optimizing multinomial logit profit functions the multinomial logit model is a standard approach for determining the probability of purchase in product line problems when the purchase probabilities are multiplied by product contribution margins the resulting profit function is generally nonconcave because of this standard nonlinear search procedures may terminate at a local optimum which is far from the global optimum we present a simple procedure designed to alleviate this problem the key idea of this procedure is to find a path of prices from the global optimum of a related but concave logit profit function to the global optimum of the true but nonconcave logit profit function

constrained assortment optimization for the nested logit model we study assortment optimization problems where customer choices are governed by the nested logit model and there are constraints on the set of products offered in each nest under the nested logit model the products are organized in nests each product in each nest has a fixed revenue associated with it the goal is to find a feasible set of products i e a feasible assortment to maximize the expected revenue per customer we consider cardinality and space constraints on the offered assortment which limit the number of products and the total space consumption of the products offered in each nest respectively we show that the optimal assortment under cardinality constraints can be obtained efficiently by solving a linear program the assortment optimization problem under space constraints is np hard we show how to obtain an assortment with a performance guarantee of 2 under space constraints this assortment also provides a performance guarantee of 1 1 when the space requirement of each produc

an equilibrium model of the business cycle with household production and fiscal policy the authors estimate a dynamic general equilibrium model of the u s economy that includes an explicit household production sector and stochastic fiscal variables they use their estimates to investigate two issues first the authors analyze how well the model accounts for aggregate fluctuations they find that household production has a significant impact and reject a nested specification in which changes in the home production technology do not matter for market variables second the authors study the effects of some simple fiscal policy experiments and show that the model generates different predictions for the effects of tax changes than similar models without home production copyright 1997 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

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

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

household saving micro theories and micro facts in this survey we review the recent theoretical and empirical literature on household saving and consumption the discussion is structured around a list of motives for saving and how well the standard theory captures these motives we show that almost all of the motives for saving that have been suggested in the informal saving literature can be captured in the standard optimizing model particular attention is given to recent work on the precautionary motive and its implications for saving and consumption behavior we also discuss the behavioral or psychological approach that eschews the use of standard optimization techniques and focuses instead on direct consideration on saving we provide a section on facts who save and how much we then discuss informally the recent decline in the u s saving rate and whether the theory is of much use in understanding this and other changes in aggregate saving rates over time we do not find any convincing explanation for the change in saving rates we also discuss some analyses of saving behavior over the life cycle addressing such questions as whether households save enough for retirement and whether the consumption patterns of older households can be rationalized within a simple life cycle model we also review a great number of studies of the consumption euler equations based on our analysis of the studies cited we conclude that there is still mixed evidence that consumption is excessively sensitive to income we also examine in depth the recent empirical literature on the precautionary motive we conclude that although some households do seem to have a significant precautionary motive at some points in their life cycle this motive is not so strong empirically as some investigators suggest

optimal pricing of correlated product options under the paired combinatorial logit model in this paper we study price optimization with price demand relationships captured by the paired combinatorial logit pcl model which overcomes restrictions of the well studied multinomial logit mnl and nested logit nl models the pcl model allows for choice correlation and like the nl model includes the mnl model as a special case compared to the nl models the pcl model does not restrict the sequence of the choice structure and allows for different covariances among all pairs of choices this additional flexibility in structure enables a more accurate representation of some choice settings and broadens its empirical applications hence it is of both theoretical and practical interests to extend the normative studies on the mnl and nl models to the pcl model and examine the pricing problem under this model due to cross nesting of choice alternatives the pricing problem under the pcl model poses a greater challenge than the mnl and nl models however using the concept of p matrix we are abl

price competition under mixed multinomial logit demand functions in this paper we postulate a general class of price competition models with mixed multinomial logit demand functions under affine cost functions in these models the market is partitioned into a finite set of market segments we characterize the equilibrium behavior of this class of models in the case where each product in the market is sold by a separate independent firm we identify a simple and very broadly satisfied condition under which a pure nash equilibrium exists and the set of nash equilibria coincides with the solutions of the system of first order condition equations a property of essential importance to empirical studies this condition specifies that in every market segment each firm captures less than 50 of the potential customer population when pricing at a specific level that under the condition is an upper bound for a rational price choice for the firm irrespective of the competitors prices we show that under a somewhat stronger but still broadly satisfied version of the abov

household production and the excess sensitivity of consumption to current income empirical research on the permanent income hypothesis pih has found that consumption growth is excessively sensitive to predictable changes in income this finding is interpreted as strong evidence against the pih we propose an explanation for apparent excess sensitivity that is based on a quantitative equilibrium model of household production in which permanent income consumers respond to shifts in sectoral wages and prices by substituting work effort and consumption across home and market sectors although the pih is true this mechanism generates apparent excess sensitivity because market consumption responds to predictable income growth

revenue management model for on demand it services abstract this paper presents a model for applying revenue management to on demand it services the multinomial logit model is used to describe customer choice over multiple classes with different service level agreements slas a nonlinear programming model is provided to determine the optimal price or service level for each class through a numerical analysis we examine the impacts of system capacity and customer waiting incentives on the service provider s profit and pricing strategies

the determinants of coupon usage this paper uses a large sample of survey data to investigate the empirical determinants of coupon usage the broad set of control variables allows for comparisons of the relative importance of indi

a constructive approach to estimating pure characteristics demand models with pricing discrete choice demand models are important and fundamental tools for understanding consumers choice behavior and for analyzing firms operations and pricing strategies in these models products are often described as a vector of observed characteristics a consumer chooses the product that maximizes her utility assumed to be a function of the observed product characteristics and the consumer s preference over these product characteristics one central task in the demand estimation literature is to infer based on observed data consumers preferences on product characteristics we consider such an estimation problem for pure characteristics models a class of random coefficients demand models without the idiosyncratic logit error term in a consumer s utility function the absence of the logit error term and the use of numerical integration to approximate the integral in aggregate market shares lead to a nonsmooth formulation of approximated market share equations as a result solving the approximated

information processing and bounded rationality a survey this paper surveys recent attempts to formulate a plausible and tractable model of bounded rationality the author focuses in particular on models that view bounded rationality as stemming from limited information processing he discusses partitional models such as computability automata perceptions and optimal networks nonpartitional models and axiomatic approaches

product line selection and pricing under a share of surplus choice model abstract product line selection and pricing decisions are critical to the profitability of many firms particularly in today s competitive business environment in which providers of goods and services are offering a broad array of products to satisfy customer needs we address the problem of selecting a set of products to offer and their prices when customers select among the offered products according to a share of surplus choice model a customer s surplus is defined as the difference between his utility willingness to pay and the price of the product under the share of surplus model the fraction of a customer segment that selects a product is defined as the ratio of the segment s surplus from this particular product to the segment s total surplus across all offered products with positive surplus for that segment we develop a heuristic procedure for this non concave mixed integer optimization problem the procedure utilizes simulated annealing to handle the binary product selection variables and a steepest ascent style procedure that relies on certain structural properties of the objective function to handle the non concave continuous portion of the problem involving the prices we also develop a variant of our procedure to handle uncertainty in customer utilities in computational studies our basic procedures perform extremely well producing solutions whose objective values are within about 5 of those obtained via enumerative methods our procedure to handle uncertain utilities also performs well producing solutions with expected profit values that are roughly 10 higher than the corresponding expected profits from solutions obtained under the assumption of deterministic utilities

assortment optimization under variants of the nested logit model we study a class of assortment optimization problems where customers choose among the offered products according to the nested logit model there is a fixed revenue associated with each product the objective is to find an assortment of products to offer so as to maximize the expected revenue per customer we show that the problem is polynomially solvable when the nest dissimilarity parameters of the choice model are less than one and the customers always make a purchase within the selected nest relaxing either of these assumptions renders the problem np hard to deal with the np hard cases we develop parsimonious collections of candidate assortments with worst case performance guarantees we also formulate a convex program whose optimal objective value is an upper bound on the optimal expected revenue thus we can compare the expected revenue provided by an assortment with the upper bound on the optimal expected revenue to get a feel for the optimality gap of the assortment by using this approach our computational experiments test the performance of the parsimonious collections of candidate assortments that we develop

optimal product line pricing in the presence of budget constrained consumers abstract the product line pricing problem is generally defined as a seller s task to determine the optimal prices for each product in a product line while accounting for both demand side and supply side restrictions in this paper we contribute to the existing literature by incorporating consumers budget considerations into the seller s optimisation problem despite playing an important role in many applications such as the pricing of tickets for sporting or theatre seasons budget constraints have not been considered in the academic literature in the context of product line pricing to date by building on the assumptions and the model formulation recently proposed in a previous study by burkart w r et al 2012 product line pricing for services with capacity constraints and dynamic substitution european journal of operational research 219 2 347 359 for standard product line pricing we propose a number of new mixed integer linear formulations assuming budget constrained consumers the formulations differ in terms of how consumers handle their individual budget limitations to solve the underlying problems we propose a customised branch and bound procedure that relies on various novel problem specific bound arguments explicitly exploiting the consumers budget limitations experimental tests show that the branch and bound procedure clearly outperforms ibm ilog cplex which is unable to solve problems for even medium sized instances furthermore based on a number of scenarios we derive managerial insights regarding e g the overall impact of considering budget constraints on the seller s revenue as well as the impact of correctly anticipating the type of consumer purchase behaviour

short run pricing strategies to increase corporate average fuel economy short run pricing strategies to increase corporate average fuel economy i introduction in 1974 the average fuel efficiency of new automobiles sold in the united states reached a low of 14 2 miles per gallon mpg close on the heels of the arab opec oil embargo of 1973 74 and the ensuing petroleum price shocks congress passed the 1975 energy policy and conservation act the act required each manufacturer to meet sales weighted corporate average fuel economy cafe standards beginning with 18 mpg in 1978 and gradually increasing each year to 27 5 mpg in 1985 figure 1 the expressed purpose of the cafe standards was to stimulate the development of technology to improve fuel efficiency the possibility of raising the relative prices of the least energy efficient models as a strategy to meet the standards was considered but only as a last resort 1 although there continues to be intense debate as to whether fuel price increases or the cafe regulations drove the fuel economy improvements of the 1970s and 80s several studies agree that improvements in automotive engineering and design rather than pricing strategies played an overwhelmingly dominant role 2 no empirical evidence supports the effectiveness of using pricing strategies to increase the overall level of automotive fuel economy every year since 1985 automobile manufacturers have successfully petitioned the national highway traffic safety administration which determines the level of the cafe standard to reduce the target from 27 5 to 26 mpg in 1986 88 and 26 5 mpg in 1989 in each case at least one manufacturer argued that it would be unable to meet the original target with its planned product offerings and would have to resort to other strategies that would result in unacceptable economic costs this paper explores a method of estimating the costs of achieving fuel economy goals when pricing strategies are used to alter the distribution of sales the method employs the closed form equation for consumers surplus derived from the multinational logit model of discrete choice discussed by mcfadden 1973 and assumes that manufacturers must bear the full cost of meeting the fuel economy target the estimated cost represents an upper bound on the losses firms would incur by setting prices to minimize loss of profit using econometric estimates of the sensitivity of vehicle choice to vehicle price together with market shares and fuel efficiencies for 1986 i estimate the costs of short term improvements in average fuel economy using pricing strategies for general motors ford and chrysler minor adjustments of up to 1 mpg cost 1 2 percent of the price of a 10 000 car for improvements of 2 mpg or more however pricing strategies become a costly way to improve fuel economy the technique also estimates the market shares for each car line that correspond to the pricing solution it thereby identifies which car lines would be most affected the technique produces precise price changes and market shares for each car line readers should not place too much weight on the apparent precision but should consider the estimates as an approximation the usefulness of which lies in measuring the difficulty of meeting fuel economy targets via pricing strategies alone one can compare the size of these estimates to the fines for failing to meet the standards 50 per mpg per car or to typical manufacturer rebates to stimulate sales often 100 to 2 000 per car ii a formulation of the pricing problem faced with the cafe requirements a firm can respond with engineering and design improvements or by raising the prices of less efficient models and lowering the prices of those that exceed the standard technological improvements generally require a lead time of three to five years very large fluctuations in fuel prices have occurred in far shorter perids figure 1 creating the risk that a manufacturer s product offering could be out of step with the market

stocking retail assortments under dynamic consumer substitution we analyze a single period stochastic inventory model newsboy like model in which a sequence of heterogeneous customers dynamically substitute among product variants within a retail assortment when inventory is depleted the customer choice decisions are based on a natural and classical utility maximization criterion faced with such substitution behavior the retailer must choose initial inventory levels for the assortment to maximize expected profits using a sample path analysis we analyze structural properties of the expected profit function we show that under very general assumptions on the demand process total sales of each product are concave in their own inventory levels and possess the so calleddecreasing differences property meaning that the marginal value of an additional unit of the given product is decreasing in the inventory levels of all other products for a continuous relaxation of the problem we then show via counterexamples that the expected profit function is in general not even quasiconcave thus global optimization may be difficult however we propose and analyze a stochastic gradient algorithm for the problem and prove that it converges to a stationary point of the expected profit function under mild conditions finally we apply the algorithm to a set of numerical examples and compare the resulting inventory decisions to those of some simpler naive heuristics the examples show that substitution effects can have a significant impact on an assortment s gross profits the examples also illustrate some systematic distortions in inventory decisions if substitution effects are ignored in particular under substitution one should stock relatively more of popular variants and relatively less of unpopular variants than a traditional newsboy analysis indicates

optimal pricing for a multinomial logit choice model with network effects we consider a seller s problem of determining revenue maximizing prices for an assortment of products that exhibit network effects customers make purchase decisions according to a multinomial logit choice model modified to incorporate network effects so that the utility each individual customer gains from purchasing a particular product depends on the market s total consumption of that product in the setting of homogeneous products we show that if the network effect is comparatively weak then the optimal pricing decision of the seller is to set identical prices for all products however if the network effect is strong then the optimal pricing decision is to set the price of one product low and to set the prices of all other products to a single high value this boosts the sales of the single low price product in comparison to the sales of all other products we also obtain comparative statics results that describe how optimal prices and sales levels vary with a parameter that determines the strengt

disability earnings income and consumption using longitudinal data for the period 1968 2005 for a sample of male household heads we determine the prevalence of disability during the working years and examine how the extent of disability affects a range of outcomes including earnings income and consumption we have seven main findings first disability rates are high we divide the disabled along two dimensions based on the persistence and severity of their work limiting condition we estimate that a person reaching age 56 has a 53 percent chance of having been disabled at least once during his working years and a 19 percent chance that he has begun a chronic and severe disability second the economic consequences of disability are frequently profound ten years after disability onset a person with a chronic and severe disability on average experiences a 68 percent decline in earnings a 32 percent decline in after tax income a 22 percent decline in food and housing consumption and a 21 percent decline in food consumption third the various economic consequences differ sharply across disability groups the outcome declines for those with a chronic and severe disability are often more than twice as large as those for the average disabled fourth our findings show the partial and incomplete roles that individual savings family support and social insurance play in reducing the consumption drop that follows disability only about half of this most disabled group reports receiving social security disability insurance or supplemental security income fifth we find a noticeable fall in earnings and income prior to the onset of a reported disability consumption also falls somewhat suggesting that future disability is partially but incompletely predictable in the short run sixth time use and detailed consumption data further indicate that disability is associated with a decline in well being seventh the quantities we have estimated combined with elasticities from the literature allow us to examine the optimality of current compensation for the disabled we find that the current compensation for our most disabled group appears to be lower than is optimal

heuristics for pricing and positioning a product line using conjoint and cost data designing and pricing a product line is the very essence of every business in recent years quantitative methods to assist managers in this task have been gaining in popularity conjoint analysis is already widely used to measure preferences for different product profiles and build market simulation models in the last few years several papers have been published that suggest how to optimally choose a product line based on such data we formalize this problem as a mathematical program where the objective of the firm is either profit or total welfare unlike alternative published approaches we introduce fixed and variable costs for each product profile the number of products to be introduced is endogenously determined on the basis of their desirability fixed and variable costs and in the case of profits their cannibalization effect on other products while the problem is difficult np complete we show that the maximum welfare problem is equivalent to the uncapacitated plant location problem which can be solved very efficiently using the greedy interchange heuristic based on past published experience with this problem and on simulations we perform we show that optimal or near optimal solutions are obtained in seconds for large problems we develop a new greedy heuristic for the profit problem and its application to simulated problems shows that it too runs quickly and with better performance than various alternatives and previously published heuristics we also show how the methodology can be applied taking existing products of both the firm and the competition into account

distinguishing income from substitution effects in disability insurance a set of studies conducted over the last 15 years has produced a near consensus that the social security disability insurance system ssdi has substantial disincentive effects on the labor supply of near elderly males diminishing labor force participation increasing the sensitivity of labor force exit decisions to adverse economic shocks and encouraging those nearing retirement to claim disability benefits and subsequently transfer into the social security retirement program yet efforts by the social security administration ssa to encourage labor supply among the disabled by removing the work disincentives built into ssdi have been almost entirely unsuccessful most notably in 1999 congress authorized the ticket to work program which provides an array of inducements for current ssdi beneficiaries to take up employment including permitting a trial work period of up to nine months providing 7 75 years of ongoing medicare eligibility following return to work and providing three years of automatic benefit reinstatement when claimants workplace earnings fall below a threshold level each of these steps reduces the implicit tax placed on labor supply by the ssdi program despite these lures fewer than 1 400 0 01 percent of the 12 2 million tickets issued to date have led to successful workforce integration autor and duggan 2006

taxes and time allocation evidence from single women and men the classic model of becker 1965 suggests that labor supply decisions should be analyzed within the broader context of time allocation and market good consumption choices but most empirical work on policy has focused exclusively on measuring impacts on market work this paper examines how income taxes affect time allocation during the entire day and how these time allocation decisions interact with expenditure patterns using the panel study of income dynamics from 1975 to 2004 we analyze the response of single women s housework labor supply and other time to variation in tax and transfer schedules across income levels number of children states and time we find that when the economic reward to participating in the labor force increases market work increases and housework decreases with the decrease in housework accounting for approximately two thirds of the increase in market work analysis of repeated cross sections of time diary data from 1975 to 2004 shows that home production decreases substantially when market hours of work increase in response to policy changes data on expenditures from the consumer expenditure survey from 1980 to 2003 show some evidence that expenditures on market goods likely to substitute for housework increase in response to a greater incentive to join the labor force the baseline estimates imply that the elasticity of substitution between consumption of home and market goods is 2 61 the results are consistent with the becker model meanwhile single men show little response to changes in tax policy and we are able to rule out an elasticity of substitution between home and market goods for this group of more than 1 52

competition based dynamic pricing in online retailing a methodology validated with field experiments a retailer following a competition based dynamic pricing strategy tracks competitors price changes and then must answer the following questions i should we respond ii if so to whom iii how much of a response iv and on which products the answers require unbiased measures of price elasticity as well as accurate estimates of competitor significance and the extent to which consumers compare prices across retailers there are two key challenges to quantify these factors empirically first the endogeneity associated with almost any type of observational data where prices are correlated with demand shocks observable to pricing managers but not to researchers and second the absence of competitor sales information which prevents efficient estimation of a full consumer choice model we address the first issue by conducting a field experiment with randomized prices we resolve the second issue by exploiting the retailer s own and competitors stockouts as a source of variation to the consumer cho

what accounts for the variation in retirement wealth among u s households even among households with similar socioeconomic characteristics saving and wealth vary considerably life cycle models attribute this variation to differences in time preference rates risk tolerance exposure to uncertainty relative tastes for work and leisure at advanced ages and income replacement rates these factors have testable implications concerning the relation between accumulated wealth and the shape of the consumption profile using the panel study of income dynamics and the consumer expenditure survey we find little support for these implications the data are instead consistent with rule of thumb mental accounting or hyperbolic discounting theories of wealth accumulation jel di d91 e21

the demand for food and calories we investigate nutrition and expenditure in rural maharashtra in india we estimate that the elasticity of calorie consumption with respect to total expenditure is 0 3 0 5 a range that is in accord with conventional wisdom the elasticity declines only slowly with levels of living and is far from the value of zero suggested by a recent revisionist literature in these indian data the calories necessary for a day s activity cost less than 5 percent of the daily wage which makes it implausible that income is constrained by nutrition rather than the other way around

the long run consumption effects of earnings shocks although prior studies of job displacement and disability have measured the impact of these shocks in terms of lost earnings no previous research has linked these permanent earnings shocks to the

technical note pricing under the nested attraction model with a multistage choice structure we develop a solution approach to the centralized pricing problem of a nested attraction model with a multistage tree structure we identify conditions under which the optimal solution can be uniquely determined and we characterize the optimal solution as a fixed point of a single variable in the special case of a multistage nested logit model we show the impact of asymmetry in price sensitivity and adjustment index also known as the dissimilarity index and we derive a closed form solution when the tree structure is symmetric many existing results in the literature regarding the single or two stage nested attraction model are shown to be special cases of the results we have derived we show that the equal markup property which holds for the single stage logit model with symmetric price sensitivity in general does not hold for products that do not share the same immediate parent node in the nested choice structure even when price sensitivities are the same for all products

the demand for local telephone service a fully discrete model of residential calling patterns and service choices we present an empirical model of households choices among local telephone service options for example between flat rate and measured service and the interrelation of these choices with the number and average duration of local calls households make at each time of day to each geographical zone using a nested logit model with estimation performed on a randomly selected subset of the households calling patterns we calculate elasticities of demand for each local service option number of calls average duration and revenues with respect to the fixed monthly charges and the usage charges for calling under each option we find moderate price elasticities of number of calls with respect to usage charges for households subscribing to measured service nevertheless raising usage charges has a negligible effect on revenues since a sufficient number of households either originally subscribe to flat rate service or convert to flat rate service in response to higher usage charges we find a high elasticity of demandfor each service option with respect to itsfixed monthlyfee this indicates high substitutability among service options the shift among service options induces new calling patterns which wefind to be a small but not negligible indirect effect e most telephone operating companies offer residential customers several options for local service there are two general categories of service flat rate service under which a household can for a fixed monthly charge make an unlimited number of calls within a specified geographical area and measured service for which the household pays a lower fixed monthly fee but can make only a specified number or dollar value of calls at no extra charge after which charges are incurred for additional calls various flat rate services differ in the size of the geographical area in which calling is at no extra charge with higher monthly fees for larger areas measured services differ with respect to the threshold number or dollar value of calls beyond which the customer is charged

the d level nested logit model assortment and price optimization problems we consider assortment and price optimization problems under the d level nested logit model in the assortment optimization problem the goal is to find the revenue maximizing assortment of products to offer when the prices of the products are fixed using a novel formulation of the d level nested logit model as a tree of depth d we provide an efficient algorithm to find the optimal assortment for a d level nested logit model with n products the algorithm runs in o d n log n time in the price optimization problem the goal is to find the revenue maximizing prices for the products when the assortment of offered products is fixed although the expected revenue is not concave in the product prices we develop an iterative algorithm that generates a sequence of prices converging to a stationary point numerical experiments show that our method converges faster than gradient based methods by many orders of magnitude in addition to providing solutions for the assortment and price optimization problems

homework in labor economics household production and intertemporal substitution abstract we argue that estimates of intertemporal substitution elasticities obtained from standard life cycle models are subject to a downward bias because they neglect changes in work done at home over the life cycle we extend the standard life cycle model to include home production and estimate it using data from three time use surveys we find that the downward bias is large

consumption versus expenditure previous authors have documented a dramatic decline in food expenditures at the time of retirement we show that this is matched by an equally dramatic rise in time spent shopping for and preparing meals using a novel data set that collects detailed food diaries for a large cross section of u s households we show that neither the quality nor the quantity of food intake deteriorates with retirement status we also show that unemployed households experience a decline in food expenditure and food consumption commensurate with the impact of job displacement on permanent income these results highlight how direct measures of consumption distinguish between anticipated and unanticipated shocks to income whereas measures of expenditures obscure the distinction