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

the optimality of consumer stockpiling strategies the ability of consumers to make rational sequential purchase quantity decisions under imperfect knowledge about future prices in a product category is explored normatively a consumer should make such decisions by defining a series of reservation prices which define how many buying periods supply should be held given an observed price an experiment is reported in which consumers make sequential purchase quantity decisions under variations in the shape of the distribution of prices and its trend over time results suggest a number of systematic deviations from optimality when facing stationary uniform and bimodal price distributions for example subjects tend to systematically overbuy when small purchases are called for and underbuy when large purchases are called for likewise when facing ascending or descending series behavior is the opposite of that predicted by the normative analysis there is an increasing tendency to defer purchases given increasing prices and accelerate purchases given descending prices an explanation for the findings in terms of a prospect theory type loss function in expenditures is offered

home production and social security reform this paper incorporates home production into a dynamic general equilibrium model of overlapping generations with endogenous retirement to study social se curity reforms as such the model dierentiates both consumption goods and labor eort according to their respective roles in home production and market activities using a calibrated model we nd that eliminating the current pay as you go social security system has important implications for both labor supply and consumption decisions and that these decisions are in uenced by the presence of a home production technology comparing our benchmark economy to one with dierentiated goods but no home production we nd that eliminating social security bene ts generates larger welfare gains in the presence of home produc tion this result is due to the self insurance aspects generated by the presence of home production comparing our economy to a one good economy without home production we show that the welfare gains of eliminating social security are magni ed even further these policy analyses suggest the importance of mod eling home production and distinguishing between both time use and consumption goods depending on whether they are involved in market or home production

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

families and social security abstract the present paper quantifies the importance of family insurance for the analysis of social security we therefore augment the standard overlapping generations model with idiosyncratic labor productivity and longevity risk in that we account for gender and marital status we simulate the abolition of pay as you go pension payments calculate the resulting intergenerational welfare changes and isolate aggregate efficiency effects for singles and families by means of compensating transfers we find that abolishing social security creates significant efficiency losses which are substantially higher for singles compared to married couples a decomposition of the efficiency loss reveals that this difference can be almost exclusively attributed to the insurance role of the family with respect to longevity risk neglecting differences in family structure when studying the privatization of social security one overestimates the long run change in the capital stock by about 40 percent the decline in labor supply by about 30 percent and the aggregate efficiency loss by even 36 percent given rising divorce rates and less stable marriages in almost all western societies our results also indicate that social security should not be reduced but strengthened in the future

taxing capital not a bad idea after all we quantitatively characterize the optimal capital and labor income tax in an overlapping generations model with idiosyncratic uninsurable income shocks and permanent productivity difierences of households the optimal capital income tax rate is signiflcantly positive at 36 percent the optimal progressive labor income tax is roughly a at tax of 23 percent with a deduction of 7 200 relative to average household income of 42 000 the high optimal capital income tax is mainly driven by the life cycle structure of the model whereas the optimal progressivity of the labor income tax is attributable to the insurance and redistribution role of the tax system jel e62 h21 h24

please or squeeze brand performance implications of constrained and unconstrained multi item promotions existing research on price promotions typically investigates the effects of single product promotions however brand managers often promote multiple items simultaneously to bolster the performance of a complete brand line this paper investigates the brand performance implications of such multi item promotions we distinguish between two types of multi item promotions traditional unconstrained multi item promotions that grant a discount irrespective of the size or composition of the purchase set and constrained multi item promotions that require consumers to purchase specific quantities self bundling or even predetermined combinations fixed bundling of promoted items using a normative consumer decision model the authors analyze the relative effectiveness of these promotions in terms of unit sales and revenue impact and show that promotion performance is moderated by consumers preference for variety the authors find that unconstrained multi item promotions outperform single item promotions especially in markets without variety seeking in markets with variety seeking unconstrained multi item promotions are not as effective in stealing extra sales from competition because consumers prefer to spread their purchases across all items including competitive ones however in those markets self bundling promotions are particularly effective because they force consumers to adopt larger amounts of the promoted items at the expense of competitors finally in neither type of market does fixed bundling substantially improve promotion performance

social security life insurance and annuities for families abstract in this paper we ask whether an aspect of social security namely its role as a provider of insurance against uncertain life spans is welfare enhancing to this end we use an olg model where agents have a bequest motive and differ in sex and marital status and where families are formed and destroyed and their characteristics evolve exogenously according to u s demographic patterns of marriage divorce fertility and mortality we compare the implications of social security under a variety of market structures that differ in the extent to which life insurance and annuities are available we find that social security is a bad idea in economies where the private sector provides annuities and life insurance it is a bad idea for the standard reason that it distorts the intertemporal margin by lowering the capital stock in the absence of such securities social security is still a very bad idea only marginally less so compared with economies with annuities and life insurance we also explore these issues in a world where people live longer and we find no differences in our answers as a by product of our analysis we find that the existence of life insurance opportunities for people is important in welfare terms while that of annuities is not

optimal inventory policies when ordering prices are random we consider a single item inventory model with deterministic demands at the beginning of each period a random ordering price is received according to a known distribution function a decision must be made as to how much if any of the item to order in each period so as to minimize total expected costs while satisfying all demands we show that in each period a sequence of critical price levels determines the optimal ordering strategy so that it is optimal to satisfy the demands of the next n periods if and only if the random price falls between the nth and the n 1st levels we derive recursive expressions that describe the critical price numbers and demonstrate the relationship of these expressions to minimal expected cost we study finite horizon as well as infinite horizon models and show that the critical number strategy is also average cost optimal

flexible and risk sharing supply contracts under price uncertainty we study supply contracts for deterministic demand but in an environment of uncertain prices we develop valuation methodologies for different types of supply contracts a time inflexible contract requires the firm to specify not only how many units it will purchase but also the timing of the purchase a time flexible contract allows the firm to specify the purchase amount over a given period of time without specifying the exact time of purchase other than time flexibility the suppliers may offer quantity flexibility to the firm as well i e purchase quantities could be within a prespecified quantity window finally risk sharing features can be incorporated in the contract in terms of the purchase price that the firm eventually pays to a supplier within a prespecified price window the firm pays the realized price but outside of it the firm shares in an agreed way added costs or benefits given the structure of a supply contract we study the firm s decision when to purchase and how many units in each purchase such that the expected net present value of the purchase cost plus inventory holding cost is minimized we discuss optimal purchasing strategies for both time flexible and time inflexible contracts with risk sharing features other interesting results include the analysis of two supplier sourcing environments and the exploitation of quantity flexibility in such contracts our discussion illustrates how time flexibility quantity flexibility supplier selection and risk sharing when carefully exercised can effectively reduce the sourcing cost in environments of price uncertainty

differential mortality and the progressivity of social security abstract there is a well established negative correlation between earnings and mortality risk using a calibrated general equilibrium macroeconomic model this paper examines how this correlation interacts with the welfare implications of social security s benefit earnings rule my primary findings suggest that the welfare ranking of alternative benefit earnings rules is somewhat sensitive to differential mortality due to their relatively high mortality risk households with unfavorable earnings histories heavily discount the expected utility from old age consumption and therefore do not put much weight on better work retirement consumption smoothing because of this reason social security s benefit earnings rule warrants less redistribution in the presence of differential mortality compared to when mortality risk is uncorrelated to earnings i find that this result continues to hold when household level labor supply distortions are ignored and also when an alternative maximin welfare criterion is considered but not when accidental bequests from the deceased are redistributed to the survivors

sources of lifetime inequality is lifetime inequality mainly due to differences across people established early in life or to differences in luck experienced over the working lifetime we answer this question within a model that features idiosyncratic shocks to human capital estimated directly from data as well as heterogeneity in ability to learn initial human capital and initial wealth we find that as of age 23 differences in initial conditions account for more of the variation in lifetime earnings lifetime wealth and lifetime utility than do differences in shocks received over the working lifetime jel d31 d91 j24 j31 to what degree is lifetime inequality due to differences across people established early in life as opposed to differences in luck experienced over the working lifetime among the individual differences established early in life which ones are the most important a convincing answer to these questions is of fundamental importance first and most simply an answer serves to contrast the potential importance of the myriad policies directed at modifying or at providing insurance for initial conditions e g public education against those directed at shocks over the working lifetime e g unemployment insurance second a discussion of lifetime inequality cannot go too far before discussing which specific type of initial condition is the most critical for determining how one fares in life third a useful framework for answering these questions should also be central in the analysis of a wide range of policies considered in macroeconomics public finance and labor economics we view lifetime inequality through the lens of a risky human capital model agents differ in terms of three initial conditions initial human capital learning ability and financial wealth initial human capital can be viewed as controlling the intercept of an agent s mean earnings profile whereas learning ability acts to rotate

the life cycle and the business cycle of wage risk cross country comparisons abstract we provide evidence on life cycle and business cycle fluctuations in the dispersion of household level wage innovations comparing the us the uk and germany first we find that household characteristics explain about 25 of the dispersion in wages within an age group in all three countries second the cross sectional variance of wages is almost linearly increasing in household age in all three countries but with increments being smaller in the european data third wage risk is procyclical in germany while it is countercyclical in the us and acyclical in the uk

mitigating america s demographic dilemma by pre funding social security abstract financing social security benefits at current levels implies significant increases in payroll taxes within the next 20 years under current us demographic developments using a general equilibrium overlapping generations model with realistic patterns of fertility and lifespan extension this study shows that future generations would be harmed during the demographic transition due to rising payroll taxes which crowd out savings and slow real wage growth below the rate of technological progress a faster rate of technological progress would mitigate only some of the payroll tax increase and its economic consequences but could not overcome them addressing the financing problem by reducing social security benefits as needed or by raising the eligibility age for benefits imposes major welfare losses on current or near term retirees by contrast a pre funding of social security financed with consumption taxes more evenly spreads the welfare losses across generations and it helps future generations especially the poor by stimulating capital formation

marketing models and the lucas critique the lucas critique has been largely ignored in the marketing literature we present a number of conditions under which the critique is most likely to also apply in marketing settings next we provide some perspectives on how to diagnose and accommodate the lucas critique and identify various avenues for future research

mean variance theory in complete markets two paradigms in the pricing of risky assets are the complete markets model of arrow and debreu and mean variance pricing as embodied in the capital asset pricing model capm the former is primarily of theoretical interest in fact prior to the recent work of banz and miller 1978 and breeden and litzenberger 1978 there was little thought or hope of practical applications on the other hand the hegemony of the capm is due mostly to its apparent ease of applicability and to a lesser extent its empirical justification in a competitive market with no taxes transactions costs or institutional constraints on portfolio holdings the allocation of the available assets will be pareto optimal the end of period distribution of wealth or the consumption goods however will typically be pareto optimal only when there is available an arrow debreu security for each contingency since by definition a pareto superior reallocation is weakly preferred by all investors a complete set of arrow debreu markets should naturally arise provided they are not too costly to establish the complete markets model of arrow and debreu and the meanvariance capital asset pricing model capm are two paradigms of risky asset markets this paper provides an integration of these two theories we prove that the standard meanvariance separation theorem obtains in a complete market only if all investors have quadratic utility in addition the familiar capm pricing relation can hold for all assets in a complete market only if arbitrage opportunities exist on the positive side we show that the validity of this relation for the primary assets in a complete market is unaffected by the distribution of returns on the created financial assets

smoking cessation a model of planned vs actual behavior for time inconsistent consumers we offer a simple model of intertemporal choice to characterize how planned versus actual behaviors evolve for time inconsistent smokers our results suggest that smokers participation and cessation decisions are governed by the interplay between three effects the cessation effect leads smokers to advance their plans to quit smoking whereas the procrastination effect leads them to consecutively revise their planned quitting age upwards consequently the duration of smoking is effectively governed by which one of these two effects is dominant finally for certain consumer segments a threshold effect causes an all or nothing type of extreme smoking behavior based on certain critical values of present biased preferences our results provide some preliminary evidence that both marketing efforts by tobacco firms and public policy initiatives can have a significant influence on smoking behavior in particular we find that reductions in the age at which individuals start smoking may not only vastly extend their duration of smoking but also convert potential never smokers into lifetime smokers finally we estimate a hazard model using survey data from over 800 smokers to provide evidence in support of our theoretical model

modeling asymmetric competition the effects of the marketing actions of one brand can be distributed among its competitors market shares in a complex manner this paper presents and illustrates methods for modeling brand competition and brand strategies in markets where competitive effects can be differentially and asymmetrically distributed we discuss the empirical specification parameter estimation and competitive strategy implications of the models proposed price and advertising competition among eleven brands of an australian household product is used to illustrate the application of these procedures

the family as an incomplete annuities market families can self insure against uncertain dates of death through implicit or explicit agreements with respect to consumption and interfamily transfers interfamily transfers need have nothing to do with altruistic feelings they may simply reflect risk sharing behavior of completely selfish family members although family annuity markets are incomplete even small families can substitute by more than 70 percent for perfect market annuities given adverse selection and transaction costs family risk pooling may be preferred to public market annuities in the absence of public annuities these risk sharing arrangements provide powerful incentives for marriage and family formation

the category demand effects of price promotions although price promotions have increased in both commercial use and quantity of academic research over the last decade most of the attention has been focused on their effects on brand choice and brand sales by contrast little is known about the conditions under which price promotions expand short run and long run category demand even though the benefits of category expansion can be substantial to manufacturers and retailers alike this paper studies the category demand effects of consumer price promotions across 560 consumer product categories over a 4 year period the data describe national sales in dutch supermarkets and cover virtually the entire marketing mix i e prices promotions advertising distribution and new product activity we focus on the estimation of main effects i e the dynamic category expansive impact of price promotions as well as the moderating effects of marketing intensity and competition both conduct and structure on short and long run promotional effectiveness the research design uses modern multivariate time series analysis to disentangle short run and long run effects first we conduct a series of unit root tests to determine whether or not category demand is stationary or evolving over time the results are incorporated in the specification of vector autoregressive models with exogenous variables varx models the impulse response functions derived from these varx models provide estimates of the short and long term effects of price promotions on category demand these estimates in turn are used as dependent variables in a series of second stage regressions that assess the explanatory power of marketing intensity and competition several model validation tests support the robustness of the empirical findings we present our results in the form of empirical generalizations on the main effects of price promotions on category demand in the short and the long run and through statistical tests on how these effects change with marketing intensity and competition the findings generate an overall picture of the power and limitations of consumer price promotions in expanding category demand as follows category demand is found to be predominantly stationary either around a fixed mean or a deterministic trend although the total net short term effects of price promotions are generally strong with an average elasticity of 2 21 and a more conservative median elasticity of 1 75 they rarely exhibit persistent effects instead the effects dissipate over a time period lasting approximately 10 weeks on average and their long term impact is essentially zero by contrast the successful introduction of new products into a category is more frequently associated with a permanent category demand increase several moderating effects on price promotion effectiveness exist more frequent promotions increase their effectiveness but only in the short run the use of nonprice advertising reduces the category demand effects of price promotions both in the short run and in the long run competitive structure matters as well the less oligopolistic the category the smaller the short run effectiveness of price promotions at the same time we find that the dominant form of competitive reaction either in price promotion or in advertising is no reaction short run category demand effectiveness of price promotions is lower in categories experiencing major new product introductions finally both the short and long run price promotion effectiveness is higher in perishable product categories the paper discusses several managerial implications of these empirical findings and suggests various avenues for future research overall we conclude that the power of price promotions lies primarily in the preservation of the status quo in the category

the state preference approach to general equilibrium in corporate finance abstract this paper attempts to implement the state preference approach in a multiperiod exchange economy the procedure is relevant for a further investigation of various important issues in corporate finance such as the results of modigliani and miller and the integration of the state preference and the mean variance approach to asset pricing

an equilibrium model of asset pricing with progressive personal taxes this paper examines how the progressive personal tax rate affects the equilibrium asset pricing model in a continuous time framework with progressive taxation it can be shown that the expected excess rate of return on a risky asset is an increasing function of i the covariance of asset return with aggregate consumption rate changes and ii the covariance of asset return with the aggregation of individual wealth change weighted by the investor s tax scheme progressivity index the capital asset pricing model derived in the absence of tax is shown to understate the expected excess rate of return and to have a misspecification error under the progressive tax scheme furthermore the expected excess rate of return can be decomposed as the consumption risk premium and tax premium the tax premium depends on the tax structure prevailing in the economy

retail competition and the dynamics of demand for tied goods we present a demand system for tied goods incorporating dynamics arising from the tied nature of the products and the stockpiling induced by storability and durability we accommodate competition across tied good systems and competing downstream retail formats by endogenizing the retail format at which consumers choose to stockpile inventory this facilitates measurement of long run retail substitution effects and yields estimates of complementarities within and substitution across competing systems of tied goods we present an empirical application to an archetypal tied goods category razors and blades we discuss the implications of measured effects for manufacturer pricing when selling the tied products through an oligopolistic downstream retail channel and assess the extent to which retail substitution reduces channel conflict

intertemporal pricing and consumer stockpiling we study a dynamic pricing problem for a class of products with stable consumption patterns e g household items staple foods consumers may stock up the product at current prices for future consumption but they incur inventory holding costs we model this situation as a dynamic game over an infinite time horizon in each period the seller sets a price and each consumer chooses how many units to buy we develop a solution methodology based on rational expectations by endowing each player with beliefs we decouple the dynamic game into individual dynamic programs for each player we solve for the rational expectations equilibrium where all players make optimal dynamic decisions given correct beliefs about others behavior in equilibrium the seller may either charge a constant fixed price or offer periodic price promotions at predictable time intervals we show that promotions are useful when frequent shoppers are willing to pay more for the product than are occasional shoppers we also develop several model extensions to study the impact of consumer stockpiling on the seller s inventory production and rationing strategies

two views of inequality over the life cycle data on the life cycle profiles of inequality in wages earnings hours worked and consumption contain precious information for answering questions about the ability of households to insure labor market risk and about the sources of this risk this paper demonstrates that the choice of whether to control for cohort effects or for time effects has a drastic impact on the estimated age profiles for inequality and thus on the answers to those questions it also shows that time effects are required to account of the observed trends in inequality in 30 years of u s data whereas there is no evidence that cohort effects have been important jel c13 d31 d91 j22 j31

taxes and marriage a two sided search analysis this article analyzes the effects of differential tax treatment of married and single individuals in the united states on marriage formation and composition divorce and labor supply we develop a marriage market model with search frictions and heterogeneous agents that is sufficiently rich to capture key elements of the problem under consideration we then calibrate the model and use it to evaluate the quantitative effects of several tax reforms aimed at making the tax law neutral with respect to marital status we find that these reforms i systematically increase the labor supply of married females with changes ranging from 0 3 to 10 1 percent ii have substantial effects on the correlation of spouses incomes which changes from 0 2 to values between 0 185 and 0 334 iii can lead to either an increase or decrease in the fraction of people married with changes that range from 0 6 to 2 4 percent

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

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

does unemployment insurance crowd out spousal labor supply previous research on unemployment insurance ui has emphasized the program s effect on individual search behavior this state contingent income may also reduce the labor supply of family members during the unemployment spell we investigate this question within the context of wives labor supply responses to their husbands unemployment spells we find strong crowdout of this form of family self insurance our estimates imply that for each dollar of ui receipt wives earn up to 73 cents less the reduction in spousal hours of work is over 40 as large as previous estimates of the effect of ui on search time of husbands

measuring the impact of promotions on brand switching when consumers are forward looking abstract logit choice models have been used extensively to study promotion response this article examines whether brand switching elasticities derived from these models are overestimated as a result of rational consumer adjustment of purchase timing to coincide with promotion schedules and whether a dynamic structural model can address this bias using simulated data the authors first show that if the structural model is correct brand switching elasticities are overestimated by stand alone logit models a nested logit model improves the estimates but not completely second the authors estimate the models on real data the results indicate that the structural model fits better and produces sensible coefficient estimates the authors then observe the same pattern in switching elasticities as they do in the simulation third the authors predict sales assuming a 50 increase in promotion frequency the reduced form models predict much higher sales levels than does the dynamic structural model the autho

the pricing of stock index options in a general equilibrium model this paper analyzes the pricing of stock index options in a simple general equilibrium model in this model the volatility of the stock index and the spot rate of interest are functions of a stochastic variable the paper investigates the biases that arise when using the black scholes model with the assumed volatility and interest rate dynamics it is shown that the model can in principle explain the biases observed in empirical work on stock index options

taxing capital along the transition not a bad idea after all this paper quantitatively characterizes optimal tax systems in a model of overlapping generations when transitional cohorts are explicitly taken into account we use the recent study of conesa et al 2009 as an example but extend it by transitional dynamics we furthermore develop a general and coherent way of aggregating welfare effects of different individuals and cohorts in the short and long run our welfare measure includes the case of a utilitarian social welfare function yet is not limited to this perspective we show that the optimality of a high capital income tax rate along the transition crucially depends on the assumption of a utilitarian social welfare function this objective of the policy maker comprises implicit redistributive objectives across and within cohorts based on pure economic efficiency and insurance effects however we find a zero capital income tax rate and a less progressive labor income tax schedule to be optimal such a tax system receives political support from initial cohorts a high capital income tax regime on the other hand doesn t

social security and individual welfare precautionary saving borrowing constraints and the payroll tax this paper examines the impact of social security on national saving and individual welfare in the presence of realistic capital market imperfections market failure in the private provision of annuities and restrictions on borrowing against anticipated future wages the introduction of social security increases lifetime welfare and reduces national saving if borrowing restrictions are absent however the increase in individual welfare is reduced and in some cases eliminated when borrowing constraints are taken into consideration the substantial difference suggests the importance of reexamining the proportional payroll tax finance of social security copyright 1987 by american economic association

engines of liberation electricity was born at the dawn of the last century households were inundated with a flood of new consumer durables what was the impact of this consumer durable goods revolution it is argued here that the consumer goods revolution was conducive to liberating women from the home to analyse this hypothesis a beckerian model of household production is developed households must decide whether or not to adopt the new technologies and whether a married woman should work can such a model help to explain the rise in married female labour force participation that occurred in the last century yes the housewife of the future will be neither a slave to servants nor herself a drudge she will give less attention to the home because the home will need less she will be rather a domestic engineer than a domestic labourer with the greatest of all handmaidens electricity at her service this and other mechanical forces will so revolutionize the woman s world that a large portion of the aggregate of woman s energy will be conserved for use in broader more constructive fields thomas alva edison as interviewed in good housekeeping magazine lv no 4 october 1912 p 436

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

the effect of promotion on consumption buying more and consuming it faster the authors empirically demonstrate the existence of flexible consumption rates in packaged goods products how this phenomenon can be modeled and its importance in assessing the effectiveness of

arbitrage and the existence of competitive equilibrium a general equilibrium model of markets for commodities and assets is considered the author develops the notion of a price system that admits no arbitrage opportunity and demonstrates the fundamenta l role of this concept for the theory of the existence of a competiti ve equilibrium a price system admits no arbitrage opportunity for a consumer if every bundle of desired commodities has a positive market value the author proves that the existence of a price system that a dmits no arbitrage opportunity for all consumers is sufficient for th e existence of an equilibrium copyright 1987 by the econometric society

more on marriage fertility and the distribution of income according to pareto 1896 the distribution of income depends on the nature of the people comprising a society on the organization of the latter and also in part on chance in the model developed here the nature of the people is captured by attitudes toward marriage divorce fertility and children singles search for mates in a marriage market married agents bargain about work and the quantity and quality of children they can divorce social policies such as child support requirements reflect the organization of the society finally chance is modeled by randomness in income marriage opportunities and marital bliss

the valuation of multivariate contingent claims in discrete time models there are several examples in the literature of contingent claims whose payoffs depend on the outcomes of two or more stochastic variables familiar cases of such claims include options on a portfolio of options options whose exercise price is stochastic and options to exchange one asset for another this paper derives risk neutral valuation relationships rnvrs in a discrete time setting that facilitate the pricing of such complex contingent claims in two specific cases joint lognormally distributed underlying variables and constant proportional risk aversion on the part of investors and joint normally distributed underlying variables and constant absolute risk aversion preferences respectively this methodology is then applied to the valuation of several interesting complex contingent claims such as multiperiod bonds multicurrency option bonds and investment options

stockpiling under price uncertainty and storage capacity constraints abstract a model is presented for the operation of an agent whose responsibility is to purchase and perhaps stockpile sufficient quantities of a certain commodity in order to satisfy an exogenous constant demand per time period this is the situation faced by a state agency which is responsible for the purchasing of oil products to satisfy the demand of a country in which demand for energy has stabilized at a certain level an important feature of the model is that the price of the commodity is described by a stochastic process this reflects the volatility of prices of oil products furthermore the model takes storage capacity constraints explicitly into account and thus can help to assess the optimal level of storage capacity expansion the relevant stochastic dynamic programming equations are derived and solved for the least cost function which turns out to be piecewise linear in the inventory level the storage capacity enters only in the computation of the constant term of the value function the solution of the dynamic programming equation leads also to the optimal purchasing strategy of agencies with different levels of flexibility in their policy in the model an agency can be allowed or not to resell from the stock and it can have finite or infinite storage capacity

the relationship between market characteristics and promotional price elasticities many empirical studies in marketing and economics have estimated brand price elasticities for specific products in markets their results indicate that price elasticities seem to differ across brands product categories retail outlets and regions however there has been very little research which examines the factors associated with these observed differences this paper focuses on the promotional price elasticities of established major brands in stable categories it identifies some characteristics of markets which may be associated with differences in price elasticities for frequently purchased nondurables a cross sectional model of the effect of these market characteristics on price elasticities is developed and estimated utilizing own price elasticity estimates for brands at twelve stores the results indicate market characteristics such as brand market share couponing activity display activity and feature activity explain a substantial amount of the variation in promotional price elasticities

how important is intra household risk sharing for savings and labor supply abstract while it is recognized that the family is a risk sharing institution little is known about the quantitative effects of this source of insurance on savings and labor supply in this paper we present a model where workers females and males are subject to idiosyncratic employment risk and where capital markets are incomplete a household is formed by a female and a male who decide on consumption savings and labor supplies in a calibrated version of our model we find that intra household risk sharing has its largest impact among wealth poor households while the wealth rich use mainly savings to smooth consumption across unemployment spells wealth poor households rely on spousal labor supply for instance for low wealth households average hours worked by wives of unemployed husbands are 8 higher than those worked by wives of employed husbands this response in wives hours makes up 9 of lost family income we also study consumption losses upon an unemployment spell precautionary savings and the crowding out effects of the public unemployment insurance program on the extent of risk sharing within the household

population aging social security and fiscal limits abstract we use an overlapping generations olg life cycle model with distortionary taxation on labor and capital to derive a threshold dependency ratio i e a point in the cross section distribution of the population beyond which tax revenues can no longer sustain the planned level of transfers to retirees we quantify the level of the threshold the distance of the economy from the threshold and the probability of reaching the threshold at some point in the future the model is calibrated on the united states and fourteen european countries which have dependency ratios among the highest in the world we examine the effects on the threshold and welfare of a number of policies often advocated to improve the sustainability of pension systems new tax data on dynamic laffer effects are provided

a decision support system for planning manufacturers sales promotion calendars a common event in the consumer packaged goods industry is the negotiation between a manufacturer and a retailer ofthe sales promotion calendar determining the promotion calendar involves a large number of decisions regarding levels of temporary price reductions feature ads and in store displays each executed at the level of individual retail accounts and brand skus over several months or a year though manufacturers spend much of their marketing budget on trade promotions they lack decision support systems to address the complexity and dynamics of promotion planning previous research has produced insights into how to evaluate the effectiveness of promotional events but has not addressed the planning problem in a dynamic environment this paper develops a disaggregate level econometric model to capture the dynamics and heterogeneity of consumer response by modeling the purchase incidence timing choice and quantity decisions of consumers we decompose total sales into incremental and nonincremental baseline plus borrowed the response model forms the basis of a market simulator that permits us to search for the manufacturer s optimal promotion calendar subject to a set of constraints some of them imposed by the retailer via the simulated annealing algorithm calendar profits are the net result of the contribution from incremental sales minus the opportunity cost from giving away discounts to nonincremental sales and the fixed costs associated with implementing promotional events e g retagging features displays incremental sales result from promotion induced switching the acceleration and quantity promotion effects on those switchers increased consumption and the carryover effect from purchase event feedback we applied our approach to the promotion planning problem of a large consumer packaged goods company in a nonperishable staple product category suggested by company executives canned tomato sauce subject to a retailer pass through constant rate of 80 provided to us by the collaborating firm the optimal promotion calendar produced by the modeling system followed a pattern of frequent and shallow temporary price reductions with no feature or display activity we also analyze how that result would change under different retailer pass through scenarios our findings indicated that the manufacturer could substantially improve the profitability of its sales promotion activity and that there would be a concurrent positive effect on retailer profit and volume levels management reported to us that the insights from the use of the system were implemented in their promotion planning process and produced positive results a validation analysis on follow up data for one market showed that promotion activity could be significantly reduced as recommended with no adverse effect on the brand s market share as predicted to generalize the model beyond the specific category where it was implemented we conducted a sensitivity analysis on the profile of the calendar i e frequency depth and duration of deals with respect to changes in market response competitive activity and retailer pass through first we found that the optimal depth frequency and timing of discounts is stable for price elasticities ranging from near zero to around four in absolute magnitude we also found no systematic impact of competitive promotions on the profile of the optimal calendar for example variation in competitive activity did not affect the optimal depth or frequency of discounts lastly we found changes in retailer pass through to have a significant effect on the optimal depth and number of weeks of trade promotion that a manufacturer should offer this emphasizes the importance to manufacturers of having accurate estimates of pass through for purposes of promotion budgeting and planning

why does consumption fall at retirement evidence from germany abstract analyzing the consumption behavior over retirement in germany this paper finds a negative correlation between income replacement and the increase in home production related activities this might reconcile the observed drop in consumption at retirement with the predictions of the standard life cycle model however since individuals with fairly stable income over retirement also increase home production this increase cannot be entirely attributed to a substitution effect

rational shopping behavior and the option value of variable pricing when a product s price fluctuates at a store how should rational cost minimizing shoppers shop for it specifically how frequently should they visit the store and how much of the product should they buy when they get there would this rational shopping behavior differ across every day low price edlp and promotional pricing hilo stores if shoppers are rational which retail price format is more profitable edlp or hilo to answer these questions we develop a normative model that shows how rational customers should shop when the price of the product is random we derive a closed form expression for the optimal purchasing policy and show that the optimal quantity to purchase under a given price scenario is linearly decreasing in the difference between the price under that scenario and the average price this purchase flexibility due to price variability has a direct impact on shopping frequency indeed the benefit of this purchase flexibility can be captured via an option value that implicitly reduces the fixed cost associated with each shopping trip consequently rational shoppers should shop more often and buy fewer units per trip when they face higher price variability our results suggest that if two stores charge the same average price for a product rational shoppers incur a lower level of expenditure at the store with a higher price variability since stores with different price variabilities coexist in practice we expect stores with higher price variability to charge a higher average price thus given two stores a higher relative mean price for a given item should be indicative of higher price variability and vice versa these model implications are tested using multicategory scanner panel data from 513 households and pricing data for three stores two edlp stores and one hilo store and 33 product categories over a two year period we find strong empirical support for the model implications

competitive promotional strategies this article analyzes the equilibrium pricing strategies of brands engaged in a pricing game each brand has a monopoly market loyal consumers and competes with others in a common market called brand switchers in the case of a duopoly it is shown that the behavior of the brand switchers characterizes the equilibrium behavior of the duopolists this article focuses on two key comparative statics namely the depth of discounts away from a regular high price and the probability of giving a deal or the frequency of deals how these properties vary with the size of the loyal markets and the behavior of the brand switching population is discussed copyright 1988 by the university of chicago

comparing labor supply elasticities in europe and the united states new results we suggest the first large scale international comparison of labor supply elasticities for 17 european countries and the united states using a harmonized empirical approach we find that own wage elasticities are relatively small and more uniform across countries than previously considered nonetheless such differences do exist and are found not to arise from different tax benefit systems wage hour levels or demographic compositions across countries suggesting genuine differences in work preferences across countries furthermore three other findings are consistent across countries the extensive margin dominates the intensive margin for singles this leads to larger responses in low income groups and income elasticities are extremely small

does social security privatization produce efficiency gains while privatizing social security can improve labor supply incentives it can also reduce risk sharing we analyze a 50 privatization using an overlapping generations model where heterogeneous agents with elastic labor supply face idiosyncratic earnings shocks and longevity uncertainty when wage shocks are insurable privatization produces about 18 100 of extra resources for each future household after all transitional losses have been compensated for with lump sum taxes when wages are not insurable privatization reduces efficiency by about 2 400 per future household we check the robustness of these results to different model specifications as well as policy reforms and arrive at several surprising conclusions first privatization performs better in a closed economy where interest rates decline with capital accumulation than in an open economy second privatization also performs better when an actuarially fair private annuity market does not exist third government matching of private contributions on a progressive basis is not very effective at restoring efficiency and can actually cause harm

retirement pensions and ageing we study the effects of demographic shocks and changes in the pension system on the macroeconomic performance of an advanced small open economy facing a given world interest rate we construct an overlapping generations model which includes a realistic description of the mortality process individual agents choose their optimal retirement age taking into account the time and age profiles of wages taxes and the public pension system the early retirement provision in most pension systems acts as a trap inducing most workers to retire well before the normal retirement age simulations show that pension reform must be drastic for it to have any effects on the retirement behaviour of workers

capital structure equilibrium under market imperfections and incompleteness this paper generalizes miller s supply side equilibrium argument to other forms of capital market imperfections and incompleteness if corporations possess a comparative advantage in dealing with these imperfections they have an incentive to act as financial intermediaries corporations attempts to profit from these intermediation activities dictate an optimal capital structure for the corporate sector as a whole but in equilibrium the capital structure of any single firm is a matter of indifference in addition the positive role that corporate finance plays in completing the market restores standard perfect market results on asset pricing and the associated portfolio separation properties

currency options hedging and social value in early september 1982 a conference on exchange rate determination organized by l klein and w krelle took place at the deutsche bundesbank in frankfurt at this conference i presented a paper currency options theory and practicability this paper gave formulas for the pricing and hedging of currency options and showed by means of ex post simulations their practicability examples were given of how to hedge dm options on either the spot bond or forward market cp sondermann 1985a at that time markets for currency options did not yet exist but i was convinced that these markets would soon emerge since i the theory for pricing and hedging of currency options was now available ii the computational facilities were available and most importantly iii currency options do have a social value the stormy development of these markets which started soon after has proved this expectation correct that currency options have a social value has been questioned both on practical and theoretical grounds the first type of arguments stress the speculative element of such options and refer to the forward exchange markets as the approved means of hedging against foreign exchange risks this view overlooks the fact that only future currency streams which are expected with certainty can be hedged on forward markets if for some reason these future payments fail to realize or deviate from their expected value the hedger on the forward market may end up with a costly open position this may e g be the case in a tender situation currency options as a non redundant alternative to forward markets allow for a better allocation of exchange risks the social value of currency options is

dynamic pricing with online learning and strategic consumers an application of the aggregating algorithm we study the problem faced by a monopolistic company that is dynamically pricing a perishable product or service and simultaneously learning the demand characteristics of its customers in the learning procedure the company observes the sales history over consecutive learning stages and predicts consumer demand by applying an aggregating algorithm aa to a pool of online stochastic predictors numerical implementation uses finite sample distribution approximations that are periodically updated using the most recent sales data these are subsequently altered with a random step characterizing the stochastic predictors the company s pricing policy is optimized with a simulation based procedure integrated with aa the methodology of the paper is general and independent of specific distributional assumptions we illustrate this procedure on a demand model for a market in which customers are aware that pricing is dynamic may time their purchases strategically and compete for a limited product supply we derive the form of this demand model using a game theoretic consumer choice model and study its structural properties numerical experiments demonstrate that the learning procedure is robust to deviations of the actual market from the model of the market used in learning

labor supply elasticity and social security reform abstract previous literature on social security reform has used a variety of period utility functions and calibrated values for the intertemporal elasticity of substitution ies in labor in this paper we show that the effects of social security reforms on aggregate labor supply are invariant to plausible values of the ies but the effect of such reforms on the profile of hours over the life cycle is highly sensitive to the ies we first establish these results analytically in a simple partial equilibrium setting and then demonstrate their robustness in a general equilibrium model calibrated to match key u s macroeconomic indicators we find that the aggregate effects are similar regardless of the wide range of the values of ies used in calibrated economies however social security reform leads to a large reallocation of hours worked over the life cycle from early years to later working years and the size of this reallocation significantly increases with the ies

the long term effects of price promotions on category incidence brand choice and purchase quantity abstract to what extent do price promotions have a long term effect on the components of brand sales namely category incidence brand choice and purchase quantity the authors answer this question by using persistence modeling on weekly sales data of a perishable and a storable product derived from a scanner panel their analysis reveals first that permanent promotion effects are virtually absent for each sales component next the authors develop and apply an impulse response approach to estimate the promotional adjustment period and the total dynamic effects of a price promotion specifically they calculate the long term equivalent of gupta s 1988 14 84 2 breakdown of promotional effects because of positive adjustment effects for incidence but negative adjustment effects for choice the authors find a reversal of the importance of category incidence and brand choice 66 11 23 for the storable product and 58 39 3 for the perishable product the authors discuss the implications of the findings an

letter to the editor comments on on optimal inventory policies when ordering prices are random by kamal golabi comments on on optimal inventory policies when ordering prices are random by kamal golabi golabi k 1985 optimal inventory policies when ordering prices are random opns res 33 575 588

price dispersion and stockpiling by consumers this paper presents a model of equilibrium price dispersion in which buyers do not search however they are able to store the non durable commodity for future use such behaviour implies sellers demand curves are endogenously generated by the observed price distribution equilibrium is shown to exist although more than one price may be charged in equilibrium the monopoly price will occur with positive probability comparative static results are derived with a linear version of the model some of which are perverse this paper demonstrates that the possibility of stockpiling of a commodity by consumers can cause equilibrium price dispersion in the market for that commodity this dispersion may occur even when all consumers are identical all firms have identical cost functions and no search takes place thus the stockpiling model presented here provides an alternative explanation of phenomena explained by the more familiar search models of course one expects that storage and search both occur in many markets salop and stiglitz 1982 develop a simple stockpiling model similar to the one presented here and discuss the role that search might play the main point developed here also emphasized in salop and stiglitz 1982 is that price dispersion may occur despite the complete symmetry among sellers and among buyers most search models rely on differences among buyers or among sellers to generate multiple price equilibria the stockpiling model demonstrates such heterogeneity is not necessary each firm has the same cost curve and faces the same demand curve in equilibrium firms choose a price where the demand curve is tangent to the average cost curve thus for there to be price dispersion more than one such tangency must exist that may be the case when stockpiling occurs for then the demand curves are endogenous they are generated by the stocks of goods held by buyers which themselves depend on the observed price distribution and under reasonably weak assumptions a property of the equilibrium price distribution is that the demand curves it generates be tangent to sellers cost curves at several points in section 1 of this paper optimal storage rules for buyers are developed section 2 uses these rules to derive market demand curves in section 3 conditions for equilibrium are presented and in section 4 the possibility of that equilibrium involving only one price is discussed section 5 proves an equilibrium must exist section 6 gives examples of two price equilibria and presents some comparative statics with a simple linearized version of the model some of these comparative results are quite surprising and show the policy implications of stockpiling models may differ from alternative models of price dispersion prior to the formal analysis a brief discussion of the assumptions of the model seem in order buyers are assumed to visit exactly one seller in each period they live forever and consume exactly one unit of the commodity in each period if its price does not

economic aspects of optimal disability benefits this paper analyzes optimal disability and retirement or welfare benefits with imperfect disability evaluation with some able workers judged disabled and some disabled workers judged able thus the levels of both disability and retirement benefits affect labor supply with anyone not working eligible for retirement benefits we analyze the optimal structure of benefits for a given disability screening mechanism and briefly consider the problem of optimal evaluations of disability evidence in the united states there is an overlap in eligibility for disability and retirement portions of social security more generally welfare is sometimes available to people denied disability benefits

aching to retire the rise in the full retirement age and its impact on the social security disability rolls abstract the social security amendments of 1983 reduced the generosity of social security retired worker benefits in the u s by increasing the program s full retirement age from 65 to 67 and increasing the penalty for claiming benefits at the early retirement age of 62 these changes were phased in gradually so that individuals born in or before 1937 were unaffected and those born in 1960 or later were fully affected no corresponding changes were made to the program s disabled worker benefits and thus the relative generosity of social security disability insurance ssdi benefits increased in this paper we investigate the effect of the amendments on ssdi enrollment by exploiting variation across birth cohorts in the policy induced reduction in the present value of retired worker benefits our findings indicate that the amendments significantly increased ssdi enrollment since 1983 with an additional 0 6 of men and 0 9 of women between the ages of 45 and 64 receiving ssdi benefits in 2005 as a result of the changes our results further indicate that these effects will continue to increase during the next two decades as those fully exposed to the reduction in retirement benefit generosity reach their fifties and early sixties

redistribution of individual pension wealth to survivor pensions evidence from a stated preferences analysis abstract pension schemes in the netherlands allow workers to redistribute their own pension wealth to increase the survivor pension of their partner however due to lacking communication and knowledge of survivor pensions among workers and also due to the lack of transparent products and choice architecture redistribution remains limited this paper uses a stated preferences experiment that is explicitly designed for workers with a partner in the age group of 55 to 65 years to elicit their pension redistribution preferences we find that on average the preferred pension wealth redistribution amounts to 50 35 of all individuals have such a preference 33 of all individuals would prefer less redistribution and 32 percent prefers to redistribute more pension income to the partner upon one s death we further show that total family income during working life does not affect the redistribution to survivor pensions however the distribution of the contribution to total family income before retirement across partners as well as the survival likelihood of the partner and the number of years the partner is expected to survive have a significant causal impact on the preferred pension redistribution decision the preference for redistribution to survivor pensions also depends significantly on personal characteristics preferences and social attitude males have a significantly stronger preference for redistribution compared to females moreover forward looking more risk averse and more altruistic individuals have a stronger preference to redistribute part of their pension wealth to a survivor pension finally in particular when employees have the perception that their partner is more forward looking they are willing to invest more in a survivor pension

estimating the impact of consumer expectations of coupons on purchase behavior a dynamic structural model we examine the basic premise that consumers may anticipate future promotions and adjust their purchase behavior accordingly we develop a structural model of households who make purchase decisions to minimize their expenditure over a finite period the model allows for future expectations of promotions to enter the purchase decision households with adequate inventory of the product may face a trade off of buying in the current period with a coupon or defer the purchase until next period given their expectations of future promotions thus we provide a framework for examining the impact of consumer expectations on choice behavior the target audiences for our paper are a empirical researchers who intend to make structural models part of their applied research agenda and b managers who value and seek to understand the impact of consumers coupon expectations on current purchase behavior our research objective is to provide an empirical framework to examine whether and to what extent consumers anticipate future coupon promotions and adjust purchase behavior the central premise of our approach is that a rational consumer minimizes the present discounted value of the cost of a purchase where cost in a single period consists of purchase price inventory holding cost gains from coupons and potential stockout cost we aim to test whether our hypotheses regarding the various elements of the cost structure are supported and that whether consumers take into account future discounted cost when making current purchase decisions the research methodology we adopt is relatively new in econometrics and known as the estimable stochastic structural dynamic programming method the methodology amounts to incorporating a maximum likelihood routine embedded in a dynamic programming problem the dynamic programming problem is solved several times within a maximum likelihood iteration for each value of the state space elements and for each value of the parameters in the parameter set the state space in our model consists of purchase and nonpurchase alternatives in each time period coupon availability and no coupon availability in each time period level of inventory in each time period for each household and consumption rate of each household we use scanner panel data on purchases in the disposable diaper product category and promotions we estimate the inventory holding and stockout costs brand specific value of coupons and consumers expectations of future coupons the key insights and lessons learned can be summarized as follows 1 our results are consistent with the notion that consumers hold beliefs about future coupons and that such beliefs affect the purchase decision we find that the dynamic optimization model performs significantly better than a single period optimization model and a naive benchmark model 2 we find a high and significant stockout cost consistent with the essential nature of the product category our estimate of the holding cost yields a reasonable annualized percentage value when converted to the cost of capital we find that consumer valuation of coupons differ markedly across brands 3 our empirical evidence supports the notion that consumers hold beliefs about future coupon availability we also find that the expectations about future coupons estimated endogenously differ depending upon whether or not a coupon was available in the current period thus the proposed model structure yields rich managerial insights and facilitates several what if scenarios a possible limitation of our model and estimable structural models in general is the computational cost while it is possible to conceptually extend the state space to accommodate variations across households and add a richer parameter structure each addition multiplies the size of the state space and the computation time for this reason we have kept the state space as tight as possible and refrained from additions that would otherwise enable us to incorporate heterogeneity in consumer decisions for example we assumed that consumers are similar other than reflected by their purchase behavior we built a category purchase incidence model rather than a brand choice model we refrained from including unobserved heterogeneity in the parameters we chose to opt out of modeling autocorrelation and other time dependent error term patterns in the likelihood function thus we have made an effort to build a structural model that reasonably reflects consumer purchase behavior without requiring expensive computation currently there are developments in econometrics to approximate the computation of the valuation functions without sacrificing much accuracy when these methods are well developed we expect that structural models will become more commonplace in marketing

decomposing the sales promotion bump with store data sales promotions generate substantial short term sales increases to determine whether the sales promotion bump is truly beneficial from a managerial perspective we propose a system of store level regression models that decomposes the sales promotion bump into three parts cross brand effects secondary demand cross period effects primary demand borrowed from other time periods and category expansion effects remaining primary demand across four store level scanner datasets we find that each of these three parts contribute about one third on average one extension we propose is the separation of the category expansion effect into cross store and market expansion effects another one is to split the cross item effect total across all other items into cannibalization and between brand effects we also allow for a flexible decomposition by allowing all effects to depend on the feature display support condition and on the magnitude of the price discount the latter dependence is achieved by local polynomial regression we find that feature supported price discounts are strongly associated with cross period effects while display only supported price discounts have especially strong category expansion effects while the role of the category expansion effect tends to increase with higher price discounts the roles of cross brand and cross period effects both tend to decrease

families as shocks in this paper we show the quantitative importance of the process that determines changes in family composition to determine the main macroeconomic magnitudes we do so by modelling family type as a stochastic process that affects households in a way similar to shocks to earnings agents respond to these process by optimally choosing savings we show that the size of savings differs dramatically depending on the details of the stochastic process the model is quantitative its fundamental parameters are estimated using u s data

stack them high let em fly lot sizing policies when inventories stimulate demand in some retail contexts stocking large quantities of inventory may not only improve service levels but can also stimulate demand for products having demand rates that increase with inventory levels we analyze the effect of stocking decisions on firm profitability to develop managerial insights regarding the structure of the optimal inventory policy and to understand how this policy differs from traditional approaches when inventories stimulate demand iteratively applying the standard economic order quantity eoq model by setting the demand rate parameter equal to the observed average demand rate in prior cycles yields an equilibrium order quantity that is robust to demand parameter misestimation but is suboptimal the profit maximizing policy orders larger quantities and can replenish inventory even before on hand stock fully depletes using an extension of a standard inventory dependent demand model from the literature we first provide a convenient characterization of products that require early replenishment we demonstrate that the optimal cycle time is largely governed by the conventional trade off between ordering and holding costs whereas the reorder point relates to a promotions oriented cost benefit perspective we show that the optimal policy yields significantly higher profits than cost based inventory policies underscoring the importance of profit driven inventory management

consumption and risk sharing over the life cycle a striking feature of u s data on income and consumption is that inequality increases with age this paper asks if individual specific earnings risk can provide a coherent explanation we find that it can we construct an overlapping generations general equilibrium model in which households face uninsurable earnings shocks over the course of their lifetimes earnings inequality is exogenous and is calibrated to match data from the u s panel study on income dynamics consumption inequality is endogenous and matches well data from the u s consumer expenditure survey the total risk households face is decomposed into that realized before entering the labor market and that realized throughout the working years in welfare terms the latter is found to be more important than the former

risk sharing and efficiency implications of progressive pension arrangements the present paper aims to quantify the welfare effects of progressive pension arrangements in germany starting from a purely contribution related benefit system we introduce basic allowances for contributions and a flat benefit fraction since our overlapping generations model takes into account variable labor supply borrowing constraints as well as stochastic income risk we can compare the labor supply the liquidity and the insurance effects of the policy reform our simulations indicate that for a realistic parameter combination an increase in pension progressivity would yield an aggregate efficiency gain of more than 2 percent of resources however such a reform would not be implemented because it would not find political support of the currently living generations

social security and two earner households in the past decades elimination of the pay as you go system in u s has been extensively discussed and studied such an elimination would also eliminate the intra cohort redistribution done by the following policies of social security due to spousal and survivor s beneflt provisions the system redistributes mostly to single earner married households not necessarily progressive retirement beneflts are a concave function of past mean earnings hence the system redistributes from high earners to low earners finally the existence of a cap on social security taxable earnings makes the system regressive this is the flrst paper that quantifles redistributive labor supply and welfare implications of these policies using a general equilibrium life cycle model agents start out as permanently married or single and with education levels and wage proflles where the latter depend both on education and gender the household is the decision maker and decides on the labor supply of its member s and saving the aggregate production function has as inputs capital and labor aggregated by e ciency elimination of these policies results in a 6 1 increase in married female labor force participation rate the middle income single earner married households experience the largest welfare losses whereas the high income two earner households together with high income single households experience the largest welfare gains

joint purchasing decisions a multivariate negative binomial approach the analysis of household purchasing decisions for understanding consumption behaviour has received much attention recently mainly because of the measurement error problems that appear when using expenditure data to approximate consumption this paper discusses some empirical regularities of the household purchasing behaviour based on information about the number of purchases a household has declared having done during the survey period the concern of this paper is two fold first to show how to recover purchase frequency data from the spanish budget survey 1990 1991 second to discuss some empirical regularities of the joint purchasing decisions based on multivariate negative binomial models

does unemployment insurance crowd out home production abstract in this paper we study the interaction between self insurance and public insurance in particular we provide evidence on a negative correlation between unemployment insurance benefits and home production using the american time use survey atus and the state level unemployment insurance data of the u s the empirical results suggest that moving to a two times more generous state would decrease time spent on home production about 22 for the unemployed then we pursue a quantitative assessment of this empirical finding using a dynamic competitive equilibrium model in which households do home production as well as market production the model is able to generate the empirical facts regarding the unemployment benefits and home production the fact that unemployment insurance benefits crowd out home production is interpreted as a substitution between the two insurance mechanisms against loss of earnings during unemployment spells

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

dealing temporary price cuts by seller as a buyer discrimination mechanism this paper is concerned with temporary price cuts deals sales and specials as a mechanism for the seller to price discriminate between buyers with different intensities of demand we analyze why a seller offers such price cuts which buyers take advantage of them and what the parameters are that determine the amount and frequency of the discount offered in the remainder of this section we briefly review the literature on price deals 1 in section ii simple models of buyer and seller behavior are developed and we show why and how a seller adopts a dealing strategy section iii summarizes the key implications of the model and indicates how the price discrimination hypothesis could be tested in practice section iv suggests possible extensions of the model finally section v gives our conclusions in the marketing literature the issue of who is deal prone has been extensively researched an explanation for temporary price cuts usually called deals sales or specials is provided we hypothesize that they are a mechanism that discriminates between more intense and less intense demanders we further hypothesize a positive relationship between demand elasticity and holding costs buyers with more intense demand with high holding costs are those who will be buying the product at its regular price the low holdingcost buyers take advantage of deals by forward buying the model is applicable to three relationships 1 manufacturer reseller where the reseller may be a wholesaler or a retailer 2 resellerreseller for example wholesaler retailer and 3 retailer consumer we are grateful to michael mussa and albert madansky for their comments we also benefited from comments made by the marketing faculty of the wharton school at a seminar where an earlier version of this paper was presented neil beckwith in particular is acknowledged 1 for a more detailed review of deals and similar pricecutting mechanisms e g mail in rebates cents off labels coupons etc see narsimhan 1982 chan 2 journal of business 1985 vol 58 no 3 1985 by the university of chicago all rights reserved 0021 9398185 5803 0004 01 50

the decomposition of promotional response an empirical generalization price promotions are used extensively in marketing for one simple reason consumers respond the sales increase for a brand on promotion could be due to consumers accelerating their purchases i e buying earlier than usual and or buying more than usual and or consumers switching their choice from other brands purchase acceleration and brand switching relate to the primary demand and secondary demand effects of a promotion gupta 1988 captures these effects in a single model and decomposes a brand s total price elasticity into these components he reports for the coffee product category that the main impact of a price promotion is on brand choice 84 and that there is a smaller impact on purchase incidence 14 and stockpiling 2 in other words the majority of the effect of a promotion is at the secondary level 84 and there is a relatively small primary demand effect 16 this paper reports the decomposition of total price elasticity for 173 brands across 13 different product categories on average we find that 25 of the elasticity is due to primary demand expansion i e purchase acceleration and 75 to secondary demand effects or brand switching thus while gupta s finding that the majority of promotional response stems from brand switching is supported the average magnitude of the effect appears to be smaller than first thought more important there is ample evidence that promotions have a significant primary demand effect the relative emphasis on purchase acceleration and brand switching varies systematically across categories and the second goal of the paper is to explain this variation as a function of exogeneous covariates in doing this we recognize that promotional response is the consumer s reaction to a price promotion and therefore develop a framework for understanding variability in promotional response that is based on the consumer s perspective of the benefits from a price promotion these benefits are posited to be a function of i category specific factors ii brand specific factors and iii consumer characteristics the framework is formalized as a generalized least squares meta analysis in which the brand s price elasticity is the dependent variable several interesting results emerge from this analysis category specific factors brand specific factors and consumer demographics explain a significant amount of the variance in promotional response for a brand at both the primary and secondary demand levels category specific factors have greater influence on variability in promotional response and its decomposition than do brand specific factors there are several instances where exogenous variables do not affect total elasticities yet significantly affect individual components of total elasticity in fact the lack of a significant relationship between the variables and total elasticity is often due to offsetting effects within two or more of the three behavioral components of elasticity this is particularly true for brand specific factors which typically have no effect on total elasticity yet have important effects on the individual behaviors there is some evidence to suggest that not all promotion related increases in primary demand are due to forward buying in some cases promotions appear to increase consumption we use these results to illustrate how category and brand specific factors work to drive primary and secondary demand elasticities in different directions in short this paper offers an empirical generalization of a key finding on promotional response how elasticities decompose across brand choice purchase incidence and stockpiling and new insights into factors that explain variance in promotional response these findings are likely to be of interest to researchers who are concerned with theory development and the generalizability of marketing phenomena and to managers who plan promotion campaigns

price competition under stockpiling and flexible consumption abstract conventional wisdom suggests that the main effect of price promotion is on brand switching i e secondary demand however some recent studies demonstrate that the primary demand expansion effect can be considerably larger than previously believed a significant driver of this primary demand effect is consumer stockpiling in response to price promotions indeed experimental studies have shown that additional inventory on hand can lead to an endogenous increase in consumption the authors develop a model of price competition between firms in response to the stockpiling and subsequent consumption dynamics of consumers in this setting the flexible consumption effect causes more intense price competition deeper promotions and an increase in the frequency of promotions the authors use two years of scanner panel data from eight product categories and 4313 stockkeeping units to test three implications of the theoretical model they find strong support for each

female labor supply as insurance against idiosyncratic risk in this paper we explore the role of female labor supply as an insurance mechanism against idiosyncratic earnings risk within the family we use a life cycle model in which a unitary family makes consumption saving and labor supply decisions additional uncertainty increases female participation rates this effect on participation is greatest when the ability to borrow and hence to smooth consumption is limited we calculate the welfare cost of increases in uncertainty and show that the welfare cost is greater when households are unable to adjust female labor supply jel j22 d91

should pensions be progressive abstract the present paper quantitatively characterizes the consequences of rising pension progressivity in an overlapping generations model with idiosyncratic income disability and longevity risk as well as endogenous labor supply at the intensive and extensive margin focusing on the german pension system which is purely earnings related we increase the degree of progressivity and compute the optimal mix between flat and earnings related pensions we find that a flat rate pension share of roughly 30 maximizes aggregate economic efficiency since improved insurance provision dominates higher labor supply distortions disability risk significantly increases the optimal progressivity level while endogenous retirement has important macroeconomic implications since our results are robust for a wide range of parameter specifications they indicate that at least in germany a move towards more redistribution within the pension system is efficient

promotion effect on endogenous consumption over the years researchers have found that promotion makes consumers switch brands and purchase earlier or more however it is unclear how promotion affects consumption especially for product categories that are perceived to be versatile and substitutable in this paper we propose a dynamic structural model with endogenous consumption under promotion uncertainty to analyze the promotion effect on consumption this model recognizes consumers as rational decision makers who form promotion expectations and plan their purchase and consumption decisions in light of promotion schedule applying the proposed model to packaged tuna and yogurt we find that endogenous consumption responds to promotion as a result of forward looking and stockpiling behavior this is the first empirical paper that recognizes consumption as an endogenous decision variable and proposes a structural model to offer behavioral explanations on whether how and why promotion encourages consumption for product categories with flexible consumption