optimal pricing and return policies for perishable commodities this paper considers the pricing decision faced by a producer of a commodity with a short shelf or demand life a hierarchical model is developed and the results of the single period inventory model are used to examine possible pricing and return policies the paper shows that several such policies currently in effect are suboptimal these include those where the manufacturer offers retailers full credit for all unsold goods or where no returns of unsold goods are permitted the paper also demonstrates that a policy whereby a manufacturer offers retailers full credit for a partial return of goods may achieve channel coordination but that the optimal return allowance will be a function of retailer demand therefore such a policy cannot be optimal in a multi retailer environment it is proven however that a pricing and return policy in which a manufacturer offers retailers a partial credit for all unsold goods can achieve channel coordination in a multi retailer environment this article was originally published in marketing science volume 4 issue 2 pages 166 176 in 1985

coordinating a decentralized supply chain with customer returns and price dependent stochastic demand using a buyback policy abstract we investigate a decentralized supply chain that consists of a manufacturer and a retailer where the retailer simultaneously determines the retail price and order quantity while experiencing customer returns and price dependent stochastic demand we propose an agreement between the manufacturer and the retailer that includes two buyback prices one for unsold inventory and a second for customer returns and show that this type of easy to implement agreement can achieve perfect supply chain coordination and be a win win for both manufacturer and retailer when a complementary profit sharing agreement is included

distribution of personal income development of a new model and its application to u s income data summary this paper proposes a four parameter statistical model of the personalized distribution of income using the income share elasticity approach suggested by esteban 1986 our proposed model includes the singh maddala 1976 and dagum 1977 distributions as special cases the generalized beta ii distribution of mcdonald 1984 is also a variant of this model it appears to give an excellent fit to us income data and its empirical performance turns out to be superior to those of the singh maddala 1976 dagum 1977 the five parameter champernowne 1953 distributions and the generalized beta ii distribution of mcdonald 1984 on some data

analysis of the impact of price sensitivity factors on the returns policy in coordinating supply chain this paper analyzes the impact of price sensitivity factors on characteristics of returns policy contracts in a single period product supply chain the contract considers stochastic and price dependent demand we present an analytical model and then use numerical methods with the stackelberg game to identify the contract properties we numerically show that a returns policy indeed improves supply chain performance however the benefits earned from the returns policy under price sensitive and variable demand are different for different supply chain partners first when price sensitivity is high profit of the manufacturer decreases with increase in demand variability second when price sensitivity is sufficiently high and demand variability increases the manufacturer has to surrender part of the profits to the retailer in order to continue sales however even after surrendering part of the profits to the retailer the manufacturer still earns profits that are higher than those available in a wholesale price contract last from the perspective of division of channel profits the retailer is always worse off in case of returns policies than in a wholesale price contract therefore to apply this form of incentive in practice managements should consider the impact of price sensitivity on the returns policy and its performance

optimal inventory decisions for a risk averse retailer when offering layaway abstract layaway allows economically disadvantaged budget constrained consumers to purchase expensive items through amortized payments and nominal program fees as opposed to using high interest financing options such as credit cards and payday loans we consider a risk averse retailer s ordering decisions when offering a layaway program we use the net loss and total loss functions found in the literature to determine a risk averse retailer s optimal order quantity under conditional value at risk cvar we next analyze the effects of the model parameters retailer s risk aversion the market default rate enrollment fee cancellation fee and so on on the optimal order quantity decisions we show that the optimal order quantity depends on different loss functions and different demand distribution functions further we show that as market default rate increases or the retailer becomes more risk averse then a rational retailer will not offer a layaway program

the evolution of income inequality in the european union during the period 1993 1996 the objective of this work is to analyse the income inequality in the 15 eu countries during the convergence process to the monetary union using the information contained in the european community household panel corresponding to the four first waves using the inverse second order stochastic dominance concept an ordering of these countries has been carried out furthermore this ranking allows one to determine if the differences among eu country members have increased or decreased during this particular period whether the inequality of income has diminished within and between countries over time was studied gini s generalized family indices proposed by donaldson and weymark journal of economic theory 22 67 86 1980 and 29 353 8 1983 and yitzhaki international economic review 24 617 28 1983 have been used this allows one to test the sensitivity of the results obtained to different degrees of inequality aversion and to different equivalence scales taking into account household sizes

the effect of risk aversion on distribution channel contracts implications for return policies the return policy is often used in retailing supply chains however it is controversial in judging their practical value in the literature various theoretical and modeling explanations of why the return policy is used in practice and is preferred by the retailer and manufacturer have been put forth the literature focusing on the channel agents risk attitudes to explain the adoption seems to have led to the conclusion that the two agents preferences for adopting the full return policy over the no return policy are always in conflict and thus the risk attitudes do not explain the adoption of return policy in practice in this paper we reinvestigate this issue we first identify two distinct phases of risk averseness high or low for each of the two agents we show distinct behaviors of how the wholesale price and order size are set in each phase then we show that the full return policy can be preferred over the no return policy by both the agents if both of them are high risk averse this implies that the agents risk attitudes can explain the adoption of return policy this is a new theoretical result which is contrary to the existing understanding in the literature our result highlights the importance and intricacy of channel policies especially when the risk attitudes of agents are considered

using the dagum model to explain changes in personal income distribution this article studies the evolution of personal income distribution in spain from 1995 to 2005 using the dagum model dagum s three parameter model type i provides a good fitting to empirical income distributions in spain moreover its parameters can be interpreted as economic indicators of income distribution changes after studying the economic interpretation of the dagum model parameters we analyse the impact of parameter changes on different income percentiles and also on the evolution of inequality in spain using data from the european community household panel echp and the european union statistics on income and living conditions eu silc

technical note a risk averse newsvendor model under the cvar criterion the classical risk neutral newsvendor problem is to decide the order quantity that maximizes the one period expected profit in this note we consider a risk averse newsvendor with stochastic price dependent demand we adopt conditional value at risk cvar a risk measure commonly used in finance as the decision criterion the aim of our study is to investigate the optimal pricing and ordering decisions in such a setting for both additive and multiplicative demand models we provide sufficient conditions for the uniqueness and existence of the optimal policy comparative statics show the monotonicity properties and other characteristics of the optimal pricing and ordering decisions we also compare our results with those of the newsvendor with a risk neutral attitude and a general utility function

efficient supply contracts for fashion goods with forecast updating and two production modes we examine the problem of developing supply contracts that encourage proper coordination of forecast information and production decisions between a manufacturer and distributor of high fashion seasonal products operating in a two mode production environment the first production mode is relatively cheap but requires a long lead time while the second is expensive but offers quick turnaround we focus on contracts of the form w1 w2 b wherewi is the wholesale price offered for production modei andb is a return price offered for items left over at the end of the season we find that such a contract can coordinate the manufacturer and distributor to act in the best interest of the channel the pricing conditions needed to ensure an efficient solution vary depending on the degree of demand forecast improvement between periods and the manufacturer s access to forecast information we also examine whether these conditions ensure a pareto optimal solution with respect to two traditional production settings

the right to return this article studies the allocation of responsibility for unsold inventory provision for which is made in practically every distribution contract the two extreme cases are the consignment contract which allocates all the burden to the manufacturer and the no return contract in which retailers purchase the merchandise outright and assume responsibility for unsold inventory contract choices are shown to vary across countries industries products and types of transactions the article identifies six main factors affecting this choice optimal inventory policy in a stochastic retail demand environment relative advantage in disposing of the unsold inventory optimal risk allocation incentives to invest in promotions and provide services to increase consumer demand information asymmetry and costs associated with the consignment contract per se several testable implications are presented and the choice of contracts in the publishing industry is shown to be consistent with the predictions of the model

the distribution of personal income revisited in a recent paper majumder and chakravarty 1990 propose a four parameter model which they find provides a better fit to some income data than the lognormal gamma singh maddala dagum and generalized beta of the second kind gb2 distributions this note 1 demonstrates that the model proposed by majumder and chakravarty is a reparameterization of the gb2 and 2 reconciles the corresponding contradictory empirical findings reported by majumder and chakravarty

returns policy new model introduction and consumer welfare abstract this paper investigates how economic outcomes differ for new model introduction between two extreme contracts outright sales contract and returns policy contract with full credit under the outright sales contract we show that the retailer s incentive to introduce a new model can lead to a reduction of consumer welfare when the retailer is moderately risk averse the primary conclusion from this study is that the returns policy contract resolves this conflict between firms and consumers and that the supply chain introduces the new model only when consumer surplus from the new model is higher than that from the old model

leaders and followers perspectives on the nordic model and the economics of innovation abstract what kinds of social and economic systems are most conducive to innovation we formulate a simple model in which countries can close the gap with the technological leader but where the cost of doing so may be so high that the country chooses to remain laggards observed disparities in productivity may be the result of a recognition that the cost of closing the gap exceeds benefit and there may therefore exist an international equilibrium in which there are leaders and followers even if it is granted that the united states is the leader and scandinavia are followers there are theoretical grounds for arguing that the nordic model may in fact be better for innovation suggesting that if the us adopted some of the nordic institutions innovations would be higher and societal welfare would be improved even more

opening a can of worms the pitfalls of time series regression analyses of income inequality this paper argues that time series regression analysis is of only very limited use for understanding the determinants of income inequality the argument is based on a combination of results from the time series econometrics literature and several characteristics of inequality itself principally nonstationarity of the data in most inequality regression models and the weak theoretical foundations underlying the models a sample of postwar us data is used to illustrate the problems involved

manufacturer s return policies and retail competition manufacturers returns policies are a common feature in the distribution of many products the obvious rationale for returns policies is insurance practitioners not surprisingly have a different perspective and view returns as a cost of doing business in this paper we study the strategic effect of returns policies on retail competition and highlight its profitability implications for a manufacturer the setting for our research is the distribution of products with uncertain demand limited shelf lives and retail competition our objective is to provide a better understanding of when manufacturers should adopt returns policies the insights are obtained with a model based on the economics of strategy and decision making under uncertainty we show that when retailing is competitive and there is no uncertainty in demand a returns policy subtly induces retailers to compete more intensely the provision of a returns policy reduces retail prices without affecting wholesale prices thereby reducing retailer margins and improving manufacturer profitability the intuition is that with a returns policy cournot like levels of retail stocks cannot be sustained each retailer will order stocks so that it will not be constrained by stocks and so intensifying retail competition when however demand is uncertain and there is a single retailer a returns policy encourages the retailer to over stock and so decreases upstream manufacturer profits while the provision of a returns policy leads to lower retail margins the optimality of returns policy depends on the overall uncertainty and marginal cost a returns policy reduces the dispersion in retail prices between the high and low states of demand and the range of retail prices in the returns case is contained within the range of retail prices for the no returns case in the general setting when there are competing retailers and demand is uncertain there is a trade off for the manufacturer between the benefits more intense retail competition and the costs excessive stocking of a returns policy we find that a manufacturer should accept returns when the marginal production cost is sufficiently low and demand uncertainty is not too great to validate the results of our theory we conduct an empirical test with data from a major u s retailer the tests confirm our prediction that a returns policy intensifies retail competition and reduces retailer margins our theory and empirical test should interest practitioners and researchers in distribution especially those concerned with managing retail competition

equilibrium returns policies in the presence of supplier competition the pioneering pasternack returns policy model analyzed channel coordination with a single supplier catering to a retailer facing stochastic demand for a perishable product with a fixed price and the model showed that giving partial returns of unsold stock to the retailer is the optimal policy for the entire supply chain the result thus begs the question as to why manufacturers of perishable commodities widely accept full returns of unsold stock as the norm we model the environment as one where two capacity constrained manufacturers compete for shelf space with the same retailer and we show that a complete credit returns policy is in fact the only possible equilibrium of the game our results obviate the need for knowing the exact functional form of the demand distribution in order to compute the returns credit as pasternack s results would require from a retailer s standpoint we establish a simple procurement strategy and show that it is optimal the same game with price only contracting has a pure strategy equilibrium when the supplier capacities are below a threshold value and a mixed strategy equilibrium when the supplier capacities cross this threshold but are still so limited that no single supplier can with certainty supply all the quantity demanded

when should a manufacturer set its direct price and wholesale price in dual channel supply chains abstract applying an observable delay game framework developed in noncooperative game theory we investigate the timing problem concerning when a manufacturer managing dual channel supply chains consisting of a retail channel and a direct channel should post its wholesale price and direct price conventionally operational research models describing dual channel supply chains examine price competition where the retailer and the manufacturer simultaneously determine the retail and direct prices respectively in contrast to this conventional setting our model demonstrates that such simultaneous price competition never arises if the manufacturer and retailer can choose not only the level of the price but also the timing of pricing if the manufacturer sets the direct price after setting the wholesale price to the retailer the retailer accelerates the timing of retail pricing prior to the direct price setting by the manufacturer our findings suggest that the manufacturer should post the direct price before or upon but not after setting the wholesale price for the retailer this upfront posting of the direct price not only constitutes the subgame perfect nash equilibrium of the noncooperative game between channel members but also maximizes the profits for a manufacturer employing multichannel sales strategies

mean variance analysis of a single supplier and retailer supply chain under a returns policy abstract in the literature most of the supply chain coordinating policies target at improving the supply chain s efficiency in terms of expected cost reduction or expected profit improvement however optimizing the expected performance alone cannot guarantee that the realized performance measure will fall within a small neighborhood of its expected value when the corresponding variance is high moreover it ignores the risk aversion of supply chain members which may affect the achievability of channel coordination as a result we carry out in this paper a mean variance mv analysis of supply chains under a returns policy we first propose an mv formulation for a single supplier single retailer supply chain with a newsvendor type of product the objective of each supply chain decision maker is to maximize the expected profit such that the standard deviation of profit is under the decision maker s control we study both the cases with centralized and decentralized supply chains we illustrate how a returns policy can be applied for managing the supply chains to address the issues such as channel coordination and risk control extensive numerical studies are conducted and managerial findings are proposed

dagum vs singh maddala income distributions this letter shows that the dagum and the singh maddala income distributions are closely related it exploits this relationship to derive lorenz ordering results for the dagum distributions from known results for the singh maddala family

optimal decisions for the loss averse newsvendor problem under cvar abstract most of the existing literature about the newsvendor problem mainly focused on choosing an optimal order quantity to maximize the expected profit of a risk neutral newsvendor however some studies pointed out that in practice managers decisions as to order quantities always deviate from the profit maximization order quantity which is referred to as decision bias in the newsvendor problem then many studies introduced other preferences rather than risk neutrality of the newsvendor to explain such a decision bias this paper thus introduces loss aversion to the research of the newsvendor decision bias we propose a new definition to the loss averse newsvendor problem legacy loss which is defined either as the loss for excess order or the shortage penalty for lost sales when sales time is due the optimal decisions of a loss averse newsvendor are obtained through the following three ways i minimizing the expected legacy loss ii minimizing cvar of legacy loss by combining the cvar measure in risk management iii minimizing the combination of expected legacy loss and cvar of legacy loss and are compared with other existing results besides we present some properties of the optimal decisions as well as relations among them some numerical examples are given to illustrate the obtained results

a risk averse competitive newsvendor problem under the cvar criterion abstract we study a risk averse newsvendor problem with quantity competition and price competition under the conditional value at risk cvar criterion we characterize the optimal quantity and pricing decisions under both quantity and price competition for quantity competition we consider two demand splitting rules namely proportional demand allocation and demand reallocation although competition always leads to overstocking interestingly it does not necessarily lead to a profit loss in certain competitive environments such as demand reallocation by avoiding reducing overstocking that results from competition under the risk neutral criterion for price competition we consider both additive and multiplicative demand we find that the order quantity sale price and the expected profit decrease in the degree of risk aversion further both high price sensitivity and competition intensity force decision makers to lower their prices however high price sensitivity always reduces the order quantity while competition can have the opposite effect

buyback contracts with price dependent demands effects of demand uncertainty chapter 2 examines buyback contracts in a supplier retailer supply chain where the retailer faces a price dependent downward sloping demand curve subject to uncertainty compared with classical research a fundamental difference of this research lies in its analytical examination of the effects of demand uncertainty on the applicability of buyback contracts to this end the research seeks to characterize the buyback contract model in terms of only demand uncertainty level with such a new research perspective some new and interesting findings are obtained for such issues as how demand uncertainty level affects the applicability of buyback practice and how to apply this practice to improve supply chain members own interests or the supply chain system s efficiency the research in this chapter demonstrates that the uncertainty level inherent in market demand can be a critical factor influencing the applicability of supply chain contracts as well as the contract s administrative cost cachon 2003 and the uncertainty type marvel and peck 1995

on returns policies with exogenous price we contribute to current research on single period returns policies by making a clear distinction between models in which transfer price is exogenous and models in which one dominant party unilaterally declares a price we compare the equilibrium contracts that result from these two approaches and derive conditions for the equilibrium returns policy to be pareto efficient when transfer price is exogenous our main result is distribution free but we make some interesting observations on channel performance when demand is uniformly distributed

the impacts of the full returns policy on a supply chain with information asymmetry abstract in contrast to the existing return policies literature assuming that information is symmetrical between the manufacturer and the retailer we study the full returns policy s impact on supply chains with information asymmetry we first study the case that the base level of the demand follows a discrete distribution with two states we find that the retailer benefits from the full returns policy in all circumstances while the manufacturer and the supply chain are better off under some conditions we then consider the situation in which the base level of the demand is a type of ar 1 process

note the role of returns policies in pricing and inventory decisions for catalogue goods manufacturers often use returns policies to encourage retailers to stock and price items more aggressively we focus on the effect that such policies have on both a retailer s and a manufacturer s profits when the retailer must commit prior to the selling season to both a stocking quantity and a price at which to sell an item such a commitment is often necessary for retailers who sell primarily through catalogues

a risk averse newsvendor model under marketing dependency and price dependency abstract in this paper we analyze a single period inventory model where a risk averse newsvendor makes a joint decision on ordering pricing and marketing under the cvar risk measure criterion the newsvendor can exert marketing effort to enhance market demand we assume that the newsvendor s marketing effort affects the scale of the demand distribution and hence to model the marketing dependent demand as a multiplicative form we characterize sufficient conditions that guarantee existence and uniqueness of the optimal solutions under some mild assumptions on demand distribution expected demand function and marketing effort cost which are widely used in the related literature we show that the optimal order quantity increases in the newsvendor s marketing effort but the optimal price remains unchanged whether the demand is marketing dependent or not additionally we explore impact of exogenous parameters such as unit order cost salvage value and the newsvendor s risk aversion coefficient on the optimal decision variables and find that the optimal marketing effort always keeps the same changing direction with the optimal marketing independent order quantity as the exogenous parameters change this suggests that impact of the parameters on the optimal order quantity gets strengthened in the case of marketing dependent demand

demand uncertainty and returns policies manufacturers facing uncertain demand may induce distributors to carry ample stocks of their products by agreeing to accept returns of unsold goods for credit the authors model the manufacturer s decision to accept returns showing that this decision depends crucially on the nature of the demand uncertainty uncertainty over customer arrivals favors returns while uncertainty over consumers valuation of the manufacturer s product leads distributors to set retail prices too high from the manufacturer s standpoint when returns are allowed the authors show that returns can be expected to raise retail prices while maintaining shrinking distributor margins copyright 1995 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association