conditions that cause risk pooling to increase inventory abstract we say product a is a partial substitute for product b if a fraction of the customers who prefer b are willing to accept a when b is out of stock when demand is uncertain it is intuitive and true that a larger willing to substitute fraction implies larger expected profits a higher willing to substitute fraction allows one to pool the risk of individual products it may also be intuitive that a larger willing to substitute fraction might result in lower optimal total inventory for the full substitution structure several researchers have shown that for certain distributions such as the exponential this latter intuition is not true we show that this full substitution anomaly can occur with any right skewed demand distribution we assume i i d demand distributions unless we indicate otherwise we also show that the anomaly can occur for a number of realistic situations of partial substitution with commonly used demand distributions such as normal exponential poisson and uniform we also demonstrate the anomaly for more than one period with backlogging lost sales more than two products and with setup costs

estimation of consumer demand with stock out based substitution an application to vending machine products the occurrence of temporary stock outs at retail is common in frequently purchased product categories available empirical evidence suggests that when faced with stock outs consumers are often willing to buy substitute items an important implication of this consumer behavior is that observed sales of an item no longer provide a good measure of its core demand rate sales of items that stock out are right censored while sales of other items are inflated because of substitutions knowledge of the true demand rates and substitution rates is important for the retailer for a variety of category management decisions such as the ideal assortment to carry how much to stock of each item and how often to replenish the stock the estimated substitution rates can also be used to infer patterns of competition between items in the category in this paper we propose methods to estimate demand rates and substitution rates in such contexts we develop a model of customer arrivals and choice between goods that explicitly allows for possible product substitution and lost sales when a customer faces a stock out the model is developed in the context of retail vending an industry that accounts for a sizable part of the retail sales of many consumer products we consider the information set available from two kinds of inventory tracking systems in the best case scenario of a perpetual inventory system in which times of stock out occurrence and cumulative sales of all goods up to these times are observed we derive maximum likelihood estimates mles of the demand parameters and show that they are especially simple and intuitive however state of the art inventory systems in retail vend ing provide only periodic data i e data in which times of stock out occurrence are unobserved or missing for these data we show how the expectation maximization em algorithm can be employed to obtain the mles of the demand parameters by treating the stock out times as missing data we show an application of the model to daily sales and stocking data pooled across multiple beverage vending machines in a midwestern u s city the vending machines in the application carry identical assortments of six brands since the number of parameters to be estimated is too large given the available data we discuss possible restrictions of the consumer choice model to accomplish the estimation our results indicate that demand rates estimated naively by using observed sales rates are biased even for items that have very few occurrences of stock outs we also find significant differences among the substitution rates of the six brands the methods proposed in our paper can be modified to apply to many nonvending retail settings in which consumer choices are observed not their preferences and choices are constrained because of unavailability of items in the choice set one such context is in store grocery retailing where similar issues of information availability arise in this context an important issue that would need to be dealt with is changes in the retail environment caused by retail promotions

single period multiproduct inventory models with substitution we study a single period multiproduct inventory problem with substitution and proportional costs and revenues we consider n products and n demand classes with full downward substitution i e excess demand for class i can be satisfied using product j for i j we first discuss a two stage profit maximization formulation for the multiproduct substitution problem we show that a greedy allocation policy is optimal we use this to write the expected profits and its first partials explicitly this in turn enables us to prove additional properties of the profit function and several interesting properties of the optimal solution in a limited computational study using two products we illustrate the benefits of solving for the optimal quantities when substitution is considered at the ordering stage over similar computations without considering substitution while ordering specifically we show that the benefits are higher with high demand variability low substitution cost low profit margins or low price to cost ratio high salvage values and similarity of products in terms of prices and costs

can unobserved land quality explain the inverse productivity relationship abstract an inverse relationship between both farm productivity and labor intensity and farm size is a common empirical finding in developing country agriculture the traditional explanation has been imperfect labor markets recently it has been suggested instead that the inverse relationship is a statistical artifact resulting from omitted land quality using a farm level data set from java i investigate whether omitted variable bias can explain the inverse relationship i show that the inverse relationship and accompanying wage responses are inconsistent with a model of neoclassical farm behavior that ignores omitted variable bias instrumental variables techniques yield parameter estimates in which the inverse relationship is eliminated and the estimated wage elasticities are more in line with economic theory further econometric investigation hints that a model of omitted land quality may be a possible source of the inverse relationship these results emphasize the importance of considering the sources of cross sectional variation in estimating microeconomic relationships

a two item newsboy problem with substitutability previous research on the newsboy problem is based on the assumption that in case of a shortage unsatisfied demand is lost such an assumption is inappropriate for items that have a close substitute in this paper we formulate a two item newsboy problem with substitutability tinps upper and lower bounds on the optimal order quantities of the two items are derived since analytical solutions to the problem are difficult to obtain a monte carlo simulation is used to identify the optimal solution to the tinps order quantities identified by the simulation provide higher expected profit than would have been obtainable without considering substitutability

the effects of selling packaged goods on inventory decisions in this paper we study within a newsboy type modeling framework the common business practice of retail firms to sell products not only as independent items but also as part of multiproduct packets packaged goods our emphasis is on understanding the effects of such practices on the inventory decisions of the firm we provide insights on the resulting level of suboptimality when inventory decisions are made with demand information only on the independent items and without accounting for the demand substitution structure induced between independent items and packaged goods our stylized model studies an environment with two products that are not direct substitutes for each other sold either independently or as part of a packet that contains one unit of each we provide necessary and sufficient optimality conditions for this model and suggest an efficient numerical search for obtaining the optimal stocking levels an extensive computational study allowed us to provide insights on the nature of the optimal stocking policies the suboptimality of independent newsboy policies the effects of demand correlation among individual products and multiproduct packets and the determining role of induced substitution structure among products during stockout occasions on the profitability of the inventory system

joint inventory and pricing decisions for an assortment we seek optimal inventory levels and prices of multiple products in a given assortment in a newsvendor model single period stochastic demand under price based substitution but not stockout based substitution we address a demand model involving multiplicative uncertainty motivated by market share models often used in marketing the pricing problem that arises is known not to be well behaved in the sense that in its deterministic version the objective function is not jointly quasi concave in prices however we find that the objective function is still reasonably well behaved in the sense that there is a unique solution to the first order conditions and this solution is optimal for our problem

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

joint pricing and procurement of fashion products in the existence of clearance markets abstract this paper focuses on the joint pricing and procurement of fashion products in the existence of clearance markets it is assumed that the expected regular season demand is a linear decreasing function of the price and the end of period excess inventory is sold at a known discounted price in a clearance market where the demand is a random variable that follows a general distribution it is shown that the expected profit function is unimodal and the optimal procurement quantity and price can be found from the first order conditions existence of a clearance market increases the profit price and the procurement quantity in order to prove this the optimal procurement and pricing policy of a price setting retailer who does not have a clearance market is provided as opposed to the literature it is shown that the expected profit function of this problem is unimodal as well a numerical study demonstrating the magnitude of the increase in profit procurement quantity and price is reported

technical allocative and economic efficiencies in swine production in hawaii a comparison of parametric and nonparametric approaches abstract technical allocative and economic efficiency measures are derived for a sample of swine producers in hawaii using the parametric stochastic efficiency decomposition technique and nonparametric data envelopment analysis dea efficiency measures obtained from the two frontier approaches are compared firm specific factors affecting productive efficiencies are also analyzed finally swine producers potential for reducing cost through improved efficiency is also examined under the specification of variable returns to scale vrs the mean technical allocative and economic efficiency indices are 75 9 75 8 and 57 1 respectively for the parametric approach and 75 9 80 3 and 60 3 for dea while for the constant returns to scale crs they are 74 5 73 9 and 54 7 respectively for the parametric approach and 64 3 71 4 and 45 7 for dea thus the results from both approaches reveal considerable inefficiencies in swine production in hawaii the removal of potential outliers increases the technical efficiencies in the parametric approach and allocative efficiencies in dea but overall contrary to popular belief the results obtained from dea are found to be more robust than those from the parametric approach the estimated mean technical and economic efficiencies obtained from the parametric technique are higher than those from dea for crs models but quite similar for vrs models while allocative efficiencies are generally higher in dea however the efficiency rankings of the sample producers based on the two approaches are highly correlated with the highest correlation being achieved for the technical efficiency rankings under crs based on mean comparison and rank correlation analyses the return to scale assumption is found to be crucial in assessing the similarities or differences in efficiency measures obtained from the two approaches analysis of the role of various firm specific factors on productive efficiency shows that farm size has strong positive effects on efficiency levels similarly farms producing market hogs are more efficient than those producing feeder pigs based on these results by operating at the efficient frontier the sample swine producers would be able to reduce their production costs by 38 46 depending upon the method and returns to scale considered

a static approximation for dynamic demand substitution with applications in a competitive market we propose a static approximation of dynamic demand substitution behavior based on a fluid network model and a service inventory mapping this approximation greatly enhances our ability to analyze the interdependent inventory service price and product assortment decisions in noncompetitive and competitive scenarios with demand substitution we demonstrate that the approximation is well behaved and then apply it to two previously intractable applications first we study a price and service competition between single product retailers after establishing a unique pure strategy nash equilibrium we find that competition results in lower price higher demand and a higher level of inventory we also observe that the aggregate profit and inventory level increase to positive constants as the number of retailers goes to infinity second we study a duopolistic competition on price service and product assortment we establish a pure strategy nash equilibrium for the product assortment competition and identify a condition for uniqueness we find that competition on both price and product assortment results in lower price and less variety for each competitor but the total number of products and the aggregate inventory level in a duopoly market are both likely to be higher than in a monopolistic market

inverse productivity land quality labor markets and measurement error abstract this paper examines the role that land quality and imperfect markets play in generating the inverse productivity relationship in the international crop research institute for the semi arid tropics icrisat data differences in land quality largely explain the inverse productivity ip relationship in the random effects profit regression but not in labor demand regressions controlling for labor and land market failures and differences in soil quality eliminates the ip relationship for male labor but not female labor in the random effects estimates the inverse relationship is much stronger in fixed effects than random effects estimates suggesting that the farm size variable may be subject to measurement error a view supported by the results of instrumental variables estimation

the implications of costs capacity and competition on product line selection we consider a situation in which a manufacturer has to select the product s to sell as well as the selling price and production quantity of each selected product there are two substitutable products in the consideration set where product 2 has a higher quality and reservation price than that of product 1 by considering the cannibalization effect that depends on the selling price of each product the manufacturer needs to evaluate the profit function associated with three different product line options sell both products or only one of the 2 products in order to examine the impact of costs capacity and competition on the optimal product line selection optimal price and optimal production quantity analytically we present a stylized model in this paper so that we can determine the conditions under which a particular option is optimal

too small to be beautiful the farm size and productivity relationship in bangladesh this paper examines the agricultural productivity farm size relationship in the context of bangladesh features of bangladesh s agriculture help overcome several limitations in testing the inverse farm size productivity relationship in other developing country settings a stochastic production frontier model is applied using data from three rounds of a household panel survey to estimate simultaneously the production frontier and the technical inefficiency functions the correlated random effects approach is used to control for unobserved heterogeneous household effects methodologically the results suggest that the stochastic production frontier models that ignore the inefficiency function are likely mis specified and may result in misleading conclusions on the farm size productivity relationship empirically the findings confirm that the farm size and productivity relationship is negative but with the inverse relationship diminishing over time total factor productivity growth driven by technical change is found to have been robust across the sample across farm size groups the relatively larger farmers experienced faster technical change which helped them to catch up and narrow the productivity gap with the smaller farmers

inverse productivity or inverse efficiency evidence from mexico abstractusing a unique panel data set from rural mexico we find strong evidence of a negative relationship between farm size and both productivity and technical efficiency large farms not only have a lower value of output per hectare than small farms they also produce further from the efficiency frontier our findings suggest that in spite of the ongoing transformation of agricultural supply chains and economists recommendations for small farmers to exit crop production there may be sustained advantages for smallholder farms our analysis offers new insights into inverse farm size relationship the productivity efficiency relationship and the use of stochastic frontier techniques

the decline in the number of school districts in the u s 1950 1980 between 1950 and 1980 the number of school districts fell from 83 642 to 15 987 data for the fifty states for 1950 1960 1970 and 1980 are used to identify the factors that contributed to this decline the focus is on the tradeoff between cost savings through scale economies a few large districts and a diverse population s demand for choice in public schooling many small districts we find that much of the decline in the number of school districts has resulted from 1 the decline in the farm population and increase in population density which has made it easier to take advantage of scale economies 2 the growing importance of state aid which reduces quality variation among districts within a state and 3 the increase in the fraction of teachers that belong to the national education association teacher s union which may reflect increased political influence used to lower the costs of organizing

joint pricing and procurement of substitutable products with random demands a technical note abstract single period joint pricing and procurement of substitutable products entails one time procurement and pricing decisions for substitutable products that face price dependent stochastic demands recently karakul and chan karakul m chan l 2008 analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem european journal of operational research 190 179 204 considered this problem for two one way substitutable products authors model the demands for each product in the well known additive form where the mean demands are linear functions of the price of the high grade new product plus an additive stochastic noise term by assuming that the noise term for the low grade existing product follows a general discrete distribution and the noise term for the high grade product follows a general continuous distribution authors are able to show the unimodality of the expected profit function with respect to the procurement quantities and the price of the new product in this paper we extend this result to the case where the noise term in the demand of the low grade product follows a general continuous distribution as well

category management and coordination in retail assortment planning in the presence of basket shopping consumers this paper studies the assortment planning problem with multiple merchandise categories and basket shopping consumers i e consumers who desire to purchase from multiple categories we present a duopoly model in which retailers choose prices and variety level in each category and consumers make their store choice between retail stores and a no purchase alternative based on their utilities from each category the common practice of category management cm is an example of a decentralized regime for controlling assortment because each category manager is responsible for maximizing his or her assigned category s profit alternatively a retailer can make category decisions across the store with a centralized regime we show that cm never finds the optimal solution and provides both less variety and higher prices than optimal in a numerical study we demonstrate that profit loss due to cm can be significant finally we propose a decentralized regime that uses basket profits a new metric rather than accounting profits basket profits are easily evaluated using point of sale data and the proposed method produces near optimal solutions

can unobserved heterogeneity in farmer ability explain the inverse relationship between farm size and productivity abstract the well known inverse relationship between farm size and productivity is usually explained in terms of diminishing returns with respect to land and other inputs coupled with various types of market frictions that prevent the efficient allocation of land across farms we show that even in the absence of diminishing returns one can provide an alternative explanation for this phenomenon using endogenous occupational choice and heterogeneity with respect to farming skills

a model of optimal plant size with an application to the demand for cognitive achievement and for school size a model of optimal plant size is developed which predicts that 1 plants experience increasing returns to in plants inputs 2 the relative price of plant output is greater in rural areas than in urban areas and 3 plants are larger in urban areas than in rural areas the model s predictions appear to be consistent with behavior in a number of consumer services e g grocery movie and library services these predictions are more rigorously tested and are strongly supported when demand functions for cognitive achievement and for school size are estimated these regressions also lend support to the quality quantity model of fertility

does restricting choice in referenda enable governments to spend more if school boards represent the preferences of the median voter referendums to approve school expenditures should not constrain school expenditures if school boards would choose expenditures larger than the median voter s preference referendums that restrict voters to approving or disapproving a school board s recommended expenditure level will result in expenditures larger than the median voter would prefer however florida used a unique referendum system which guaranteed the median voter s most preferred outcome using florida education expenditures as a benchmark the evidence suggests that spending was slightly higher in restricted choice referendum states than in florida

managing inventories with one way substitution a newsvendor analysis abstract this paper presents an insightful approach to analyze two item periodic inventory systems with one way substitution the objective is to minimize the expected total cost per period which consists of expected purchasing costs expected inventory holding costs expected shortage costs and expected adjustment costs this approach helps derive the optimality conditions in both single period and infinite horizon settings and yields useful insights into the impact of substitution on the service level the optimality of a borderline case in which the order up to level of the inflexible item is reduced to zero and the pivotal role of the purchasing cost

a classification of the literature on the planning of substitutable products abstract a company s assortment of products and corresponding inventory levels are constrained by available resources such as production capacity storage space and capital to acquire the inventory thus customers may not always be able to find a most preferred product at the time of purchase this unsatisfied demand is often substituted with an alternative in the extant literature there have been an increasing number of studies that consider product substitution when planning product assortment inventory and capacity in conjunction with pricing in this paper we classify the literature on the planning of substitutable products published in the major om and marketing journals during the past thirty years 1974 2013 and present a comprehensive taxonomy of the literature one criterion is adopted to discuss modeling objectives and three major criteria are provided to define the nature of product substitution including substitution mechanism substitution decision maker and direction of substitutability we also identify research gaps to provide guidance for related research in the future

product availability in competitive and cooperative dual channel distribution with stock out based substitution abstract this paper investigates the impact of customers stock out based substitution on the product availability and the channel efficiency of a dual channel supply chain which consists of a supplier distributing a single product to customers through both its wholly owned direct channel and an independent retailer the supplier and its retailer with the objective of optimizing their own profit simultaneously choose their own base stock level to satisfy the stochastic demand from the customers whose channel preferences are heterogeneous and may be affected by each channel s product availability the customers dynamically substitute between the two channels in the event of a stock out the result shows that the effect of the stock out based substitution may increase or decrease the efficiency of a decentralized supply chain it is found that while the integrated supplier retailer may consolidate the base stock levels to benefit from stock out based substitution the independent supplier and retailer are more inattentive to customers stock out based substitution thus the competitive base stock levels of the decentralized dual channel supply chain rarely agree with the system optimal levels various contracts are examined to shed light on channel coordination mechanisms in addition it is shown that the channel efficiency of the dual channel distribution can be improved by the emergence of stackelberg leadership from either the supplier or the retailer

evidence on the impact of state government on primary and secondary education and the equity efficiency trade off abstract state governments may affect the productivity of primary and secondary education in two ways first various regulations imposed on local school districts are expected to make schools less efficient second state efforts to reduce inequality in education spending make it more difficult for voters to increase school quality which should lead to less voter monitoring of schools and thus less efficient schools our empirical analysis of state scholastic aptitude test sat scores from 1987 to 1992 provides evidence on both effects the state s revenue share which captures state meddling in local decisions has the expected negative impact on school efficiency but our novel result is that state induced spending equalization also lowers average test scores but has had little if any effect on reducing the disparity in student achievement these results bring into question policy efforts designed to shift education responsibilities from local governments to state and federal governments

inventory decisions for substitutable products with stock dependent demand abstract we study a retailer s inventory policy for two products the products are substitutable and have inventory dependent demand so a higher inventory level of a product increases its sales we model the joint effect of demand stimulation and product substitution on inventory decisions by considering a single period stochastic demand setting we provide the first order optimality conditions for the profit maximizing order quantities and interpret them using marginal analysis we also consider two heuristic solutions that separately account for either demand stimulation or product substitution our numerical analysis reveals that the optimal policy by appropriately using sales information that quantifies substitution and demand stimulation can produce significantly higher profits the profit benefits are lessened under certain circumstances such as when the two products have similar critical fractile values suggesting that in such instances the heuristics may be used effectively

optimizing product assortment under customer driven demand substitution abstract the problem of product assortment and inventory planning under customer driven demand substitution is analyzed and a mathematical model for this problem is provided in this paper realistic issues in a retail context such as supplier selection shelf space constraints and poor quality procurement are also taken into account the performance of three modified models one that neglects customers substitution behavior another that excludes supplier selection decision and one that ignores shelf space limitations are analyzed separately with computational experiments the results of the analysis demonstrate that neglecting customer driven substitution or excluding supplier selection or ignoring shelf space limitations may lead to significantly inefficient assortments the effects of demand variability and substitution cost on optimal assortment and supplier selection decisions as well as on the optimal revenue are also investigated the main contribution of this paper is the development of a practical and flexible model to aid retailers in finding optimal assortments to maximize the expected profit

incorporating one way substitution policy into the newsboy problem with imprecise customer demand this paper presents an approach for solving an inventory model for single period products with maximizing its expected profit in a fuzzy environment in which the retailer has the opportunity for substitution though various structures of substitution arise in real life in this study we consider the fuzzy model for two item with one way substitution policy this one way substitutability is reasonable when the products can be stored according to certain attribute levels such as quality brand or package size again to describe uncertainty usually probability density functions are being used however there are many situations in real world that utilize knowledge based information to describe the uncertainty the objective of this study is to provide an analysis of single period inventory model in a fuzzy environment that enables us to compute the expected resultant profit under substitution an efficient numerical search procedure is provided to identify the optimal order quantities in which the utilization of imprecise demand and the use of one way substitution policy increase the average expected profit the benefit of product substitution is illustrated through numerical example

an industry equilibrium analysis of downstream vertical integration this paper investigates the effect of product substitutability on nash equilibrium distribution structures in a duopoly where each manufacturer distributes its goods through a single exclusive retailer which may be either a franchised outlet or a factory store static linear demand and cost functions are assumed and a number of rules about players expectations of competitors behavior are examined it is found that for most specifications product substitutability does influence the equilibrium distribution structure for low degrees of substitutability each manufacturer will distribute its product through a company store for more highly competitive goods manufacturers will be more likely to use a decentralized distribution system this article was originally published in marketing science volume 2 issue 2 pages 161 191 in 1983

market deregulation trade liberalization and productive efficiency in bangladesh agriculture an empirical analysis the impact of trade liberalization and of market deregulation in general on the performance of agriculture remains contentious and empirical issue in the literature following the random coefficient frontier modelling framework this paper attempts to contribute to this debate by computing the farm specific productive efficiency indices in bangladesh agriculture before and after reform it also examines the impact of some farm specific and policy variables on productive efficiency the empirical results show that there are wide variations in productive efficiency across farms and regions and the average efficiency of all regions increased modestly by 8 percentage points from the pre reform to post reform period the efficiency differentials are largely explained by farm size infrastructure households off farm income and the reduction of government anti agricultural bias in relation to trade and domestic policies the implication of these results suggests the need for further policy reform to augment p

the legacy of serrano the impact of mandated equal spending on private school enrollment 1 introduction the california supreme court decision in serrano v priest in 1971 was the first state supreme court ruling to declare a state s education finance system unconstitutional 1 the suit originally filed by a class of los angeles county public school children and their parents argued that the california public school finance system was unconstitutional because of its reliance on a local property tax system under this system large differences in property wealth created enormous variations in educational resources across the state in its subsequent 1976 serrano h decision the california supreme court found that the state legislature s response to the first serrano decision was insufficient the court ordered the state legislature to follow a trial court s requirement to implement a funding formula that reduces wealth related per pupil expenditure disparities i e property tax revenue exclusive of categorical aid and special needs to 100 across school districts the serrano ii decision resulted in a nearly complete shift of the fiscal responsibility for k 12 education in california from local to state government in the aftermath of the initial serrano decision suits were filed in several other states claiming unconstitutional inequities in the state education system many of these suits were successful between 1973 and 1983 six state supreme courts new jersey 1973 connecticut 1977 washington 1978 west virginia 1979 wyoming 1980 arkansas 1983 found their systems of educational finance unconstitutional similar rulings followed in 1989 in kentucky montana and texas in 1993 in massachusetts and tennessee in 1994 in arizona and in 1997 in new hampshire ohio and vermont a third of the states education finance systems now have been ruled unconstitutional as a result of these rulings and legislative based education reforms in a number of other states education expenditure inequality has been reduced 2 this in turn has left local districts with less latitude in determining spending levels parents in richer districts are expected to be especially frustrated with the limits on spending that accompany equalization changes in state educational finance systems to gain greater equity affected average spending on education in these states the initial research on this issue focused on the california experience where raw expenditure figures reveal the dramatic change in per pupil spending in california since the initial serrano decision in 1971 in academic year ay 1969 1970 per pupil spending in california s public elementary and secondary schools was slightly greater than the national average 106 25 of the national average ranking 14th among all states however by ay 1992 1993 education expenditures in california had fallen to 85 6 of the national average and its rank had dropped to 34th silva and sonstelie 1995 concluded that education spending in california in 1989 1990 was significantly lower than they would have otherwise predicted they attributed about half of the lowered spending to the legislation following serrano ii and the other half to the growth of the student population in california but the california experience of reduced expenditures appears to be atypical manwaring and sheffrin 1997 found spending to be higher in many states as a result of litigation or legislativebased educational finance reform downes and shah 1995 similarly estimated that school finance reform raised spending in some states and lowered spending in other states murray evans and schwab 1998 found state per pupil spending rose with successful state education finance litigation the variation across states in the spending effects of education finance reforms may be due to the source court ordered or legislative and or degree e g weak reform strong reform etc of the reforms in any case there should be greater interest in supplementing what the public schools do or opting out of the public system if reforms cause spending in a state to fall

sequential decision making in production models single equation estimates of production models usually are justified by the assumption that production inputs are chosen as part of a one period decision problem yet most production decisions in agriculture are made sequentially in this paper the farmer s optimal input choices are modeled as optimal controls in a stochastic control problem a two period cobb douglas example is used to show that sequential solutions to production problems may yield models which require either single equation or simultaneous equation estimators functional separability stochastic specification and behavior under uncertainty are discussed in the context of dynamic production models

optimal capacity for substitutable products under operational postponement abstract we consider a monopolist producing two substitutable products with one flexible shared capacity the demand of each product is a linear function of the prices of both products and is subject to an additive shock we study the impact of two key drivers namely the degree of substitution between the products and the level of operational postponement on the optimal capacity and the resulting expected profit we show that the relationship between the optimal capacity and the degree of product substitution is not impacted by the different postponement strategies the firm can utilize or by the different settings forced clearance versus holdback considered in the previous literature on the other hand how capacity is affected by postponement critically depends on how closely substitutable the products are in particular we show that the well known result that operational postponement and capacity are strategic complements in a single product setting van mieghem and dada 1999 no longer holds in our setting because the two substitutable products are now linked through consumer driven substitution which the firm can influence through pricing in particular capacity and operational postponement in the form of quantity postponement can be either strategic substitutes or strategic complements and this depends on both the firm s cost structure and the degree of substitution between the products we also study the impact of forced clearance on the firm s expected profit and find that clearance deteriorates the firm s earnings more when the products it offers are highly differentiated

relative export competitiveness of agricultural commodities and its determinants some evidence from india abstract in this paper we derive time varying relative export competitiveness rec of india s top agricultural exports rice wheat cotton and sugar against india s share of world agricultural exports rec wa and world exports rec we from 1961 to 2012 we reveal that india s exports of all four commodities became relatively competitive over time but these were not as competitive as the top or selected emerging exporters of the four commodities we also examine the determinants of rec in these four commodities focusing on factors including crop specific and aggregate factor endowments domestic price export prices and gdp per capital preferential trade agreements export restrictions and bans and india s green revolution the regression analysis was mainly confined to the 1981 2012 due to data constraints we find that the time series regression results are similar in sign and significance for rec we and rec wa our key findings suggest the rec in wheat rice and cotton deteriorated as a result of export restrictions capital had negative effects on cotton rec labor and farm size did not influence the rec in the commodities the green revolution improved the rec in rice and cotton in phase 3 the wto had a positive effect on the rec in rice the south asian free trade area safta agreement adversely affected the rec in wheat and rice but strengthened the rec in cotton and sugar higher domestic price reduced the rec in cotton higher per capita income strengthens the rec in wheat with a lag we explain these results and suggest policy implications

profit efficiency among bangladeshi rice farmers abstract production inefficiency is usually analyzed by its three components technical allocative and scale efficiency in this study we provide a direct measure of production efficiency of the bangladeshi rice farmers using a stochastic profit frontier and inefficiency effects model the data which are for 1996 include seven conventional inputs and several other background factors affecting production of modern or high yielding varieties hyvs of rice spread across 21 villages in three agro ecological regions of bangladesh the results show that there are high levels of inefficiency in modern rice cultivation the mean level of profit efficiency is 77 suggesting that an estimated 23 of the profit is lost due to a combination of technical allocative and scale inefficiency in modern rice production the efficiency differences are explained largely by infrastructure soil fertility experience extension services tenancy and share of non agricultural income

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

rising real wages mechanization and growing advantage of large farms evidence from indonesia this paper examines dynamic patterns of land use capital investments and wages in agriculture using farm panel data from indonesia the empirical analysis shows that with an increase in real wages that prevailed in both agricultural and non agricultural sectors in rural areas relatively larger farmers increased the size of operational farm land by renting in land as well as used more hired in machines through machine rental and or service providers which induces the substitution of labor by machines machines and land are complementary and consistently the inverse farm size productivity relationship tends to be reversed among relatively large holders the results support growing diminishing advantage of large small farms in the presence of rapidly rising real wages and have food security policy implications to many asian countries where real wages are rapidly rising and small farms are predominant

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

the impact of product substitution on retail merchandising abstract we analyze the impact of product substitution on two key aspects of retail merchandising order quantities and expected profits to perform this analysis we extend the basic news vendor model to include the possibility that a product with surplus inventory can be used as a substitute for out of stock products this extension requires a definition and an approximation for the resulting effective demand under substitution a service rate heuristic is developed to solve the extended problem the performance of this heuristic is evaluated using an upper bound generated by solving the associated lagrangian dual problem our analysis suggests that this heuristic provides a tractable and accurate method to determine order quantities and expected profits under substitution we apply this heuristic to examine how the level of demand uncertainty and correlation and the degree of substitution between products affect order quantities and expected profits under substitutable demand in addition we use the heuristic to better understand the mechanism by which substitution improves expected profits

on the relationship between inventory costs and variety benefits in retailassortments consider a category of product variants distinguished by some attribute such as color or flavor a retailer must construct an assortment for the category i e select a subset variants to stock and determine purchase quantities for each offered variant we analyze this problem using a multinomial logit model to describe the consumer choice process and a newsboy model to represent the retailer s inventory cost we show that the optimal assortment has a simple structure and provide insights on how various factors affect the optimal level of assortment variety we also develop a formal definition of the level of fashion in a category using the theory of majorization and examine its implications for category profits

coordinated decisions for substitutable products in a common retailer supply chain abstract this paper studies coordination mechanisms in a supply chain which consists of two suppliers with capacity uncertainties selling differential yet substitutable products through a common retailer who faces price sensitive random demand of these two products we develop in a noncompetitive setting three coordination models revenue sharing return policy and combination of revenue sharing and return policy and contrast them with a basic and uncoordinated model we are able to establish the ordinal relationship among the retailer s ordering and pricing decisions and analytically compare the performances between certain models when two suppliers are identical we find that the retailer s ordering and pricing decisions in the model with return policy in the case of identical suppliers are independent of demand or supply uncertainty our numerical results reveal that the performances of coordination models in the case of nonidentical suppliers resemble those in the case of identical suppliers we find that the retailer will place a larger order quantity in models where her average cost per unit sold is smaller we also find that product substitutability and uncertainties have different effects on chain performances

testing household specific explanations for the inverse productivity relationship the inverse relationship between land productivity and farm size is an old and puzzling empirical regularity most explanations for this relationship rely on market imperfections that jointly determine the farm size and the household s shadow price of some productive inputs we use plot level data from the icrisat vls to assess whether these household specific theories can explain the puzzle the data exhibit plots of different sizes being simultaneously cropped by the same household the inverse relationship is shown to hold true with the same magnitude across the plots of each household thus cross household heterogeneity does not suffice to explain the puzzle

flexible service capacity optimal investment and the impact of demand correlation we consider a firm that provides multiple services using both specialized and flexible capacity the problem is formulated as a two stage single period stochastic program the firm invests in capacity before the actual demand is known and optimally assigns capacity to customers when demand is realized sample applications include a car rental company s use of mid sized cars to satisfy unexpectedly high demand for compact cars and an airline s use of business class seats to satisfy economy class demand we obtain an analytical solution for a particular case when services may be upgraded by one class the simple form of the solution allows us to compare the optimal capacities explicitly with a solution that does not anticipate flexibility given that demand follows a multivariate normal distribution we analytically characterize the effects of increasing demand correlation on the optimal solution for the case with two customer classes the effects of demand correlation are intuitive increasing correlation induces a shift from flexible to dedicated capacity when there are three or more classes there are also adjustments to the resources not directly affected by the correlation change as correlation rises these changes follow an alternating pattern for example if the optimal capacity of one resource rises then the optimal capacity of the adjacent resource falls these results make precise conjectures based on numerical experiments that have existed in the literature for some time

co production processes with random yields in the semiconductor industry a wide variety of manufacturing operations can be characterized as co production with substitutable demand that is there are many situations in which the availability of two or more items are related and because of randomness in either supply or demand it can be advantageous to substitute one of these items for another our research was motivated by the semiconductor industry where chips are produced in large batches because of the presence of randomness in the process individual chips in a given batch can perform differently because some customers have stricter specifications than others chips within the same batch can be classified and sold as different products according to their measurable performance we model the production and inventory problem as a stochastic dynamic program in which the objective is to minimize the costs of meeting contractual obligations after developing heuristic methods of solving the problem in practice we validate them against a lower bound on the cost of an optim

the inverse relationship between productivity and farm size a test using regional data from india the farm size productivity debate for india needs little introduction it has occupied a prominent position in the agricultural economics literature since 1962 when sen observed that indian farm management data revealed an inverse relationship between farm size and yields per acre since then no fewer than twenty journal papers have appeared on this subject sen 1975 the objective of this paper is to test two hypotheses that were either not given enough attention or left unresolved in the debate the first is that the inverse relationship is valid for all of indian agriculture it is not merely a phenomenon observed in a few sample villages this means a test of the hypothesis that the small farm sector as a whole is more productive than the large farm sector in indian agriculture the second hypothesis is that the inverse relationship is true only of a traditional agriculture and that it breaks down with technical progress a methodology is developed below which uses cross sectional regional data to test the two hypotheses simultaneously on applying this methodology to indian district level data 272 districts for 1970 71 it is found that the hypothesis of the small farm sector being more productive than the large farm sector cannot be rejected at low levels of agricultural technology but can be rejected at higher levels this suggests that the inverse relationship between yields and farm size although valid for a traditional agriculture cannot be assumed to exist in an agriculture experiencing technical change

farm size productivity and returns to scale in agriculture revisited a case study of wine producers in south africa abstract the inverse relationship between farm size and productivity has almost become a stylised fact in the economic development literature most of the studies contributing to this preception have been flawed by methodological shortcomings and the request is that these studies be treated with caution using recent farm survey data from the wine producing areas of the western cape of south africa this study attempts to overcome some of the methodological problems distinguishing between partial and total productivity measures using data envelopment analysis most of the wine grape producers were found to operate under constant returns to scale co operative membership seemed to overcome the economies of scale associated with processing and marketing the inverse relationship between farm size and both land productivity and total factor productivity is weak not consistently negative and differs between regions thus caution must be used when advocating rural development policies based on the inevitability of an inverse relationship existing in all sectors and production regions of agriculture

assortment planning and inventory decisions under a locational choice model we consider a single period assortment planning and inventory management problem for a retailer using a locational choice model to represent consumer demand we first determine the optimal variety product location and inventory decisions under static substitution and show that the optimal assortment consists of products equally spaced out such that there is no substitution among them regardless of the distribution of consumer preferences the optimal solution can be such that some customers prefer not to buy any product in the assortment and such that the most popular product is not offered we then obtain bounds on profit when customers dynamically substitute using the static substitution for the lower bound and a retailer controlled substitution for the upper bound we thus define two heuristics to solve the problem under dynamic substitution and numerically evaluate their performance this analysis shows the value of modeling dynamic substitution and identifies conditions in which the static substitution solution serves as a good approximation