optimal supply diversification under general supply risks we analyze a planning model for a firm or public organization that needs to cover uncertain demand for a given item by procuring supplies from multiple sources the necessity to employ multiple suppliers arises from the fact that when an order is placed with any of the suppliers only a random fraction of the order size is usable the model considers a single demand season with a given demand distribution where all supplies need to be ordered simultaneously before the start of the season the suppliers differ from one another in terms of their yield distributions their procurement costs and capacity levels the planning model determines which of the potential suppliers are to be retained and what size order is to be placed with each we consider two versions of the planning model in the first the service constraint model scm the orders must be such that the available supply of usable units covers the random demand during the season with at least a given probability in the second version of the model the total cost model tcm the orders are determined so as to minimize the aggregate of procurement costs and end of the season inventory and shortage costs in the classical inventory model with a single fully reliable supplier these two models are known to be equivalent but the equivalency breaks down under multiple suppliers with unreliable yields for both the service constraint and total cost models we develop a highly efficient procedure that generates the optimal set of suppliers as well as the optimal orders to be assigned to each most importantly these procedures generate a variety of important qualitative insights for example regarding which sets of suppliers allow for a feasible solution both when they have ample supply and when they are capacitated and how various model parameters influence the selected set of suppliers the aggregate order size and the optimal cost values

an economic model of representative democracy this paper develops an approach to the study of democratic policy making where politicians are selected by the people from those citizens who present themselves as candidates for public office the approach has a number of attractive features first it is a conceptualization of a pure form of representative democracy in which government is by as well as of the people second the model is analytically tractable being able to handle multidimensional issue and policy spaces very naturally third it provides a vehicle for answering normative questions about the performance of representative democracy

job creation process in a transition economy in many european countries sme policy is close to being a synonym for job creation most empirical research on the job generation potential of small firms over the last decade has been done in the stable and favorable economic conditions of market economies the paper investigates the role of small firms in more difficult circumstances on an empirical data set for slovenia the paper tries to show that small firms have been the most important employer during the transition period a finding that very likely can be extrapolated for other european transition economies over the last decade slovenia has transformed from a labor managed economic system to a market oriented economy if we compare the firm size structure in a socialist like economy to the firm size structure in a mature market economy close to equilibrium we notice a typical absence of small and medium sized firms with the exception of craft shops that was how slovenia appeared in the early nineties charac terized by the removal of administrative barriers transition encouraged a spontaneous entrepreneurial wave through an expanding small business sector the ensuing changes in employment distribution changed the firm size structure

job creation and job destruction in great britain in the 1980s using data from the workplace industrial relations surveys of 1980 1984 and 1990 the authors investigate processes of job creation and job destruction in britain they find that rates of employment growth job creation and job destruction were higher at the end of the 1980s than at the beginning bothjob creation and job destruction were extremely concentrated about 50 of each was accounted for by just 4 of continuing establishments employment growth was apparently more variable in manufacturing plants than in private service sector workplaces some variables negatively related to employment growth were unionization establishment size establishment age and location in the private manufacturing sector versus private service sector

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

majority voting with single crossing preferences we clarify and extend a number of sufficient conditions for the existence of a majority voting equilibrium on one dimensional choice domains these conditions variously stated in the previous literature all impose order restrictions on voter preferences for instance monotone marginal rates of substitution which we show to imply or be equivalent to a general ordinal version of the single crossing condition this simple property is economically intuitive and easily checked in applications this ease of application is demonstrated through an examination of voting models of redistributive income taxation and trade union bargaining behaviour

jobs and the business life cycle in the uk there have been a number of statistical studies in recent years of the firm life cycle its effects on employment and the role of small firms in the job generation process they have all followed the changes which take place in a population of firms through time birch based his usa national analysis on the dun and bradstreet computer files for 5 6 million establishments covering 80 of all private sector employment and some of his findings were of a controversial nature most british studies to date have been limited to single regions looking at aspects of job generation in detail there is now a series of local studies for the regions of glasgow the midlands cleveland manchester and merseyside the dti ganguly 1982a has carried out an important national study based on vat data and a sectoral study macey 1982 of manufacturing the study described here used the data of dun and bradstreet uk the commercial credit rating market research and information company to estimate job generation pe

why has the investment performance of technology specialist european venture capital funds been so poor abstract this paper seeks to identify and model the key parameters which impact on the commercial performance of a specialist technology focused early stage venture capital fund using both input costs and output expected values data provided by a number of specialist independent venture capital firms a spreadsheet model of a 10 year term fund is developed these figures are used to generate internal rate of return irr and net present value npv performance calculations for the investment commitments of both the institutional limited partners and venture capitalist general partner the generically defined model allows the user to address both conceptual and pragmatic questions regarding the relationship between fund structure and performance the model is further developed to determine the effect on fund performance of two venture capital related indirect state support schemes guarantee and leverage options iterative interrogations of the model demonstrate the sensitivity of economic returns to the scale of the investment activity state supported schemes mitigate but do not remove the negative performance consequences of small fund size a fund with under 15 million us 25 million or ecu21 million under management is of increasing economic vulnerability

diversification under supply uncertainty supply chain management is becoming an increasingly important issue especially when in most industries the cost of materials purchased comprises 40 60 of the total sales revenue despite the benefits cited for single sourcing in the popular literature there is enough evidence of industries having two three sources for most parts in this paper we address the operational issue of quantity allocation between two uncertain suppliers and its effects on the inventory policies of the buyer based on the type of delivery contract a buyer has with the suppliers we suggest three models for the supply process model i is a one delivery contract with all of the order quantity delivered either in the current period with probability or in the next period with probability 1 model ii is also a one delivery contract with a random fraction of the order quantity delivered in the current period the portion of the order quantity not delivered is cancelled model iii is similar to model ii with the remaining quantity delivered in the next period we derive the optimal ordering policies that minimize the total ordering holding and penalty costs with backlogging we show that the optimal ordering policy in period n for each of these models is as follows for x a n order nothing for vi n x a n use only one supplier and for x vi n order from both suppliers for the limiting case in the single period version of model i we derive conditions under which one would continue ordering from one or the other or both suppliers for model ii we give sufficient conditions for not using the second more expensive supplier when the demand and yield distributions have some special form for the single period version of models ii and iii with equal marginal ordering costs we show that the optimal order quantities follow a ratio rule when demand is exponential and yields are either normal or gamma distributed

political competition within and between parties an application to environmental policy this paper presents a political economy model that explains the low rate of emission taxes in the u s as well as the fact that neither democrats nor republicans propose to increase them the voters differ according to their wage and capital incomes which are assumed to have a bivariate lognormal distribution they vote over the emission tax rate and a budgetary rule that specifies how to redistribute the tax proceeds the political competition is modeled a la roemer 2001 where the two parties care for the policies they propose as well as the probability of winning the equilibrium solution concept is the party unanimity nash equilibrium pune we calibrate the model using u s data and compute the punes numerically two main results emerge all viable punes entail subsidies on emissions as opposed to taxes this indicates the importance of distributional concerns in garnering political support for environmental policies second parties always propose an interior value for the budgetary rule even though all citizens prefer extreme values this illustrates the emergence of political compromise to attract voters

majority voting in a model of means testing abstract we study a model of endogenous means testing where households differ in their income and where the in kind transfer received by each household declines with income majority voting determines the two dimensions of public policy the size of the welfare program and the means testing rate we establish the existence of a sequential majority voting equilibrium and show that the means testing rate increases with the size of the program but the fraction and the identity of the households receiving the transfers are independent of the program size furthermore the set of subsidy recipients does not depend on households preferences but depends only on income heterogeneity

majority support for progressive income taxation with corner preferences this paper studies voting over quadratic taxation when incomeis fixed and taxation non distortionary the set of feasibletaxes is compact and self interested voters have cornerpreferences we first show that if a majority winning taxpolicy exists it involves maximum progressivity we then givea necessary and sufficient condition on the incomedistribution for a majority winner to exist this conditionappears to be satisfied for a large class of distributionfunctions

infinite horizon strategies for replenishment systems with a general pool of suppliers we consider a general infinite horizon inventory control model that combines demand and supply risks and the firm s ability to mitigate the supply risks by diversifying its procurement orders among a set of n potential suppliers supply risks arise because only a random percentage of any given replenishment order is delivered as useable units the suppliers are characterized by the price they charge and the distribution of their yield factor assuming unsatisfied demand is backlogged the firm incurs as in standard inventory models three types of costs i procurement costs ii inventory carrying costs for units carried over from one period to the next and iii backlogging costs we establish the existence of an optimal stationary policy under both the long run discounted and average cost criteria and characterize its structure assuming each period s inventory level distribution can be approximated as a normal we develop an efficient solution method identifying additional structural properties finally we identify a simple class of heuristic policies that come close to being optimal

taxes budgetary rule and majority voting this paper studies majority voting outcomes fora specific class of two dimensional policies one policyinstrument influences efficiency and the other redistribution absent the political process the two dimensions can beaddressed separately with a two dimensional vote the twoaspects will interact in a non trivial way the illustrativepolicy we consider requires taxing an externality generatinggood and determining a budgetary rule which specifies theproportions of the tax proceeds that go to wage earners and tocapital owners we show first a sequential vote wherein thetax rate is determined first and the budgetary rule second always possesses an equilibrium and that this equilibrium isthe median endowed individual s most preferred policy second the reverse sequential choice implies that the median endowedindividual may but need not be decisive third the shepsle procedure also implies that the equilibrium is thepolicy most favored by the median individual fourth thisequilibrium constitutes under certain circumstances thecondorcet winner for the unrestricted simultaneous votinggame

average cost single stage inventory models an analysis using a vanishing discount approach an important problem in the theory of dynamic programming is that of characterizing sufficient conditions under which the optimal policies for markov decision processes mdps under the infinite horizon discounted cost criterion converge to an optimal policy under the average cost criterion as the discount factor approaches 1 in this paper we provide for stochastic inventory models a set of such sufficient conditions these conditions unlike many others in the dynamic programming literature hold when the action space is noncompact and the underlying transition law is weakly continuous moreover we verify that these conditions hold for almost all conceivable single stage inventory models with few assumptions on cost and demand parameters as a consequence of our analysis we partially characterize for the first time optimal policies for the following inventory systems under the infinite horizon average cost criterion which have thus far been a challenge a capacitated systems with setup costs b uncapacitated systems with convex ordering costs plus a setup cost and c systems with lost sales and lead times

selecting a portfolio of suppliers under demand and supply risks we analyze a planning model for a firm or public organization that needs to cover uncertain demand for a given item by procuring supplies from multiple sources each source faces a random yield factor with a general probability distribution the model considers a single demand season all supplies need to be ordered before the start of the season the planning problem amounts to selecting which of the given set of suppliers to retain and how much to order from each so as to minimize total procurement costs while ensuring that the uncertain demand is met with a given probability the total procurement costs consist of variable costs that are proportional to the total quantity delivered by the suppliers and a fixed cost for each participating supplier incurred irrespective of his supply level each potential supplier is characterized by a given fixed cost and a given distribution of his random yield factor the yield factors at different suppliers are assumed to be independent of the season s demand which is described by a general probability distribution determining the optimal set of suppliers the aggregate order and its allocation among the suppliers on the basis of the exact shortfall probability is prohibitively difficult we have therefore developed two approximations for the shortfall probability although both approximations are shown to be highly accurate the first based on a large deviations technique ldt has the advantage of resulting in a rigorous upper bound for the required total order and associated costs the second approximation is based on a central limit theorem clt and is shown to be asymptotically accurate whereas the order quantities determined by this method are asymptotically optimal as the number of suppliers grows most importantly this clt based approximation permits many important qualitative insights

employment change in the small business sector evidence from five manufacturing industries this paper examines the scale and nature of employment flows into and out of the small business sector sbs in five united kingdom manufacturing industries over the period 1979 85 it first provides a taxonomic framework for analysing these flows it then draws on specially prepared analyses from the annual census of production acop for the uk to show that the sbs in each industry has experienced very substantial turbulence although the sbs across all five industries lost only four per cent of 1979 employment over the period movement in and out each represented about half of 1979 employment most gains and losses were in the very small size bands the paper also briefly explores the relationship between births and deaths and industrial characteristics across the five industries the study raises questions about the causes and costs of high turbulence in the sbs it also demonstrates the potential value of the acop data base for longitudinal studies of business in the uk 1

technical note linear inflation rules for the random yield problem analysis and computations in this paper we propose a simple heuristic approach for the inventory control problem with stochastic demand and multiplicative random yield our heuristic tries to find the best candidate within a class of policies that are referred to in the literature as the linear inflation rule lir policies our approach is computationally fast easy to implement and intuitive to understand moreover we find that in a significant number of instances our heuristic performs better than several other well known heuristics that are available in the literature

coordinating inventory control and pricing strategies with random demand and fixed ordering cost the finite horizon case we analyze a finite horizon single product periodic review model in which pricing and production inventory decisions are made simultaneously demands in different periods are random variables that are independent of each other and their distributions depend on the product price pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered the objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon we show that when the demand model is additive the profit to go functions arek concave and hence an s s p policy is optimal in such a policy the period inventory is managed based on the classical s s policy and price is determined based on the inventory position at the beginning of each period for more general demand functions i e multiplicative plus additive functions we demonstrate that the profit to go function is not necessarilyk concave and an s s p policy is not necessarily optimal we introduce a new concept the symmetrick concave functions and apply it to provide a characterization of the optimal policy

a model of political competition with citizen candidates the authors develop a model of electoral competition in which citizens choose whether or not to run as candidates a winner implements her favorite policy the equilibrium number of candidates depends negatively on the cost of running and positively on the benefits of winning for some parameter values all equilibria under plurality rule have exactly two candidates whose positions are distinct two candidate elections are more likely under plurality rule than under a runoff system the candidates positions are less differentiated under a runoff system there exist equilibria under both systems in which some candidates have no chance of winning

the growth of uk companies and their contribution to job generation 1985 1987 theories of firm growth are reviewed and various models examined the firm growth and job generation process in the uk over the period 1985 87 is examined empirically by using the very large data files of the dun and bradstreet credit rating organisation in the analysis four computer processes were carried out the sorting and matching of files the cleaning of the data the validation of the cleaned data and the scaling up the results the final adjusted data were grossed up to provide an overview of the growth and job generation potential of uk firms this is compared with past results for the periods 1971 81 and 1982 84 small firms performed well providing 48 of all new jobs although consisting of only 21 of all employment in 1985 the 1000 employee range provided only 13 of all new jobs over the period although consisting of 37 of all employment in 1985 an overall trend of positive performance in smaller firms and negative in larger firms was apparent the 20 49 employee cohort performed unusually poorly in firm and job creation against the expected pattern the effect of takeovers mergers and rationalisations on employment was examined as expected there was negligible restructuring of small firms but over 5 of employees in the largest 1000 cohort were involved in some form of reorganisation

taxation as a social choice problem the scope of the laffer argument abstract this paper studies the form of the tax equilibrium set in simple diamond mirrlees models and characterizes the corresponding laffer curves the curves need not ever slope downward and can have multiple local maxima local information about them is thus not sufficient to place restrictions on optimal choice among tax systems in this simple framework the problem of choice among tax systems is shown to have no more structure than an abstract social choice problem