a note on unionization and the elasticity of substitution if unions force employers off their demand curves the measured elasticity of substitutio n should be lower where unionization is stronger estimates based on pooled data for twenty two digit sic canadian manufacturing industrie s over the period 1971 81 support this proposition point estimates a re that the elasticity is 1 98 in the absence of unions 1 04 if empl oyees are fifty percent unionized and only 0 10 if employees are one hundred percent unionized however the results are not very robust to specification changes

uncertainty in the theory of renewable resource markets the natural growth rate of most renewable resource stocks is in part stochastic this paper examines the implications of such ecological uncertainty for competitive equilibrium in a market with property rights we show that stochastic fluctuations add a risk premium to the rate of return required to keep a unit of stock in situ and we examine the effects of fluctuations on resource rent examples are used to show that extraction can increase decrease or be left unchanged as the variance of the fluctuations increases depending on the extent of market self correction regulatory implications are also discussed renewable resource economics has traditionally been concerned with the study of dynamically optimal harvesting policies given a deterministic function for the natural growth of the resource stock issues have included the existence and characteristics of steady state equilibria for the optimally managed resource the need for and design of regulatory policies to prevent over exploitation and conditions under which as a social optimum or otherwise the resource will be exploited to extinction 1 much of this work has been based on the assumption of a fixed and exogenous price for the harvested resource typically resulting in bang bang solutions for the harvesting policy however some recent papers make price endogenous and thereby describe how the extraction rate and the rate of return and asset value of the resource behave in a competitive market with property rights 2

an analysis of technological change factor substitution and economies of scale in manufacturing industries in india the biases of technological change factor substitution and economies of scale in four major manufacturing industries viz cement electricity and gas cotton textiles and iron and steel in india are examined the translog cost functions are estimated using annual time series data covering the period 1960 61 to 1982 83 the study reveals that technical change has been biased towards the use of labour and materials and against the use of capital and energy in electricity and gas industries in cotton textiles the technological change has shown the opposity biases significant economies of sclae exist in the production of electricity and gas enough evidence of substitution possibilities among factors of production in all the four industries was also found

analyzing the indirect production function for u s manufacturing in recent years there has been considerable research conducted in applied production economics to estimate the firm s structure of technology and its production characteristics the main concept used in this research is the duality principle relating production and cost or profit together with the use of flexible form econometric specifications for estimating production technologies under the assumption of cost minimization or proft maximization duality implies that for any production function there exists a cost or profit function that provides an equivalent description of the technology what is less well known however is that the firm s technology can be equally well described by the indirect production function a production analog of the indirect utility function in consumer theory 5 8 9 the indirect production function is based on the firm s output maximization subject to a budget constraint on input costs of course it is evident enough that a firm choosing inputs to maximize output for a given input cost produces that output at the minimum cost by implication the indirect production and cost functions are equivalent ways of characterizing the firm s technology and as will be seen there exists a unique correspondence between the two functions in empirical application however the choice between the two functions hinges on the exogeneity or endogeneity of output for the indirect production function the level of output is an endogenous variable in the case of the cost function on the other hand output is exogenously given in most situations it is the indirect production function not the cost function that is more compatible with observed behavior of firms and industries while numerous studies have been conducted recently to estimate the cost or profit function in a variety of firms and industries 1 2 3 6 no attempts have been made to employ the indirect production function as a working tool in applied production analysis this paper attempts to provide empirical evidence from analyzing the indirect production function within the context of an application of the duality principle using the well known data set utilized by berndt and wood 3 and berndt and khaled 2 it reexamines the production structure of u s manufacturing based on a translog specification of the indirect production function for the underlying technology an important question is how the choice of a model the indirect production or cost function

common property resources storage facilities and ownership structures a cournot model of the oil market during the last decade economists have tried hard to convince meadows and his followers that market forces do not tend to exhaust our natural resources too rapidly as compared with the requirements of an intertemporal pareto optimum it is well known now that under well defined property rights and correct price expectations a competitive extraction industry brings about a pareto optimal depletion path and it has been shown that oligopolistic and monopolistic market structures may even produce a bias towards conservation 1 it is still an unresolved issue however which extraction path will result if property rights are imperfectly defined following the pioneering work of gordon 1954 there has been a large body of literature demonstrating that in the extreme case of free entry and myopic profit maximization there are strong reasons for excessive extraction 2 but this literature hardly yields reliable conclusions for the perhaps more realistic case where firms derive their behaviour from intertemporal optimization and where there is a common ownership but limited access to the resource the basic intuition behind the common pool problem is that the individual agent chooses an extraction policy other than the one he would choose under well defined property rights since he is afraid that part of the resource he leaves underground will be extracted and sold by others 3 despite the simplicity of this intuition there does not seem to be any publication that analyses it within an intertemporal equilibrium model with rational and far sighted agents this is the motivation for the present approach the approach studies the common pool problem in the context of an oligopolistic world market for oil it posits a given number of identical firms extracting oil from holdings between some of which there is mutual seepage the firms sell the extracted oil in the same market or they store it in privately owned seepage proof tanks each firm derives its behaviour from intertemporal optimization under perfect foresight of the time paths of the model variables but cournotesque conjectures about the reactions of its competitors except for the assumption of storage facilities this specification is closely related to models previously studied by khalatbari 1977 and kemp and long 1980 essay 10 4 the two models are very similar but they yield strikingly different conclusions while kemp and long find that the extraction path chosen by the firms is pareto optimal i e that the price of the resource rises at a rate given by the market rate of interest khalatbari contends that there is over extraction kemp and long convincingly demonstrate that khalatbari s model suffers from an inconsistency in the way the individual firm expects its rivals to respond to its own actions and they argue that this inconsistency is the reason for the divergence in results thus the casual reader gets the

factor substitution average firm size and economic growth this paper extends the lucas 1978 the bell journal of economics 9 2 508 523 analysis of firm size by taking into account a normalised aggregate ces production function in a general equilibrium framework it is proved that there is an inverse relation between the elasticity of substitution and average firm size if interpreted together with the fact that richer countries are characterised by a higher elasticity of substitution this result can explain why the recent literature finds a positive association between the importance of smes in an economy and its stage of development but seems to fail in finding causality between the two both have a common origin a high value of the elasticity of substitution this paper also provides a first empirical test of the theory proposed using cross country data from both developed and developing countries

capital accumulation games of infinite duration abstract consider a market in which firms accumulate capital according to the nerlove arrow capital accumulation equation each player chooses a path of investment and thus an induced path of capital to maximize his total discounted profits which depend on his own capital and the capital stocks of his rivals existence is proved for such a nonzero sum infinite horizon differential game and conditions under which the game converges to a particular stationary point regardless of the initial conditions are shown thus the game possesses the property of conditional global asymptotic stability

the elasticity of substitution in india s manufacturing sector abstract using cross section data and the translog cost function this paper examines the substitution possibilities between capital and materials and labor and materials since raw materials might be used to overcome the bottlenecks caused by shortages of physical capital and skilled labor three significant conclusions are a since materials are substitutable for both capital and labor to a considerable extent capital and skilled labor may not be a binding constraint on growth agricultural materials expansion may substitute for these inputs and lead to expansion in the industrial sector b fixed proportion models are not warranted in india without modification and c separability tests showed that materials must be included in the production function

oligopoly equilibria in nonrenewable resource markets abstract most nash cournot oligopoly models of nonrenewable resources apply open loop equilibrium concepts and are based on physical resource depletion this paper studies feedback equilibria and economic depletion assuming affine quadratic functional forms the existence uniqueness and explicit solutions for the equilibria are derived for duopoly and n player oligopoly with multiple resource stocks for the cases of nonquadratic criteria we develop a numeric solution scheme for the nash feedback equilibrium this scheme is an application of a discrete time discrete state controlled markov chain approximation method originally developed for solving deterministic and stochastic dynamic optimization problems in our nash cournot equilibrium the degree of concentration in supply declines over time whereas the previous models with physical depletion and open loop equilibrium concepts predict that a nash cournot resource market will develop in the direction of monopoly supply

open loop and feedback models of dynamic oligopoly abstract a simple method of estimating the degree of oligopoly power in dynamic markets using either open loop or feedback subgame perfect strategies is developed new theoretical results are presented for families of oligopoly models differences between discrete time and continuoustime models and open loop and feedback models are demonstrated the effects of increasing the number of firms or adjustment costs are examined

ces production functions and economic growth we examine inconsistencies and controversies related to the use of ces production functions in growth models first we show that not all variants of ces functions commonly used are consistently specified second using a simple growth model we find that a higher elasticity of substitution leads to a higher steady state and makes the emergence of permanent growth more probable it is also pointed out that the effect of a higher elasticity of substitution on the speed of convergence depends on the relative scarcity of the factors of production finally we discuss possible explanations of variations in the elasticity of substitution jel classification o41 o11

does firm growth increase corruption evidence from an instrumental variable approach prior literature on the role that firm heterogeneity plays in corruption finds that larger firms pay smaller bribes and are less likely to pay bribes than smaller firms these studies however often overlook the plausible reverse causality between firm growth or firm size and corruption utilizing an innovative identification strategy that accounts for this source of endogeneity this study finds that increased firm size actually causes greater corruption and bureaucratic burdens on a typical firm and provides evidence against the argument for a uniform corruption burden regardless of size it was determined that a one standard deviation increase in sales leads to 0 33 standard deviation increase in bribes and to 0 36 standard deviation increase in management time spent dealing with public officials moreover although corruption burden increases with increasing firm size we find that this relationship is non linear and diminishes in magnitude as firm size approaches to medium and large we conclude with implications and policy considerations

policy reform and labour demand in branches of sri lankan manufacturing industry many policy reforms in developing countries aim to remove factor market distortions whether such reforms reduce unemployment depends partly on the substitution possibilities between labour and other factors of production this paper examines labour demand in seven branches of sri lankan manufacturing industry using data on 4 digit industrial categories over the 1990 to 1997 period the box cox transformation is used to allow for flexible and data dependent elasticities the elasticity of capital labour substitution varies widely across the branches of industry and is usually variable rather than constant the average long run own wage elasticity of labour demand for the manufacturing sector is estimated as 0 80 so factor price policy should have an important effect on labour demand in this setting

unemployment wage bargaining and capital labour substitution many economists believe that capital accumulation technical progress and labour force expansion have no lasting effect on unemployment this view rests on the empirically doubtful assumption that the elasticity of substitution between labour and capital is equal to unity i e production is cobb douglas using a simple model based on the work of layard nickell and jackman this paper demonstrates that with a lower elasticity of substitution the equilibrium unemployment rate is affected by all of the above factors it considers briefly how capital accumulation may be endogenised and what long run implications this has for unemployment copyright 1999 by oxford university press

economic growth and the elasticity of substitution two theorems and some suggestions at the beginning of the twentieth century the work of the swedish economist knut wicksell 1901 marked an important advance in our understanding of the relationship between the structure of production functions and income distribution wicksell had asked the following question among many others suppose that the marginal productivities are equal to the remuneration rates of each factor what then should be the form of the corresponding production function he pointed out p 125 that the general integral of the partial differential equation implied by this relationship was of the form y lf kil which meant in turn that the product y was necessarily a homogeneous of degree one function of capital k and labor l as an example he gave a function where the shares of k and l in y were constant and wrote down the function which would be rediscovered decades later by charles w cobb and paul h douglas 1928 however it is only half a century later in robert m solow s nobel prize winning 1956 essay that implications between the structure of the production function and long run equilibrium or disequilibrium of the economy were drawn in his classic article a contribution to the theory of economic growth solow had considered three cases analytically other cases were also discussed geometrically using a phase diagram he had labeled the two first cases 1hlarrod domar and cobb douglas respectively and he referred to the third type of production function as offering a bit of variety it was y ak 2 l 2 2 a particular case of y akp lp 1p in those early days solow had not pointed out to the reader that his cases could have been numbered 0 1 and 2 following the elasticity of substitution of the corresponding production function it would be only five years later in 1961 that with his coauthors kenneth j arrow et al he would find the general form of the two factor constant elasticity of substitution ces production function by integrating the differential equation corresponding to the observed relationship between output per capita and the wage rate solow s third case was indeed highly interesting since it allowed the possibility of everincreasing income per head even without any technical progress indeed solow showed that due to the efficiency of the system entailed by the particular production function he had chosen there existed a threshold for the savings rates s to generate investment per head large enough for income per head to grow forever that threshold was s nla2 where n is the growth rate of the population it was then natural to ask whether one could express that threshold in terms of the elasticity of substitution a the value of that threshold was determined by de la grandville 1989 to be equal to s no3 or where a is k s coefficient in a normalized ces function equal to a in solow s third case where u 2 for any s and n values this relationship gives also the threshold value in implicit form by the solution of ao1 1 log 3q or ilog nls by totally differentiating the last relationship one could observe that the threshold for the elasticity of substitution to entail ever sustained growth was an in klump faculty of mathematics and economics university of ulm helmholtzstrasse 20 d 89081 ulm germany de la grandville department of economics university of geneva 102 boulevard carl vogt ch 1211 geneva 4 switzerland we gratefully acknowledge the comments of seminar participants at stanford university and at the universities of stuttgart hohenheim and munich where parts of the paper were presented also we would like to thank without implicating in any way robert solow for his insightful remarks and an anonymous referee for very helnfuil supgestions wicksell cobb and douglas would no doubt burst with pride if they knew that one of our first year students wrote in a paper of his of course we recognize here a kirk douglas production function

common pool equities an arbitrage based non cooperative solution to the common pool resource problem abstract it is proposed that a new type of property right termed a common pool equity can solve the common pool resource problem this equity may be presented to any firm that extracts from the resource for a share in profits it is shown that a profit arbitrage condition ensures that the market and socially efficient solutions correspond whenever market power is absent the cost externalities are fully internalized

an econometric estimation of hicksian and marshallian elasticities in indian manufacturing the knowledge of substitution possibilities between different factors of production is essential in evaluating the impact of public policies on productivity employment industrial growth and factor intensity since the advent of flexible functional forms in the early 1970s a large number of studies have estimated the ease of factor substitution however to date most of the empirical evidence on factor substitution is based on a cost function a drawback with the cost function

inefficiency of credible strategies in oligopolistic resource markets with uncertainty abstract the implications of different information patterns for firms in oligopolistic resource markets are considered the traditional open loop nash equilibrium with static information sets is one of many possible nash equilibria and is not suitable for stochastic environments when shocks to resource growth are serially uncorrelated there are no gains from conditioning the harvest on past stock levels and the feedback or credible nash equilibrium is the appropriate nash equilibrium concept this credible equilibrium assumes that firms have knowledge of current stocks of reserves which typically leads to more rapid extraction of the resource and possibly extinction since the open loop nash equilibrium is efficient when demand is iso elastic and extraction costs are zero it is clear that an increase in information can be detrimental to firms in the industry

a one line proof of the slutsky equation one focus of the usual classroom discussion of consumer theory is the demonstration that the individual consumer s reaction to a change in the market price of a commodity can be usefully broken down into vectors of substitution effects and income effects the slutskv equation relating the price effect to the substitution and income effects can be simply nmotivated by j r hicks graphical presentation p 31 but the usual proof see paul samuelson is very tedious and nonintuitive if the instructor includes a discussion of the expenditure function in his curriculum however he has available a concise intuitively appealing proof of the slutsky equation 1 suppose a consumer with income y faces a vector of commoditv prices p his marshallian demand curve for commodity j is given by xj dj y p the minimum expenditure necessary for the consumer to achieve any utility level u is given by his expenditure function y m u p here y is in units of the jth good his hicksian income compensated demand for commodity j is represented xj hi u p if m is differentiable we have the well known result that

an open access fishery with rational expectations explain the evolution of the fish stock and the boat fleet as well as determine their equilibrium levels 2 while the changes in the fish stock are described by a biological rule entry and exit from the fishing industry are determined by how expectations are formed we examine a general model in which entry and exit are proportional to the present value of expected profits and compare two special cases of adaptive myopic expectations and rational expectations although both expectations mechanisms lead to the same equilibrium values they lead to different adjustment paths where expectations solely depend on current values myopic expectations it is well known that boats enter the fishery only when the fish stock is greater than its steady state stock 3 with rational expectations however boats may enter when the fish stock is much lower than its steady state value provided the boat fleet is sufficiently small this difference in adjustment is observable and in principle leads to an obvious test on how agents form expectations section 2 develops a general dynamic model for studying fisheries in section 3 we show that the model standardly used in the literature is equivalent to a myopic adaptive expectations model a rational expectations model is analyzed in section 4 the standard and rational expectations models are compared in section 5 section 6 illustrates this comparison using a simulation based on a schaefer model of the pacific halibut fishery section 7 presents the conclusions

efficiency inducing tax for a common property oligopoly the author characterizes the markov perfect tax that induces a common property oligopoly to extract efficiently a nonrenewable resource for linear and isoelastic demand he provides closed form expressions of the unique specific tax industry profits may be higher or lower in the oligopoly with the tax relative to the competitive equilibrium with property rights for linear or isoelastic demand there exists no feasible open loop tax that induces efficient extraction in this case the policymaker gains no advantage from being able to make binding commitments copyright 1992 by royal economic society

competitive versus efficient extraction of a common property resource the groundwater case abstract in this paper socially optimal and private extraction of a common property aquifer are compared open loop equilibrium and feedback equilibrium in linear strategies have been computed to characterize private extraction the use of these two equilibrium concepts allows us to distinguish between cost and strategic externalities as long as the open loop solution captures only the cost externality and the feedback solution captures both the results show that strategic behaviour increases the overexploitation of the aquifer compared to the open loop solution however if the groundwater storage capacity is large the difference between the socially optimal and private extraction the latter characterized by a feedback equilibrium is negligible

economic growth technical change biases and the elasticity of substitution a test of the de la grandville hypothesis a recent development in microeconomic theory suggests that the size of the elasticity of substitution between factors is relevant to economic growth this study undertakes an empirical investigation of this proposition comparing two economies the united states and south korea the authors test results support the de la grandville hypothesis that the elasticity of substitution is a potent explanatory variable of economic growth this inquiry also provides a clue to the puzzle that the u s elasticity of substitution between labor and capital is well below unity whereas that of south korea is close to unity nonetheless the u s factor shares have tended to remain fairly stable whereas the distributive shares of south korea seem to have changed in favor of capital their findings indicate that a high elasticity of substitution is a bad signal for the distribution of income under the paradigm of modern technology copyright 1991 by mit press

optimality and consistency in a differential game with non renewable resources abstract imperfect competition amongst buyers for a non renewable resource is modeled as a stackelberg differential game the buyers may act as a cartel or behave non cooperatively in setting tariffs which the sellers take as given the buyer s optimal policy is not consistent when extraction costs depend on the stock level both optimal and consistent unit and ad valorem tariff s are analyzed when a buyers cartel uses a consistent tariff the sellers may prefer to behave as perfect competitors or a monopolist depending on the functional form of demand and cost non cooperative buyers who are constrained to act consistently are unable to extract any rent from competitive sellers

functional separability and the existence of consistent aggregates in u s manufacturing comment this paper examines the relationship between separability of the direct production function in inputs and separability of the indirect production function in input prices in particular it shows that simultaneous direct and indirect weak separability implies homotheticity of the direct production function and hence homotheticity of the indirect production function thus inferences regarding direct separability based on empirical tests for indirect separability would be valid only if homotheticity is also imposed and treated as maintained hypothesis copyright 1996 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

appropriation of common access natural resources through exploration the relevance of the open loop concept in this paper the open loop equilibrium is rehabilitated as a sensible concept for analyzing common property situations in a model of natur al resource exploration in which the sole motivation to explore prior to extraction arises from a strategic incentive to preempt competito rs a consistency rule to the exploration game is applied under which the commonality of reserves is preserved even if strategies are open loop under this rule the so often claimed efficiency of the common property open loop equilibrium is lost copyright 1988 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

scale biased technological development in canada s industrialization 1900 1929 the relationships between factor use and scale and technological change and scale are emphasized in a translog cost function analysis of technological development in four sectors of canadian manufacturing 1900 29 by paying particular attention to the role of electrification in this technological development the major findings are that the increased use of electricity was not in general scale dependent and that electrification may have been a factor in increasing the relative productivity of smaller scale units over the period a hypothesis that states that technical change is partially induced by increased scale is however confirmed copyright 1990 by mit press

measures of capacity utilization and its determinants a study of indian manufacturing we estimate capacity utilization cu rates in for selected industries in indian manufacturing for the 20 year period 1976 1996 we estimate a generalized leontief variable cost function with capital as a quasi fixed input to derive our cu measures using error component techniques we note substantial variations in cu both across industries and over time in general we find that cu rates were higher in the earlier time period dropped in the mid 80s and started rising again in the early 90s cu rates in our analysis are sensitive to input prices with the sole exception of the price of labor we also confirm the standard result that variations in demand are a significant driving force for variations in cu we find that cu is positively related to the magnitude of labor intensity in production this holds for both between industries and within industries empirical results also indicate that traditional measures of cu such as minimum capital output ratio and peak to peak are not appropriate proxies for

dynamic oligopoly with capacity adjustment costs abstract the literature on strategic investment emphasized the case of completely irreversible investment this paper considers an oligopoly model in which investment is reversible and capacity is subject to adjustment costs an n player linear quadratic differential game is analyzed existence and characterization results for perfect equilibrium feedback strategies are provided feedback strategies provide incentives for each player to invest strategically so as to preempt subsequent expansion by rivals a larger set of perfect equilibria is constructed by using memory dependent trigger strategies equilibria of this type are shown to support joint value maximization for some initial states and asymmetric steady states

oligopoly extraction of a common property natural resource the importance of the period of commitment in dynamic games the theory of noncooperative dynamic games has provided an extremely powerful framework for studying many of the classic questions in industrial organization for example questions about resource extraction advertising research and development investment in new capacity and barriers to entry where interactions over time among few firms are involved however an important methodological issue arises when economic competition over time is modeled as a dynamic game the issue is the appropriate formulation of the players strategy spaces

constrained output maximization and us agriculture this paper presents a framework for estimating an indirect production function and then applies it to aggregate us agriculture issues addressed include tests of standard hypotheses about the underlying technology homotheticity neutral technical change etc as well as examination of consistency in aggregation and the effects of changes in the level of aggregate expenditure on farm output since there already exist several studies empirically describing agricultural production technologies with indirect objective functions one might fairly ask whether this paper really breaks any new ground we feel that it does one reason is that existing studies e g binswanger 1974 lopez 1980 ball and chambers 1982 ray 1982 and weaver 1983 all rely on either profit or cost functions to date there appears to be only one study using an indirect production appelbaum 1979 and it is not in agriculture this seems unfortunate because there are many instances in agriculture for which an indirect productio

aggressive oil extraction and precautionary saving coping with volatility the effects of stochastic oil demand on optimal oil extraction paths and tax spending and government debt policies are analyzed when the oil demand schedule is linear and preferences quadratic without prudence optimal oil extraction is governed by the hotelling rule and optimal budgetary policies by the tax and consumption smoothing principle volatile oil demand brings forward oil extraction and induces a bigger government surplus with prudence the government depletes oil reserves even more aggressively and engages in additional precautionary saving financed by postponing spending and bringing taxes forward especially if it has substantial monopoly power on the oil market gives high priority to the public spending target is very prudent and future oil demand has high variance uncertain economic prospects induce even higher precautionary saving and if non oil revenue shocks and oil revenue shocks are positively correlated even more aggressive oil extraction in contrast prudent governments deliberately underestimate oil reserves which induce less aggressive oil depletion and less government saving but less so if uncertainty about reserves and oil demand are positively correlated

international aspects of pollution control pollution is a by product of production is only gradually dissolved by the environment and crosses national borders the market outcome ignores the adverse effects of pollution and thus yields higher levels of output and pollution than would prevail under a supranational social planner which does care about pollution in practice governments often do not cooperate and this leads to outcomes of pollution and production in between the market outcomes and the outcomes under supra national social planning absence of precommitment leads to lower emission charges less cleaning up activities and more pollution appropriate levels of emission charges under the various outcomes are a result of this analysis attention is also paid to investment in clean technology the debate between optimists who believe that higher production is compatible with sound environmental policy and pessimists can be analysed in this way