the effect of supply uncertainty in price setting newsvendor models abstract we consider a price setting newsvendor model in which a firm needs to make joint inventory and pricing decisions before the selling season the supply process is uncertain such that the received quantity is the product of the order quantity and a random yield rate two cost structures are investigated the in house production case in which the firm pays for the input quantity and the procurement case in which the firm pays for the quantity received only our objective is to investigate the effect of yield randomness on optimal decisions and expected profit by using the theory of stochastic comparisons we find that under both cost structures a less variable yield rate leads to a lower optimal price and a higher expected profit moreover we show that in the in house production case a stochastically larger yield rate also results in a lower optimal price and a higher profit but this is not true in the procurement case examples show that the effect of supply uncertainty on optimal order quantity is not universal

demand for money in open economies abstract the demand for real cash balances deduced from an underlying portfolio model of the financial market is shown to depend upon domestic variables and foreign monetary developments the model is estimated using quarterly postwar data for canada germany uk and us there is clear evidence that demand for money is affected not only by changes in domestic variables such as permanent income domestic interest rate and price expectations but also by fluctuations in exchange rate expectations and foreign interest rates the conclusion that domestic monetary policy is fairly ineffective and domestic financial markets are highly vulnerable to changes in foreign financial and monetary developments need to be modified in light of the results presented in this paper

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

re examining the buffer stock model of money this paper critically examines recent papers in the buffer stock or supply side disequilibrium models of money the paper first investigates the assumptions at the m icroeconomic level and concludes that even with these assumptions aggregate behavior does not necessarily follow buffer stock models in which excess cash balances are held involuntarily in a simple model with uncertain cash flows it is shown that in the aggregate short run involuntary cash holdings are negligible if the buffer stock story is applicable it is to a broader definition of money than used in most empirical work the second part of the paper examines empirical work and argues that the buffer stock idea cannot be implemented using single equation techniques and that when viewed appropriately current empirical result s refute the buffer stock idea as it is currently modeled copyright 1987 by royal economic society

effects of financial innovations on the money demand function a canadian evidence a money demand function for the candian economy has been estimated to explore if recent financial innovations have caused any significant change in the structural relationship between the demand for money and its determinants two sets of estimation results have been analysed the first set is obtained by estimating a standard money demand function for several overlapping sample periods and the other set is obtained by estimating a modified version which included a dummy or a ratchet variable to capture the effects of innovations the estimated equations have been used to generate ex post simulations and forecasts the results suggest that innovations have displaced the money demand function in the early 1980s it also appears that the incorporation of approriate innovation variables improves the predictive performance of the money demand function

a path dependent contingent claims approach to capacity investments this note presents a contingent claims approach to strategic capacity planning we develop models for capacity choice and expansion decisions in a single firm environment where investment is irreversible and demand is uncertain these models illustrate specifically the relevance of path dependent options analysis to planning capacity investments when the firm adopts demand tracking or average capacity strategies it is argued that asian average type real options can explain hysteresis phenomena in addition to providing superior control of assets in place

us business credit sources demand deposits and the missing money abstract this study accounts for much of the missing money in the us through compensating balances business lending by banks affects demand deposit growth standard money demand models include variables that likely pick up income and interest rate effects on the transactions demand for demand deposits and on compensating balance requirements provided that bank lending to firms is stable however during the missing money period business shifted toward nonbank sources of short term credit causing a decline in compensating balances empirical finding support this hypothesis as a partial explanation for the missing money using the federal reserve board s demand deposit model

cointegration structural breaks and the demand for money in bangladesh this article allows for endogenous structural breaks in the cointegration equation and investigates if there is a stable demand for money for bangladesh we have used the gregory and hansen framework and found that there was an intercept shift and a well determined and stable demand for money in bangladesh exists

estimating money demand functions the question of which functional forms of money demand regression equations are useful for empirical work is addressed here specifically it is argued that a functional form that focuses attention on the ability of the growth rate of nominal money to predict the inflation rate is a useful way of summarizing empirical evidence on the existence of a stable money demand function the results of estimating and simulating this functional form as well as standard functional forms are presented in the final part of this paper a typical equation expressing the public s demand for real money balances m is as follows

the identification of monetary policy disturbances explaining the liquidity puzzle abstract this paper examines recent work on the identification of monetary policy disturbances its main finding is that the empirical anomalies found in the literature reflect a failure to properly address the federal reserve s policy of accommodating reserve demand shocks a new method of identifying monetary policy using nonborrowed reserves is proposed using this specification policy has a strong persistent liquidity effect regardless of subsample policy granger causes output even in the presence of interest rates explaining approximately 49 of the variance in output at a two year horizon and the residual explanatory power of interest rates for output is negligible

on the effect of demand randomness on inventories and costs we explore analytically cardinal effects of the extent of demand randomness on optimal inventory levels and the associated expected costs to model changes in demand randomness we make extensive use of a mean preserving transformation commonly used in probabilistic microeconomics as well as the notion of risk pooling aggregating independent demands for the single period news vendor model the order quantity and associated costs are shown to depend on the randomness parameter in a simple and highly interpretable manner we show by a simple example that in some situations risk pooling might neither reduce inventories nor move them closer to the mean or median demand the managerial relevance of such analyses is discussed

inventory pooling under heavy tailed demand risk pooling has been studied extensively in the operations management literature as the basic driver behind strategies such as transshipment manufacturing flexibility component commonality and drop shipping this paper explores the benefit of risk pooling in the context of inventory management using the canonical model first studied in eppen eppen gd 1979 effects of centralization on expected costs in a multi location newsboy problem management sci 25 5 498 501 specifically we consider a single period multilocation newsvendor model where n different locations face independent and identically distributed demands and linear holding and backorder costs we show that eppen s celebrated result i e that the expected cost savings from centralized inventory management scale with the square root of the number of locations depends critically on the light tailed nature of the demand uncertainty in particular we establish that the benefit from pooling relative to the decentralized case in term

inflation interest rate policy and currency substitutions in developing economies a discussion of some major issues abstract this paper deals with the management of interest rates in an open economy under rapid inflation and reviews the links between interest and exchange rate policies to prevent current substitution the rate of interest paid to lenders must equal the equivalent rate after adjusting for differential taxation and intermediation costs this would probably induce capital inflows and consequent monetary growth exchange risks are also considered in this context the paper concludes that under inflationary conditions it is difficult to use only interest rates to achieve both proper resource allocation and prevention of currency substitution some policy measures to cope with this problem are discussed

stochastic comparisons in production yield management manufacturing firms routinely commit resources to increase yield rates through product and process improvement initiatives champions of such yield improvement projects may assume that stochastically larger yield rates are beneficial in this note we show that this need not hold even when the contingent production lot sizes are chosen optimally we employ stochastic comparison techniques to show that a yield rate that is smaller in the convex order ensures higher expected profit and we provide a distribution free bound on the size of increase in expected profit we also identify properties of yield rate distributions that do make stochastically larger yield rates beneficial

the ricardian equivalence hypothesis evidence from bangladesh this article examines the ricardian equivalence hypothesis reh and its sources of failure in the case of bangladesh using various theoretical specifications annual data from 1974 2001 and linear and nonlinear time series techniques the general findings tend to invalidate the reh a finite time horizon and the presence of liquidity constrained individuals are the sources of deviation from the reh empirical results reveal that real per capita private consumption c under various specifications is cointegrated generally at the 5 level with real per capita income y government expenditure before and after interest rate repayments g and g2 taxes t and the interest rate r results reveal that an increase in g g2 t and r reduces c and that an increase in budget deficits raises trade deficits these results highlight the importance of fiscal policies in boosting private consumption and controlling trade deficits which are the prime goals of stabilization policies being followed by bangladesh

comparative statics of changes in risk on monotonically and partially responsive kinked payoffs abstract this paper derives two sets of necessary and sufficient conditions on the comparative statics of changes in risk under kinked payoff functions that are monotonically responsive and partially responsive to the realization of risk respectively the former case includes the newsboy problem with backorder the latter case includes the newsboy problem without backorder and under some restrictions also includes the optimal deductible insurance problem some relatively non restrictive conditions derived from the necessary and sufficient conditions reveal that the three problems can be quite different even though they are often viewed in the literature as being congruous these conditions lead to simple predictions of the direction of change in any risk averse agent s optimal choice upon a change in risk without assuming specific functional forms for the utility function

the structure of periodic review policies in the presence of random yield this work provides a comprehensive analysis of a general periodic review production inventory model with random variable yield existence of an order point whose value does not depend on yield being random is proved in the single period case without specifying the yield model and using a very general cost structure when yield is a random multiple of lot size the nonorder up to optimal policy is characterized for a finite horizon model the finite horizon value functions are shown to converge to the solution of an infinite horizon functional equation and the infinite horizon order point is shown to be no smaller than when yield is certain

money demand instability has it ended abstract some researchers suggest that much of the seeming instability in the post 1973 money demand occurred because of financial innovation and deregulation money demand was in transition further unprecedented declines in the income velocity of circulation during 1985 and 1986 indicate that this hypothesized transition continues have the effects of financial innovation and deregulation run their course do additional unexpected shifts in velocity loom in the near future or has the transition come to a halt these questions are examined using the methodology of hafer and hein 1982 as modified by miller 1986 no evidence of structural shifts exists beyond 1986 m1 growth may have become a reliable monetary aggregate target again further the missing money has more than returned more money is held today than predicted by the pre 1973 money demand function since m1 now includes interest bearing transactions accounts and incorporates a saving motive the finding is not counterintuitive

sound taxation on the use of self declared value abstract in the 16th century foreign ships passing through the sound had to pay ad valorem taxes known as the sound dues to give skippers an incentive to declare the true value of their cargo the danish crown reserved the right to purchase it at the declared value we show that this rule does not induce truth telling but does allow the authorities to effectively implement a given tax rate

intergenerational transfers and the social discount rate this paper investigates the relationship between intergenerational asset transfers and the choice of the discount rate for use in cost benefit analysis in a model of a competitive overlapping generations economy constrained by a socially managed exhaustible resource provided that there are no distortions in capital markets and that all agents hold perfect foresight cost benefit techniques will result in a pareto efficient resource allocation if the discount rate is set equal to the market rate of interest but since the path of the interest rate depends on the level of intergenerational transfers cost benefit techniques do not ensure a socially desirable distribution of welfare between generations a social optimum will result only if intergenerational transfers are properly chosen and enforced decentralized private altruism may result in intergenerational transfers that both present and future individuals would agree are too small if members of the present generation attach positive weight to the general welfare of future generations not simply their personal descendants in a world where intergenerational transfers are non optimal second best policy making may imply a constrained optimum that is inefficient together these findings suggest that cost benefit analysis is at best a partial criterion to policy formulation that should be used only in conjunction with ethical principles that define the proper distribution of welfare between present and future generations

cross country estimates of the demand for money and its components the demand for money aggregates m1 m2 and their components currency demand deposits and time deposits are estimated using a sample of 103 countries at two time periods money demand is found to be affected by age literacy industrial development and political structure as well as income and inflation this expanded demand function helps to explain the considerable changes in money demand that have occurred over long periods and the large variation in money demand found across countries the knowledge thus gained is useful for understanding differences in monetary and taxation policies across countries

on the relationship between entropy demand uncertainty and expected loss abstract we analyze the effect of demand uncertainty as measured by entropy on expected costs in a stochastic inventory model existing models studying demand variability s impact use either stochastic ordering techniques or use variance as a measure of uncertainty due to both axiomatic appeal and recent use of entropy in the operations management literature this paper develops entropy s use as a demand uncertainty measure our key contribution is an insightful proof quantifying how costs are non increasing when entropy is reduced

portfolio behaviour in a flow of funds model for the household sector in india we estimate a flow of funds model for the household sector in india within the almost ideal demand system aids framework and examine the demand for money and the substitution effects between money and other financial assets the restricted long run model obtained using cointegration techniques provides stable equilibrium relationship between i 1 variables and broadly satisfies the axioms of rational choice in consumer demand theory we find that financial sector reform exerts a significant impact on the interest rate structure and household portfolio preferences specifically there is strong substitutability among risk free assets and a possible speculative effect in the stock market while the exchange rate strongly influences the demand for money these findings all have important policy implications

modeling the demand for narrow money in the united kingdom and the united states abstract despite the importance of well specified empirical money demand functions for inference forecasting and policy problems in modeling have arisen concerning the economic theories of money demand the data institutional frameworks financial innovation and econometric implementation by developing constant data coherent m 1 demand equations for the u k and the u s we investigate these issues and explain such puzzles as missing money the great velocity decline and the recent explosion in m 1 the endogeneity of money the lucas critique and the non invertibility of our m 1 models are also discussed

optimal value declaration in buy sell situations buy sell shotgun clauses call for a partner who wishes to discontinue a partnership to declare a value for the business and for the other partner to then buy her out or sell to her at this value the resulting decision model for an expected utility maximizing individual who is uncertain of the business valuation by the partner is analyzed this model is also applicable to a divide and choose fair division method as well as some historical tax customs schemes and is more general than comparable bidding auctions models after showing that the optimal declaration is always between the declarer s valuation and the fractile of the subjective distribution corresponding to the share owned we show that the optimal declaration is always increasing in the valuation and for a risk neutral declarer also increasing in the share owned we prove that the more risk averse the declarer the closer is the optimal declaration to the valuation and the higher the probability that the partner who values the busine

the risk averse and prudent newsboy the effects of risk and risk aversion in the single period inventory newsboy problem are examined comparative static effects of changes in the various price and cost parameters are determined and related to the newsboy s risk aversion the addition of a random background wealth and of an increase in the riskiness of newspaper demand are also examined although many of the comparative effects generally are ambiguous some fairly simple restrictions on preferences and or risk increases are shown to lead to qualitatively deterministic results

the scourge of the monetarists kaldor on monetarism and on money nicolas kaldor s critique of monetarism from 1970 until his death is described and evaluated it is argued that subsequent events as well as empirical research vindicate his critique kaldor s critique of john maynard keynes s monetary theory is then seen as an extension of his radcliffe views and this paper argues that in this matter kaldor was mechanical in his modeling of the endogeneity of money supply it is suggested that the work of hyman minsky and victoria chick has the potential for further work in this area copyright 1989 by oxford university press

who benefits from transshipment exogenous vs endogenous wholesale prices this paper studies how transshipments affect manufacturers and retailers considering both exogenous and endogenous wholesale prices for a distribution system where a single manufacturer sells to multiple identical cost retailers we consider both the manufacturer being a price taker and the manufacturer being a price setter in a single period setup under multivariate normal demand distribution in the case of the manufacturer being a price taker we provide several analytical results regarding the effects of key parameters on order quantities and profits in the case of the manufacturer being a price setter we characterize the stackelberg game that arises and provide several insights into how the game dynamics are affected by transshipments specifically we find that risk pooling makes retailers order quantities less sensitive to the wholesale price set by the manufacturer hence in general the manufacturer benefits from retailers transshipments by charging a higher wholesale price while retailers are often worse off the paper captures the effect of demand correlation and the effect of the number of retailers throughout and it illustrates the findings by a numerical example we also provide an interactive web page for numerical experiments

new concepts of aggregated money the federal reserve board s recent redefinition of its monetary aggregates followed three years of intensive board staff research on monetary aggregation while the new aggregates ultimately were selected along conventional lines some of the staff s research was oriented towards more fundamental changes in monetary aggregation methods this paper reviews such proposals which are based upon the rigorous application of index number and aggregation theory and of principal components analysis in the construction of economic monetary aggregates the usefulness of aggregation and index number theory in acquiring price indices is widely known the theory of the true cost of living index is an application of aggregation theory examples of applied index number theory include the commerce department s implicit price deflator which is a paasche index and the labor department s consumer price index which is a laspeyres index somewhat less well known is the fact that dual to the theory of economic price aggregates and indices is a theory of economic quantity aggregates and indices an example of a highly reputable quantity index is the divisia quantity index the monetary aggregates traditionally are thought to measure the supplied quantity of an economic good called money whenever monetary aggregates are used in the context of economic theory rather than as simple accounting identities the theory of economic quantity aggregation is specifically applicable however published monetary aggregates in all countries have always been computed as simple sums but as fisher 1922 p 29 observed in the conclusion to his classic treatise on index number theory the simple arithmetic average produces one of the very worst of index numbers and if this book has no other effect than to lead to the total abandonment of the simple arithmetic type of index number it will have served a useful purpose with an example of the simple sum index fisher 1922 p 363 found that the bias alone reaches 36 percent although index number theory has not yet found its way into the monetary theory literature all of the literature on index number theory and aggregation theory for the past half century supports the result long ago deduced by fisher 1922 p 361 that the simple arithmetic index should not be used the views expressed herein are solely those of the authors and do not necessarily represent the views of the board of governors of the federal reserve system this research was partially supported by national science foundation grant soc 76 84459 we are deeply indebted to the conference session s discussant of this paper w erwin diewert for volunteering to cede his allocated journal space to us so that the paper could take its current extended form federal reserve board washington d c

the search for a stable money demand function a survey of the post 1973 literature phe question of whether the demnand function for money is stable is one of the most important recurring issues in the theory and application of macroeconomic policy what is being sought in a stable demand function is a set of necessary conditions for money to exert a predictable influence on the economy so that the central bank s control of the money supply can be a useful instrument of economic policy as such the notion of a stable demand function appears to involve three key elements e g john t boorman 1976 p 317 and david e w laidler 1977 pp 34 35 first the demand for money relation should be highly predictable in a statistical sense as measured by the usual goodness of fit statistics precision of estimated coefficients and presumably its ability to forecast accurately out of sample second a stable demand function for money has relatively few arguments a relationship that requires knowledge about a large number of variables in order to pin it down is in effect not predictable finally the variables that appear as arguments in the function should represent significant links to spending and economic activity in the real sector in sum a stable demand function for money means that the quantity of money is predictably related to a small set of key variables linking money to the real sector of the economy the importance of a stable money demand function for monetary policy can be illustrated with the standard is lm model in which interest rates and gnp are the endogenous variables in this context a stable demand function for money translates into a well defined relationship between money interest rates and gnp

policies for sustainability lessons from an overlapping generations model discounting is often considered inimical to sustainability reliance on the assumption that endowments regulate the transfer of assets to the future in standard growth models interprets the interest rate in the intergenerational context as a partial reflection of myopia a more complete market model that allows agents from different generations to engage in long term contracts with one another severs the movement of capital to the future from the endowment assumption adherence to the endowment assumption as a de facto market structure not simply a modeling convenience endorses sustainability policies that injure the future

the stochastic ordering of mean preserving transformations and its applications abstract the stochastic variability measures the degree of uncertainty for random demand and or price in various operations problems its ordering property under mean preserving transformation allows us to study the impact of demand price uncertainty on the optimal decisions and the associated objective values based on chebyshev s algebraic inequality we provide a general framework for stochastic variability ordering under any mean preserving transformation that can be parameterized by a single scalar and apply it to a broad class of specific transformations including the widely used mean preserving affine transformation truncation and capping the application to mean preserving affine transformation rectifies an incorrect proof of an important result in the inventory literature which has gone unnoticed for more than two decades the application to mean preserving truncation addresses inventory strategies in decentralized supply chains and the application to mean preserving capping sheds light on using option contracts for procurement risk management

cointegration and structural change an application to the u s demand for money wankeun oh i perform the cointegration tests for the trivariate model of real monetary aggregates real personal income and short term interest rate i find the existence of a long run relationship among these three variables to check the stability of a long run money demand relationship i implement a rank constancy test and cusum test the test results show that real mi is relatively more stable than other aggregates but structural change occurred during the 1970s and early 1980s this is consistent with prior research on money demand jel e41 i introduction incorporating structural change when performing tests on the properties of stochastic processes is important because structural breaks may cause misspecification problems most tests of structural change consider the stability of the parameters over time tests for structural breaks and parameter stability have been studied extensively a partial list includes chow 1966 brown et al 1975 harvey and collier 1977 king 1987 ploberger et al 1989 in the context of unit root processes perron 1989 showed that the presence of a one time change in the level or slope of the trend function can severely distort the results of unit root tests and it is natural to ask how structural change can distort the results of cointegration tests 1 traditional tests of parameter stability ask if the parameters of the model are constant in contrast quintos 1993 proposed a test for stability of the long run relationship s in a cointegrating regression the test is based on johansen s 1988 framework and the test statistic is simply the weighted sum of the likelihood ratio test as given in johansen 1988 quintos s rank test is very different from the traditional cusum and chow tests for parameter stability because her rank test checks for stability of the cointegrating relationship between variables in other words the rank test checks whether cointegration holds for the full period the traditional cusum and chow tests assume that cointegration holds for the full period or does not hold for the full period and tests simply whether the cointegration vector changes for example if there is cointegration from 1960 1990 between revenues and expenditures with cointegrating vector 1 1 then the cusum and chow tests check whether the cointegra ting vector 1 1 is stable throughout the period the rank constancy test checks whether the cointegration rank is stable throughout the period not whether the cointegrating vector is stable at 1 1 in other words the rank test will check whether for example there is cointegration from 1960 1980 and no cointegration from 1980 onward the chow and cusum tests are not designed to check for this the structural stability of money demand relationships has been the issue of a substantial number of empirical studies 2 in general structural stability means stability of the underlying behavioral equations 3 this term includes parameter stability and stability of functional form friedman s 1990 research on the money demand function assumes that a long run equilibrium relationship exists between real money balances real income or real wealth and the opportunity cost of holding real money balances recently there has been strong evidence of cointegration between real income real money balances and a nominal interest rate for instance engle and granger 1987 dickey et al 1991 hafer and jansen 1991 hoffman and rasche 1991 mehra 1993 miller 1991 fischer and nicoletti 1993 and baba et al 1992 report on cointegration among variables in u s aggregate money demand jain and moon 1994 report on cointegration in u s sectoral money demand yashiv 1994 and engsted 1993 on money demand in a high inflation country and hoffman et al 1995 report on international money demand comparison this article asks if long run money demand relationship is stable and if so for which measure of money is it stable over time

incentive contracts and competitive bidding an increasing segment of economic activity is taking place in nonmarket situations in which economic agents act outside the traditional markets or create markets to deal with specific resource allocation problems one such problem involves the selection by a buyer of a contractor using a competitive bidding process competitive bidding is used extensively by the government for the selection of suppliers of goods and services and for the sale of resources such as offshore oil leases firms may use competitive bidding for the selection of certain suppliers of factor inputs and may attempt to sell certain products in markets in which competitive price quoting is the established market mechanism this paper is concerned with a bidding process in which a firm has an opportunity to bid on a project under the terms of an incentive contract incentive contracts

finance capital in dynamic factor demand models the lagged partial adjusment money demand function has been studied theoretically and empirically for the aggregate economy this paper focuses on a sectoral analysis of two partial adjustment functions one for optimal money demand and another for optimal loans demand the two partial adjustment equations are derived employing a representive firm approach a dynamic factor demand model with internal costs of adjustment is utilized to generate euler equations for the demand for money and short term business loans these euler equations parallel the aggregate partial adjustment money demand equations typically employed in applied monetary research the significant difference between the ad hocderivation and the microtheoretic derivation employed here is that desired money and loan holdings are found by solving the euler equations these particular definition of desired money and loan holding are model consistent and depend upon the predetermined and exogeneous variables of the model empirical analysis ge

macroeconomic disequilibrium structural changes and the household savings and money demand in china abstract this paper presents an empirical study of the chinese personal money demand and savings in an economy of disequilibrium and structural changes we propose specifications capable of encompassing and testing the two competing hypotheses which have been advanced to explain the case of the chinese household money demand and savings based on the national and provincial data we find that both repressed inflation and structural changes are significant suggesting the need to capture both the possible disequilibrium and structural shifts further statistical evidence shows that there might have been multiple regime shifts during the post 1949 period which is at variance with the conventional approach of exclusive focus of the effects of the recent reforms nesting the competing hypotheses appears to be the key in providing an adequate account of the savings and money demand of the chinese household sector the evidence seems to favor the repressed inflation hypothesis

recent instability of the demand for money an international perspective aggregate money demand functions once an apparent bulwark for macroeconomic research have had to be re examined in the light of the events and discoveries of the 1970s following goldfeld s extensive analysis it now is widely recognized that the demand for mi balances in the united states cannot be explained satisfactorily by standard functions apparently because of shifts occurring in the early 1970s similar reservations see below have been expressed with respect to m3 balances in the united kingdom where the demand relationships appear to have been upset by the introduction of regulatory reforms in 1971 in both cases part of the problem can be traced to specific events but the possibility remains that a more general instability may be present the rapid inflation experienced by all major industrial countries after 1973 the concurrent collapse of the bretton woods system of fixed exchange rates and the attempts by most major central banks to control growth in domestic money stocks may all have altered the responses of the demand for money to the standard functional arguments this paper presents a range of stability tests for a set of demand functions estimated for two monetary aggregates in each of six countries in order to determine whether money demand functions more generally have been stable over the recent period and to attempt to identify the nature and causes of any observed instabilities the major conclusions are that none of the other functions examined displays instabilities as severe as those of the mi function for the united states and that the latter may be unstable in a more persistent and fundamental way than has heretofore been recognized the equations estimated for this study are based on a variant of goldfeld s log linear real balances function the deflated value of money balances is related to real income interest rates and inflation with lagged adjustments introduced via a simple koyck transformation this function obviously is in a simplified form especially with respect to the lag struc

short run money demand abstract the conventional wisdom holds that the short run demand for money is unstable this paper challenges the conventional view by finding a stable demand for m1 in u s data from 1959 through 1993 the approach follows previous work in interpreting long run money demand as a cointegrating relation and it uses goldfeld s partial adjustment model to interpret short run dynamics the key innovation is the choice of the interest rate in the money demand function most previous work uses a short term market rate but this paper uses the average return on near monies the savings accounts and money market mutual funds that are close substitutes for m1 this choice helps rationalize the behavior of money demand in particular the increase in the volatility of velocity after 1980 is explained by increased volatility in the returns on near monies

entitlements missing markets and environmental uncertainty reply abstract at one level dore and ward seem intent on immunizing received doctrine they say that i did not prove that rights violated nozick s principles of justice and that i did not prove that missing markets were the problem more telling they allege i did not prove that my story was better than the particular story favored by dore and ward that is they argue that there is an alternative approach based on the theory of public economics which is indeed operational 3 they then use the bulk of their comment to explain and defend this alternative model they hope to convince the reader that the model of public economics survives intact in the face of my alternative model to the extent that their model allows one to define the problem away it is not difficult to see why they find it so compelling more seriously dore and ward fail to make a coherent argument about the concept of rights and duties and the logic of a particular rights structure that happens to prevail they seem concerned that my article was tampering with some sacred social construct the status quo rights structure and that my article threatened the received wisdom of both public economics and paretian walrasian bliss indeed theirs seems to be a genuine fear that if economists release their grip on the certitude of received orthodoxy the floodgates will be open to all manner of bumbling regulators seeking to shift rights and wealth positions across generations my article is apparently threatening because it seems to suggest that the received wisdom may at times be misleading

regression direction and weak exogeneity abstract the absence of testing for weak exogeneity in money demand has often led to stark conditioning claims regarding the validity of price equations this paper uses the johansen procedure to explore the conditioning properties of money demand systems for nonborrowed reserves m1 and m2 our results show that irrespective of the specification of the cointegrating relation a feedback mechanism enters the equation for money the opposite however is not true for the price equations the results also cast a warning for single equation models of money demand in that weak exogeneity is sensitive to how the system is defined

delayed production and raw materials inventory under uncertainty abstract firms producing seasonal goods often make order and production choices prior to highly uncertain sales thus lending an investment quality to their decisions using specialized inputs imposes a delay in receiving them and linked with a long production period the firm makes its order production and pricing choices under successively reduced uncertainty the model shows that input and production costs have distinctive effects on the firm s order size with implications for the stock of raw materials inventory firms facing relatively low input costs are willing to risk leaving inputs unused as a bet for a good state of nature further we investigate situations of greater uncertainty and find a more nuanced explanation of firm behavior than previous research firms with relatively inexpensive inputs facing equal odds of good and bad states of nature will increase their order size a known result however a firm with a low relative cost of completing production may either raise or reduce its order size depending on the demand elasticity and the relative demand uncertainty intuitively firms with expensive inputs facing highly uncertain demand and with many substitute output goods are inhibited by the high cost of insuring against stock outs

sourcing decisions with capacity reservation contracts abstract by committing to long term supply contracts buyers seek to lower their purchasing costs and have products delivered without interruption when a long term contract is available suppliers are less pressured to find new customers and can afford to charge a price lower than the prevailing spot market price we examine sourcing decisions of a firm in the presence of a capacity reservation contract that this firm makes with its long term supplier in addition to the spot market alternative this contract entails delivery of any desired portion of a reserved fixed capacity in exchange for a guaranteed payment by the buyer we investigate rational actions of the two parties under two different types of periodic review inventory control policies used by the buyer the two number policy and the base stock policy when typical demand probability distributions are considered inclusion of the spot market source in the buyer s procurement plan significantly reduces the capacity commitments from the long term supplier

the effects of ageing and an environmental trust fund in an overlapping generations model on carbon emission reductions most currently employed integrated assessment models for climate change are of a dynastic nature they employ the ramsey rule linking the interest rate economic growth and the rate of pure time preference this paper argues that although a dynastic framework might be convenient for economic analysis it is restrictive and can be misleading overlapping generations models which do not employ the ramsey rule are more flexible and may give results different from those derived from dynastic models with the integrated assessment model alice 2 0 it is shown how various assumptions on demographic change and public institutions can affect the interest rate thereby influencing the efficient greenhouse gas emission reductions it is concluded that dynastic integrated assessment models are in many respects inappropriate for providing policy makers with quantitative figures about the costs of carbon dioxide emissions and their desirable reduction levels 2001 elsevier science b v all rights reserved

channel incentives in sharing new product demand information and robust contracts abstract demand for a new product is often highly uncertain as the developer of a new product the manufacturer may reduce the uncertainty of the product s demand through observing progress in his product development process or receiving demand signals directly from customers this paper first shows that a centralized channel always benefits from improved demand information yet to realize this benefit in a decentralized manufacturer retailer channel the manufacturer needs to disclose his private demand information to the retailer we show that the manufacturer s incentive to share his improved demand information depends on the supply contract signed with the retailer furthermore mandating the manufacturer to disclose his improved demand information can actually reduce the total channel profit we provide managerial insights by analyzing three widely used contract forms we investigate whether these contracts are robust under an unanticipated demand information update observed by the manufacturer we show that the quantity flexibility contract with a high return rate is not robust the buyback contract however is robust and always achieves information sharing while preserving channel performance

intertemporal preferences and intergenerational equity considerations in optimal resource harvesting abstract optimal resource harvesting decisions are reexamined in light of a distinction between personal discount rates reflecting individuals rate of time preference and generational discount rates reflecting considerations of equity for future generations the discount rates have partially counteracting effects upon the optimal harvesting decisions and upon the optimal distribution of benefits in any one period for instance it is the generational discount rate that determines the potential for economically optimal extinction of a renewable resource by distinguishing the two discount rates it is possible to give each generation equal consideration while still allowing for individual impatience

sensitivity analysis of the newsvendor model abstract quality of decisions in inventory management models depends on the accuracy of parameter estimates used for decision making in many situations error in decision making is unavoidable in such cases sensitivity analysis is necessary for better implementation of the model though the newsvendor model is one of the most researched inventory models little is known about its robustness in this paper we perform sensitivity analysis of the classical newsvendor model conditions for symmetry skewness of cost deviation i e deviation of expected demand supply mismatch cost from its minimum have been identified these conditions are closely linked with symmetry skewness of the demand density function a lower bound of cost deviation is established for symmetric unimodal demand distributions based on demonstrations of the lower bound we found the newsvendor model to be sensitive to sub optimal ordering decisions more sensitive than the economic order quantity model order quantity deviation i e deviation of order quantity from its optimum is explored briefly we found the magnitude of order quantity deviation to be comparable with that of parameter estimation error mean demand is identified as the most influential parameter in deciding order quantity deviation

transshipment and its impact on supply chain members performance this note extends some of the key results of dong and rudi 2004 to general demand distributions this generalization is achieved in two steps first we build on the analysis of dong and rudi to demonstrate that an inventory problem with transshipment is equivalent to a newsvendor problem with an adjusted demand then we study the impact of transshipment by comparing the adjusted demand with the original demand in addition to extending the results in the existing literature this note presents a novel approach for analyzing the impact of risk pooling

on the reinterpretation of money demand regressions a stylized fact concerning estimated money demand relationships is that lagged dependent variables have high explanatory power and large estimated coefficients which is hard to explain at a theoretical level marvin s goodfriend 1985 suggests that this may be due to the presence of serially correlated measurement errors in the independent variables the author demonstrates how consistent estimates of the short run demand function can be obtained even if the goodfriend hypothesis is accepted and also how the hypothesis might be tested application of the suggested test using the goldfeld 1973 data set leads to decisive rejection of the hypothesis copyright 1994 by ohio state university press

the role of money supply shocks in the short run demand for money abstract previous money demand models are either inconsistent with contemporaneous adjustment of the price level to expected changes in the nominal money supply or imply implausible interest rate fluctuations in response to innovations in nominal money we propose a shock absorber money demand model in which money supply shocks affect the synchronization of asset transactions and so engender a temporary increase or decrease in desired money holdings expected changes do not engender such fluctuations in real money inventories in simultaneous estimates for eight industrial countries the shock absorber model proved empirically superior

distributions of forecasting errors of forecast combinations implications for inventory management inventory control systems rely on accurate and robust forecasts of future demand to support decisions such as setting of safety stocks the combination of multiple forecasts is shown to be effective not only in reducing forecast errors but also in being less sensitive to limitations of a single model research on forecast combination has primarily focused on improving accuracy largely ignoring the overall shape and distribution of forecast errors nonetheless these are essential for managing the level of aversion to risk and uncertainty for companies this study examines the forecast error distributions of base and combination forecasts and their implications for inventory performance it explores whether forecast combinations transform the forecast error distribution towards desired properties for safety stock calculations typically based on the assumption of normally distributed errors and unbiased forecasts in addition it considers the similarity between in and out of sample characteristics of such errors and the impact of different lead times the effects of established combination methods are explored empirically using a representative set of forecasting methods and a dataset of 229 weekly demand series from a leading household and personal care uk manufacturer findings suggest that forecast combinations make the in and out of sample behaviour more consistent requiring less safety stock on average than base forecasts furthermore we find that using in sample empirical error distributions of combined forecasts approximates well the out of sample ones in contrast to base forecasts

on cash in advance models of money demand and asset pricing this paper shows how a cash in advance model of money can be written in a way that combines a simple yet empirically defensible money demand function with an asset pricing equation that is similar to the standard barter economy euler equations return premia are determined as in the barter exchange model except that a short term risk free nominal interest rate enters into the first order conditions in special cases asset prices satisfy the barter economy euler equations exactly in the empirical analysis the interest rate factor adds some explanatory power but both the barter and the monetary asset pricing model perform rather poorly copyright 1991 by ohio state university press

revisiting the us money demand function an application of the lagrange multiplier structural break unit root test and the bounds test for a long run relationship in this article we examine the issue of a levels relationship and stability of the us money demand function over the period 1959 01 to 2004 02 we use the lagrange multiplier structural break unit root test and the bounds testing approach to a long run relationship in levels of the variables namely real money demand nominal interest rate and real income we find greater evidence for a long run relationship in levels and stability of the us money demand function when we use m2 as a proxy for money demand however we find little evidence for a long run relationship between m1 and m2 with their determinants for the recent period spanning the last decade or so

unstable money demand and the monetary model of the exchange rate in this paper the authors investigate the importance for the monetary model of exchange rate determination of j frankel 1979 of allowing unrestricted dynamics and of accounting for shifts in the demand for money due to financial innovation based on estimation and simulation results for the canada u s bilateral exchange rate over the 1970 85 period the aut hors find strong evidence in favor of a generalized approach to dynamic specification but find that the shif t adjustment of official money supply data has only minor implications for the empirical results moreover neither modification is sufficient to generate a monetary model that is well supported by the data

international evidence on misspecification of the standard money demand equation abstract this paper tests the proposition that the interest rate in the standard money demand equation acts as a proxy for the expected change in interest rates if this is true the interest elasticity in the standard equation will depend on the expectations process for interest rates using cross country data we find that there does exist a relationship between the observed interest elasticity in the standard equation and the predictability of future interest rates from current interest rates

joint product durability and lot sizing models this paper concerns the simultaneous selection of product durability and order quantity for items that deteriorate over time choices of product durability are modelled as the values of a single design parameter that affects the distribution of the time to onset of deterioration tod once deterioration has begun individual items are assumed to have exponential remaining lifetimes we analyze two scenarios in the first case items are guaranteed to be good if used prior to an expiry date therefore tod is a constant and the store manager may choose an appropriate value at cost in the second case tod is a random variable then the design parameter can affect tod distribution in either mean preserving or variance preserving or mixed manner we report insightful numerical examples for each case and derive highly plausible conditions which when true imply that the corresponding expected cost per unit time is strictly quasi convex

asymmetric responses of money demand to oil price shocks in saudi arabia a non linear ardl approach saudi arabia is an open oil based economy with fixed exchange rates therefore it has limited monetary policy autonomy using non linear autoregressive distributed lag approach this article inves

are price equations really money demand equations on their heads it is often argued that the dependent variable in money demand functions is really the price level the money stock itself being exogenous a recent approach which stresses the theme is the buffer stock hypothesis in which money supply shocks explicitly appear in the demand for money function because prices and interest rates do not adjust rapidly enough to bring about short run equilibrium in the money market although this approach has been adopted by a number of authors it is not been subjected to much econometric testing in this paper we outline the economic and econometric issues involved in testing the exogenous money buffer stock hypothesis and subject it to a variety of tests using three different data sets none of our results supports the hypothesis fundamental restrictions are rejected at very high levels of significance and a reasonably good money demand equation is seen to be badly misspecified if interpreted as a price equation this abstract was borrowed from another version of this item

demand for money in bangladesh a cointegration analysis the aim of this study is to estimate the demand for real broad m2 money in bangladesh using the most recently developed autoregressive distributed lag approach to cointegration analyses the empirical results show that there is a unique cointegrated and stable long run relationship among real per capita broad money demand real per capita income domestic interest rates and unofficial exchange rate um premiums which act as a surrogate for foreign interest rates with money as the dependent variable the results show that the income and interest elasticities are positive while the um premium elasticity is negative these results suggest that distortions in the financial and foreign exchange markets should be reduced in order to increase financial saving or monetary accumulation our results also reveal that the demand for money in bangladesh is stable despite the changes in financial and exchange rate policies between 1975 and 1995

the black market for dollars in brazil the model of the black market for dollars focuses on the interaction of portfolio decisions relevant to the holding of asset stocks and the determinants of net flows of dollars associated with tourism and smuggling a partial equilibrium model of the black market shows that the level of the premium is determined by the official real exchange rate and the official depreciation adjusted interest differential as well as seasonal factors associated with tourism expectations of future exchange rate changes under rational expectations are shown to affect the current level of the black market premium the empirical evidence provides ample support for the role of the key determinants of the premium as well as for an important seasonal pattern the magnitude of the seasonal variation is evidence of the imperfect substitutability between black dollars and cruzeiro assets in portfolios

the persistence of interest rate effects on the demand for currency note since the end of world war ii there has been a trend decline in the demand for real currency balances part of the decrease is due to the rise in interest rates to unprecedented heights yet this is not the complete answer since a trend term included in a simple and conventional currency demand equation that already includes an interest rate still emerges with a significant negative coefficient for example using quarterly data from 1950 i to 1981 iii a demand for currency equation can be estimated as

risk aversion and plant size theory and application to tar sands oil plants motivated by canadian tar sands oil plants we investigate the dependence of plant size on various parameters for a risk averse firm assuming that construction lead time is increasing in size we show that optimal plant size decreases with risk aversion increases in mean price and decreases in price uncertainty if the firm s share in the plant is above optimal we show that plant size increases as the share is decreased thus risk sharing can offset the effect of risk aversion on the optimal plant size

a closer look at long run u s money demand linear or nonlinear error correction with m0 m1 or m2 i introduction the stability of money demand has been a long standing issue 1 lucas 1988 informally analyzes the stability of a log linear m1 money demand function and concludes that real money demand is a stable function and he supports earlier findings of meltzer 1963 with an income or wealth elasticity of around unity 2 with the development of cointegration methods engle and granger 1987 numerous empirical studies have applied these techniques to long run u s money demand examples are baba hendry and starr 1992 haferand jansen 1991 hoffman and rasche 1991 and miller 1991 who find support for a cointegrated money demand model with either m1 or m2 3 king et al 1991 also find support for cointegration with m2 and a short term interest rate in contrast to these studies others have argued against a stable u s money demand function in the postwar period for example friedman and kuttner 1992 do not find support for cointegration particularly when the period march 1970 to april 1990 is considered similarly miyao 1996 studies the behavior of the m2 money demand function over the period from 1959 to 1993 with quarterly data and various interest rates in levels and in logs miyao concludes that m2 is not a useful intermediate target for monetary policy in the 1990s 4 however carlson et al 2000 reach the conclusion that m2 does have predictive content for nominal economic activity and that the real m2 money demand function is stable but only after accounting for financial innovation in the first half of the 1990s two recent papers ball 2001 and stock and watson 1993 focus on especially long data sets for the united states and m1 stock and watson 1993 analyze various estimation methods for cointegrating relationships and illustrate their performance for money demand functions with annual data from 1900 to 1987 they pay particular attention to the postwar period and use monthly data in addition to annual data for this period they employ a semi log linear real m1 money demand model with real net national product and the level of the 6 mo commercial paper rate for the postwar period they also consider the 90 day treasury bill rate and the 10 yr treasury bond rate they compare and contrast their results to those of various others they also carry out recursive estimations to check their results for stability stock and watson 1993 conclude that a long span of data is needed to estimate long run money demand functions precisely their overall evidence is in favor of a stable long run money demand function with an income elasticity near one and an interest rate semielasticity near 0 10 however the postwar data are found to be not very informative a lack of low frequency variation in the postwar data as suggested by lucas 1988 does not allow a disentangling of the effects of output and interest rates on money demand for this time period estimates are imprecise and sensitive to subsample specifications due to substantial colinearity ball 2001 revisits the m1 money demand model of stock and watson 1993 using the same data set but extended through 1996 he applies the same array of estimation techniques as stock and watson did ball obtains precise estimates over the postwar period for his extended data set an income elasticity of approximately 0 5 and a semielasticity of 0 05 for the interest rate he does not find support for a velocity specification the m1 model is not stable over the period 1900 1996 lutkepohl terasvirta and wolters 1999 apply a nonlinear error correction model with smooth transition adjustment to capture instabilities in the linear cointegration model the long run equilibrium is described by a linear cointegrating relation and the adjustment to this long run equilibrium is nonlinear they analyze german m1 money demand granger and terisvirta 1993 terasvirta 1998 and van dijk terasvirta and franses 2002 provide details on the econometric theory for estimating and testing such nonlinear models

modelling money demand for a panel of eight transitional economies in this article we estimate money demand functions for a panel of eight transitional economies using quarterly data for the period 1995 01 1995 to 2005 03 we find that real m1 and real m2 and their determinants namely real income and short term domestic interest rate are cointegrated both for individual countries as well as for the panel long run elasticities suggest that consistent with theory real income positively and nominal interest rate negatively impact real money demand our test for panel granger causality suggests short run bidirectional causality between m1 and m2 and their determinants finally our tests for stability of the money demand functions reveal more cases of unstable money demand functions when m2 is used as a proxy for money demand

on the markov switching welfare cost of inflation abstract this paper uses the markov switching approach to account for instabilities in the long run money demand function and compute the welfare cost of inflation in the united states in doing so it circumvents the problem of data mining of some earlier seminal contributions on these issues allowing for complicated nonlinear dynamics and sudden changes in the parameters of the money demand function moreover it extends the sample period and investigates the robustness of results to alternative money demand specifications monetary aggregation procedures and assumptions regarding dynamics aspects of the money demand specification

inventory service level measures convexity and approximation we argue that standard approximations for two often used inventory service level measures may perform poorly in many situations then we confirm the long standing conjecture that the relatively exact formulas for these quantities are convex functions of the relevant control variables both results suggest the exact expressions should be seriously considered in practical work

the newsvendor problem review and directions for future research in this paper we review the contributions to date for analyzing the newsvendor problem our focus is on examining the specific extensions for analyzing this problem in the context of modeling customer demand supplier costs and the buyer risk profile more specifically we analyze the impact of market price marketing effort and stocking quantity on customer demand how supplier prices can serve as a coordination mechanism in a supply chain setting integrating alternative supplier pricing policies within the newsvendor framework and how the buyer s risk profile moderates the newsvendor order quantity decision for each of these areas we summarize the current literature and develop extensions finally we also propose directions for future research

a comparison among partial adjustment rational expectations and error correction estimates of the canadian demand for money starting from a dynamic optimization principle the currently most popular approaches to modelling money demand functions are derived the partial adjustment adaptive expectations rational expectations and error correction mechanism formulations are then estimated using a common data set the error correction mechanism equation is found to dominate the others either because their implicit restrictions are rejected rational expectations or by employing the encompassing principle partial adjustment adaptive expectations surprisingly all three forms have similar long run solutions since the short run dynamics differ substantially the results have important implications for the conduct of monetary policy

component commonality with service level requirements this paper extends recent results of baker et al baker k r m j magazine h l w nuttle 1986 the effect of commonality on safety stocks in a simple inventory model management sci 32 982 988 in understanding the impact of component commonality on stocking levels under service level constraints a model is formulated for an arbitrary number of products with general joint demand distribution the results obtained are not all intuitive while utilizing commonality is beneficial nothing general can be said about the resulting change in the components stock levels when the cost structure is of a particular simple form though some interesting general patterns do emerge we also discuss the case of using a service level measure where rationing of common components might be required and characterize the implied rationing rule

intergenerational resource rights efficiency and social optimality the discipline of economics is generally defined as the science of the allocation of scarce resources between competing social objectives given an initial distribution of resources between economic agents how would they behave so as to improve their welfare according to the pareto criterion the agents would exchange commodities until the opportunities for fruitful exchange were fully exhausted and no agent could be made better off without rendering at least one other agent worse off pareto efficiency is a powerful concept in microeconomic analysis provided that the initial distribution of property rights is equitable allocative efficiency gives rise to the best of all possible worlds acknowledging that the assumptions of perfect competition are often violated firms are monopolistic information is incomplete and externalities exist economists have argued for the modification of institutions so that economic reality will conform more closely to the assumptions of the model that yields such gratifying results but microeconomic theory has always maintained that allocative efficiency is in itself insufficient to maximize social welfare bator 1957 a social welfare function is required to discriminate a social optimum among the array of efficient allocations that correspond to alternative assignments of property rights though economists have posited alternative functional forms for the sake of pursuing conceptual arguments welfare functions have remained elusive constructs for well known theoretical and practical reasons consequently a sharp line of demarcation has been drawn between questions of efficiency the province of economics and equity the principal focus of ethical and political discourse in resource economics however the line demarcating efficiency and equity is often crossed the term optimal depletion appears regularly where only efficient depletion is meant while political debates about resource exploitation over time are laden with questions of the proper distribution of our natural patrimony between generations resource economists have predominantly espoused particular use rules that guarantee efficiency but overlook potential improvements in social welfare achievable through the reassignment of property rights across generations we document the evolution and current status of the misuse of the term optimal depletion in section ii we develop a simple two generation three period general equilibrium model in section iii to illustrate how alternative distributions of resource rights between generations relate to alternative pareto efficient solutions in section iv we demonstrate how different social welfare functions affect the optimal solution and associated assignment of resource rights between generations

sector level decisions in a sustainability constrained economy despite two decades of debate there remains little consensus about what sustainability is and how it should be achieved economists primarily portray sustainability as a macro level concern but there has been less attention on the implications of this social objective for policies related to the management of individual resources this paper derives guidance for sector level planning and project analysis from a macro level norm of intergenerational fairness optimal sustainable management involves making tradeoffs between sectors we derive a criteria for sector level planning and project analysis that help make those tradeoffs without losing site of the sustainability goal

optimal quality and quantity provisions for centralized vs decentralized distribution market size uncertainty effects abstract we provide insights on how market size uncertainty affects the optimal quality quantity provision in distribution channels when consumers are heterogeneous in their willingness to pay for product quality in this context we denote the difference between the manufacturer s optimal quality quantity provision for a centralized channel and its optimal analog for a decentralized channel as the quality quantity differential we find that market size uncertainty creates or increases the quantity differential but it does not affect the differential s polarity in contrast market size uncertainty decreases the quality differential and it does so to the extent that depending on the level of consumer heterogeneity it reverses the differential s polarity moreover we find that the higher the inherent uncertainty level the more pronounced are the effects we likewise find that the effects of market size uncertainty are amplified if the notion of consumer heterogeneity is replaced with retail level competition