a multiobjective approach to vendor selection abstract purchases from vendors involve significant costs for many firms decisions related to these purchases include the selection of vendors and the determination of order quantities to be placed with the selected vendors such decisions are frequently multiobjective in nature that is they are evaluated by more than one criterion at least 23 criteria for various vendor selection problems have been identified in this article we present a multiobjective approach to systematically analyze the inherent tradeoffs involved in multicriteria vendor selection problems the approach is motivated by and demonstrated with an actual purchasing problem facing a division of a fortune 500 company

a weighted additive fuzzy multiobjective model for the supplier selection problem under price breaks in a supply chain abstract supplier selection is one of the most critical activities of purchasing management in a supply chain because of the key role of supplier s performance on cost quality delivery and service in achieving the objectives of a supply chain supplier selection is a multiple criteria decision making mcdm problem that is affected by several conflicting factors depending on the purchasing situations criteria have varying importance and there is a need to weight criteria in practice for supplier selection problems most of the input information is not known precisely in these cases the theory of fuzzy sets is one of the best tools for handling uncertainty the fuzzy multiobjective model is formulated in such a way as to simultaneously consider the imprecision of information and determine the order quantities to each supplier based on price breaks the problem includes the three objective functions minimizing the net cost minimizing the net rejected items and minimizing the net late deliveries while satisfying capacity and demand requirement constraints in order to solve the problem a fuzzy weighted additive and mixed integer linear programming is developed the model aggregates weighted membership functions of objectives to construct the relevant decision functions in which objectives have different relative importance a numerical example is given to illustrate how the model is applied finally the conclusions and recommendations are presented

order splitting with multiple capacitated suppliers this paper studies an integrated decision making model for a supply chain system where a manufacturer faces a price sensitive demand and multiple capacitated suppliers two issues that are often considered separately in the literature the goal is to maximize total profit by determining an optimal selling price and at the same time acquiring enough supplying capacity the problem is proved to be np hard in the ordinary sense a heuristic algorithm and an optimal dynamic programming algorithm are developed computational experiments are conducted to study the efficiency and effectiveness of the algorithms some managerial insights are observed

fuzzy multiobjective linear model for supplier selection in a supply chain abstract within new strategies for purchasing and manufacturing suppliers play a key role in achieving corporate competition hence selecting the right suppliers is a vital component of these strategies in practice vagueness and imprecision of the goals constraints and parameters in this problem make the decision making complicated in spite of the importance of the problem the literature on this subject is relatively scarce in this paper a fuzzy multiobjective linear model is developed to overcome the vagueness of the information for the first time in a fuzzy supplier selection problem an asymmetric fuzzy decision making technique is applied to enable the decision maker to assign different weights to various criteria the model is explained by an illustrative example

economic measurement progress and challenges the national income accounts together with the source data which they use form the core of our economic measurement system the development of the concepts and measurements of national income are among the most important achievements of modern economics replacing the older notions of national wealth of the physiocrats and mercantilists for example is national income and product confined to market activity the appropriate fundamental concept yes but we ask a lot of national income and product accounting it is used most importantly to gauge economic progress how much better off are we than our parents or grandparents is the economy growing adequately slowly or rapidly in recent years and are we at a cyclical turning point the information requirements of course will differ depending on the question gaps in inventory measurement may be an appropriate resource claimant to those interested in cyclical issues whereas finding identifying and incorporating new products and quality change more rapidly may be far more significant to long term economic growth we also tend to have a survivor selection bias in our concern with the speed with which new ideas and concepts are incorporated into the national accounts and other data series superlative indexes hedonic regression methods for quality change and many others were much more obvious after some years of diffusion throughout the profession than at their inculcation as a result the gap between major suggested improvements and their adoption by statistical agencies can be extensive often decades erwin diewert 1999 should national accounts be extended to nonmarket activity nonmarket work time is perhaps the most important area for supplemental information natural resources and the environment are close behind william d nordhaus and edward kokkenlenberg 1999 r d capital environmental capital human capital and other intangibles are high priority items but should be dealt with in the form of satellite accounting so i applaud the bea s recent initiatives in this direction i come to this conclusion for a variety of reasons not to suggest that technological capital and human capital are less important than tangible capital in fact perhaps quite the opposite they are all complementary boskin and lawrence lau 2000 but the issues in definition classification and measurements are still more problematic for these items than for traditional items and therefore i believe they should not be added directly to the national income and product accounts nipa in short my own view is that substantial improvements can and should be made in the traditional domain of the national accounts improvements in the core national accounts should not be sacrificed to a proliferation of satellite accounts in principle we should do both and sufficient resources should be provided to accomplish these tasks

an improved model for supplier selection under capacity constraint and multiple criteria abstract ghodsypour and o brien 2001 the total cost of logistics in supplier selection under conditions of multiple sourcing multiple criteria and capacity constraint international journal of production economics 73 1 15 27 study multiple sourcing problem with multiple criteria and capacitated suppliers considering the buyer s quality requirements as a constraint they develop a mixed integer non linear programming model to find the least cost cyclic ordering policy for the buyer they propose to solve the model by enumerating over all possible supplier combinations although the problem is interesting and their analysis is correct we point out two issues with their assumptions namely capacitated suppliers and cyclic ordering policy we discuss two different capacitated supplier settings i long run average annual capacity and ii exact annual capacity first under long run average annual capacity assumption we propose a model which provides the same or a better solution and is much easier to solve than their model then we discuss how to modify our and their models to handle exact annual capacity assumption

purchasing raw materials with uncertain fluctuating prices on identifie les differentes etapes de la decision d achat des matieres premieres ainsi que les differentes approches et les aptitudes requises on decrit plusieurs methodes et modeles proposes et appliques aux differentes etapes les aspects importants etant l inadequation des modeles de stocks classiques l application de la programmation lineaire au probleme de melange la prevision des prix a l aide de l econometrie et de l analyse des series temporelles et la prise de decision sequentielle pour l achat au jour le jour

a serial inventory system with supplier selection and order quantity allocation given the prevalence of both supplier selection and inventory control problems in supply chain management this article addresses these problems simultaneously by developing a mathematical model for a serial system this model determines an optimal inventory policy that coordinates the transfer of items between consecutive stages of the system while properly allocating orders to selected suppliers in stage 1 in addition a lower bound on the minimum total cost per time unit is obtained and a 98 effective power of two pot inventory policy is derived for the system under consideration this pot algorithm is advantageous since it is simple to compute and yields near optimal solutions

supply chain focus dependent supplier selection problem increasing globalization diversity of the product range and increasing customer awareness are making the market s highly competitive thereby forcing different supply chains to adapt to different stimuli on a continuous basis it is also well recognized that overall supply chain focus should be given an overriding priority over the individual goals of the players if one were to improve overall supply chain surplus among all the possible order winners cost and responsiveness seem to be the most significant metrics based on which majority of the supply chains compete with each other supplier selection problem is one of the crucial problems that need to be addressed in configuring a supply chain that could have far reaching ramifications on the total supply chain costs and order winnability our model that considers inventory costs and the supply chain cycle time reduction costs would aid a supply chain manager to make informed decisions with regard to supplier selection problem at any stage dependent upon the priorities attached to supply chain costs and cycle time inventory related costs and responsiveness related costs are the two primary cost elements that are considered in this model we are also making use of a novel dimensionless quantity called the coefficient of inverse responsiveness that not only facilitates the introduction of responsiveness related costs into the model but also improves the scalability and simplifies the analysis and interpretation of the results based on the strategic model developed we offer some very interesting managerial insights with respect to the effect of cost efficient operations and or location and cost of volume related flexibility at a stage on alternate suppliers which in turn affects the overall supply chain performance

compensating differentials in emerging labor and housing markets estimates of quality of life in russian cities abstract the purpose of this paper is to see if an equilibrium model of compensating differences for amenities can be applied to a major transition economy russia we analyze russian labor and housing markets using data from the russian longitudinal monitoring survey rlms augmented by city and regional specific characteristics from other sources our estimated wage and housing value equations suggest that workers are compensated for differences in climate environmental conditions ethnic conflicts crime rates and health conditions after controlling for worker characteristics occupation industry and economic conditions and various housing characteristics we find evidence that these compensating differentials exist even after controlling for the regional pay differences regional coefficients used by the russian government to compensate public sector workers for living in regions that are designated as less desirable quality of life as measured by a group of eleven amenities varies substantially the highest ranked cities tend to be in relatively warm areas and areas in the western european part of the country our quality of life index is positively correlated with net migration into a region suggesting workers are attracted to amenity rich locations overall we find that a model of compensating differentials with controls for disequilibrium yields useful information about compensation for location specific amenities and quality of life in this large transition economy

the voting analytic hierarchy process method for selecting supplier abstract supplier selection has received extensive attention in supply chain management yahya et al j oper res soc 50 1999 916 930 integrate a collaborative purchasing programme where one of the aims is to select suppliers they illustrate a new approach based on the use of saaty s analytic hierarchy process ahp method that was developed to assist in multi criteria decision making problems in order to decide the total ranking of the suppliers we compare the weighted sum of the selection number of rank vote after determining the weights in a selected rank this investigation presents a novel weighting procedure in place of ahp s paired comparison for selecting suppliers it provides a simpler method than ahp that is called voting analytic hierarchy process but which does not lose the systematic approach of deriving the weights to be used and for scoring the performance of suppliers

the income distribution frontier and taxation of migrants abstract the output distribution frontier which traces out the economy s output and income distribution options is used to confirm and explain intuitively the bhagwati hamada results on the taxation of migrants from ldcs by their native country it is shown that freedom of migration without taxation may reduce the welfare of those who remain in the ldc but that taxation and free migration can be superior for them to either prevention of migration or freedom of migration without taxation an externalities argument shows why even migrants may benefit

just in time purchasing single or multiple sourcing abstract we consider two just in time jit purchasing models one utilizing a few sources and the other using the more conventional single source we address the issue of splitting a large order quantity into multiple deliveries taking account of the increase in the aggregate ordering transportation and inspection costs for multiple sourcing we formulate and solve a mathematical programming problem to obtain the optimal selection of suppliers and the size of the split orders for single sourcing we provide a procedure that yields the optimal number of deliveries

integrated fuzzy multi criteria decision making method and multi objective programming approach for supplier selection and order allocation in a green supply chain abstract an organization s environmental performance is affected by its suppliers environmental performance and selecting green suppliers is a strategic decision in order to be more competitive in today s global market the supplier selection problem involves several quantitative and qualitative criteria in the supplier selection process if suppliers have limited capacity or other constraints it is necessary to determine the best supplier and order quantity of each supplier in this paper we present an integrated approach of fuzzy multi attribute utility theory and multi objective programming for rating and selecting the best green suppliers according to economic and environmental criteria and then allocating the optimum order quantities among them at first the fuzzy analytic hierarchy process and fuzzy technique for order preference by similarity to ideal solution is applied in order to analyze the importance of multiple criteria by incorporating experts opinion and to determine the best green suppliers next multi objective linear programming is used to consider and to formulate various constraints such as quality control capacity and other objectives the objective of the mathematical model is simultaneously to maximize the total value of purchasing and to minimize the total cost of purchasing to handle the subjectivity of decision makers preferences fuzzy logic has been applied the efficiency and application of the proposed approach has been illustrated with a case study in an automobile manufacturing company the obtained results help firms establish a systematic approach for tackling green supplier selection and order allocation problems in a realistic situation finally managerial implications conclusions and directions for additional research are introduced

modeling synergies in multi criteria supplier selection and order allocation an application to commodity trading abstract we propose a novel meta approach to support collaborative multi objective supplier selection and order allocation ssoa decisions by integrating multi criteria decision analysis and linear programming lp the proposed model accounts for suppliers performance synergy effects within a hierarchical decision structure it incorporates both heterogeneous objective data and subjective judgments of the decision makers dms representing various groups with different voting powers vps we maximize the total value of purchasing tvp by optimizing order quantity assignment to suppliers and taking into consideration their synergies encountered in different time horizons we apply the proposed model to a contractor selection and order quantity assignment problem in an agricultural commodity trading act company we maximize the strategic effectiveness of both the customers and the suppliers minimize risks increase the degree of cooperation between trading partners on all levels of supply chain integration enhance transparent knowledge sharing and aggregation and support collaborative decision making

multi objective models for lot sizing with supplier selection abstract in this paper two multi objective mixed integer non linear models are developed for multi period lot sizing problems involving multiple products and multiple suppliers each model is constructed on the basis of three objective functions cost quality and service level and a set of constraints the total costs consist of purchasing ordering holding and backordering and transportation costs ordering cost is seen as an ordering frequency dependent function whereas total quality and service level are seen as time dependent functions the first model represents this problem in situations where shortage is not allowed while in the second model all the demand during the stock out period is backordered considering the complexity of these models on the one hand and the ability of genetic algorithms to obtain a set of pareto optimal solutions we apply a genetic algorithm in an innovative approach to solve the models comparison results indicate that in a backordering situation buyers are better able to optimize their objectives compared to situations where there is no shortage if we take ordering frequency into account the total costs are reduced significantly

supplier selection order allocation a two stage multiple criteria dynamic programming approach this paper proposes a two stage multiple criteria dynamic programming approach for two of the most critical tasks in supply chain management namely supplier selection and order allocation in the first stage to address multiple decision criteria in supplier ranking the analytic hierarchy process ahp is employed in the second stage supplier ranks are fed into an order allocation model that aims at maximizing a utility function for the firm as well as minimizing the total supply chain costs subject to constraints on demand capacity and inventory levels a dynamic programming approach is crafted to solve the proposed bi objective model

the concept of income in a general equilibrium this paper derives a concept of aggregate real income for a competitive economy in general equilibrium consisting of heterogeneous infinitely lived people and relates it to current and future consumption possibilities an important characteristic of our measure of income which we call real income is that deflation is carried out using a consumption deflator rather than any price index of output we suggest that it may be inappropriate to regard capital gains as income we also present a coherent treatment of the effects of changes to the terms of trade on real income and explain the implications of this for resourceexporting economies hicks 1939 defined income as the maximum amount a man can spend and still be as well off at the end of the week as at the beginning since then there has been a succession of attempts to apply this definition the problem is as hicks acknowledged that the correct interpretation of as well off is by no means clear weitzman 1976 and asheim 1997 suggest that income is equal to the level of consumption which could be sustained indefinitely out of the capitalized value of current income and equate this to being as well off at the end of the week as at the beginning eisner 1988 argues specifically that in a total incomes system effects arising from asset price changes and conventionally regarded as capital gains should be included with income here building on earlier work by sefton and weale 1996 asheim and weitzman 2001 and pemberton and ulph 2001 we provide a comprehensive account of the implications of the idea that as well off should be understood to mean that the present discounted value of current and future utility should be unchanged over the interval considered we work in the context of a general equilibrium taking the prices established in the general equilibrium as given we first look at income from the production side showing that in an economy where prices and the interest rates satisfy an intertemporal efficiency condition income along an equilibrium path can be interpreted as a weighted average of the value of the current and future consumption bundle plus a term adjusting for changes in the nominal price level converting prices to real prices by deflating by the divisia consumption price index removes the need for this adjustment these results are suggestive first they offer a way of defining the income of a household entirely in terms of its consumption possibilities second they indicate that to calculate real income deflation is best carried out using a price index of consumption this is a substantial divergence from current national accounting practice third because we have assumed constant returns there is a trivial aggregation result that aggregate income is equal to the sum of the incomes from the individual sectors

a general equilibrium model of guest worker migration the source country perspective abstract this paper examines the problem of guest worker migration from an economy populated by identical utility maximizing individuals with finite working lives the decision to migrate the rate of saving while abroad as well as the length of a migrant s stay in the foreign country are all viewed as part of a solution to an intertemporal optimization problem in addition to studying the microeconomic aspects of temporary migration the paper analyses the determinants of the equilibrium flow of migrants the corresponding domestic wage and the level of welfare enjoyed by a typical worker effects of an emigration tax are also investigated

the real real price of nonrenewable resources copper 1870 2000 over the past 40 years economists have devoted considerable effort to estimating long run trends in real commodity prices the results indicate that the real prices for many commodities have fallen suggesting to the surprise of many that resource scarcity is declining over time almost all of this work however uses the u s producer price index or other standard price deflators which recent research shows overestimate inflation for several reasons this article examines copper prices with adjusted deflators designed to eliminate this bias it finds that the trend over time which is significantly downward when no adjustment is made to the deflator displays no tendency in either direction or is significantly upward depending on the magnitude of the deflator adjustment employed these findings suggest that real resources prices provide less support than widely assumed for the hypothesis that resources are becoming more available or less scarce over time

the total cost of logistics in supplier selection under conditions of multiple sourcing multiple criteria and capacity constraint abstract little attention is given in the literature to decisions on the appropriate selection of suppliers and on assigning order quantities to these suppliers in the case of multiple sourcing with multiple criteria and with suppliers capacity constraints only a few mathematical programming models to analyse such decisions have been published to date and these have tended to consider only net price as the cost of purchasing although the costs of transportation ordering and storage may be significantly important to the decision in this paper a mixed integer non linear programming model is presented to solve the multiple sourcing problem which takes into account the total cost of logistics including net price storage transportation and ordering costs buyer limitations on budget quality service etc can also be considered in the model an algorithm is proposed to solve the model and the model is illustrated using a numerical example

vendor selection with price breaks abstract we study the problem of vendor selection where a buyer must choose order quantities to place with vendors in a multiple sourcing network the selection process is influenced by the price delivery and quality objectives of the buyer as well as by the production or rationing constraints of the vendors vendors are assumed to offer price breaks which depend on the sizes of the order quantities each proce break schedule is characterized by two attributes it represents either quantity discounts or surcharges and is either cumulative all units or noncumulative incremental we present linear and mixed binary integer programming models that provide unifying frameworks for models of vendor performance measures from the purchasing literature and models of price breaks from the operations research literature we argue that our models offer viable approaches to vendor selection with price breaks because of the availability of commercial software packages for personal computers that provide flexible and efficient computational tools for solving the models this implies that vendor selection with price breaks can be performed at the fingertips of purchasing managers

new directions in national economic accounting the national income and product accounts nipa are the most important measures of overall economic activity for a nation much as a satellite in space can survey the weather across an entire continent so can the gdp give an overall picture of the state of the economy nevertheless since their inception there have been concerns that the accounts are incomplete and misleading because they omit vast continents of nonmarket activity such as unpaid work the value of leisure time investment in human capital and most recently the environment the threshold question is why should we devote scarce intellectual resources to studying nonmarket sectors the basic insight behind nonmarket accounts is that economic and social welfare does not stop at the market s border but extends to many nonmarket activities three particular areas are worth emphasizing one important reason why we need better measures of nonmarket activity is because we spend increasingly fewer of our lifetime hours in market activities a second and more speculative reason concerns the growing importance or at least the great importance of nonmarket assets or mispriced market assets such as the environment and technology a third point is that current measures of national saving and investment are highly defective the examples later in this paper address each of these issues many of these issues were reviewed in a recent report on augmented accounting by the national academy of sciences see nordhaus and edward kokkelenberg 1999

newsvendor with multiple options of expediting we consider a manufacturer facing single period inventory planning problem with uncertain demand and multiple options of expediting the demand comes at a certain time in the future the manufacturer may order the product in advance with a relatively low cost she can order additional amount by expediting after the demand is realized there are a number of expediting options each of which corresponds to a certain delivery lead time and a unit procurement price the unit procurement price is decreasing over delivery lead time the selling price is also decreasing over time in this paper we assume that the manufacturer must deliver all products to the customer in a single shipment the problem can be formulated as a profit maximization problem we develop structural properties and show how the optimal solution can be identified efficiently in addition we compare our model with the classical newsvendor model and obtain a number of managerial insights

a conceptual exploration and critical inquiry into the theoretical foundation s of economic welfare measures abstract economic welfare measures ewm such as the isew and the gpi are often argued to lack a sound theoretical foundation however we observe that the initial ewm were jointly inspired by hicksian and fisherian income welfare s experiential nature is fisherian inspired whereas seeing the consumption of community capital e g the ecosystem as a cost is hicksian inspired as most scholars do not recognize this double theoretical foundation two distinct welfare interpretations with different time and boundary dimensions are often conflated ewm can be seen as either capturing the benefits and costs experienced or as reflecting the benefits and costs of present economic activities bcpa the former interpretation excludes future costs costs shifted abroad and capital changes as they are not experienced in the present while the latter includes them recent developments reveal that ewm are converging toward the ex post established experiential fisherian foundation formulated by lawn 2003 yet this is not the only way forward as the bcpa view offers an alternative to account for for instance the costs of present activities shifted abroad or to the future whether they are experienced or not to avoid inconsistencies ewm s standardization would greatly benefit from making explicit in future studies which interpretation is taken

migration and optimal income taxes abstract the issue addressed in this paper is the optimal taxation of incomes earned in the home economy and of incomes earned abroad when people can migrate as a preliminary the optimal taxation of home incomes when there is migration and no taxation of foreign incomes is discussed then in a more general setting we deal with optimal taxation of different kinds of labour when another kind of labour is not taxable and show how this bears on the taxation of foreign incomes the last sections of the paper analyse a simple model in which people choose between taxable labour at home taxable labour abroad and untaxable labour a condition is found implying that the optimal tax on foreign income is higher than on the home income of a person of equal utility

tax policy in the presence of emigration recent policy and theoretical discussions of the effects of highly skilled migration from the underdeveloped countries the so called brain drain have focused on a proposal bhagwati 1972 to levy a supplementary income tax on those who migrate the proceeds of such a tax to be transmitted to the developing country of origin or to developing countries en bloc for developmental spending the welfare implications of such a tax were analyzed in an earlier paper of ours bhagwati and hamada 1974 in the context of a model of the country of emigration characterized by sticky wages and harrisstodaro 1971 type of unemployment in subsequent papers the tax has been analyzed also in the context of modified models still incorporating the unemployment phenomena by rodriguez 1975 and mcculloch yellen 1975 2 essentially these models analyze the impact of the income tax on emigrants incomes as arising primarily through the reduced differential

a multicriteria model for assigning new orders to service suppliers abstract this paper describes a multicriteria model developed to support decisions on the assignment of new orders to service suppliers in this case contractors for the construction or renewal of pipeline networks for gas distribution the model comprises two phases i computation of a quota expressed as a percentage of total work orders budget for each supplier ii assignment of each particular order to a supplier selected on the basis of a multi attribute preference index evaluated for each candidate contractor the first phase is executed at the beginning of each year and then reviewed quarterly and the quotas are defined by a two criteria model the prices quoted by the supplier for standard works and the past performance of the constructor given by a performance appraisal system the paper describes the structuring phase of the model as well as the descriptors and corresponding partial value functions used in each stage to perform the evaluation within an additive aggregation framework

a weighted max min model for fuzzy multi objective supplier selection in a supply chain abstract supplier selection is one of the most important activities of purchasing departments this importance is increased even more by new strategies in a supply chain supplier selection is a multi criteria decision making problem in which criteria have different relative importance in practice for supplier selection problems many input information are not known precisely the fuzzy set theories can be employed due to the presence of vagueness and imprecision of information a weighted max min fuzzy model is developed to handle effectively the vagueness of input data and different weights of criteria in this problem due to this model the achievement level of objective functions matches the relative importance of the objective functions in this paper an analytic hierarchy process ahp is used to determine the weights of criteria the proposed model can help the decision maker dm to find out the appropriate order to each supplier and allows the purchasing manager s to manage supply chain performance on cost quality and service the model is explained by an illustrative example

optimal linear income taxation in the presence of emigration abstract this paper examines optimal linear income taxation when individuals are able to escape taxation by migrating a model is presented in which closing the economy to migration must raise the optimal marginal tax however this result may be reversed under an alternative definition of a closed economy

on the choice between capital and labour mobility trade theorists since the pioneering work of kemp 1966 have considered the question of national advantage from international factor mobility by considering only one factor to be so mobile kemp analyzed elegantly the question of optimal policies in 2 x 2 x 2 model and showed that since monopoly power could exist in both the goods and factor markets in consequence of international capital mobility the optimal policy intervention would generally involve two policy instruments tariffs cum subsidies on goods and duties cum subsidies on international capital flows jones 1967 subsequently extended kemp s argument to the secondbest context by examining the optimal level of one of these instruments when the other was arbitrarily set at zero elsewhere in this issue brecher 1983 shows in an elegant and original contribution that the jones policy problem is in fact a third best rather than a second best problem as generally believed and that if only one of the tariff and capital mobility taxes cumsubsidies can be used it is generally possible to improve welfare further by admitting an altogether different domestic policy instrument namely a production or consumption tax cum subsidy as the case may be the research of bhagwati was supported by the german marshall fund grant no l 34015 the problem analyzed in the paper was posed in bhagwati 1979 and an early ingenious and neglected analysis in ramaswami 1968 was noted by bhagwati we have profited greatly from these contributions also from reading webb 1970 ramaswami 1970 and a recent paper of calvo and wellisz 1983 on this problem this result is in consonance with the results of bhagwati ramaswami and srinivasan 1969 for the case without international capital mobility but the consonance is intuitive only after the result was established for the case with international capital mobility