a committed delivery strategy with fixed frequency and quantity abstract we analyze a supply chain environment in which a distributor facing price sensitive demand has the opportunity to contractually commit to a delivery quantity at regular intervals over a finite horizon in exchange for a per unit cost reduction for units acquired via committed delivery supplemental orders needed to meet demand are purchased at an additional unit cost for normally distributed demand we use a simulation based approximation to develop models yielding closed form solutions for the optimal order quantity and resell price for the distributor inventory ordering and pricing implications for this committed delivery strategy are investigated

approximating wtp and wta for environmental goods from marginal willingness to pay functions abstract willingness to pay wtp and willingness to accept wta for a change in the quantity of an environmental good can be represented by corresponding hicksian welfare measures the paper suggests a simple method of approximating wtp and wta given the information about the marginal willingness to pay mwtp for it it demonstrates that a polynomial based on the mwtp function allows to approximate the hicksian measures which may differ considerably much better than consumer s surplus in quantity space

returns with wholesale price discount contract in a newsvendor problem abstract we consider a newsvendor problem in a supply chain that consists of a manufacturer and a retailer the manufacturer is the stackelberg leader and the retailer is the follower we examine how the manufacturer can contract a wholesale price only agreement with its retailer that maximizes its profit we also propose a returns policy with a wholesale price discount scheme returns discount contract that can achieve supply chain coordination using the wholesale price only contract as a benchmark we show how the manufacturer sets a discounted wholesale price in a returns discount contract that enhances both profits of the manufacturer and the retailer as well as improves the supply chain efficiency

efficient methods of measuring welfare change and compensated income in terms of ordinary demand functions a utility maximizing consumer with a completely known system of ordinary demand functions q h p c is considered let p qo and p q be two arbitrary equilibrium situations the problem is to evaluate in which of the situations the utility is higher without knowing the utility function revealed preference theory tells that the ordinary demand functions which are in principle observable contain enough information to solve the problem remaining difficulties are therefore mainly computational we present how the compensated income c i c p qo and the compensated demand h p cl1 are calculated with arbitrary accuracy using only the ordinary demand system our two efficient algorithms also have interesting interpretations in terms of index numbers and consumer surplus measures

capacity allocation ordering and pricing decisions in a supply chain with demand and supply uncertainties abstract this paper studies coordinated decisions in a decentralized supply chain that consists of one original equipment manufacturer oem one manufacturer and one distributor and possesses uncertainties at both demand and supply sides these uncertainties emerge respectively from random demand the distributor faces and randomness of capacity with which the oem processes the manufacturer s outsourced quantity sharing supply and demand uncertainty information along the supply chain enables us to develop three models with different coordination efforts the oem and manufacturer coordination the manufacturer and distributor coordination and the oem manufacturer and distributor coordination and quantify the coordinated decisions in these three models our analysis of these coordination models suggests that coordinating with the oem improves the manufacturer s probability of meeting downstream demand and his expected profit yet coordinating with the manufacturer is not necessarily beneficial to the oem when downstream coordination is lacking

reform of the coal sector in an open economy the case of china cheap abundant and easy to transport and store coal has been produced and consumed to meet people s energy needs the last decade s growth in global coal use has been driven mainly by developing economies like china whose phenomenal economic growth has been powered by coal fired electricity and promoted by the export of manufactured goods a recent reform focus in china s coal sector is on coal taxation the paper develops a game theoretic model tailored to the context of china where coal taxation reform takes place against the background of privatisation of coal firms and an open economy it finds that the adoption of special coal taxes is optimal for social welfare under most circumstances but may induce coal firms to commit opportunistic behaviour in the process of privatisation the paper also cautions about potential resistance to the reform from consumers coal firms and government officials

second best carbon taxation in the global economy the green paradox and carbon leakage revisited acceleration of global warming resulting from a future carbon tax is large if the price elasticities of oil demand are large and that of oil supply is small the fall in the world interest rate weakens this weak green paradox effect especially if intertemporal substitution is weak still social damages from greenhouse gases drop if the fall in oil supply and cumulative emissions is strong enough if the current carbon tax is set too low the second best future carbon tax is set below the first best too to mitigate adverse green paradox effects unilateral second best optimal carbon taxes exceed the first best taxes due to an import tariff component the intertemporal terms of trade effects of the future carbon tax increase current and future tariffs and those of the current tax lower the current tariff finally carbon leakage and globally altruistic and unilateral second best optimal carbon taxes if non kyoto oil importers price carbon too low are analysed in a three country model of the global economy

ex ante consumer welfare evaluation in cost benefit analysis abstract public projects and policies are normally evaluated ex ante i e while consumers may still be uncertain about future prices income levels interest rates and preferences this paper extends the theory of ex ante consumer welfare evaluation by developing a 2 period model with multiple sources of uncertainty it provides insights into the influence of temporal uncertainty on the empirical measurement of ex ante willingness to pay

an economic order quantity model with partial backordering and all units discount abstract the classic economic order quantity model assumes that the unit purchasing cost is not based on the order quantity in practice a supplier may offer purchasers an all units discount we develop a model and solution procedure for the eoq with all unit discounts and partial backordering at a constant rate we show and illustrate with a numerical example how that model can be used to find the solution for the eoq with discount and full backordering a multi factor experiment is used to gain insights into the improvement in performance of the proposed procedure relative to using the basic eoq or the eoq with full backordering and to identify the model parameters that have the greatest impact on the model s performance

designing a firm s coordinated manufacturing and supply decisions with short product life cycles in this paper we consider a problem of joint coordination between a firm s manufacturing and supply departments the manufacturing department is responsible for meeting random demand of a product with a short life cycle the supply department s responsibility is to provide the sufficient amount of raw materials so that the required production level can be achieved when coordination prevails both departments decisions are jointly made otherwise decisions are made independently without an exchange of information if the random demand exceeds the amount produced a second production run can be expedited at a substantially higher cost our analysis yields insightful results to such a coordination problem between the two departments we provide conditions under which it is desirable to coordinate resulting in a significant increase in expected profit if coordination is optimal then the supply department would purchase additional reserved material for the second run under this scenario we analyze the effects of joint coordination on the expected profit we also find explicit conditions for which joint coordination is not beneficial i e the supply department should only order sufficient material to meet the first production run requirements we provide a detailed set of numerical examples and generate response surfaces indicating the desirability of coordination for different pairs of parameter combinations

a generalized quantity discount pricing model to increase supplier s profits in this paper the joint problem of ordering and offering price discount by a supplier to his sole major buyer is analyzed the objective is to induce the buyer to alter his order schedule and size so that the supplier can benefit from lower set up ordering and inventory holding costs we generalize the quantity discount pricing model of monahan monahan j p 1984 a quantity discount pricing model to increase vendor profits management sci 30 6 720 726 to 1 explicitly incorporate constraints imposed on the amount of discount that can be offered and 2 relax the implicit assumption of a lot for lot or order for order policy adopted by the supplier an algorithm is developed to solve the supplier s joint ordering and price discount problem

dynamic climate policy with both strategic and non strategic agents taxes versus quantities we study a dynamic game where blocs of fossil fuel importers and exporters exercise market power using taxes or quotas a non strategic fringe of emerging and developing countries consume and produce fossil fuels cumulated emissions from fossil fuel consumption create climate damages we examine markov perfect equilibria under the four combinations of trade policies and compare these to the corresponding static games taxes dominate quotas for both the strategic importer and exporter the fringe is better off under taxes than quotas because taxes result in lower fuel prices and less consumption by the strategic importer lowering climate damages

capture and ideology in the economic theory of politics the economic theory of regulation long ago put public interest theories of politics to rest these theories have correctly been viewed as normative wishings rather than explanations of real world phenomena they have been replaced by models of political behavior that are consistent with the rest of microeconomics anthony downs 1957 james buchanan and gordon tullock 1965 george stigler 1971 sam peltzman 1976 recently however debate has arisen over whether some version of a public interest theory of regulation will have to be readmitted to our thinking about actions and results in the political arena what is at issue is the empirical importance of the altruistic publicly interested goals of rational actors in determining legislative and regulatory outcomes james kau and paul rubin 1979 kalt 1981 peltzman 1982 this study assesses the nature and significance of publicly interested objectives in a particular instance of economic policymaking u s senate voting on coal strip mining regulations the existence of such objectives is of course no contradiction of the economic view of human behavior kenneth arrow 1972 gary becker 1974 and may well be rooted in genetic biological history becker 1976 jack hirshleifer 1978 generally however individuals altruistic publicly interested goals have been given little attention this reflects the judgment that such goals are so empirically unimportant as to allow the use of occam s razor in positive models or well founded apprehensions that these goals are unusually difficult to identify measure and analyze notwithstanding the latter problem we find that approaches which confine themselves to a view of political actors as narrowly egocentric maximizers explain and predict legislative outcomes poorly the tracking and dissecting of the determinants of voting on coal strip mining policy suggest that the economic theory of politics has been prematurely closed to a broader conception of political behavior

an explanation for why senators from the same state vote differently so frequently abstract this paper explains why rational well informed voters elect politicians with divergent platforms given well defined constituencies and the costliness of any individual politician creating transfers across all interest groups we show that different politicians from the same district can successfully represent vastly different constituencies and still have each politician producing the support maximizing level of transfers our explanation focuses on how obtaining wealth transfers reduces successful constituencies returns to obtaining additional transfers the evidence strongly rejects alternative explanations based upon the median voter and polarized policy preference approaches

dynamically consistent oil import tariffs the standard solution of the open loop optimal import tariff is normally time inconsistent the paper shows why and derives the dynamically consistent markov perfect tariff the two tariffs are compared they differ except for a special class of import demands the time paths of tariffs and the welfare cost of an inability to commit are calculated for a dominant importer the welfare costs of the inability to commit are small if its market share

planning and approximation models for delivery route based services with price sensitive demands abstract classical vehicle routing problems typically do not consider the impact of delivery price on the demand for delivery services existing models seek the minimum sum of tour lengths in order to serve the demands of a given set of customers this paper proposes approximation models to estimate the impacts of price on delivery services when demand for delivery service is price dependent such models can serve as useful tools in the planning phase for delivery service providers and can assist in understanding the economics of delivery services these models seek to maximize profit from delivery service where price determines demand for deliveries as well as the total revenue generated by satisfying demand we consider a variant of the model in which each customer s delivery volume is price sensitive as well as the case in which customer delivery volumes are fixed but the total number of customers who select the delivery service provider is price sensitive a third model variant allows the delivery service provider to select a subset of delivery requests at the offered price in order to maximize profit

constituent interest vs legislator ideology the role of political opportunity cost this paper applies the economic model of legislative voting to the automobile industry domestic content vote in the u s house of representatives in 1982 we consider constituent interests for and against the ml and compare the predictive powers of alternative indicators of ideological preferences we also examine the role of political opportunity cost and find that lame ducks were significantly less likely to vote for the bill than were returnees to congress given the political advantages of voting for the bill this is consistent with the view that legislators were influenced by the case for freer trade

some two echelon supply chain games improving from deterministic symmetric information to stochastic asymmetric information models abstract many supply chain and inventory models use the following two echelon symmetric information and deterministic gaming structure a manufacturer wholesales a product to a retailer who in turn retails it to the consumer the retail market demand varies with the retail price according to a deterministic demand function that is known to both the manufacturer and the retailer it is then assumed that the players the manufacturer and the retailer arrive at their pricing and batch size decisions through a stackelberg game or a fixed markup percentage game the first part of this paper reveals many implausible effects of demand curve forms on the behavior of these gaming models however we do not merely conclude that two echelon gaming results obtained via assuming one convenient demand curve form can often become invalid under other demand curve forms more importantly we argue in the second part of the paper that the various implausible effects revealed here suggest a different but more fundamental conclusion the assumed non cooperative games are themselves flawed because gaming is meaningless and logically circular in a deterministic and symmetrical information system we then present an introductory illustration on how the introduction of stochasticity and information a symmetry leads to more plausible two echelon supply chain gaming models together the two parts demonstrate the necessity and practicality of using a stochastic and asymmetric information instead of the prevalent deterministic symmetric information approach in many supply chain models

an analysis of the impact of congressional term limits we examine the impact of a six term tenure limit on members of the u s house of representatives the first part of this study develops a methodological framework for simulating the quantitative impact of term limits the second part of this study uses this framework to estimate the effects of term limits on i the value of holding office ii turnover and iii the size of the democratic majority in the house both steady state and transition period effects are explored i introduction the widespread support for term limitations seems to have caught both popular commentators and academic researchers by surprise 1 why do voters want them and what is the likely impact of such legislation a small but growing literature concentrates on the first of these two questions adams and kenny 1986 dick and loft 1993 in contrast this paper addresses the second in particular it investigates the empirical consequences of imposing a twelve year six term tenure limit on the members of the u s house of representatives both the degree and timing of the impact of the alternative regimes are investigated here the issue of timing arises because term limits can have very different effects depending upon how they treat currently serving congressmen we focus our investigation on the two legislative regimes that we believe have the greatest chance of being implemented limited grandfathering and complete grandfathering 2 assuming term limit legislation is passed in 1992 we trace out the time paths of the effects associated with each of these regimes as we shall see there are important transitional differences between the two the paper proceeds as follows section ii addresses the methodology used in this analysis section iii considers the impact of term limits on i the value of holding office ii turnover and iii the democratic majority in the house section iv concludes ii methodology the first concern of this paper is to model the seniority structure of the house in the absence of congressional term limits let n t identify the number of congressmen in their nth term at time t let r define the proportion of congressmen that successfully move from term n to term n l note that there are a number of reasons for not continuing to an additional term besides electoral defeats there are voluntary departures to seek other elective office or private sector employment retirements and deaths given any set of continuation rates r sub 1 r sub 2 and an initial distribution of representatives across terms n sub 1 t n sub 2 t one can construct what the seniority structure of congress will look like any number of periods into the future for instance the number of congressmen in their jth term at time t m is given by mathematical expression omitted where n sub 1 t 1 m j identifies the number of representatives who enter congress in time period t 1 m j t 1 and j and m o ifj m 1 one simply takes the number of congressmen currently serving their j m th term and multiplies this by the appropriate product of continuation rates if j m 1 one needs to identify the number of congressmen who will enter congress in time period t l m since congress always has 435 members the number of arrivals must always equal the number of departures the number of first term congressmen who leave office at the end of time period t is given by 1 r sub 1 n sub 1 t similarly the number of second term congressmen who leave office at the end of time period t is given by 1 r sub 2 n sub 2 t thus the number of representatives who will enter congress in time period t l is given by mathematical expression omitted equations 1 and 2 allow one to recursively solve for n sub 1 t 1 m j for all m j 1 i

exhaustible resources and the dynamics of comparative advantage abstract this paper analyses the role of international differences in factor endowments and rates of time preference in determining the pattern of trade and specialization when one of the factors of production is an exhaustible resource the length of the period over which a country exports the resource is found to be directly related to the fraction of the world s resource stock under its control while the relative endowments of the inexhaustible factor influence only the volume of trade the direction of trade is determined by the rates of time preference with the more impatient country being the first to export the resource effects of trade on factor rewards are also examined

arbitrating a dispute a decision analytic approach many collective decision making and bargaining situations can be described through the set of the feasible joint evaluations of all conceivable settlements attention should then be restricted to that subset pareto optimal frontier from which no joint gains are possible hence the focal issue becomes which element of the pareto optimal subset should be chosen as a solution to the dispute this paper proposes an arbitration procedure to address this issue the proposed approach decision analytic in its nature is inspired by lavalle s lavalle i h 1978 fundamentals of decision analysis holt rinehart and winston new york allocation function approach which is not specific on how to obtain an allocation function and by eliashberg and winkler s eliashberg j r l winkler 1981 risk sharing and group decision making management sci 27 november 1221 1235 work which does not accommodate probability differences within the group after the new approach is presented its implications are examined for some likely scenarios and examples are considered

the effects of logrolling on congressional voting the theoretical public choice literature suggests that vote trading is an important determinant of congressional voting behavior yet empirical voting models do not allow for vote trading these models recognize that observed ideology may influence legislative behavior but do not correct for unobserved ideology this study devises new tests for logrolling and ideology the empirical model controls for logroll agreements and unobserved ideological interest via the correlation of unobserved variables the results reflect the presence of vote trading coalitions on some votes but not on others the results cast doubt on the importance of personal ideological interests of legislators copyright 1992 by american economic association

an approach for developing an optimal discount pricing policy this paper addresses the problem of why and how a seller should develop a discount pricing structure even if such a pricing structure does not alter ultimate demand the situation modeled is most appropriate where the seller s product does not represent a major component of the buyer s final product where the demand for the product is derived or where the price is only one of many factors considered in making a purchase decision a model of buyer reaction to any given pricing scheme is developed to show that there exists a unified pricing policy which motivates the buyer to increase its ordering quantity per order thereby reducing the joint buyer and seller ordering and holding costs as a result the seller is able to reduce its costs while leaving the buyer no worse off and often better off the model is extended to handle variable ordering and shipping costs and situations where the seller faces numerous groups of buyers each having different ordering policies finally a case study is presented explicitly showing how the proposed pricing policy can be applied to the situation of a large seller selling to a number of different buyer groups

the eoq models modified by introducing discount of purchase price or increase of setup cost abstract the eoq model of inventory problem can determine ordering cycle and quantity when the purchase unit price is constant ordering cycle and ordering quantity which minimize the one day s average inventory cost is not dependent on the purchase price but if purchase price may change the eoq model must be modified the purchase unit price is discounted as the ordering becomes larger the discount of purchase price is described with a decreasing function of ordering quantity this function is not always continuous with respect to the ordering quantity under this condition one day s average profit can be defined and we can determine ordering cycle and ordering quantity which maximize one day s average profit moreover we consider the situations under which the setup cost depends on the ordering quantity in this case the setup can be described with the increasing function of ordering quantity we show that the eoq model can be applied if it is modified by introducing the continuous setup cost function this function is not differentiable at some levels of ordering quantity

note comments on a quantity discount pricing model to increase vendor profits monahan monahan j p 1984 a quantity discount pricing model to increase vendor profits management sci june 720 726 adapted the quantity discount model of inventory theory to the problem of determining an optimal quantity discount schedule from a vendor s point of view and opened up an important direction of research however his one item one customer one vendor model is based on several implicit assumptions that must be judged unreasonable monahan must account for the vendor s inventory carrying charges and redefine his variable s2 it is shown that a rational vendor s manufacturing frequency would not be identical to the buyer s ordering frequency if the vendor s manufacturing setup costs are substantially larger than the buyer s ordering costs a numerical example presented in this note also questions the practical usefulness of monahan s model even after its theoretical inaccuracies axe corrected monahan s model may explain discounts that are a fraction of 1 of the price of an item but it fails to explain commonly observed magnitudes of quantity discounts such as 10 of the unit price

public and private returns from joint venture research an example from agriculture public research institutions are turning increasingly to the private sector for additional financial support such a trend in the short run lessens the need for public research expenditures but may in the long run prove to be very costly to the economy as a whole this is because private funding increases the chance that the direction of research will shift so that private benefits are enhanced such a shift is especially costly if public research funds are then not forthcoming that would have the potential of producing the maximum level of benefits to the economy as a whole a case study of canadian barley research is used to illustrate this problem

a critical review and an extension of the political shirking literature after substituting actual and real changes for proposed and nominal changes in budgetary and employment levels it is clear that the size and scope of the federal leviathon had not been reduced over 1982 83 it is also clear that the agencies which witnessed real budget cuts over this period were of minor importance in terms of the total u s budget future research on why only small agencies receive real budget cuts will provide us with a better understanding of the budgetary process

discount pricing decisions in distribution channels with price sensitive demand abstract in this paper we evaluate the effectiveness of quantity discounts and volume discounts as coordination mechanisms in distribution channels with demand that is price sensitive we consider a single vendor single retailer distribution channel demand for the product arises only at the retailer the demand faced by the retailer is assumed to be deterministic but price elastic the retailer in turn buys the product from the vendor the vendor and the retailer act independently and rationally each maximizing their own respective profit the equilibrium point that specifies the vendor s and buyer s inventory and pricing policy is determined by the solution to a stackelberg game we consider the cases when quantity discount and volume discount respectively are offered we develop methods to determine the optimal discount policy for these cases we then consider the case where both volume and quantity discounts are offered simultaneously and develop a method to determine the optimal simultaneous discount offer the relative performance of the alternative discount schemes is then evaluated through a numerical study the results of the study demonstrate that the effectiveness of volume discount as a coordination mechanism is higher when the sensitivity of demand to price changes is higher the effectiveness of quantity discount on the other hand is higher with lower price sensitivity of demand finally the results also demonstrate that perfect coordination is achieved when volume and quantity discounts are offered simultaneously

coordination and profit sharing between a manufacturer and a buyer with target profit under credit option several studies have focused on buyer vendor coordination through quantity discount credit option mechanism but few quantitative models and investigations are available that have explored the mechanism for transfer of surplus generated due to coordination in this paper we develop a coordination mechanism through credit option such that both the parties can divide the surplus equitably after satisfying their own profit targets two situations are explored here in the first situation both the parties have no individual profit target from the business whereas in the second situation there are individual profit target for both the parties the proposed mechanism for division of surplus is studied through a numerical study and the impact of different parameter values on the results are examined

the grey paradox how fossil fuel owners can benefit from carbon taxation abstract this paper considers the distributional impact of optimal carbon taxation on fossil fuel owners a carbon emitting exhaustible resource competes with a dirtier abundant resource and a clean backstop a time dependent carbon tax is set to optimally use these resources under a cap constraint over co 2 atmospheric concentration as the cap is tightened the dirtier resource becomes less competitive compared to the exhaustible resource the competition effect but the timing and duration of extraction of the exhaustible resource is modified the timing effect we provide analytical expressions of these effects and determine conditions over size of reserves pollution contents extraction costs and demand elasticity such that the exhaustible resource owners profits increase as the ceiling is tightened calibrations for the transport and power sectors suggest that the profits of conventional oil and natural gas owners increase compared to a baseline without regulation for plausible carbon ceiling values

endogenous growth asymmetric trade and resource dependence the aggregate income of oil exporting countries relative to that of oil poor countries has been remarkably constant in recent decades despite the existence of structural gaps in productivity growth rates this stylized fact is rationalized in an endogenous growth model of asymmetric trade where resource poor and resource rich economies display productivity differences but stable income shares due to terms of trade dynamics the model yields two testable predictions that deserve empirical scrutiny i the asymmetric impact between exporters and importers of national taxes on resource use on income shares and ii the inverse relation between terms of trade dynamics and total factor productivity growth

on the meaning of economic efficiency in policy analysis there are crucial differences in the normative foundations of alternative economic cri teria used to assess the efficiency of policy pro posals differences between pareto and potential pareto measures are emphasized in this comparison of efficiency standards technical distinctions be tween these two criteria are examined and illus trated it is argued that potential pareto criteria have greater disciplinary acceptance than their nor mative foundations merit and further that the pareto measure has suffered undue criticism from association with its potential pareto namesake jel all

term limits causes and consequences this paper consults multiple literatures to specify andevaluate the economic rationales for term limitation particularly on congress i first consider theories that aroseto explain among related issues why individual states mightunilaterally self impose term limits on their own delegationsto congress next i consider two main lines of argument foruniversal limits both of which begin with the empiricalphenomenon of high and rising congressional tenure first supporters of term limits argue that higher tenure biaseslegislatures toward inefficiency big government highspending second higher tenure creates inefficient anti competitive conditions in the legislative election market term limitation would remedy these inefficiencies by virtue ofdecreasing average tenure these claims are then evaluated inlight of the evidence amassed in the literature based on theliterature reviewed this paper finds that while term limitswill reduce average tenure there is no evidence to suggestthat term limits will affect the underlying causes of theseinefficiencies further research on a more general reform which would strike deeper at these underlying causes isimplied

compensating variation consumer s surplus and welfare the compensating variation was defined by j r hicks 1942 as the amount one would have to deduct from a person s income to make him just as well off after a change in prices and income as he had been in the initial situation if the compensating variation is positive the individual is better off under the new situation since the compensating variation furnishes a uniquely defined numerical cardinal indicator of welfare improvement it provides an implicit ranking of alternative prospective situations not only relative to the initial situation but also relative to each other in practice this appears to be how this and other tools of cost benefit analysis are actually used one is interested in knowing not only whether a particular bridge or a particular excise tax will lead to an improvement in welfare but which out of a set of alternative bridges or alternative tax systems will improve welfare the most 1 in this paper we analyze conditions under which the compensating variation can be validly used in this generalized sense these turn out to be precisely the same as conditions previously derived see our 1976 paper for the valid use of consumer s surplus as a welfare measure in our final section we analyze the problem of deriving the generalized equivalent and compensating variations either exactly or approximately from observable demand functions by means of generalizations of or alternatives to consumer s surplus

does legislative turnover adversely affect state expenditure policy evidence from indian state elections the effect of legislative turnover on the size and composition of government expenditures in indian states over the 1980 2000 period is examined the paper finds that excessive turnover in indian state elections results in inefficient government expenditure policy first the higher the turnover the larger the government size second excessive turnover affects the allocative efficiency of government expenditures by skewing the composition of government spending toward pure consumption and away from more productive investment expenditures third the effect of turnover on fiscal policy is not linear public consumption expenditure is convex in turnover while public investment expenditure is concave in turnover

strategic institutional choice voters states and congressional term limits states choices on term limits are quantified as a multiple categorical variable capturing variation in the type of limits passed measures of relative political influence in congress explain much of this variation using 1992 data on the american states the model controls for unobserved heterogeneity due to voter access to direct democracy in some states at 2002 values for congressional tenure and federal spending the model predicts approximately eight to ten additional states would choose to limit their own members terms but cannot under a supreme court ruling we discuss implications for institutional federalism and the potential passage of similar political institutions across the states

welfare measurement in the household production framework the household production approach to consumer behavior developed from the work of gary becker william gorman and kelvin lancaster has considerable descriptive appeal in modelling the decisions of households the approach derives from the observation that households frequently purchase market goods that do not yield utility directly but are combined to produce commodity service flows which the household values thus observed behavior is determined by household production technology as well as by tastes the advantage of this distinction is that we can pose reasonable hypotheses about characteristics of technology though we rarely possess useful a priori information regarding tastes the putative advantages of the household production approach are questioned on empirical and conceptual grounds by robert pollak and michael wachter 1975 they show that jointness in production or nonconstant returns to scale cause implicit commodity prices to depend on both tastes and technology raising serious econometric difficulties in the estimation of commodity demand functions in addition since commodity prices become functions of the commodity bundle consumed the analogy to traditional demand theory breaks down joint production occurs when a good enters several production processes simultaneously or equivalently when a good in one production process also enters directly into the individual s utility function the most common example is time which provides the context for all production processes and is often associated with the production of several commodities simultaneously since joint production in the household is likely to be pervasive the critique by pollak and wachter cannot be ignored in response to the comment by william barnett pollak and wachter 1977 suggest dispensing with the notion of commodity prices and treating the demand for commodities as a function of goods prices this approach confounds tastes and technology but it eliminates the troublesome concept of commodity prices as parameters when in fact they are likely to be endogenous in this paper we show that results from positive analysis such as the critique by pollak and wachter have implications for the use of the household production framework for welfare analysis the household production function approach has had considerable appeal for measuring welfare effects of public actions in the environmental and natural resource areas gardner brown john charbonneau and michael hay elizabeth wilman yet traditional approaches to welfare measurement are frequently inapplicable we argue that welfare measurement in this framework is complicated by the difficulties of unravelling tastes and technology we extend pollak and wachter s results by demonstrating that marshallian demand functions for commodities cannot be uniquely defined thus marshallian functions cannot be used to derive exact compensated functions in the manner of jerry hausman and of george mckenzie and i f pearce nor can compensating and equivalent variation measures be bounded by marshallian consumer s surplus estimates following robert willig in fact duality results that normally allow us to move between marshallian and hicksian functions are not assistant and associate professors respectively department of agricultural and resource economics university of maryland college park md 20742 this paper is scientific article no a3404 contribution no 6476 of the maryland agricultural experiment station we wish to thank darrell hueth james opaluch v kerry smith and elizabeth wilman for comments on an earlier draft

reconciling voters behavior with legislative term limits a puzzle exists over why voters continually re elect their congressional and state representatives although these same voters often support initiatives to limit the number of terms that their legislators may serve residents of california colorado and oklahoma voted in 1990 to limit the terms of their state legislators to tenures ranging from six to twelve years 1 in california these same voters however re elected 87 of 91 or 96 percent of all incumbent state representatives and senators whose terms they sought to limit 2 among re elected incumbents 67 or 77 percent had served as long as or longer than the maximum term prescribed under their state s term limit initiative voters defeated only two incumbents who would have been removed under the terms of california s tenure restrictions had they been in effect similar voter behavior characterized recent state elections in colorado and oklahoma 3 more generally these seemingly contradictory voter preferences also are apparent in public opinion polls at the federal level while 62 percent of voters immediately prior to the 1990 general elections indicated their intentions to reelect their congressman that same poll showed that only 24 percent said they approve of the way congress is handling its job gallup and newport 1990 pp 36 37 support for term limit initiatives and the low public esteem of legislators as a group both appear to be inconsistent with voters strong preferences for their own representative and the regular reelection of incumbents

shifting foundations of agricultural policy analysis welfare economics when risk markets are incomplete the neat alignment of resources output and prices specified by the perfect competition model is far from duplicated in free markets and the equally neat alignment assumed under the constraints of a program is not experienced when programs are in effect in particular areas under empirically determined supply curves are unlikely to represent opportunity costs the basic theory is invaluable in providing a conceptual orientation for the analysis of programs but the assumptions implicit in the literal use of simple forms of it for policy conclusions are breathtakingly heroic

modeling quantity discounts under general price sensitive demand functions optimal policies and relationships this paper presents models for determining optimal all unit and incremental quantity discount policies and investigates the effect of quantity discounts on increasing demand and ensuring pareto efficient transactions under general price sensitive demand functions the paper develops optimal quantity discount policies investigates their interrelationships and their benefits to both the supplier and the buyer and gains managerial insights for the scenarios of maximizing the supplier s profit and the joint profit we develop simple and efficient solution approaches for determining the all unit and the incremental optimal decision policies for general price sensitive demand functions we have three main findings first with price sensitive demand there are two incentives in offering quantity discounts increasing demand and ensuring pareto efficient transactions in most cases increasing demand dominates in justifying the offering of quantity discounts second using a single lot size associated with all efficient transactions as with the constant demand case does not hold with the price sensitive demand case third the optimal all unit quantity discount policy is equivalent to the optimal incremental quantity discount policy in benefiting both the supplier and the buyer

coordinating ordering and pricing decisions in a two stage distribution system with price sensitive demand through short term discounting abstract we consider a short term discounting model in which the distributor offers a discounted price for the retailers orders placed at the beginning of its replenishment cycle in a non cooperative distribution system with one distributor and multiple retailers each facing price sensitive demand we examine the value of the price discount strategy as a mechanism for the distributor to coordinate the retailers ordering and pricing decisions under two common types of demand linear demand in price and constant elasticity demand in price our numerical study reveals that in the presence of homogeneous retailers namely retailers with identical demand rates the distributor s profit improvement due to coordination generally decreases as the number of retailers or the inventory holding cost rate increases but increases as price elasticity increases although an increase in the inventory holding cost rate has a negative effect on the distributor s profit it may have a positive effect on the retailers profits we further find that with heterogeneous retailers namely retailers with different demand rates offering a discounted price under linear demand benefits the distributor when both the inventory holding cost rate and the variation in demand are either small or large this cross effect however is absent under constant elasticity demand

seniority political experience and support for government spending in the us house a culture of spending payne 1991a postulates that there is a culture of spending in the us congress whereby members of congress are socialized to increase their roll call support for more spending as a function of length of service and exposure to the washington culture in this article we develop and test an expanded model of roll call voting on spending matters focusing on two potential sources of socialization effects 1 exposure to the washington culture of spending primarily through seniority and proximity to washington dc and 2 previous political experiences developed before members are elected to congress using data for us house members from the 93rd through the 107th congresses we estimate a series of models in which we explain national taxpayer union scores as a function of seniority previous political experience personal attributes and a range of constituency variables we find strong and consistent seniority and political experience effects with senior members and those with extensive political experience more likely to support greater spending than other members these findings withstand a range of robustness tests

rent extracting tariffs and the management of exhaustible resources this paper examines the interaction between a resource exporting and a resource importing country the exporting country must choose the optimal rate of depletion of an exhaustible resource and also must decide on the allocation of the extracted resource between exports and domestic use optimal management from a national point of view entails inefficiency from a global perspective in that too little resource is exported as the supplying country exploits its monopoly power the importing country however has an incentive to extract some of the resource rent by using a tariff although rent extraction is limited by the exporter s ability to use the resource domestically the optimal tariff is positive and induces greater overall inefficiency

the political economy of benefits and costs a neoclassical approach to distributive politics this essay offers a rational political explanation for the notorious inefficiency of pork barrel projects with an optimization model of legislative behavior and legislative institutions the model emphasizes the economically arbitrary from a welfare point of view importance of the geographic incidence of benefits and costs owing to the geographic basis for political representation we explore the implications of a legislator s objective function and derive conditions under which a representative legislature will select an omnibus of projects each of which exceeds the efficient scale

on capturing oil rents with a national excise tax this paper argues that since the supply of oil in the ground is inelastic the incidence of a sales tax on oil maintained forever at a fixed rate would fall entirely on the oil suppliers in the world economy however the elasticity of supply of oil to a single country depends on that country s imports as a share of world output and on the elasticity of demand for that country the paper calculates optimal tax rates for a country as a function of these variables and estimates optimal oil tax rates for the u s for some oecd countries separately and for the u s plus the oecd collectively current u s tax rates are shown to be far below optimal values

the relationship between congressional spending and tenure with an application to term limits whether term limits would increase or decrease federal spending depends on the reason for the causal relationship between tenure and spending we investigate this subject by empirically studying congressional spending and tenure for all united states house and senate members who entered congress between the 94th and 102nd congresses 1975 1992 as our measure of congressional spending we use the national taxpayers union s congressional spending scores our study finds that a statistically significant relationship exists between congressional spending and tenure for some groups of congressmen we then test three hypotheses relating tenure and spending no single hypothesis is consistent with all of our empirical results nevertheless the small sizes of the empirical effects estimated in this study suggest that term limits would have an inconsequential impact on the level of federal spending at least via the moral hazard mechanisms described in this paper

quantity discounts managerial issues and research opportunities marketing managers frequently administer pricing policies involving substantial quantity discounts however our understanding of the precise role of these discounts and their design is quite limited this paper reviews and integrates the economics and marketing literature and presents a detailed analysis of the policies of four firms in order to i specify the variety of motivations for quantity discounts ii provide guidelines to managers in designing quantity discount schedules and iii set out the most fruitful directions for future research

a stochastic and asymmetric information framework for a dominant manufacturer supply chain abstract consider a dominant manufacturer wholesaling a product to a retailer who in turn retails it to the consumers at p unit the retail market demand volume varies with p according to a given demand curve this basic system is commonly modeled as a manufacturer stackelberg ms game under a deterministic and symmetric information det sym i framework we first explain the logical flaws of this framework which are i the dominant manufacturer leader will have a lower profit than the retailer under an iso elastic demand curve ii in some situations the system s correct solution can be hyper sensitive to minute changes in the demand curve iii applying volume discounting while keeping the original ms profit maximizing objective leads to an implausible degenerate solution in which the manufacturer has dictatorial power over the channel we then present an extension of the stochastic and asymmetric information sto asy i framework proposed in lau and lau lau a lau h s 2005 some two echelon supply chain games improving from deterministic symmetric information to stochastic asymmetric information models european journal of operational research 161 1 203 223 coupled with the notion that a profit maximizing dominant manufacturer may implement not only ms but also pm i e using a manufacturer imposed maximum retail price we show that this new framework resolves all the logical flaws stated above along the way we also present a procedure for the dominant manufacturer to design a profit maximizing volume discount scheme using stochastic and asymmetric demand information using our sto asy i framework to resolve the logical flaws of the det sym i framework also reveals two noteworthy points i the attractiveness of the perfectly legal but overlooked channel coordination mechanism pm and ii volume discounting as a means for the dominant manufacturer to benefit from information known only to the retailer

multi buyer discount pricing abstract this article gives an exact optimal solution to the problem of finding the optimal discount price and price break quantity for a seller dealing with one buyer it also gives a method for solving the problem when one seller offers a single quantity discount schedule to many buyers the discount is of the all quantity type and the model of the cost structure was originally proposed by crowther

consumer s surplus and welfare change in a simple dynamic model la somme escomptee d equivalents instantanes ou les variations compensees n est jamais un indicateur du bien etre economique exact pour un consommateur dont les preferences sont representees par une fonction utilite inter temporelle croissant

measuring economic welfare new methods preface 1 an introduction to the money metric 2 the marginal utility of money as an integrating factor 3 calculation of the money metric 4 the approach of dupuit and marshall 5 the hicksian approach 6 approximations based on consumer surplus 7 a reconsideration of the theory of index numbers 8 the money metric as a basis for calculation of social welfare functions 9 measurement of the social costs of monopoly 10 a final comment and conclusion references index

an optimization approach for supply chain management models with quantity discount policy abstract owing to the difficulty of treating nonlinear functions many supply chain management scm models assume that the average prices of materials production transportation and inventory are constant this assumption however is not practical vendors usually offer quantity discounts to encourage the buyers to order more and the producer intends to discount the unit production cost if the amount of production is large this study solves a nonlinear scm model capable of treating various quantity discount functions simultaneously including linear single breakpoint step and multiple breakpoint functions by utilizing the presented linearization techniques such a nonlinear model is approximated to a linear mixed 0 1 program solvable to obtain a global optimum

consumer s surplus without apology the purpose of this paper is to settle the controversy surrounding consumer s surplus and by so doing to validate its use as a tool of welfare economics i will show that observed consumer s surplus can be rigorously utilized to estimate the unobservable compensating and equivalent variations the correct theoretical measures of the welfare impact of changes in prices and income on an individual i derive precise upper and lower bounds on the percentage errors of approximating the compensating and equivalent variations with consumer s surplus these bounds can be explicitly calculated from observable demand data and it is clear that in most applications the error of approximation will be very small in fact the error will often be overshadowed by the errors involved in estimating the demand curve the results in no way depend upon arguments about the constancy of the marginal utility of income consequently this paper supplies specific empirical criteria which can replace the apologetic caveats frequently employed by those who presently apply consumer s surplus moreover the results imply that consumer s surplus is usually a very good approximation to the appropriate welfare measures to preview below i establish the validity of these rules of thumb for a

legislative term limits and state spending supporters of legislative term limits often claim that they will lower state spending levels using fiscal data from 48 states from 1977 to 2001 this paper finds little support for this assertion instead this analysis finds that states with term limits have higher spending levels than states without term limits these results suggest that term limits give legislators greater incentives to deviate from socially optimal fiscal policy by altering the legislative environment in which such policy is formulated

legislator voting and shirking a critical review of the literature we set out to critically review the progress in answering two related questions what determines how legislators vote and how can shirking by legislators be measured in the first category the hypothesis that legislators shirk in order to indulge their personal ideological preferences has led researchers astray the theoretical underpinning is shaky on two counts first legislators who indulge their preferences at the expense of their constituents preferences put themselves at a competitive electoral disadvantage second the original two stage procedure used to measure ideological shirking is severely flawed among many other problems the residual measure of shirking implicitly assumes that the median voter is the relevant constituent principal for the legislator agent

a test for pure or apparent ideology in congressional voting a politician s preferences do matter he is not simply a captured agent speaking only for his constituent s interests some latitude exists for him to shirk his responsibility to serve his constituents interests and to cast votes consistent with his own personal ideology more important to our understanding and modeling of voting behavior shirking for ideological consumption is seen to increase with age once a threshold of about 53 years old is reached shirking is not a phenomena of the politicians final term in office rather it likely exists in every term and begins to increase significantly two terms prior to the expected horizon sixty percent of the sample of senators were seen to exhibit increasing ideological consumption with age

trade and depletable resources the small open economy a two sector two factor small open economy intertemporal trade model is examined in which one of the factors is an exhaustible resource unlike the static model complete specialization in production will occur at any date with the economy switching at some date from resource intensive goods to less resource intensive goods a complete set of comparative dynamic results for the model are given one surprising result is that an increase in the price of the resource intensive good leads to a reduction in the quantity of output supplied at each date but an increase in the length of time over which the economy specializes in resource intensive production commerce international et ressources epuisables le cas d une petite economie ouverte l auteur developpe un modele de petite economie ouverte a deux secteurs et avec deux facteurs de production dont l un est une ressource epuisable c est un modele qui met l accent sur le commerce international en contexte intertemporel et dynamique contrairement a ce qui se produit en contexte statique il y a a tout moment specialisation complete de la production l economie se d6placant a certains moments de la production de biens dependant plus ou moins de la ressource epuisable le memoire presente un ensemble de resultats de dynamique comparee a partir du modele un resultat surprenant est que une augmentation dans le prix du bien dependant le plus de la ressource epuisable entraine une r6duction de la quantite produite a chacune des periodes mais aussi un accroissement dans la longueur de la periode de specialisation de l economie dans la production de ce bien

effects of a demand curve s shape on the optimal solutions of a multi echelon inventory pricing model abstract when a price demand relationship is needed in inventory pricing models very often a convenient typically linear function is arbitrarily chosen the common wisdom implication is that any downward sloping demand curve would lead to similar conclusions this paper applies different demand curve functions to a simple inventory pricing model and shows that while the common wisdom implication is valid for a single echelon system assuming different demand curve functions can lead to very different results in a multi echelon system in some situations a very small change in the demand curve appearance leads to very large changes in the model s optimal solutions other significant but counter intuitive effects of the demand curve form are also revealed this paper does not completely resolve the difficulties revealed by the counter intuitive effects reported here but establishing the existence of these effects represents a first step towards developing procedures to handle such effects these procedures will be necessary to ensure the reliability of many multi echelon models for products having price sensitive demands

inventory investment product cycles and the imperfectly competitive firm we consider a profit maximizing imperfectly competitive firm with downward sloping demand functions that can produce multiple products at a single facility we show that if the firm dedicates production to a single product both dynamic production which exploits inventory and static production which does not can be optimal we also consider sharing the production facility by multiple products we evaluate the efficiency of scheduling production using simple rotation cycle scheduling and give a condition for guaranteeing optimality of this scheduling rule we conclude by studying when dedicated production is preferred over shared production

a cooperative game theory model of quantity discounts quantity discounts offered by a monopolist are considered in the context of a bargaining problem in which the buyer and the seller negotiate over the order quantity and the average unit price all units and incremental quantity discounts that permit transaction at a negotiated outcome are described the effects of risk sensitivity and bargaining power on quantity discounts are discussed for alternative bargaining models

a model of trade in exhaustible resources what distinguishes exhaustible resources from most other goods is not only their non renewable nature but also a combination of two other important characteristics related to their economic functions in their role as an input resources serve as an esseptial factor in the production of final goods moreover because their usefulness remains intact until they are consumed in the process of production they may also serve as a store of value in the absence of other types of marketable assets this latter characteristic enables the owner of the resource to achieve through optimal resource management his desired time profile of consumption corresponding to these two economic functions are two possible motives for international trade in exhaustible resources first in connection with their role as a productive input trade in resources promotes efficiency in the allocation of factors of production throughout the world economy on the basis of this motive for trade countries with a relatively high per capita endowment of the resource should be expected to export the resource in exchange for final goods second in connection with their asset function trade in resources may be viewed as a means of achieving efficiency in the intertemporal allocation of consumption goods among countries economies with a relatively high rate of time preference desire a relatively high ratio of current to future consumption accordingly impatient countries might be expected to import consumption goods in exchange for the resource in the present and export consumption goods in the future the interaction between these two motives for trade is examined in the present paper within a simple two period two country model traded objects are assumed to be an exhaustible resource and a single consumption good although the possibility of trade in consumption loans is also considered later in the paper the consumption good is produced in both countries with the aid of labor and the resource because the latter has the dual role of being a productive input as well as a store of value in the model international trade is viewed both as a means of reallocating the world s endowment of the resource so as to ensure

mr smith and the economy the influence of economic conditions on individual legislator voting this paper estimates the influence of macroeconomic conditions on individual legislator voting over time previous work shows legislator voting to be stable over careers in this paper voting on an ideological issue space ada scores and a fiscal issue space ntu scores from 1976 to 2002 exhibits significant short term cyclicality with economic conditions individual legislators polarize by party in response to rising unemployment and converge in response to rising inflation as legislators accumulate tenure they become more ideologically conservative but more fiscally liberal results are also reported on presidential party divided government and region all results are weaker in the senate than in the house

trends in natural resource commodity prices an analysis of the time domain abstract this paper attempts to reconcile the theoretical predictions of increasing real prices for nonrenewable natural resource commodities obtained from hotelling style models with the empirical findings of falling prices for these commodities a theoretical model for relative price movements is derived for the case of exogenous technical change and endogenous change in the grade of ores mined the model suggests a u shaped time path for relative prices the implied price movements are tested for all the major metals and fuels and the model parameters are found to be statistically significant for 11 out of the 12 commodities tested

to join or not to join group purchasing organization a vendor s decision abstract a group purchasing organization gpo is an entity that utilizes collective buying power to obtain significant discounts from vendors which can be suppliers distributors and manufacturers in the healthcare sector it is reported that about 72 of hospital purchases are settled through gpo contracts this paper seeks to examine two critical questions that vendors face 1 business strategy does partnering with a gpo to offer quantity discounts make strategic sense and if so 2 pricing policy what price will yield optimal maximum profits in such a relationship using a linear quantity discount scheme we find that the size of gpo members strongly influences the vendor s decision to contract or not with the gpo furthermore we show that vendors should price their products close to the reservation prices of the gpo members if the vendors indeed wish to pursue such partnerships

pricing strategy for deteriorating items using quantity discount when demand is price sensitive abstract this study develops an optimal pricing and ordering policy for a deteriorating item with price sensitive demand since it usually benefits the vendor more than the buyer when both the buyer and the vendor are integrated a quantity discount pricing strategy is necessary to entice the buyer to accept the alliance a negotiation factor is incorporated to balance the profit sharing between both players sensitivity analysis with the numerical example shows that the integrated total cost is very sensitive to the deterioration rate and the price sensitive parameter the analysis resulted in an increase in the total joint profit therefore it is significant to consider the integrated vendor buyer strategy with quantity discount

an inverse economic lot sizing approach to eliciting supplier cost parameters recent literature on supply chain coordination offers a wide range of game theoretic and optimization approaches that ensure efficient planning in the supply chain but assume that the involved parties have complete information about each other however in reality complete information is rarely available and those models alone do not present any incentive for the parties to reveal their private information e g the cost parameters that they use when solving their planning problems this paper proposes an inverse lot sizing model for eliciting the cost parameters of a supplier from historic demand vs optimal delivery lot size pairs gathered during repeated earlier encounters it is assumed that the supplier solves a single item multi period uncapacitated lot sizing problem with backlogs to optimality to calculate its lot sizes and the buyer is aware of this fact the inverse lot sizing problem is reformulated to an inverse shortest path problem which is in turn solved as a linear program this model is used to compute the ratios of the supplier s cost parameters i e the setup the holding and the backlog cost parameters consistent with all the historic samples the elicited cost parameters can be used as input for various game theoretic or bilevel optimization models for supply chain coordination computational experiments on randomly generated problem instances indicate that the approach is very efficient in predicting future supplier actions from the historic records 2013 elsevier b v all rights reserved

on optimal domestic processing of exhaustible natural resource exports abstract this paper is concerned with the desirability of domestic processing of natural resource exports from a small open economy completely dependent upon these exports in the framework of a malleable capital model where the services of imported capital are needed to process the resource domestically the paper examines the optimal rates of extraction domestic processing and import of capital services in different economic scenarios defined in terms of processing technology cost and market structures presence or absence of taxes and subsidies historical growth in prices etc

measuring option prices from market behavior abstract option prices can be calculated from empirical demand models given knowledge of the utility theoretic structure implied by the demand specifications and the joint density of the random variables consumers face formulas for option price are given for three common weakly complementary demand specifications because it can be difficult to assess behavioral uncertainty and calculate option prices in practice knowledge of the sign of option value is important since it is a guide to the bias from ignoring this type of uncertainty the sign of option value is determined for sources of uncertainty that have proved elusive in previous treatments

time series evidence on shirking in the u s house of representatives this paper presents time series evidence on the voting behavior of members of the u s house of representatives from 1975 to 1990 the empirical results indicate that voting behavior of individual congressmen is remarkably stable over time we find no evidence of economically significant last term effects on voting behavior nor are there important effects of legislative tenure on voting patterns the most significant deviations in voting behavior occur for congressmen who failed to win their reelection bid suggesting that sizable deviations from previous policy positions may result in swift retribution by constituents in the district

channel coordination and quantity discounts this paper presents a model for analyzing the impact of joint decision policies on channel coordination in a system consisting of a supplier and a group of homogeneous buyers the joint decision policy characterized by the unit selling price and the order quantity is coordinated through quantity discounts and franchise fees both the annual demand rate and the operating cost including the purchase ordering and inventory holding costs depend on the joint decision policy employed this paper contributes by integrating work addressing quantity discounts on inventory and ordering policies and work focusing on the control mechanism provided by quantity discounts in channel coordination it is shown that the optimal all unit quantity discount policy is equivalent to the optimal incremental quantity discount policy in achieving channel coordination furthermore it is shown that quantity discounts alone are not sufficient to guarantee joint profit maximization the analyses of the general models are illustrated by specific analytical results obtained for a given demand function