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 pricing and composition of multiple bundles a two step approach abstract this paper analyzes the problem facing a firm that must determine the optimal composition and pricing of multiple bundles it supplies to a single market segment it is assumed the firm s competitors does not react in the short run to its decisions and that their bundles prices and characteristics are known it is further assumed that potential consumers of bundles are rational and maximize a random utility function the problem is modeled as a mixed integer non linear program though such programs are normally hard to solve using traditional methods the difficulties are circumvented here by taking advantage of the problem s mathematical structure to develop a novel two phase solution approach two aspects of the solution are particularly worthy of note 1 we demonstrate that the optimal price of a bundle marketed by a firm depends on the composition of all the firm s bundles and not on their prices and on the composition and price of all the competitors bundles in the market and 2 that if the consumer choice behavior is described by a logit model then the firm s bundles should be very similar to each other

competitive targeted advertising with price discrimination this paper investigates the eects of price discrimination by means of targeted advertis ing in a duopolistic market where the distribution of consumers preferences is discrete and where advertising plays two major roles it is used by rms as a way to transmit relevant information to otherwise uninformed consumers and it is used as a price discrimination device we compare the rms optimal marketing mix advertising and pricing when they adopt mass advertising non discrimination strategies and targeted advertising price discrim ination strategies if rms are able to adopt targeted advertising strategies we nd that the symmetric price equilibrium is in mixed strategies while the advertising is chosen deter ministically our results also unveil that as long as we allow for imperfect substitutability between the goods rms do not necessarily target more ads to their own market in par ticular rms optimal marketing mix leads to higher advertising reach in the rival s market than in the rms own market provided that advertising costs are su ciently low in relation to the consumer s reservation value the comparison of the optimal marketing mix under mass advertising strategies and targeted advertising strategies reveals that targeted adver tising might constitute a tool to dampen price competition in particular if advertising costs are su ciently low in relation to the value of the goods we obtain that average prices with non discrimination mass advertising are below those with price discrimination and targeted advertising regardless of the market segment accordingly when i goods are imperfect substitutes ii advertising is not too expensive and iii targeted advertising constitutes an eective price discrimination tool price discrimination through targeted advertising may be detrimental to social welfare since it boosts industry pro ts at the expense of consumer surplus

tracking the market dynamic pricing and learning in a changing environment dynamic pricing of commodities without knowing the exact relation between price and demand is a much studied problem most existing studies assume that the parameters describing the market are constant during the selling period this severely reduces their practical applicability since in reality market characteristics may change all the time without the firm always being aware of it in the present paper we study dynamic pricing and learning in a changing market environment we introduce a methodology that enables the price manager to hedge against changes in the market and provide explicit upper bounds on the regret a measure of the performance of the firm s pricing decisions in addition this methodology guides the selection of the optimal way to estimate the market process we provide numerical examples from practically relevant situations to illustrate the methodology

pressure groups and redistribution abstract the simple pressure group model of political redistribution can predict more with less restrictive assumptions instead of ready made pressure groups composed of individuals who vote their pocketbooks we posit heterogeneous agents each of whom decides which group to join and how much effort to expend on political activity our model then examines social affinity conditions that foster pressure group formation political sympathies based on social affinity imply testable effects of growth rate and income distribution on progressive transfers effects that prove substantial in pooled time series cross section regressions for 13 oecd countries 1960 1981

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

optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices abstract consider a continuous time inventory problem in which a retailer sets the price on a fixed number of a perishable asset that must be sold prior to the time at which it perishes the retailer can dynamically adjust the price between any of a finite number of allowable prices demand for the product is poisson with an intensity that is inversely related to the price the optimal policy is piecewise constant the maximum expected revenue is nondecreasing and concave in both the remaining inventory and the time to go for a given inventory level the optimal price declines as the time at which the products perish approaches at any given time the optimal price is nonincreasing in the number of items remaining unsold these results are extended to i the case in which the prices and corresponding demand intensities depend on the time to go and ii the case in which the retailer can restock to meet demand at a unit cost after the initial inventory has been sold

robust assortment optimization in revenue management under the multinomial logit choice model we study robust formulations of assortment optimization problems under the multinomial logit choice model the novel aspect of our formulations is that the true parameters of the logit model are assumed to be unknown and we represent the set of likely parameter values by a compact uncertainty set the objective is to find an assortment that maximizes the worst case expected revenue over all parameter values in the uncertainty set we consider both static and dynamic settings the static setting ignores inventory consideration whereas in the dynamic setting there is a limited initial inventory that must be allocated over time we give a complete characterization of the optimal policy in both settings show that it can be computed efficiently and derive operational insights we also propose a family of uncertainty sets that enables the decision maker to control the trade off between increasing the average revenue and protecting against the worst case scenario numerical experiments show that our robust approach combined with our proposed family of uncertainty sets is especially beneficial when there is significant uncertainty in the parameter values when compared to other methods our robust approach yields over 10 improvement in the worst case performance but it can also maintain comparable average revenue if average revenue is the performance measure of interest

a probabilistic choice model for market segmentation and elasticity structure marketing scholars commonly characterize market structure by studying the patterns of substitution implied by brand switching though the approach is useful it typically ignores the destabilizing

intergenerational redistribution with short lived governments we study the politics of intergenerational redistribution in an overlapping generations model with short lived governments the successive governments who care about the welfare of the currently living generations and possibly about campaign contributions are unable to pre commit the future course of redistributive taxation in a stationary politico economic equilibrium the intergenerational transfer in each period depends on the current value of the state variable and all expectations about future political outcomes are fulfilled we find that there exist multiple stationary equilibria in many political settings steady state welfare is often lower than it would be in the absence of redistributive politics

the competitive newsboy we consider a competitive version of the classical newsboy problem in which a firm must choose an inventory or production level for a perishable good with random demand and the optimal solution is a fractile of the demand distribution and investigate the impact of competition upon industry inventory a splitting rule specifies how initial industry demand is allocated among competing firms and how any excess demand is allocated among firms with remaining inventory we examine the relation between equilibrium inventory levels and the splitting rule and provide conditions under which there is a unique equilibrium our most general result is that if all excess demand is reallocated i e there is perfect substitutability then competition never leads to a decrease in industry inventory

bundle pricing of inventories with stochastic demand we consider a retailer selling a fixed inventory of two perishable products over a finite horizon assuming poisson arrivals and a bivariate reservation price distribution we determine the optimal product and bundle prices that maximize the expected revenue our results indicate that the performances of mixed bundling pure bundling and unbundled sales strategies heavily depend on the parameters of the demand process and the initial inventory levels bundling appears to be most effective with negatively correlated reservation prices and high starting inventory levels when the starting inventory levels are equal and in excess of average demand most of the benefits of bundling can be achieved through pure bundling however the mixed bundling strategy dominates the other two when the starting inventory levels are not equal we also observe that an incorrect modeling of the reservation prices may lead to significant losses the model is extended to allow for price changes during the selling horizon it is shown that offering price bundles mid season may be more effective than changing individual product prices

unequal societies income distribution and the social contract this paper develops a theory of inequality and the social contract aiming to explain how countries with similar economic and political fundamentals can sustain such different systems of social insurance fiscal redistribution and education finance as those of the united states and western europe with imperfect credit and insurance markets some redistributive policies can improve ex ante welfare and this implies that their political support tends to decrease with inequality conversely with credit constraints lower redistribution translates into more persistent inequality hence the potential for multiple steady states with mutually reinforcing high inequality and low redistribution or vice versa

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

politico economic equilibrium and economic growth abstract we propose a notion of dynamic politico economic equilibrium which builds on two key assumptions policies are determined sequentially and agents are fully rational in their roles as both consumers and voters we examine a simple model of endogenous growth and infinitely lived agents where taxes on income are endogenous and where growth critically depends on the initial distribution of asset holdings we relate our equilibrium definition and results to existing literature on time consistency and on political economy and growth we show that our equilibria are time consistent and we argue that the choice of equilibrium concept might have important quantitative implications

how much income mobility is there in britain using the first four waves of the british household panel survey 1991 4 and a variety of methods we show that there is much mobility in household net income from one year to the next in britain however most income changes from one year to the next are not very large and when incomes are longitudinally averaged so that transitory variations are smoothed out substantial permanent income differences are revealed there is some evidence of greater mobility for those in the tails of the income distribution relative to the middle and for elderly persons compared to non elderly persons

relationships among three assumptions in revenue management this note discusses the relationships among three assumptions that appear frequently in the pricing revenue management literature these assumptions are mostly needed for analytical tractability and they have the common property of ensuring a well behaved revenue function the three assumptions are decreasing marginal revenue with respect to demand decreasing marginal revenue with respect to price and increasing price elasticity of demand we provide proofs and examples to show that none of these conditions implies any other however they can be ordered from strongest to weakest over restricted regions and the ordering depends upon the region

simple policies for dynamic pricing with imperfect forecasts we consider the classical single product dynamic pricing problem allowing the scale of demand intensity to be modulated by an exogenous market size stochastic process this is a natural model of dynamically changing market conditions we show that for a broad family of gaussian market size processes simple dynamic pricing rules that are essentially agnostic to the specification of this market size process perform provably well the pricing policies we develop are shown to compensate for forecast imperfections or a lack of forecast information altogether by frequent reoptimization and reestimation of the instantaneous market size

dynamic pricing with uncertain production cost an alternating move approach abstract this article studies a two firm dynamic pricing model with random production costs the firms produce the same perishable products over an infinite time horizon when production or operation costs are random in each period each firm determines its price and production levels based on its current production cost and its opponent s previous price level we use an alternating move game to model this problem and show that there exists a unique subgame perfect nash equilibrium in production and pricing decisions we provide a closed form solution for the firm s pricing policy finally we study the game in the case of incomplete information when both or one of the firms do not have access to the current prices charged by their opponents

a probabilistic approach to pricing a bundle of products or services the authors propose a probabilistic approach to optimally price a bundle of products or services that maximizes seller s profits their focus is on situations in which consumer decision making is o

intertemporal price discrimination structure and computation of optimal policies we study a firm s optimal pricing policy under commitment the firm s objective is to maximize its long term average revenue given a steady arrival of strategic customers in particular customers arrive over time are strategic in timing their purchases and are heterogeneous along two dimensions their valuation for the firm s product and their willingness to wait before purchasing or leaving the customers patience and valuation may be correlated in an arbitrary fashion for this general formulation we prove that the firm may restrict attention to cyclic pricing policies which have length at most twice the maximum willingness to wait of the customer population to efficiently compute optimal policies we develop a dynamic programming approach that uses a novel state space that is general capable of handling arbitrary problem primitives and that generalizes to finite horizon problems with nonstationary parameters we analyze the class of monotone pricing policies and establish their suboptimality in general optimal policies are in a typical scenario characterized by nested sales where the firm offers partial discounts throughout each cycle offers a significant discount halfway through the cycle and holds its largest discount at the end of the cycle we further establish a form of equivalence between the problem of pricing for a stream of heterogeneous strategic customers and pricing for a pool of heterogeneous customers who may stockpile units of the product this paper was accepted by yossi aviv operations management

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

competitive and cooperative inventory policies in a two stage supply chain we investigate a two stage serial supply chain with stationary stochastic demand and fixed transportation times inventory holding costs are charged at each stage and each stage may incur a consumer backorder penalty cost e g the upper stage the supplier may dislike backorders at the lower stage the retailer we consider two games in both the stages independently choose base stock policies to minimize their costs the games differ in how the firms track their inventory levels in one the firms are committed to tracking echelon inventory in the other they track local inventory we compare the policies chosen under this competitive regime to those selected to minimize total supply chain costs i e the optimal solution we show that the games nearly always have a unique nash equilibrium and it differs from the optimal solution hence competition reduces efficiency furthermore the two games equilibria are different so the tracking method influences strategic behavior we show that the system optimal solution can be achieved as a nash equilibrium using simple linear transfer payments the value of cooperation is context specific in some settings competition increases total cost by only a fraction of a percent whereas in other settings the cost increase is enormous we also discuss stackelberg equilibria

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

highway safety economic behavior and driving environment author s keeler theodore e abstract economic analysis has enhanced our understanding of the efficacy of highway safety regulations specifically a consumer theoretic literature has developed on drivers responses to regulations based on ideas first set forth by lester lave and w e weber 1970 and more fully thought out by sam peltzman 1975 meanwhile an empirical literature has also developed testing hypotheses relating to the effects on safety of speed limits safety device regulations and alcohol policies among other things yet despite extensive research controversies remain as to the effects of regulations on highway safety this paper contributes to the literature on economic aspects of highway safety in an four important ways first it is based on a county level data set for the u s for 1970 and 980 affording over 2 600 observations each year in a consistent panel many more observations than previous studies have used second this study uses different and more appropriate estimation procedures than most previous studies allowing for the count nature of highway fatalities and correcting for omitted variable bias otherwise possible in cross section analysis third the model used here controls for more variables in a single model than previous studies finally this study allows for important differences in the estimated coefficients between urban and rural driving environments

a theory of dynamic oligopoly ii price competition kinked demand curves and edgeworth cycles we provide game theoretic foundations for the classic kinked demand curve equilibrium and edgeworth cycle we analyze a model in which firms take turns choosing prices the model is intended to capture the idea of reactions based on short run commitment in a markov perfect equilibrium mpe a firm s move in any period depends only on the other firm s current price there are multiple mpe s consisting of both kinked demand curve equilibria and edgeworth cycles in any mpe profit is bounded away from the bertrand equilibrium level we show that a kinked demand curve at the monopoly price is the unique symmetric renegotiation proof equilibrium when there is little discounting we then endogenize the timing by allowing firms to move at any time subject to short run commitments we find that firms end up alternating thus vindicating the ad hoc timing assumption of our simpler model we also discuss how the model can be enriched to provide explanations for excess capacity and market sharing keiiwords tacit collusion markov perfect equilibrium kinked demand curve edgeworth cycle excess capacity market sharing endogenous timing

dynamic pricing with a prior on market response we study a problem of dynamic pricing faced by a vendor with limited inventory uncertain about demand and aiming to maximize expected discounted revenue over an infinite time horizon the vendor learns from purchase data so his strategy must take into account the impact of price on both revenue and future observations we focus on a model in which customers arrive according to a poisson process of uncertain rate each with an independent identically distributed reservation price upon arrival a customer purchases a unit of inventory if and only if his reservation price equals or exceeds the vendor s prevailing price we propose a simple heuristic approach to pricing in this context which we refer to as decay balancing computational results demonstrate that decay balancing offers significant revenue gains over recently studied certainty equivalent and greedy heuristics we also establish that changes in inventory and uncertainty in the arrival rate bear appropriate directional impacts on decay balancing prices in contrast to these alternatives and we derive worst case bounds on performance loss we extend the three aforementioned heuristics to address a model involving multiple customer segments and stores and provide experimental results demonstrating similar relative merits in this context

mixed bundling of two independently valued goods this paper develops analytical results and insights for the mixed bundling problem of pricing a product line consisting of two component goods with valuations distributed uniformly and independently in 0 a1 and 0 a2 respectively with a1 a2 and a bundle of the two goods this setting has previously been considered analytically intractable by deriving component good prices as exact algebraic functions of the optimal bundle price i reduce the multiproduct pricing problem to a univariate nonlinear optimization problem in the bundle price when the two component goods are sufficiently asymmetric in valuations the optimal solution is partial mixed bundling one component good is not sold separately for which i derive exact conditions and optimal prices an exact analytical solution is also given for mixed bundling of two information goods component goods with zero marginal costs for the general case i derive a closed form approximation of the optimal bundle price pb 0 5724w1 0 5695w2

speeding coordination and the 55 mph limit do laws coordinate or restrain a number of recent papers discuss the optimality of the 55 mph national maximum speed limit nmsl and evaluate the tradeoff of timelost vs lives saved resulting from the lowered speed james jondrow et al 1983 dana kamerud 1983 thomas forester et al 1984 these papers all implicitly accept the conventional wisdom speed kills slower is safer this conventional wisdom leads to laws designed as limits on behavior whereas the crucial element is often coordination people need to do the right things at the right time in relation to what others are doing thomas schelling 1978 p 121 there are indeed some traffic laws that establish conventions of expected conduct we ask that motorists drive to the right not because driving on the left is evil but because it is important that the direction of flow be commonly agreed upon likewise traffic lights are best viewed as a coordinating device allowing free flow to alternating lanes of traffic to reduce the confusion and loss of time in unsignalized intersections for peculiar historical reasons speed laws evolved as limits on driver behavior rather than as signaling devices meant to coordinate it guided by the limit rationale police concentrate on those drivers who exceed the legal speed and tend to ignore those drivers who disrupt coordination by traveling much slower than the norm this paper tests these differing views of the law by examining the current effects of the 55 mph nmsl should it be viewed as a coordinating mechanism or a limiting mechanism i measure the effects of limit defying behavior speeding and absence of coordination speed variance on the fatality rate based on analysis of 1981 and 1982 state cross section data i find that there is no statistically discernable relationship between the fatality rate and average speed though there is a strong relationship to speed variance when most cars are traveling at about the same speed whether it is a high speed or a low one the fatality rate will be low presumably because the probability of collision will be low variance kills not speed

a continuous time yield management model with multiple prices and reversible price changes this article studies a continuous time yield management model in which reversible price changes are allowed we assume that perishable assets are offered at a set of discrete price levels demand at each level is a poisson process to maximize the expected revenue management controls the price dynamically as sales evolve we show that a subset of these prices that form a concave envelope is potentially optimal we formulate the problem into an intensity control model and derive the optimal solution in closed form properties of the optimal solution and their policy implementations are discussed numerical examples are provided

social mobility and the demand for redistribution the poum hypothesis this paper examines the often stated idea that the poor do not support high levels of redistribution because of the hope that they or their offspring may make it up the income ladder this prospect of upward mobility poum hypothesis is shown to be fully compatible with rational expectations and fundamentally linked to concavity in the mobility process a steady state majority could even be simultaneously poorer than average in terms of current income and richer than average in terms of expected future incomes a e rst empirical assessment suggests on the other hand that in recent u s data the poum effect is probably dominated by the demand for social insurance in the future everyone will be world famous for e fteen minutes andy warhol 1968

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

a general equilibrium model for industries with price and service competition this paper develops a stochastic general equilibrium inventory model for an oligopoly in which all inventory constraint parameters are endogenously determined we propose several systems of demand processes whose distributions are functions of all retailers prices and all retailers service levels we proceed with the investigation of the equilibrium behavior of infinite horizon models for industries facing this type of generalized competition under demand uncertainty we systematically consider the following three competition scenarios 1 price competition only here we assume that the firms service levels are exogenously chosen but characterize how the price and inventory strategy equilibrium vary with the chosen service levels 2 simultaneous price and service level competition here each of the firms simultaneously chooses a service level and a combined price and inventory strategy 3 two stage competition the firms make their competitive choices sequentially in a first stage all firms simultaneously choose a service level in a second stage the firms simultaneously choose a combined pricing and inventory strategy with full knowledge of the service levels selected by all competitors we show that in all of the above settings a nash equilibrium of infinite horizon stationary strategies exists and that it is of a simple structure provided a nash equilibrium exists in a so called reduced game we pay particular attention to the question of whether a firm can choose its service level on the basis of its own input characteristics i e its cost parameters and demand function only we also investigate under which of the demand models a firm under simultaneous competition responds to a change in the exogenously specified characteristics of the various competitors by either i adjusting its service level and price in the same direction thereby compensating for price increases decreases by offering improved inferior service or ii adjusting them in opposite directions thereby simultaneously offering better or worse prices and service

optimal product bundling with dependent valuations the price of independence abstract in this paper we investigate the tactical problem of pricing a bundle of products when the underlying valuations of the bundle components are dependent we use copula theory to model the joint density of reservation prices and provide analytical derivations for the prices under different bundling strategies and sharp bounds for the profit function we discover that when only the bundle is offered and the marginal costs are relatively small the seller is better off by bundling products that have a negative association between their valuations while the converse is true when the marginal costs are relatively high we also show that the net benefit of offering a full product line containing both the bundle and the components decreases for mild to strong associations between the component valuations compared to offering just the bundle finally we analyze how the typical literature assumption of independence of reservation prices impacts the seller s profitability when in fact the valuations are dependent and find that this gap in profitability which we call the price of independence can be arbitrarily large

the survival of the welfare state this paper provides an analytical characterization of markov perfect equilibria in a model with repeated voting where agents vote over distortionary income redistribution a key result is that the future constituency for redistributive policies depends positively on current redistribution since this affects both private investments and the future distribution of voters the model features multiple equilibria in some equilibria positive redistribution persists forever in other equilibria even a majority of beneficiaries of redistribution vote strategically so as to induce the end of the welfare state next period skill biased technical change makes the survival of the welfare state less likely

competitive targeted advertising over networks recent advances in information technology have allowed firms to gather vast amounts of data regarding consumers preferences and the structure and intensity of their social interactions this paper examines a game theoretic model of competition between firms that can target their marketing budgets to individuals embedded in a social network we provide a sharp characterization of the optimal targeted advertising strategies and highlight their dependence on the underlying social network structure furthermore we provide conditions under which it is optimal for the firms to asymmetrically target a subset of the individuals and establish a lower bound on the ratio of their payoffs in these asymmetric equilibria finally we find that at equilibrium firms invest inefficiently high in targeted advertising and the extent of the inefficiency is increasing in the centralities of the agents they target taken together these findings shed light on the effect of the network structure on the outcome of marketing co

anyone for higher speed limits self interested and adaptive political preferences swedish survey evidence indicates that variables reflecting self interest are important in explaining people s preferred speed limits and that political preferences adapt to technological development drivers who believe they drive better than the average driver as well as drivers of cars that are newer and hence safer bigger and with better highspeed characteristics prefer higher speed limits in contrast elderly people prefer lower speed limits furthermore people report that they themselves vote more sociotropically than they believe others vote on average indicating that we may vote less sociotropically than we believe ourselves one possible reason for such self serving biases is that people desire to see themselves as socially responsible

the future of social security we analyze the effect of the projected demographic transition on the political support for social security and equilibrium outcomes embedding a probabilistic voting setup of electoral competition in the standard olg model with capital accumulation we find that intergenerational transfers arise in the absence of altruism commitment or trigger strategies closed form solutions predict population ageing to lead to higher social security tax rates a rising share of pensions in gdp but eventually lower social security benefits per retiree the response of equilibrium tax rates to demographic shocks reduces old age consumption risk calibrated to match features of the u s economy the model suggests that in response to the projected demographic transition social security tax rates will gradually increase to 16 other policies that distort labor supply will become less important labor supply therefore will rise in contrast with frequently voiced fears

dynamic and targeted bundle pricing of two independently valued products abstract bundling is when two or more products are offered as a single unit and at a price lower than the sum of the individual prices of the products we study a multi segment market in which a retailer aims to clear the inventory of an item by bundling it with a second product which is independently valued we investigate the question of how dynamic and segment specific bundle pricing impacts retailer s revenue we develop a revenue model that integrates the dynamic and segment specific aspects of the pricing decisions and present a computational study to analyze their revenue impact relative to a price promotion for the individual item only the computational results indicate that the bundle offers are most effective when the initial inventory of the item under consideration is high the results also demonstrate that dynamic pricing is beneficial when the initial inventory of the item is low an additional revenue improvement is observed when the price of the bundle is dynamically optimized in the computational study segment specific pricing is observed to have no direct impact on revenue when prices are static segment specific and dynamic pricing however can bring about substantial revenue improvements that are an increasing function of the initial inventory level of the item we consider the correlation in consumers valuations of the bundled products and show that dynamically priced and segment specific bundle offers yield a robust revenue performance mitigating the potentially revenue diminishing impact of positive correlation in consumers valuations of the products

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

using mandated speed limits to measure the value of a statistical life in 1987 the federal government permitted states to raise the speed limit on their rural interstate roads but not on their urban interstate roads from 55 mph to 65 mph since the states that adopted the higher speed limit must have valued the travel hours they saved more than the fatalities incurred this institutional change provides an opportunity to estimate an upper bound on the public s willingness to trade off wealth for a change in the probability of death our estimates indicate that the adoption of the 65 mph limit increased speeds by approximately 4 percent or 2 5 mph and fatality rates by roughly 35 percent together the estimates suggest that about 125 000 hours were saved per lost life when the time saved is valued at the average hourly wage the estimates imply that adopting states were willing to accept risks that resulted in a savings of 1 54 million 1997 dollars per fatality with a sampling error roughly one third this value we set out a simple model of states decisions to adop

democratic public good provision this paper analyzes an overlapping generation model of redistribution and public good provision under repeated voting expenditures are financed through age dependent taxation that distorts human capital investment taxes redistribute income both across skill groups and across generations we focus on politico economic markov equilibria and contrast these with the ramsey allocation under commitment the model features indeterminate equilibria with a key role of forward looking strategic voting due to the lack of commitment to future policies the tax burden may be on the wrong side of the dynamic laffer curve moreover restrictions on government policies can in some cases be welfare improving

inventory competition under dynamic consumer choice we analyze a model of inventory competition among n firms that provide competing substitutable goods each firm chooses initial inventory levels for their good in a single period newsboy like inventory model customers choose dynamically based on current availability so the inventory levels at one firm affect the demand of all competingfirms this creates a strategic interaction amongthe firms inventory decisions our work extends earlier work on variations of this problem by karjalainen 1992 lippman and mccardle 1997 and parlar 1988 specifically we model demand in a more realistic way as a stochastic sequence of heterogeneous consumers who choose dynamically from amongthe available goods or choose not to purchase based on a utility maximization criterion we also use a sample path analysis so minimal assumptions are imposed on this demand process we characterize the nash equilibrium of the resulting stocking game and prove it is unique in the symmetric case we show there is a bias toward overstocking caused by competition specifically reducing the quantity stocked at any equilibrium of the game increases total system profits and at any joint optimal set of stocking levels each firm has an individual incentive to increase its own stock for the symmetric case we show that as the number of competing firms increases the overstockingbecomes so severe that total system and individual firm profits approach zero finally we propose a stochastic gradient algorithm for computing equilibria and provide several numerical examples

a second chance at success a political economy perspective abstract this paper characterizes a stationary markov perfect political equilibrium where agents vote over income taxation that distorts educational investment agents become rich or poor through educational investment and the poor have a second chance at success the results show the following concerning the cost of a second chance first when the cost is low the economy is characterized by high levels of upward mobility and inequality and a low tax burden supported by the poor with prospects for upward mobility second when the cost is high there are multiple equilibria with various patterns of upward mobility inequality and redistribution numerical examples show that the shift from a high cost economy to a low cost economy may reduce social welfare

optimal bundle formation and pricing of two products with limited stock abstract in this study we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm one of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit product demands follow a poisson process with a price dependent rate customer reservation prices are assumed to have a joint distribution we study the impact of reservation price distributions initial inventory levels product prices demand arrival rates and cost of bundling we observe that the expected profit decreases as the correlation between the reservation prices of two products increases with negative correlation bundling cost has a significant impact on the number of bundles formed when the product prices are low the retailer sells individual products as well as the bundle mixed bundling when they are high the retailer sells only bundles pure bundling the expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases for high starting inventory levels the retailer reduces bundle price and offers more bundles the number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases impacts of substitutability and complementarity of products are also investigated the retailer forms more bundles or charges higher prices for the bundle or both as the products become more complementary and less substitutable

preferences for redistribution in the land of opportunities this paper explores how individual preferences for redistribution depend on future income prospects in addition to estimating the impact of individuals socioeconomic background and of their subjective perceptions of future mobility we employ panel data to construct dobjectivet measures of expected gains and losses from redistribution for different categories of individuals we find that such measures have considerable explanatory power and perform better than dgeneral mobilityt indexes we also find that preferences for redistribution respond to individual beliefs on what determines one s position in the social ladder ceteris paribus people who believe that the american society offers equal opportunities are more averse to redistribution d 2004 published by elsevier b v

a combined approach for segment specific market basket analysis abstract market baskets arise from consumers shopping trips and include items from multiple categories that are frequently chosen interdependently from each other explanatory models of multicategory choice behavior explicitly allow for such category purchase dependencies they typically estimate own and across category effects of marketing mix variables on purchase incidences for a predefined set of product categories because of analytical restrictions however multicategory choice models can only handle a small number of categories hence for large retail assortments the issue emerges of how to determine the composition of shopping baskets with a meaningful selection of categories traditionally this is resolved by managerial intuition in this article we combine multicategory choice models with a data driven approach for basket selection the proposed procedure also accounts for customer heterogeneity and thus can serve as a viable tool for designing target marketing programs a data compression step first derives a set of basket prototypes which are representative for classes of market baskets with internally more distinctive complementary cross category interdependencies and are responsible for the segmentation of households in a second step segment specific cross category effects are estimated for suitably selected categories using a multivariate logistic modeling framework in an empirical illustration significant differences in cross effects and price elasticities can be shown both across segments and compared to the aggregate model

a note on probability distributions with increasing generalized failure rates distributions with an increasing generalized failure rate igfr have useful applications in pricing and supply chain contracting problems we provide alternative characterizations of the igfr property that lead to simplify verifying whether the igfr condition holds we also relate the limit of the generalized failure rate and the moments of a distribution

inequality mobility and redistributive politics abstract this paper develops a model where income inequality and intergenerational mobility are jointly determined via redistributive politics the model includes two key factors accessibility of tertiary education for poor born agents and multiple self fulfilling expectations of agents given these factors the model provides predictions of cross country differences in inequality and mobility consistent with empirical observations

a graphical analysis of bundling by comparing the demand for a bundle and the vertical sum of the demands for its components this article analyzes the profitability and welfare consequences of bundling if it does not lower costs bundling tends to be profitable when reservation values are negatively correlated and high relative to costs if bundling lowers costs and costs are high relative to average reservation values positively correlated reservation values increase the incentive to bundle bundling and charging a price equal to the sum of the components prices lowers consumer surplus bundling can however increase consumer surplus when it results in lower prices copyright 1995 by university of chicago press

the dynamics of government abstract we model income redistribution with dynamic distortions as determined by rational voting without commitment among individuals of different types and income realizations we find that redistribution is too persistent relative to that chosen by a planner with commitment the difference is larger the lower is the political influence of young agents the lower is the altruistic concern for future generations and the lower is risk aversion furthermore there tends to be too much redistribution in the political equilibrium finally smooth preference aggregation as under probabilistic voting produces less persistence and does not admit multiple equilibria which occur under majority voting aggregation

resource allocation in public policy the effects of the 65 mph speed limit i background previous work lave 1985 shows that highway fatality rates are strongly related to the variation in speed between cars variance kills what matters most in setting a speed limit is choosing one that people will obey hence reducing variance between cars this paper looks at another consideration for setting a speed limit how will the limit affect the allocation of vehicles across alternative roads and the allocation of policing resources across alternative safety activities this resource allocation perspective leads to the development of a new criterion for judging safety effects instead of measuring the local effect of a speed limit change we should measure the statewide effect because a reallocation of traffic and patrol activities will have systemwide consequences this perspective is analogous to the study of offsetting behavior pioneered by peltzman 1975 a government s attempt to improve the safety characteristics of a product may be offset by behavioral changes in the use of the product thus substantially weakening the expected safety improvement and possibly even making the overall situation worse 1 if this has occurred then we should be able to detect an increase in safety when the government regulation is reversed in 1987 the federal government allowed states to raise speed limits on their rural interstate highways 40 states did so some reports show that fatalities increased baum et al 1990 national highway traffic safety administration 1989 gallagher et al 1989 however they only look at local effects fatalities on a particular highway before and after the speed limit change this is not the relevant criterion ii consequences of raising the speed limit raising the speed limit might have consequences for the allocation of policing resources and the allocation of traffic consider the policing resources first the allocation of policing resources there is strong evidence that the state highway patrols felt they had been forced to misallocate their manpower because of the federally mandated 55 mph national maximum speed limit the federal government had imposed detailed compliance requirements that required strict new enforcement efforts 2 in response highway patrols shifted resources from other safety activities e g drunk driving checkpoints and truck safety to speed enforcement on the interstate highways these highways have the densest concentration of high speed traffic hence a patrol hour of activity there will control the greatest number of potential speeders by 1983 29 of patrol hours were devoted to rural interstate highways though these were already the safest highways and produced only 9 of fatalities national research council 1984 227 the state highway patrols were well aware that this was a peculiar way to allocate manpower testifying before congress the international association of chiefs of police said federal financial sanctions force the over concentration of limited resources for the express purpose of attaining compliance rather than application of resources in a manner most effectively enhancing total highway safety tippet 1990 and following the speed limit increase to 65 mph they took the opportunity to reallocate patrol resources 3 the allocation of highway resources for physical reasons the interstates are our safest roads higher legal speeds on the interstates would be expected to lure traffic away from other roads hence reducing fatalities on the less safe roads is there evidence that traffic did shift to the interstates following the speed limit increase we need to measure change relative to some expected baseline table i does this in two different ways part a concentrates on the states that increased speed limits to 65 mph for these states it compares the growth of vehicle miles traveled vmt on specific highway types to the overall vmt growth rate in the state

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

price versus production postponement capacity and competition this article presents a comparative analysis of possible postponement strategies in a two stage decision model where firms make three decisions capacity investment production inventory quantity and price typically investments are made while the demand curve is uncertain the strategies differ in the timing of the operational decisions relative to the realization of uncertainty we show how competition uncertainty and the timing of operational decisions influence the strategic investment decision of the firm and its value in contrast to production postponement price postponement makes the investment and production inventory decisions relatively insensitive to uncertainty this suggests that managers can make optimal capacity decisions by deterministic reasoning if they have some price flexibility under price postponement additional postponement of production has relatively small incremental value therefore it may be worthwhile to consider flexible ex post pricing before production postponement reengineering while more postponement increases firm value it is counterintuitive that this also makes the optimal capacity decision more sensitive to uncertainty we highlight the different impact of more timely information which leads to higher investment and inventories and of reduced demand uncertainty which decreases investment and inventories our analysis suggests appropriateness conditions for simple make to stock and make to order strategies we also present technical sufficiency and uniqueness conditions under price postponement these results extend to oligopolistic and perfect competition for which pure equilibria are derived interestingly the relative value of operational postponement techniques seems to increase as the industry becomes more competitive

rationalizability learning and equilibrium in games with strategic complementarities we study a rich class of noncooperative games that includes models of oligopoly competition macroeconomic coordination failures arms races bank runs technology adoption and diffusion r d competition pretrial bargaining coordination in teams and many others for all these games the sets of pure strategy nash equilibria correlated equilibria and rationalizable strategies have identical bounds also for a class of models of dynamic adaptive choice behavior that encompasses both best response dynamics and bayesian learning the players choices lie eventually within the same bounds these bounds are shown to vary monotonically with certain exogenous parameters we study the class of noncooperative supermodular games introduced by topkis 1979 and further analyzed by vives 1985 1989 who also pointed out the importance of these games in industrial economics supermodular games are games in which each player s strategy set is partially ordered the marginal returns to increasing one s strategy rise with increases in the competitors strategies so that the game exhibits strategic complementarity 2 and if a player s strategies are multidimensional marginal returns to any one com ponent of the player s strategy rise with increases in the other components this class turns out to encompass many of the most important economic applications of noncooperative game theory in macroeconomics diamond s 1982 search model and bryant s 1983 1984 rational expectations models can be represented as supermodular games in each of these models more activity by some members of the economy raises the returns to increased levels of activity by others in oligopoly theory some models of bertrand oligopoly with differentiated products qualify as supermodu lar games in these games when a firm s competitors raise their prices the marginal profitability of the firm s own price increase rises a similar structure is present in games of new technology adoption such as those of dybvig and spatt 1983 farrell and saloner 1986 and katz and shapiro 1986 when more users hook into a communication system or more manufacturers adopt an interface standard the marginal return to others of doing the same often rises similarly in some specifications of the bank runs model introduced by diamond and dybvig 1983 when more depositors withdraw their funds from a bank it is more worthwhile for other depositors to do the same in the warrant exercise

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

dynamic price competition with discrete customer choices abstract for many years dynamic pricing has proven to be an effective tool to increase revenue in the airline and other service industries most studies however focused on monopolistic models and ignored the fact that nowadays consumers can easily compare prices on the internet in this paper we develop a game theoretic model to describe real time dynamic price competition between firms that sell substitutable products by assuming the real time inventory levels of all firms are public information we show the existence of nash equilibrium we then discuss how a firm can adapt if it knows only the initial but not the real time inventory levels of its competitors we compare a firm s expected revenue under different information structures through numerical experiments

growth learning and redistributive policies abstract this paper develops an endogenous growth model with redistributive taxation in which the growth rate of the economy affects the agents preferences over redistributive policies and therefore the equilibrium level of taxation the main mechanism through which the growth rate affects policy preferences is by changing the ability of the agents to learn their positions in the future distribution of incomes the main result of the paper is that during periods of growth the society opts for less taxation and less redistribution the model also predicts that growing economies are characterized by higher inequality in the distribution of income and by greater mobility of agents within income classes over time

dynamic targeted pricing with strategic consumers abstract we investigate in this paper whether dynamic targeted pricing based on consumer purchase history could benefit a practicing firm even when consumers are strategic in that they actively seek to avail themselves of a low price in the future such strategic behavior on the part of consumers has been shown in the literature to render such dynamic targeted pricing unprofitable even for a monopoly firm we show that dynamic targeted pricing can benefit competing firms when they actively pursue customer recognition based on consumer purchase history this is because in order to pursue customer recognition competing firms need to price high to screen out price sensitive consumers and hence price competition is moderated as a result all competing firms can become better off with targeted pricing than without even when consumers behave strategically interestingly because of this competition moderation effect the paradoxical outcome occurs where dynamic targeted pricing may not benefit a monopolist but it may benefit competing firms we also show that dynamic targeted pricing can expand the market such that social welfare unambiguously improves

a reexamination of resource allocation responses to the 65 mph speed limit michael greenstone i introduction in 1987 the federal government allowed states to raise speed limits from 55 mph to 65 mph on a single category of roads rural interstates of the 47 states with rural interstate roads 40 adopted the higher speed limit within a year garber and graham 1990 and ashenfelter and greenstone 2002 document that the fatality rate on rural interstates increased dramatically subsequent to its introduction these studies conclude that higher speed limits lead to higher fatality rates in a recent issue of economic inquiry lave and elias 1997 henceforth l e argue that the full effect of the 65 mph speed limit cannot be inferred by examining rural interstates in isolation from other roads they conjecture that the higher speed limits caused reallocations of drivers and state police that counterbalanced the increased fatality rates on rural interstates in particular they posit that the reduced travel times available on rural interstates induced drivers to switch from dangerous side roads to the safer rural interstates additionally they contend that the higher limits freed the state police from speed enforcement which allowed them to concentrate on activities with greater impacts on fatality rates thus l e s hypothesis is that the full effect of an increase in the speed limit requires an examination of statewide fatality rates figure 1 graphically depicts l e s hypothesis l e present evidence in favor of their hypothesized causal chain first in support of the driver reallocation conjecture they find that between 1986 and 1988 vehicle miles of travel vmt increased on rural interstates where the speed limit was increased to 65 mph second they present anecdotal evidence in favor of the trooper reallocation conjecture third they show that the introduction of the 65 mph limit was associated with a statistically significant decline in statewide fatality rates of 3 4 5 1 thus l e s surprising conclusion is that through driver and trooper reallocations the 1987 increase in speed limits reduced fatality rates this study reexamines l e s empirical results and is unable to confirm them it shows that the statewide fatality rate declined by a statistically insignificant amount in adopting states after 1987 this finding holds when the specification is virtually identical to the one that l e fit and when alternative specifications are estimated although this result directly contradicts l e s primary finding the source of the discrepancy cannot be determined because their data were unavailable it remains puzzling that the large increase in rural interstate fatality rates is not observable in statewide fatality rates an explanation that potentially reconciles this finding with l e s is that the increase on rural interstates was counterbalanced but not swamped by fatality declines induced by the hypothesized reallocations consequently this article also explores whether the 65 mph speed limit caused the reallocations that are the conjectured sources of the statewide decline in fatality rates if these links are not supported by the data it indicates that the statistically insignificant decline in statewide fatality rates cannot be causally related to the two reallocations and in turn to the higher speed limit the links between the 65 mph speed limit and the two reallocations are tested separately first the results suggest that vmt did not increase on rural interstates where the speed limit was raised this finding is derived from a regression on 1982 1990 data whereas l e only compared unadjusted means from 1986 and 1988 moreover it holds when the comparison is to rural interstates in states that did not adopt the higher limit and to both other states and other categories of roads these results fail to provide an empirical basis for the driver reallocation conjecture

purchasing pricing and quick response in the presence of strategic consumers we consider a retailer that sells a product with uncertain demand over a finite selling season the retailer sets an initial stocking quantity and at some predetermined point in the season optimally marks down remaining inventory we modify this classic setting by introducing three types of consumers myopic consumers who always purchase at the initial full price bargain hunting consumers who purchase only if the discounted price is sufficiently low and strategic consumers who strategically choose when to make their purchase a strategic consumer chooses between a purchase at the initial full price and a later purchase at an uncertain markdown price in equilibrium strategic consumers and the retailer make optimal decisions given their rational expectations regarding future prices availability of inventory and the behavior of other consumers we find that the retailer stocks less takes smaller price discounts and earns lower profit if strategic consumers are present than if there are no strategic consumers we find that a retailer should generally avoid committing to a price path over the season assuming such commitment is feasible committing to a markdown price or to not mark down at all is often too costly inventory may remain unsold even in the presence of strategic consumers the better approach is to be cautious with the initial quantity and then mark down optimally furthermore we discuss the value of quick response the ability to procure additional inventory after obtaining updated demand information albeit at a higher unit cost than the initial order we find that the value of quick response to a retailer is generally much greater in the presence of strategic consumers than without them on average 67 more valuable and as much as 558 more valuable in our sample in other words although it is well established in the literature that quick response provides value by allowing better matching of supply with demand it provides more value often substantially more value by allowing a retailer to control the negative consequences of strategic consumer behavior