity management with uncertain demand and dynamic price inspired from practices of chinese real estate firms we study dynamic capacity management problems for a firm that sells homogeneous goods over a finite or infinite selling horizon provided that demand is uncertain retail price is exogenous but changes according to an auto regressive process and there is holding cost for remaining inventory in each period the capacity problems facing the firm include to determine an initial stock at the beginning of the selling season and to allocate the remaining quantity for the current and future sale in each period to maximize the firm s total expected discounted profit by using markov decision processes we show the optimality of a so called save up to level policy i e it is optimal to allocate as much as the save up to level to future periods if possible in each period and the existence of the optimal initial stock moreover we characterize monotone properties of the optimal save up to level and the optimal initial stock numerical analysis shows that compared to the policy with zero save up to level i e always allocating all the remaining inventory to the current period the advantage of the policy proposed in the present paper is significant when price rising trend is large holding cost is low initial price is high or demand variation is either high or low

revenue management through dynamic cross selling in e commerce retailing we consider the problem of dynamically cross selling products e g books or services e g travel reservations in the e commerce setting in particular we look at a company that faces a stream of stochastic customer arrivals and may offer each customer a choice between the requested product and a package containing the requested product as well as another product what we call a packaging complement given consumer preferences and product inventories we analyze two issues 1 how to select packaging complements and 2 how to price product packages to maximize profits we formulate the cross selling problem as a stochastic dynamic program blended with combinatorial optimization we demonstrate the state dependent and dynamic nature of the optimal package selection problem and derive the structural properties of the dynamic pricing problem in particular we focus on two practical business settings with the emergency replenishment model and without the lost sales model the possibility of inventory replenishment in the case of a product stockout for the emergency replenishment model we establish that the problem is separable in the initial inventory of all products and hence the dimensionality of the dynamic program can be significantly reduced for both models we suggest several packaging pricing heuristics and test their effectiveness numerically

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

cargo capacity management with allotments and spot market demand we consider a problem faced by an airline that operates a number of parallel flights to transport cargo between a particular origin to destination pair the airline can sell its cargo capacity either through allotment contracts or on the spot market where customers exhibit choice behavior between different flights the goal is to simultaneously select allotment contracts among available bids and find a booking control policy for the spot market to maximize the sum of the profit from the allotments and the total expected profit from the spot market we formulate the booking control problem on the spot market as a dynamic program and construct approximations to its value functions which can be used to estimate the total expected profit from the spot market we show that our value function approximations provide upper bounds on the optimal total expected profit from the spot market and they allow us to solve the allotment selection problem through a sequence of linear mixed integer programs with a special structure furthermore the value function approximations are useful for constructing a booking control policy for the spot market with desirable monotonic properties computational experiments show that the proposed approach can be scaled to realistic problems and provides well performing allotment allocation and booking control decisions

determinants of price adjustment this paper reports results of an empirical study investigating the adjustment speed of prices to change in costs and demand particular emphasis is laid on the impact of concentration on the adjustment speed in addition the effects of the business cycle and capital intensity are considered it shows that concentrated industries tend to adjust prices faster while capital intensity has a negative impact prices are more flexible during an upswing than in times of a recession

optimal market making with risk aversion market makers have the obligation to trade any given amount of assets at quoted bid or ask prices and their inventories are exposed to the potential loss when the market price moves in an undesirable direction one approach to reduce the risk brought by price uncertainty is to adjust the inventory at the price of losing potential spread gain using stochastic dynamic programming we show that a threshold inventory control policy is optimal with respect to an exponential utility criterion and a mean variance trade off model symmetric and monotone properties of the threshold levels are also established

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

pricing in revenue management for multiple firms competing for customers abstract we consider the pricing strategies of multiple firms providing the same service in competition for a common pool of customers in a revenue management context the firms have finite capacity and the demand at each firm depends on the selling prices charged by all firms each of which satisfies demand up to a given capacity limit we use game theory to analyze the systems when firms face either a deterministic demand or a general stochastic demand the existence and uniqueness conditions of a nash equilibrium are derived and we calculate the explicit nash equilibrium point when the demand at each firm is a linear function of price we also conduct sensitivity analysis of the equilibrium prices with respect to cost and capacity parameters

an empirical analysis of backlog inventory production and price adjustments an application of recursive systems of log linear models this article presents an empirical analysis of firms order backlogs inventories production and price adjustments to unanticipated demand shocks the data are obtained from quarterly insee business survey tests on firms realizations expectations and appraisals of some various economic variables the analysis is based on the formulation and the estimation of a recursive system of conditional log linear probability models

seasonality in surveys a comparison of belgian french and german business tests abstract seasonal effects appear in qualitative responses of monthly business surveys the seasonal effects can be extracted like in regression or time series models via dummy variables in surveys however there is another route to extract the seasonal effects by incorporating questions on the questionnaires which force respondents to make a distinction between seasonal and cyclical effects it is shown in the paper that a comparison of these two approaches on theoretical grounds is inconclusive evidence from belgian french and german surveys is used to make a comparison the approach with survey based seasonal measures is found more desirable moreover the responses to the request to separate seasonal from cyclical effects seem to be fairly consistent

the stylized facts about the behavior of manufacturers inventories and backorders over the business cycle 1959 1980 recent theoretical work has highlighted the role of inventories in propagating business cycles this paper attempts to provide an empirical foundation for current and future research on the role inventories play in business cycles the evidence presented here indicates that inventories and backorders are major variables in predicting output fluctuations further the evidence is that disaggregating inventories by stage of fabrication is important in predicting output in concert with previous findings our results suggest that disaggregated inventories ought to be a component of models of the business cycle

disequilibrium dynamics an empirical study despite the amount of attention devoted in economics to the study of equilibria the process by which an equilibrium can be attained is not well understood stephen smale 1977 called this the fundamental problem of economic theory this paper explores the microeconomics of the adjustment process by examining empirically the disequilibrium behavior of firms implications for the microeconomic foundations of macroeconomics are stressed the data from german industry describe the month by month price and output changes of individual firms as well as the firms own assessments of the levels of their inventories and unfilled orders because the data are qualitative use is made of the multivariate conditional logit model developed by marc nerlove and s james press 1973 1976 and extended by kawasaki and zimmermann section i discusses the underlying model of firm behavior and the significance of the inquiry for macroeconomics in section ii the econometric techniques are briefly described in section iii the empirical results are summarized and interpretations of the results are offered in section iv

inventories and sticky prices more on the microfoundations of macroeconomics the role of inventories in making prices sticky is studied by analyzing a dynamic linear quadratic model of a monopoly firm facing stochastic demand but able to store its finished goods in inventory it is shown that in contrast to the usual presumption firms that exhibit the smallest output responses to demand fluctuations may also exhibit the smallest price fluctuations specifically firms which have very flexible inventory storage facilities or are subjected to very transitory demand shocks will rely on inventories as buffers and will change neither production nor price very much on the other hand firms which have very inflexible storage facilities or whose demand shocks are quite permanent will display large swings in both price and output the standard assumption about inventory carrying costs that has been used in the literature that they are linear is shown to imply that production is impervious to fluctuations in demand it is also established that prices may respond more strongly to positive demand shocks than to negative ones if it is impossible to hold negative inventories i e to have unfilled orders the model offers an explanation for stickiness in relative prices however under certain circumstances it may help explain the persistence of inflation this abstract was borrowed from another version of this item

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

emergent dynamics of a macroeconomic agent based model with capital and credit in this paper we present and discuss a macroeconomic agent based model with capital and credit cc mabm which builds upon the framework put forward by delli gatti et al 2011 the novelty of this model with respect to the previous framework consists in the introduction of a stylized supply chain where upstream firms i e producers of capital goods k firms supply a durable and sticky input capital to the downstream firms who produce consumption goods c firms to be sold to households both c firms and k firms resort to bank loans to satisfy their financing needs there are two way feedbacks between firms and markets which yield interesting emerging properties at the macro level we show that the interaction of upstream and downstream firms and the evolution of their financial conditions in a nutshell capital and credit are essential ingredients of a crisis i e a sizable slump followed by a long recovery

price and output adjustment in a model with inventories econometric evidence from categorical in this paper we investigate the role of inventories in the adjustment process of prices and output in response to demand and cost shocks using the qualitative information contained in business surveys of u k firms the discussion is organized around a model based on the assumption of monopolistic competition and which permits a production smoothing role for inventories the econometric results suggest that the stock of inventories has no impact on output decisions the effect on pricing decisions is weak at best anticipated demands shocks are the main factor accounting for output changes while both cost and demand shocks are important determinants of prices coauthors are fabio schiantarelli jon breslaw and william low copyright 1993 by mit press

price adjustment in an automobile insurance market a test of the sheshinski weiss model nominal price rigidity is explained in the sheshinski weiss sw model by costly price adjustment the predictions of the sw model which describe a firm s optimal forward looking price adjustment strategy were derived and tested using microdata on the timing and the magnitude of premium changes by sixty nine firms in the alberta automobile insurance market over the period 1974 82 the model was tested by estimating the structural equations of the model probit equations for premium changes and reduced form equations for the firm s new premium and its old premium the overall conclusion is that the sw model does not explain the price adjustments observed in the alberta automobile insurance market