the hyperinflation model of money demand revisited in this paper we propose a test of the hyperinflation model of money demand which is valid under any assumption concerning agents expectations subject only to the restriction that forecasting errors are stationary it is also demonstrated that highly efficient parameter estimates can be obtained and restrictions on them tested under the same weak assumption finally it is shown how these first stage estimates can be utilized to test the stronger assumption of rational expectations the arguments are illustrated by analysis of the classic data on european hyperinflations previously analyzed by cagan 1956 barro 1970 and abel dornbusch huizinga and marcus 1979 copyright 1991 by ohio state university press

budget deficits stability and the monetary dynamics of hyperinflation hyperinflationary processes usually occur in countries with extremely large budget deficits in models of inflationary finance with rational expectations e g buiter 1987 large budget deficits cannot lead to hyperinflation the purpose of this paper is to reconcile the standard theoretical model with the stylized facts it shows that by introducing a lag in the adjustment of the money market into the standard inflationary finance model large budget deficits are indeed the main reason for hyperinflation the paper also provides an explanation for the ineffectiveness of moderate reductions in the deficit in reducing inflation and argues that fiscal lags can be destabilizing copyright 1989 by ohio state university press

determining optimal lot size for a two warehouse system with deterioration and shortages using net present value abstract in this paper we develop a deterministic inventory model for deteriorating items with two warehouses by minimizing the net present value of the total cost deterioration rates of items in the two warehouses may be different in addition we allow for shortages and complete backlogging we then prove that the optimal replenishment policy not only exists but also is unique under some condition further the result reveals that the reorder interval based on the average total cost if it exists must be longer than that derived using net present value finally we use yang s h l yang european journal of operational research 157 2004 344 356 numerical example to illustrate the model and conclude the paper with suggestions for possible future research

multivariate measures of well being and an analysis of inequality in the michigan data we demonstrate a multidimensional approach for combining several indicators of well being including the traditional money income indicators this methodology avoids the difficult and much criticized task of computing imputed incomes for such indicators as net worth and schooling inequality in the proposed composite measures is computed using relative inequality indexes that permit simple analysis of both the contribution of each welfare indicator and its factor components and within and between components of total inequality when the population is grouped by income levels age gender or any other criteria the analysis is performed on u s data using the michigan survey of income dynamics

seigniorage operating rules and the high inflation trap there may be both a high and a low inflation equilibrium when the government finances the deficit through seigniorage under rational expectations the high inflation equilibrium is stable and the low inflation equilibrium unstable under adaptive expectations or lagged adjustment of money balances with rational expectations the low inflation equilibrium may be stable adding bond financing dual equilibria remain if the government fixes the real interest rate but a unique equilibrium is attained when the government sets a nominal anchor for the economy the existence of dual equilibria is thus a result of the government s operating rules

estimating the size of the shadow economy in spain a structural model with latent variables there has recently been a revival of international interest in measuring the size of the shadow economy the current study adopts an approach to the spanish case that is based on the theory of unobservable variables this methodology involves the estimation of structural models mimic which analyses a set of causes of the shadow economy while simultaneously taking into account its influence upon a series of indicators the proposed model permits the determination of a relative evolution over time of the size of the shadow economy which requires the calibration of the model with an exogenous estimation in order to obtain real values the exogenous estimation employed is that obtained by a monetary method based on a money demand function the results show a considerable shadow economy measuring between 8 and 18 8 of gdp in the period 1976 2002 and demonstrate that the shadow economy is significantly influenced by the tax burden the degree of regulation and unit labour costs a positive correlation is

unobserved rational expectations and the german hyperinflation with endogenous money supply a kalman filtering technique is employed to test the convergent expectation hypothesis in the great german hyperinflation when the money supply is endogenously determined after converting the model structure to a state space form the parameters are estimated via minimization of a gaussian likelihood function the result is then used in a filter smoother combination to yield smoothed estimates of the state variable associated with the arbitrary constant of the rational expectations solution bo th para metric and nonparametric tests lead us to reject the null hypothesis of convergent expectations copyright 1987 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

slipping into and out of poverty the dynamics of spells this paper examines the dynamics of poverty previous analyses have examined either fluctuations in the male heads earnings or the frequency of poverty periods over a fixed time frame our approach depends on a definition of spells of poverty using this methodology we find that the majority of poor persons at any time are in the midst of a rather long spell of poverty the methodology also allows us to estimate that less than 40 percent of poverty spells begin because of a drop in the heads earnings while 60 percent of the spells end when the heads earnings increase thus researchers must focus on household formation decisions and on the behavior of secondary family members there has been a dramatic resurgence recently of discussion of the underclass the discussion is reminiscent of debates about poverty during the 1960s when the notions of a culture of poverty particularly as popularized by michael harrington s other america 1962 dominated both intellectual and policy thinking the idea of an underclass seems inconsistent however with much of the research on the dynamics of poverty during the 1970s that research using new longitudinal data seemed to show that the bulk of the poor were poor for only a few years the research also showed that the poor were a very heterogeneous group including a small minority of persistently poor the persistence of poverty is of interest both for understanding the phenomenon and for developing policy claims about dependency and separate life styles among the poor rest on assumptions about the long term nature of poverty questions

on measuring deprivation and the standard of living in a multidimensional framework on the basis of aggregate data in measuring social deprivation in a multidimensional framework ideally one should first measure each individual s overall deprivation and then aggregate the overall deprivation levels of all individuals however given only aggregate data one is often forced to measure social deprivation in terms of each attribute separately and then to aggregate them so as to get the overall social deprivation this paper shows that it is only under extremely stringent conditions that this procedure would always yield the same result as the conceptually sound procedure referred to earlier a similar difficulty also arises in measuring a society s standard of living

identifying deprivation profiles in spain a new approach usually an indirect approach for measuring deprivation or poverty is used with poverty lines however some studies have used a direct approach to measure deprivation or poverty the aim of this study is improving the identification of the poor people the central point of the concept of deprivation used is related to the opportunity to have or do something therefore deprivation means an inability to get the goods facilities and opportunities which are usual in the household environment since all of the needed variables are categorical the latent class model is used to solve this problem because it is the best model to achieve this objective

the earnings of male immigrants in england evidence from the quarterly lfs in this paper we estimate earnings functions for native born and foreign born white and non white males in the english labour market using data from the quarterly labour force survey our results highlight the importance of distinguishing between native born and foreign born males when investigating the labour market experience of ethnic minorities furthermore the earnings performance amongst white immigrants varies considerably

testing for rational bubbles with exogenous or endogenous fundamentals the german hyperinflation once more abstract the presence of rational price bubbles during the german hyperinflation is tested under two different structural assumptions on the money process if the money supply is constrained to be exogenous to the current inflation rate the hypothesis of no bubble can be rejected however this is no longer found to be true when a feedback rule from inflation to money creation is allowed the analysis contradicts previous results presented in the literature

a deterministic order level inventory model for deteriorating items with two storage facilities abstract in this paper a deterministic inventory model is developed for a single deteriorating item which is stored in two different warehouses a rented warehouse is used to store the excess units over the fixed capacity w of the own warehouse the rented warehouse is assumed to charge higher unit holding cost than the own warehouse but to offer a better preserving facility resulting in a lower rate of deterioration for the goods than the own warehouse the optimal stock level for the beginning of the period is found and the model developed is shown to agree with the order level model for non deteriorating items with a single storage facility an illustration to show the applicability of the model is also presented

integrating deterioration and lifetime constraints in production and supply chain planning a survey abstract items with short lifetimes that are subject to deterioration are important in the business world research has a long tradition in integrating deterioration and value loss effects into mathematical models for inventory planning and control where such effects are understood as a general loss or shrinkage of inventory however there has been little work in the modeling of lifetime restrictions of items to prevent wastage and disposals especially in a dynamic planning context globalization and other trends extend the consideration of single companies to whole supply chains implying increased coordination and information needs this is important as planning decisions impact lead times and thus the quality of items in the whole supply chain products that exceed their useful lifetime can impose high costs due to inventory loss or the need to rework them this implies increased utilization of scarce resources e g machine time metals and or energy thereby increasing co 2 levels we survey the state of the art regarding depreciation effects and the modeling of lifetime constraints as well as a classification of models following business planning functions of the value chain a critical evaluation of approaches and their limitations is provided highlighting directions for future research

poverty and the distribution of material hardship public concern with poverty derives in large part from the assumption that low income families cannot afford necessities yet official poverty statistics focus on measuring income not on measuring material hardship two surveys of chicago residents measure whether families could afford food housing and medical care a family s official income to needs ratio explained 24 percent of the variance in the amount of material hardship it reported adjustments for family size age health noncash benefits home ownership and access to credit explain another 15 percent variations in permanent income explain almost none of the remaining variance in hardship among families with the same official income toneeds ratio material hardship varies by age family size and composition

how did the great recession affect gender disparity in europe an analysis by a multidimensional deprivation approach this paper analyses how the great recession affected the gender disparity in material and social deprivation in europe we propose multidimensional non monetary indexes of absolute and relative i

review of inventory systems with deterioration since 2001 abstract this paper presents an up to date review of the advances made in the field of inventory control of perishable items deteriorating inventory the last extensive review on this topic dates back to 2001 goyal s k and giri b c recent trends in modeling of deteriorating inventory european journal of operational research 134 1 16 since then over two hundred articles on this subject have been published in the major journals on inventory control indicating the need for a new review we use the classification of goyal and giri based on shelf life characteristics and demand characteristics contributions are highlighted by discussing main system characteristics including price discounts backordering or lost sales single or multiple items one or two warehouses single or multi echelon average cost or discounted cash flow and payment delay

an alternate method of estimating the cagan money demand function in hyperinflation under rational expectations abstract an alternate method of estimating the cagan money demand function under rational expectations is presented the technique utilizes the side assumptions that 1 accurate contemporaneous information on the price level and money stock is available to individuals and 2 unobservable noise in the portfolio balance schedule is neglible the procedure has three main virtues first it is implemented without imposing restrictions on the money supply process second the procedure is extremely simple and economical third it admits a simple test of a restriction implied by the cagan money demand function results are related to issues in recent hyperinflation studies

stock interest rate risk and inflation shocks abstract in this paper we proceed to estimate a measure of the flow through capability of the firms listed on the spanish stock exchange the flow through capability is defined as the ability of firms to transmit inflation shocks to the prices of the products and services sold by the company according to a strand of the literature this flow through capability can to some extent explain the so called stock duration paradox which is the difference between the theoretical stock duration derived from the ddm model and its empirical estimates the line of reasoning suggests that if a company can pass on inflation shocks to the prices of its own outputs and then to profits and dividends nominal interest rate changes due to variations in the expected inflation will have a limited impact on stock prices so in this paper we first estimate the flow through capability for different industries and find great differences among them then we analyse the link between flow through capability and stock duration and find a significant negative relationship between them as claimed by part of the literature

misspecification versus bubbles in hyperinflation data monte carlo and interwar european evidence abstract this paper analyzes some new tests of the cagan hyperinflation money demand model which have several advantages relative to those in the literature they do not confound specification error with rational bubbles can be implemented with a linear procedure and are frequently able to detect periodically collapsing bubbles which have challenged existing tests after a monte carlo analysis the tests are applied to data from hyperinflations in austria germany hungary and poland evidence of misspecification is found for austria germany and hungary while the model without a rational bubble component appears to fit the data for poland

the german hyperinflation and the demand for money revisited this paper shows that a remarkably well defined demand for real balances exists for the german hyperinflation episode including the final months which have previously been considered as outliers the authors econometric analysis exploits the theory of cointegration given the obvious nonstationarity of the data further they consider two likely sources of misspecification income variability and the necessity to distinguish between the high inflation and hyperinflation episodes copyright 1994 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

cointegration and cagan s model of hyperinflation under rational expectations when money and prices are integrated of order two philip cagan s 1956 model of hyperinflation will give rise to two different levels of cointegration in most of the literature on the german hyperinflation one of these cointegrating relationships has been ruled out a priori by assuming that velocity shocks follow a random walk using data from the german hyperinflation the author finds this assumption to be unjustified based on a straightforward extension of the cointegrated var approach suggested by john y campbell and robert j shiller 1987 a method to evaluate the cagan model under rational expectations and no bubbles is proposed and implemented to the german data copyright 1993 by ohio state university press

a deterministic order level inventory model for deteriorating items with two storage facilities abstract sarma 3 developed an inventory model for a single deteriorating item which is stored in two different warehouses an owned warehouse ow and a rented warehouse rw the rented warehouse is used for storing the excess units over the fixed capacity w of the ow and is assumed to offer better preserving facilities than the ow resulting in a lower rate of deterioration also the rw is assumed to charge higher holding cost than the ow in his paper sarma obtained an optimal replenishment schedule when the demand rate is constant over a fixed cycle length where the ow has to stock a specified known quantity in this paper we relax the assumptions of fixed cycle length and known quantity to be stocked in the ow further we find the optimal schedule that minimizes the total cost per unit time in a cycle for an arbitrary demand rate function where cycles are assumed to form a regenerative process we also present numerical examples

impact of trade credit and inflation on retailer s ordering policies for non instantaneous deteriorating items in a two warehouse environment with the advent of better technologies in manufacturing and retail industry consumer beliefs and needs have been altered supermarkets are expected to sell fresh products in good conditions which have a longer shelf life or do not begin to deteriorate immediately termed known as non instantaneous deteriorating items this characteristic is now usually observed in almost all food stuffs fashionable items electronic products among others in order to sustain in the retail sectors the managers are moving forward to store these items in warehouses moreover due to increasing competition in business world supplier offers a permissible delay in payments to retailer in order to increase demand this encourages the retailer to order a large quantity which in turn entitles the organization to rent out an additional storage space considering the importance of such a scenario the present research work develops a two warehouse inventory model for non instantaneous deteriorating items with permissible delay in payments under inflationary conditions shortages are allowed and partially backlogged since customers willingness to wait decreases over time the objective of this paper is to determine the retailer s optimal replenishment policies that maximize the present worth of total optimal profit per unit time finally the proposed inventory model has been validated with the help of numerical example sensitivity analysis of the optimal solution with respect to key parameters of the inventory system has been also presented which provides important managerial implications

multidimensional approaches to poverty measurement an empirical analysis of poverty in belgium france germany italy and spain based on the european panel this article has three goals first we wish to compare three multidimensional approaches to poverty and check to what extent they identify the same households as poor second we aim at better understanding the determinants of poverty by estimating logit regressions with five categories of explanatory variables size of the household age of the head of the household her gender marital status and status at work third we introduce a decomposition procedure proposed recently in the literature the so called shapley decomposition in order to determine the exact marginal impact of each of the categories of explanatory variables our empirical analysis is based on data made available by the european community household panel echp we used its third wave and selected five countries belgium france germany italy and spain

the conquest of south american inflation we infer determinants of latin american hyperinflations and stabilizations by using the method of maximum likelihood to estimate a hidden markov model that assigns roles both to fundamentals in the form of government deficits that are financed by money creation and to destabilizing expectations dynamics that can occasionally divorce inflation from fundamentals levels and conditional volatilities of monetized deficits drove most hyperinflations and stabilizations with a notable exception in peru where a cosmetic reform of the type emphasized by marcet and nicolini occurred

the effect of robust growth on poverty a nonlinear analysis previous research has shown that economic growth should help to reduce the rate of poverty however a number of recent studies have found that the economic expansion of the 1980s had no statistically significant effect on aggregate poverty it is shown that both a threshold regression and a fourier approximation provide a better empirical model of poverty than the standard linear model it is noteworthy that the nonlinear specifications show a large and significant effect on poverty of the 1980s expansion

multidimensional housing deprivation indices with application to spain the main aim of this article is to define a multidimensional housing deprivation index and identify the main determining characteristics of this phenomenon using spain as reference a latent variable model is used in order to overcome some of the traditional difficulties encountered in multidimensional deprivation studies the construction of a latent structure model has allowed a set of partial housing deprivation indices to be grouped together under a single index it has also enabled each individual to be assigned to a different class depending on the level and type of deprivation results show that the vector of observed variables having hot running water heating a leaky roof damp walls or floor rot in window frames and floors and overcrowding and the correlations among such variables can be explained by a single latent variable there are also specific characteristics that differentiate the population affected by housing deprivation

inflation tax and money essentiality this chapter addresses the issue of money essentiality using brock s 1975 model we present an argument which casts doubt on the conclusion reached by obstfeld and rogoff 1983 henceforth called o r based on the same theoretical framework according to o r speculative hyperinflation under a pure fiat money regime can be ruled out only when severe restrictions are placed on individual preferences e g agents must have infinitely negative utility when their real balances are zero we argue that this restriction can be tested with data from hyperinflation experiments by looking at the behavior of the inflation tax as real balances approach zero

a deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate abstract a deterministic inventory model for deteriorating items with two warehouses is developed when the replenishment rate is finite demand is at a uniform rate and shortages are allowed it is assumed that the rates of deterioration of item in the two warehouses may be different the model is analysed for the case of continuous release pattern several special cases are discussed and a numerical example is provided to illustrate the variation in optimum inventory level and optimum cost for varying shortage cost

planning for shortages net present value analysis for a deteriorating item with partial backlogging abstract this paper develops inventory models to help answer strategic questions concerning whether planning for shortages offers financial benefits a production inventory system producing a deteriorating product in batches at a finite production rate with partial backordering is considered customers pay a deposit when placing a backorder backordered items receive a discount on the sales price as lost sales may lead to customers not returning the demand rate may depend on the fraction of lost sales we develop a cash flow based profit maximising net present value npv model without the inventory cost parameters commonly used in this context unit holding cost unit backorder cost unit deterioration cost and unit lost sales cost the model finds the optimal inventory policy just like npv models that discount the traditional parameters but has the advantage of not needing to estimate the value of the traditional parameters it is shown that in models based on discounting the traditional parameters the parameters are not exogenously determinable but are non trivial functions of non financial endogenous system parameters such as the production rate annual demand rate and backorder rate extensive numerical experiments illustrate how cash flow npv models provide insights into the value of planning for shortages and strategic choices about the design of the production inventory system it also provides insight into the classical problem of how to interpret unit backorder cost and unit lost sales cost the study indicates that these insights cannot be reliably obtained from npv models based on discounting unit backorder costs and unit lost sales costs

poverty and social exclusion two sides of the same coin or dynamically interrelated processes there is growing interest in the analysis and measurement of social exclusion to complement the static and dynamic literature on income poverty on theoretical grounds social exclusion and income poverty are seen as different processes but with closely interrelated dynamics however our empirical understanding of the way these two processes dynamically interact at the individual level is still very limited to shed some light on the issue we use a dynamic bivariate probit model controlling for unobserved heterogeneity and wooldridge 2005 type initial conditions both the first and second order markov dynamics are examined we estimate the model using the italian sample of the european community household panel echp waves 1 8 and find a sizable extent of state dependence in both poverty and social exclusion moreover there are dynamic cross effects implying that poverty and social exclusion are mutually reinforcing social policies aimed at eradicating poverty and avoiding individuals social

climbing out of poverty falling back in low income stability in spain the study of the probability of entering or escaping a low income spell is not sufficient to fully describe a household s experience in deprivation if poverty spells are recurrent in time the persistency of poverty for a given household is not completely described unless the household s likelihood of a fall back into deprivation shortly after exit is considered it is found that by combining the re entry equation results with those of the exit equation one can discuss in a comprehensive way which household characteristics promote welfare stability or instability and poverty persistence or transience results indicate that one third of households who manage to leave poverty in spain return to it shortly after exit this upward income mobility if maintained for a year appears to enable a state of non poverty for a lengthy period better educated households and households with a spouse are more stable in their income level also the point reached in the income distribution after a jump out of poverty

recurrent hyperinflations and learning we use a model of boundedly rational learning to account for the observations of recurrent hyperinflations in the 1980 s in a standard monetary model we replace the assumption of full rational expectations by a formal definition of quasi rational learning the model under learning matches some crucial stylized facts observed during the recurrent hyperinflations experienced by several countries in the 1980 s remarkably well we argue that despite being a small departure from rational expectations quasi rational learning does not preclude falsifiability of the model it does not violate reasonable rationality requirements and it can be used for policy evaluation

production and inventory model using net present value using the net present value is the standard methodology in theoretical analysis and the most frequently used method for making financial decisions however net present value is rarely used in production and inventory decisions the main reasons appear to be the complexity of the formulae and the robustness of the eoq model we investigate the general multiproduct multistage production and inventory model using the net present value of its total cost as the objective function a power of two heuristic gives us a near optimal solution to this problem if the base period is fixed or varied the solution based on the best power of two heuristic will be within 6 2 or 2 1 of the optimal this result is surprisingly similar to models using the long term average cost the average cost does not reflect the time value of money does this mean that decisions based on average cost are significantly inferior to those based on net present value the answer is quite surprising if we include discounted production cost in the holding cost it turns out that the decision based on average cost is only 9 6 in terms of the net present value of the total cost worse than the decision based on the net present value however the reorder interval based on the average cost could be much longer than that derived using net present value this result shows that average cost is a good approximation to the net present value when the demands are deterministic

holding costs under push or pull conditions the impact of the anchor point holding costs are traditionally determined from the investment in physical stock during a cycle an alternative approach instead derives holding costs from net present value npv functions it is known that applying both frameworks to the same system can lead to different holding cost valuations but little explanation has been offered by introducing the anchor point in a model this paper shows for four different systems that traditional holding cost models implicitly assume pull conditions while current npv approaches model push conditions this explains in part the differences between the methods it is shown that the anchor point concept allows the construction of npv models under pull conditions giving results in better correspondence with traditional models the traditional framework is restricted to pull conditions and important considerations could be easily overlooked leading to wrong valuations of holding costs npv seems superior as such considerations are automatically incorporated the application to multi echelon inventory systems provides interesting insights on the roles of echelon stocks and lead times and offers potential for future research

composite indices of physical quality of life basic needs fulfilment and income a principal component representation abstract in the context of international comparisons the multivariate method of principal components is suggested for computing composite indices of economic development that capture per capita income basic needs fulfilment and other possible indicators of well being the method is conceptually appealing easy to apply and seems promising in several directions two illustrative applications are given one develops a composite index based on the three pqli constituents and per capita gnp for 147 countries in the other a composite index of basic needs fulfilment is first computed for 82 countries and then a more inclusive measure that also takes account of per capita gnp is derived

climbing out of poverty falling back in measuring the persistence of poverty over multiple spells this paper investigates the persistence of poverty over individuals life times using a hazard rate approach that accounts for multiple spells of poverty and incorporates spell duration individual and household characteristics and unobserved heterogeneity the findings highlight the importance of considering multiple spells in an analysis of poverty persistence with half of those who end poverty spells returning to poverty within four years accounting for multiple spells shows that approximately 50 percent of blacks and 30 percent of whites falling into poverty in some year will have family income below the poverty line in five or more of the next ten years

cagan s model of hyperinflation under rational expectations this paper studies p cagan s model of the german hyperinflation under the hypothesis that adaptive expectations are rational it shows that inference about the key money demand elasticity parameter a is very senstitive to the specification of the dynamic interaction of the unobserved money demand shock with prices and money in particular if t j sargent s 1977 specification is modified then his basic conclusions are overturned identification of a does not require prior knowledge about the covariance of unobserved shock terms and d ata on the german hyperinflation imply a sharp not loose estimate of a which is of plausible magnitude finally informal tests indicate that modifying sargent s specification gives rise to improved model fit copyright 1987 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

policy implications of new data on income mobility the existence of income mobility may moderate concerns about growing inequalities especially if income mobility has increased however the evidence for rising mobility is equivocal and its extent is not enough to offset the growth of cross sectional inequality there is a case for greater concern for and different policies towards those persistently or recurrently poor than those only temporarily poor but the data analysed here suggest that the bulk of low income observations come from the first two categories analysis of income mobility may help understand why people s incomes follow different trajectories and how policy might affect this

bubble weak and strong hyperinflation theory and empirical evidence the monthly continuous inflation rate that maximizes the inflation tax revenue varies widely from 18 3 to 143 according to semi elasticity estimates for the german hyperinflation made by several authors cagan 1956 barro 1970 frenkel 1977 sargent 1977 goodfriend 1982 burmeister and wall 1987 christiano 1987 casella 1989 taylor 1991 engsted 1993 imrohoroglu 1993 michael et al 1994 those estimates lead one to conclude that during hyperinflation the german government could have obtained more tax revenue with lower inflation rates

two warehouse inventory models for deteriorating items with shortages under inflation abstract in this paper the two warehouse inventory problem for deteriorating items with constant demand rate and shortages under inflation is considered in contrast to the traditional deterministic two warehouse inventory model with shortages at the end of each replenishment cycle an alternative model in which each cycle begins with shortages and ends without shortages is proposed here the optimal solution not only exists but also is unique comparing these two two warehouse inventory models the study shows that the proposed model is less expensive to operate than the traditional one in the case of the inflation rate is greater than zero hence under the consideration of inflationary effect the proposed model is less expensive finally some numerical examples for illustration are provided

the effects of irregular markets on macroeconomic policy some estimates for belgium abstract the paper aims at evaluating the efficiency of traditional keynesian demand or neo classical income policies in the presence of an irregular sector the analysis is applied to the belgian economy for which it is shown that the objectives of increasing output and employment and reducing the importance of the irregular economy will often lead to conflicting policy prescriptions in addition keynesian multipliers may be lowered by as much as 40 though the irregular market only represents some 10 to 15 of total activity