optimal product launch times in a duopoly balancing life cycle revenues with product cost we present a model describing the demand dynamics of two new products competing for a limited target market the demand trajectories of the two products are driven by a market saturation effect and an imitation effect reflecting the product experience of previous adopters in this general setting we provide analytical results for the sales trajectories and life cycle sales of the competing products we use these results to study the impact of launch time on overall life cycle sales we consider the perspective of one of the competing products and model the trade off between the lost revenues resulting from a delayed launch and the lower unit production costs we find that the profit maximizing launch time exhibits a counterintuitive behavior in particular we show that a firm facing a launch time delay from a competing product might benefit from accelerating its own product launch as opposed to using the softened competitive situation to further improve its cost position we identify conditions under w

a micro analytic threshold model for the timing of first purchases of durable goods a micro analytic threshold model to describe the timing of household purchases of consumer durable goods is developed and tested the model incorporates unobserved heterogeneity via a generalized gamma distribution and accounts for time varying covariates further we employ estimation methods applicable or purchase data observed at periodic intervals of time the model outperforms other competing models for predicting the timing of purchase of durable goods in terms of fit and predictive ability in particular this model outperforms the logit model and the diffusion model the generalized gamma timing model predicts well the time to purchase the durable good we show how it can be employed for micro segmentation of households several research directions and applications are described

endogenous number of firms horizontal concentration and heterogeneity of firms a note we re examine implications of heterogeneity of firms under a cournot setting on free entry equilibria concerning the number of firms heterogeneity reduces the number of firms in equilibrium the larger the cost asymmetries the smaller the free entry equilibrium number of firms in an industry

unequal treatment of identical agents in cournot equilibrium oligopoly models where prior actions by firms affect subsequent marginal costs have been useful in illuminating policy debates in areas such as antitrust regulation environmental protection and international competition we discuss properties of such models when a cournot equilibrium occurs at the second stage aggregate production costs strictly decline with no change in gross revenue or gross consumer surplus if the prior actions strictly increase the variance of marginal costs without changing the marginal cost sum therefore unless the cost of inducing second stage asymmetry more than offsets this reduction in production costs the private and social optima are asymmetric

emissions trading with profit neutral permit allocations this paper examines the impact of an emissions trading scheme ets on equilibrium emissions output price market concentration and profits in a generalized cournot model we develop formulae for the number of emissions permits that have to be freely allocated to firms to neutralize the profit impact of the ets we show that its profit impact is usually limited in a cournot oligopoly with constant marginal costs total industry profits are preserved so long as freely allocated permits cover a fraction of initial emissions that does not exceed the industry s herfindahl index

cost heterogeneity industry concentration and strategic trade policies abstract we show that if domestic firms do not have identical unit costs then the interplay between the herfindahl index of concentration and the elasticity of the slope of the demand curve is of major importance in the determination of optimal trade policies in some cases the direction of optimal policy is reversed

new product diffusion acceleration measurement and analysis it is a popular contention that products launched today diffuse faster than products launched in the past however the evidence of diffusion acceleration is rather scant and the methodology used in previous studies has several weaknesses also little is known about why such acceleration would have occurred this study investigates changes in diffusion speed in the united states over a period of 74 years 1923 1996 using data on 31 electrical household durables this study defines diffusion speed as the time it takes to go from one penetration level to a higher level and it measures speed using the slope coefficient of the logistic diffusion model this metric relates unambiguously both to speed as just defined and to the empirical growth rate a measure of instantaneous penetration growth the data are analyzed using a single stage hierarchical modeling approach for all products simultaneously in which parameters capturing the adoption ceilings are estimated jointly with diffusion speed parameters the variance in diffusion speed across and within products is represented separately but analyzed simultaneously the focus of this study is on description and explanation rather than forecasting or normative prescription there are three main findings 1 on average there has been an increase in diffusion speed that is statistically significant and rather sizable for the set of 31 consumer durables the average value of the slope parameter in the logistic model s hazard function was roughly 0 48 increasing with 0 09 about every 10 years it took an innovation reaching 5 household penetration in 1946 an estimated 13 8 years to go from 10 to 90 of its estimated maximum adoption ceiling for an innovation reaching 5 penetration in 1980 that time would have been halved to 6 9 years this corresponds to a compound growth rate in diffusion speed of roughly 2 between 1946 and 1980 2 economic conditions and demographic change are related to diffusion speed whether the innovation is an expensive item also has a sizable effect finally products that required large investments in complementary infrastructure radio black and white television color television cellular telephone and products for which multiple competing standards were available early on pcs and vcrs diffused faster than other products once 5 household penetration had been achieved 3 almost all the variance in diffusion speed among the products in this study can be explained by 1 the systematic increase in purchasing power and variations in the business cycle unemployment 2 demographic changes and 3 the changing nature of the products studied e g products with competing standards appear only late in the data set after controlling for these factors no systematic trend in diffusion speed remains unaccounted for these findings are of interest to researchers attempting to identify patterns of difference and similarity among the diffusion paths of many innovations either by jointly modeling the diffusion of multiple products as in this study or by retrospective meta analysis the finding that purchasing power demographics and the nature of the products capture nearly all the variance is of particular interest specifically one does not need to invoke unobserved changes in tastes and values as some researchers have done to account for long term changes in the speed at which households adopt new products the findings also suggest that new product diffusion modelers should attempt to control not only for marketing mix variables but also for broader environmental factors the hierarchical model structure and the findings on the systematic variance in diffusion speed across products are also of interest to forecasting applications when very little or no data are available

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

demand modeling of stochastic product diffusion over the life cycle abstract planning during the product life cycle plc poses a number of challenges for managers due to the pace of change and uncertainties in the marketplace the ability to better understand predict and make decisions based on manifestations of demand forms a set of important operational problems that ultimately affect the profitability of enterprises this paper models the stochastic diffusion of a product in the market as a geometric brownian motion gbm process that has a time varying drift rate the model is calibrated such that model parameters are able to feature different product types and diffusion conditions imperfect information on the expected peak demand is treated as model uncertainty and a bayesian approach is employed to update knowledge on it the demand model demonstrates robust performance over a wide range of conditions despite model uncertainty it provides both qualitative and quantitative information for manufacturers and service providers to design strategies for stochastic plc conditions as well as dynamic production planning

entrepreneurship and uncertainty innovation and competition among the many schumpeter stressed innovation and knight uncertainty as preconditions for entrepreneurship and productivity growth schumpeter emphasized entry in his early work but came to consider incumbent innovation the dominant mode in his later work modern growth theory emphasizes dissemination of knowledge to explain progress in the steady state the paper analyzes the effects of entry market structures and uncertainty on the incidence and diffusion of innovation the insertion of knightian uncertainty in schumpeter s model can explain why innovators are numerous and arrive unexpectedly uncertainty spurs diffusion and improves the utilization of human capital combining the ideas of schumpeter and knight also elucidates several stylized facts of entrepreneurship such as small entry size low chances of survival and high growth rates

managing demand and sales dynamics in new product diffusion under supply constraint the bass diffusion model is a well known parametric approach to estimating new product demand trajectory over time this paper generalizes the bass model by allowing for a supply constraint in the presence of a supply constraint potential customers who are not able to obtain the new product join the waiting queue generating backorders and potentially reversing their adoption decision resulting in lost sales consequently they do not generate the positive word of mouth that is typically assumed in the bass model leading to significant changes in the new product diffusion dynamics we study how a firm should manage its supply processes in a new product diffusion environment with backorders and lost sales we consider a make to stock production environment and use optimal control theory to establish that it is never optimal to delay demand fulfillment this result is interesting because immediate fulfillment may accelerate the diffusion process and thereby result in a greater loss of customers in the future using this result we derive closed form expressions for the resulting demand and sales dynamics over the product life cycle we then use these expressions to investigate how the firm should determine the size of its capacity and the time to market its new product we show that delaying a product launch to build up an initial inventory may be optimal and can be used as a substitute for capacity also the optimal time to market and capacity increase with the coefficients of innovation and imitation in the adoption population we compare our optimal capacity and time to market policies with those resulting from exogeneous demand forecasts in order to quantify the value of endogenizing demand

buying ecological services nature s harmonies fragmented reserves and the agricultural extensification debate growing demand for cropland products has placed intense pressure on the ability of land resources to support nature straining public budgets to purchase environmental goods fixing overall agricultural output two policy options are whether to promote more extensive and nature friendly farming practices or to produce intensively on some land and leave the rest wild microeconomic models of the topic have not accommodated widely recognized complementary spatial externalities in providing ecological services this article does so identifying also a third policy possibility this is that environmental services can follow a smoothly varying spatial path characterized by harmonic functions

the impact of standards competition on consumers effectiveness of product information and advertising formats abstract compared with other markets those with competing technological standards exhibit certain fundamental characteristics that make a consumer s decision to adopt a new product more risky and more complex this article examines how standards competition affects consumer behavior an issue that has been relatively neglected by previous research in this area the results show that consumers depend on different types of information in their adoption decisions and respond differently to advertising specifically the authors find that standards competition motivates consumers to pay more attention to information that is comparative in nature thus information about the relative absolute performance of a product has a stronger weaker impact on a product s share in markets with standards competition study 1 standards competition also moderates the effectiveness of different advertising formats it strengthens the effect of comparative advertisements but weakens the effect of noncomparative advertis

cost manipulation games in oligopoly with costs of manipulating we analyze a class of two stage games where rival firms incur real resource costs in manipulating their marginal costs so as to influence the outcome of the game they want to play in stage two marginal costs may be manipulated by various means such as redistribution of productive assets choice of location or creation of an internal input market a general formulation of the game is provided and several applications are analyzed we show that the optimal allocation of resources within an oligopoly can be asymmetric even for ex ante symmetric firms this is an additional explanation of heterogeneity in oligopoly

estimating efficiency in the hospital sector a comparison of three statistical cost frontier models this paper reports the results of an empirical comparison of three statistical cost frontier models using data from 49 spanish public hospitals the models estimated include the deterministic cost frontier a cross section stochastic cost frontier scf in which inefficiency is assumed to follow a half normal distribution and a panel data scf in which inefficiency is assumed to remain constant over time a non frontier model is also estimated the paper compares the estimates of average inefficiency obtained from the frontier models and the implied rankings of hospitals in terms of their costliness actual cost as a proportion of expected cost

a theory of oil igopoly cournot equilibrium in exhaustible resource markets with fixed supplies the emergence of an effective and powerful cartel in the international petroleum market has stimulated considerable effort among economists to develop models of pricing and supply behavior for this industry 2 this modeling task poses two basic difficulties first as in the standard oligopoly problem one must characterize the behavior of several sellers in a market aware of each other and of their effect on market price second there is here the added difficulty of treating the explicitly intertemporal nature of suppliers decision wherein a limited stock must be optimally allocated over time this paper studies the implications of the simplest non trivial postulates about these two aspects of the problem it is assumed that suppliers are non cooperative cournot nash players each of whom is imagined to select an optimal supply strategy taking as given the strategies of the others moreover it is hypothesized that the feasible strategies are limited to open loop paths chosen at the initial date to maximize the present value of profits in light of the paths of supply which the others have chosen 3 these basic postulates together with a few technical assumptions concerning the structure of resource demand permit one to demonstrate the existence of at least one non cooperative equilibrium concerning thisequilibrium we show that 1 the average and marginal return on resource stocks is inversely related to the size of a player s initial endowment 2 aggregate production decreases over time until all stocks are exhausted while firms with smaller stocks exhaust their supplies no later than firms with larger stocks do 3 the present value of price net of extraction cost declines over time 4 industry production maximizes a weighted average of intertemporal consumer s surplus and producers profits

the power of money wealth effects in contests abstract the relationship between wealth and power has long been debated nevertheless this relationship has been rarely studied in a strategic game in this paper we study wealth effects in a strategic contest game two opposing effects arise wealth reduces the marginal cost of effort but it also reduces the marginal benefit of winning the contest we consider three types of contests which vary depending on whether rents and efforts are commensurable with wealth our theoretical analysis shows that the effects of wealth are strongly contest dependent it thus does not support general claims that the rich lobby more or that low economic growth and wealth inequality spur conflicts

an analysis of cooperative research and development i analyze the effects of cooperative research whereby member firms agree to share the costs andfruits of a research project before they undertake it in this model industrywide agreements tend to have socially beneficial effects when the degree ofproduct market competition is low when there are r d spillovers in the absence of cooperation when a high degree of sharing is technologically feasible and when the agreement concerns basic research rather than development activities i show that a royalty free cross licensing agreement among any number offirms lowers the equilibrium level of innovation even though it increases the efficiency of r d through sharing

noncooperative versus cooperative r d with endogenous spillover rates this paper deals with a general version of a two stage model of r d and product market competition we provide a thorough generalization of previous results on the comparative performance of noncooperative and cooperative r d dispensing in particular with ex post firm symmetry and linear demand assumptions we also characterize the structure of profit maximizing r d cartels where firms competing in a product market jointly decide r d expenditure as well as internal spillover levels we establish the firms would essentially always prefer extremal spillovers and within the context of a standard specification derive conditions for the optimality of minimal spillover

will it ever fly modeling the takeoff of really new consumer durables a consistent pattern observed for really new household consumer durables is a takeoff or dramatic increase in sales early in their history the takeoff tends to appear as an elbow shaped discontinuity in the sales curve showing an average sales increase of over 400 in contrast most marketing textbooks as well as diffusion models generally depict the growth of new consumer durables as a smooth sales curve our discussions with managers indicate that they have little idea about the takeoff and its associated characteristics many managers did not even know that most successful new consumer durables had a distinct takeoff their sales forecasts tend to show linear growth yet knowledge about the takeoff is crucial for managers to decide whether to maintain increase or withdraw support of new products it is equally important for industry analysts who advise investors and manufacturers of complementary and substitute products although previous studies have urged researchers to examine the takeoff no research has addressed this critical event while diffusion models are commonly used to study new product sales growth they do not explicitly consider a new product s takeoff in sales indeed diffusion researchers frequently use data only from the point of takeoff therefore nothing is known about the takeoff or models appropriate for this event our study provides the first analysis of the takeoff in particular we address three key questions i how much time does a newly introduced product need to takeoff ii does the takeoff have any systematic patterns iii can we predict the takeoff we begin our study by developing an operational measure to determine when the takeoff occurs we found that when the base level of sales is small a relatively large percentage increase could occur without signaling the takeoff conversely when the base level of sales is large the takeoff sometimes occurs with a relatively small percentage increase in sales therefore we developed a threshold for takeoff this is a plot of percentage sales growth relative to a base level of sales common across all categories we define the takeoff as the first year in which an individual category s growth rate relative to base sales crosses this threshold the threshold measure correctly identifies the takeoff in over 90 of our categories we model the takeoff with a hazard model because of its advantages for analyzing time based events we consider three primary independent variables price year of introduction and market penetration as well as several control variables the hazard model fits the pattern of takeoffs very well with price and market penetration being strong correlates of takeoff our results provide potential generalizations about the time to takeoff and the price reduction nominal price and penetration at takeoff in particular we found that on average for 16 post world war ii categories the price at takeoff is 63 of the introductory price the time to takeoff from introduction is six years the penetration at takeoff is 1 7 the time to takeoff is decreasing for more recent categories for example the time to takeoff is 18 years for categories introduced before world war ii but only six years for those introduced after world war ii many of the products in our sample had a takeoff near three specific price points in nominal dollars 1000 500 and 100 in addition we show how the hazard model can be used to predict the takeoff the model predicts takeoff one year ahead with an expected average error of 1 2 years it predicts takeoff at a product s introduction with an expected average error of 1 9 years even against the simple mean time to takeoff of six years for recent categories the model s performance represents a tremendous improvement in prediction it represents an immeasurable improvement in prediction for managers who currently have no idea about how long it takes for a new product to takeoff the threshold rule for determining takeoff can be used to distinguish between a large increase in sales and a real takeoff some limitations of this study could provide fruitful areas for future research our independent variables suffer from endogeneity bias so alternative variables or methods could address this limitation also the takeoff may be related to additional variables such as relative advantage over substitutes and the presence of complementary products finally examination of sales from takeoff to their leveling off could be done with an integrated model of takeoff and sales growth or with the hazard model we propose generalizations about this period of sales growth could also be of tremendous importance to managers of new products

technology asymmetries group algebra and multiplant cost minimization for a homogeneous good this article studies firm level production activities when the firm controls a plural number of plants through careful construction of cost function technology asymmetries we inquire into the ordinal structure of the production vector for multiplant cost minimizers when schur convexity of a reference pseudo cost technology is the principal functional assumption then ordinal concepts of technical asymmetries map into rank order on the equilibrium production vector under a more generalized characterization of the technical asymmetries a multiplant firm encounters group theory is used to map a cardinal concept of asymmetries into cardinal bounds on the optimum allocation

social contagion and income heterogeneity in new product diffusion a meta analytic test standard diffusion models capture social contagion only coarsely and do not allow one to operationalize different contagion mechanisms moreover there is increasing skepticism about the importance of contagion and as has long been known s shaped diffusion curves can also result from heterogeneity in the propensity to adopt we present hypotheses about conditions under which specific contagion mechanisms and income heterogeneity are more pronounced and test these hypotheses using a meta analysis of the q p ratio in applications of the bass diffusion model the ratio is positively associated with the gini index of income inequality in a country supporting the heterogeneity in thresholds interpretation the ratio also varies as predicted by the gamma shifted gompertz diffusion model but the evidence vanishes after controlling for national culture as to contagion the q p ratio varies with the four hofstede dimensions of national culture for three of them in a direction consistent with the social contagion interpretation furthermore products with competing standards have a higher q p ratio which is again consistent with the social contagion interpretation finally we find effects of national culture only for products without competing standards suggesting that technological effects and culturally moderated social contagion effects might not operate independently from each other

global takeoff of new products culture wealth or vanishing differences the authors study the takeoff of 16 new products across 31 countries 430 categories to analyze how and why takeoff varies across products and countries they test the effect of 12 hypothesized drivers of takeoff using a parametric hazard model the authors find that the average time to takeoff varies substantially between developed and developing countries between work and fun products across cultural clusters and over calendar time products take off fastest in japan and norway followed by other nordic countries the united states and some countries of midwestern europe takeoff is driven by culture and wealth plus product class product vintage and prior takeoff most importantly time to takeoff is shortening over time and takeoff is converging across countries the authors discuss the implications of these findings

partial vertical ownership abstract a backward ownership interest held by a downstream firm yields a partial rebate of the upstream margin input demand increases with backward ownership and the upstream firm optimally responds by raising price with symmetric costs every downstream firm s equilibrium input output choice is invariant across a class of ownership profiles including uniform ownership moreover equity trading results in uniform holdings so partial vertical ownership may have no real effects with asymmetric costs ex ante equity trading amplifies the asymmetries and shifts output toward lower cost firms with homogeneous goods this improves producer and total surplus with differentiated goods it may harm consumers

impure public goods and transfers in a three agent model abstract this paper extends previous models of non cooperative private funding of pure public goods by allowing for impure public goods the analysis is developed in the context of international public goods under certain conditions the consequences of transfers on utility are paradoxical if the preferences are divergent a country may gain by giving a transfer the receiver may lose and these two phenomena may appear at the same time

oligopoly and welfare a unified presentation with applications to trade and development abstract we develop a unified sequence of models to examine the determinants of price output profitability and concentration for different kinds of oligopolistic market we relate various magnitudes of significance to judges of welfare and to policy makers such as consumer surplus profit or added benefits of employment or trade surplus to observable magnitudes such as the size and concentration of the market it emerges that various appropriately formulated herfindahl indices are useful in several of these relations we attempt to present results in a way that is useful for empirical investigations and pay particular attention to applications in trade and development

price elasticity dynamics over the adoption life cycle little empirical research has been conducted to test the dynamic behavior of elasticities over the product life cycle competing specifications of price elasticity dynamics are examined to test the

two remarks on cournot equilibria abstract we describe two simple results in the theory of cournot equilibria the first has to do with the effect of taxation in a cournot industry and the second describes under what conditions a cournot equilibrium will implicity maximize an objective function these results are probably known but are not well known and they seem useful enough to be worth spelling out

symmetric research joint ventures cooperative substitutes and complements we introduce the concepts of cooperative substitutes and complements and use them to explain when all firms in a research joint venture will choose equal levels of r d we show that the second order conditions for a symmetric optimum take a particularly simple form ruling out both excessive cooperative substitutability and excessive cooperative complementarity and nesting conditions already derived in the literature finally we apply our results to the comparison between cooperative and non cooperative r d and show in an important special case that asymmetric outcomes are only optimal for a very limited range of parameter values

a free lunch in the commons we derive conditions under which raising costs through a regulatory constraint or a fully expropriated tax can increase the profits arising from a common pool resource the basic model assumes a fixed number of identical agents with linear costs selling in a single period at an exogenous price a necessary and sufficient condition for a cost increase to be profitable is that aggregate output from the resource be locally convex in aggregate effort we also show that cost increases can be profitable even if price is endogenous agents are heterogeneous entry is costless or agents are playing a markov perfect equilibrium of a dynamic game we also discuss more general welfare implications of the result along with its relation to existing results for a cournot oligopoly

input price discrimination with downstream cournot competitors abstract this paper addresses third degree price discrimination in input markets i decompose the upstream monopolist s profit into two parts one that depends on average input prices and one that depends on their distribution this decomposition is useful in comparing the welfare properties of price discrimination against uniform pricing under reasonable assumptions input price discrimination negatively affects both consumer surplus and total welfare

growing growing gone cascades diffusion and turning points in the product life cycle research on the product life cycle plc has focused primarily on the role of diffusion this study takes a broader theoretical perspective on the plc by incorporating informational cascades and developing and testing many new hypotheses based on this theory on average across 30 product categories the authors find that i new consumer durables have a typical pattern of rapid growth of 45 per year over 8 years ii this period of growth is followed by a slowdown when sales decline by 15 and stay below those of the previous peak for 5 years iii slowdown occurs at 34 population penetration and about 50 of ultimate market penetration iv products with large sales increases at takeoff tend to have larger sales declines at slowdown v leisure enhancing products tend to have higher growth rates and shorter growth stages than nonleisure enhancing products time saving products tend to have lower growth rates and longer growth stages than nontime saving products vi lower probability of slowdown is associated with steeper price reductions lower penetration and higher economic growth vii a hazard model can provide reasonable predictions of the slowdown as early as the takeoff the authors discuss the implications of these findings

when are nash equilibria independent of the distribution of agents characteristics author s bergstrom ted varian hal r abstract we present examples of nash equilibria that do not vary with the distribution of a parameter across agents and then offer a general theorem that characterizes this independence

systems competition and network effects this paper discusses firm behavior market performance and the public and private institutions that arise in systems markets i e markets where consumers use compatible components together to generate benefits in such markets which include communications networks and hardware software networks popular products are inherently more valuable these network effects can drive corporate strategies and are critical in understanding innovation in many high technology markets the discussion here emphasizes the dynamics of consumer adoption decisions in the presence of network effects competition between incompatible systems and how suppliers choose which components are compatible and which are not

modeling multinational diffusion patterns an efficient methodology the objective of this study is to develop an econometric model for the diffusion of innovations at the individual country level but which also allows the parameters of the process to differ systematically across countries the conceptualization rests on behavioral and spatial theories of diffusion and extends the domain to international markets the cross national model of innovation diffusion which is developed highlights substantive differences and similarities among international markets it also provides estimates for the diffusion parameters even for countries where sales data are not available thereby yielding some insights into the nature of the expected diffusion pattern in these countries prior to market entry