civil unrest in north africa risks for natural gas supply abstract the uprising and military confrontation in libya that began in february 2011 has led to disruptions of gas supplies to europe an analysis of how europe has compensated for these missing gas volumes shows that this situation has not affected security of supply however this situation would change if the north african uprising were to spread to algeria since algeria is a much more important gas supplier to europe than is libya more severe consequences would be likely applying a natural gas infrastructure model we investigate the impact of supplier disruptions from both countries for a summer and winter period our analysis shows that disruptions in the low demand summer months could be compensated for mainly by lng imports into several european countries an investigation of a similar situation at the beginning of the winter shows that security of supply would be severely compromised and that disruptions to italian consumers would be unavoidable the analysis thereby highlights the importance of taking the political stability of supply countries into account when assessing the security of european gas imports

strategic eurasian natural gas market model for energy security and policy analysis formulation and application to south stream abstract the mathematical formulation of a strategic eurasian natural gas market model is presented the model represents horizontal oligopolistic relationships among producers bilateral market power between producer russia and transit ukraine countries detailed transport constraints and operation decisions over a 20 year time horizon to demonstrate the model s capabilities a financial and market analysis of the proposed south stream gas pipeline from russia via the black sea to south europe is summarized insights obtained include the following first expectations of high demand growth in europe and or transit risks do not justify the construction of the south stream pipeline because under all demand and ukraine transit interruption scenarios the net benefits to the south stream participants are negative the npv ranges from 1 9 billion bn to 7 4 bn second ukraine s perception of high transit market power vis a vis russia may trigger the construction of the otherwise unprofitable south stream project thus under ukraine s high transit market power scenario the npv of south stream ranges between 2 4 bn and 24 5 bn third we find that the south stream investment increases the efficiency of the european gas market under the following conditions i when gas demand in europe grows 2 per year up to 2030 ii when ukraine poses high transit market power or iii under a combination of severe transit risks through ukraine and low demand scenarios in europe it should be noted that the value of south stream to both its project sponsors and the market as a whole is much higher when ukraine exercises transit market power than under the high demand scenario therefore whether ukraine is likely to wield market power is crucial to the success of the south stream project because that is the only scenario in which the project yields both a positive expected npv to its sponsors and the highest value to the market as a whole

china s co2 emission structure for 1957 2017 through transitions in economic and environmental policies abstract this paper provides an insight into the structure of co 2 emissions in china through transitions in economic and environmental policies for the period of 1957 2017 by using input output and network analysis with newly compiled environmentally extended historical input output tables of china these tables which include firm level industry level and macro level statistical data are the first environmentally extended input output tables covering the years in the early stage of the people s republic of china the results present the following two main findings the first is due to the stable economic structure associated with the independent economic policy china s emission structure has been stable for more than 60 years heavy industry has contributed about 80 of co 2 emissions since the 1950s on a second account although the emission structure was stable stricter environmental controls and regulations led to a decrease of the growth rate of co 2 emissions after 2010 against this background as a policy choice of china instead of carbon leakage that could break up the stable economic structure balanced technology upgrading across all sectors induced by stricter environmental controls is a realistic way for china to achieve increased energy efficiency emission mitigation and economic development so that the country can keep the promise of reducing co 2 emissions after they peak around 2030

a new product growth for model consumer durables this article originally appeared in management science january 1969 volume 15 number 5 pp 215 227 published by the institute of management sciences a growth model for the timing of initial purchase of new products is developed and tested empirically against data for eleven consumer durables the basic assumption of the model is that the timing of a consumer s initial purchase is related to the number of previous buyers a behavioral rationale for the model is offered in terms of innovative and imitative behavior the model yields good predictions of the sales peak and the timing of the peak when applied to historical data a long range forecast is developed for the sales of color television sets

what drives the change in china s energy intensity combining decomposition analysis and econometric analysis at the provincial level abstract we employ decomposition analysis and econometric analysis to investigate the driving forces behind china s changing energy intensity using a provincial level panel data set for the period from 1995 to 2009 the decomposition analysis indicates that a all of the provinces except for a few experienced efficiency improvement while around three fourths of the provinces economics became more energy intensive or remained unchanged b consequently the efficiency improvement accounts for more than 90 of china s energy intensity change as opposed to the economic structural change the econometric analysis shows that the rising income plays a significant role in the reduction of energy intensity while the effect of energy price is relatively limited the result may reflect the urgency of deregulating the price and establishing a market oriented pricing system in china s energy sector the implementation of the energy intensity reduction policies in the eleventh five year plan fyp has helped reverse the increasing trend of energy intensity since 2002 although the chinese government intended to change the industry led economic growth pattern it seems that most of the policy effects flow through the efficiency improvement as opposed to the economic structure adjustment more fundamental changes to the economic structure are needed to achieve more sustainable progress in energy intensity reduction

a mixed complementarity based equilibrium model of natural gas markets we present a new multiseasonal multiyear natural gas market equilibrium model based on the concept of a competitive equilibrium involving the market participants producers storage reservoir operators peak gas operators pipeline operators marketers and consumers the first three classes are depicted as price takers consistent with perfect competition the pipeline operations are described with regulated tariffs but also involve congestion pricing as a mechanism to allocate scarce pipeline capacity the marketers are price takers in all markets except in sales to consumers in which they compete as nash cournot players finally consumers are described by demand curves for each of the four sectors residential commercial industrial and electric power we show that the equilibrium model is an instance of a mixed nonlinear complementarity problem ncp and provide sufficient detail not generally seen in previous complementarity models of natural gas the ncp formulation is derived from considering the karush kuhn tucker optimality conditions of the optimization problems faced by these participants under mild conditions we show that this ncp has a solution and under additional reasonable conditions we show that the market prices are unique we also validate the model on a representative sample network with nine market participants and three seasons using four scenarios

comparing structural decomposition analysis and index to analyze and understand historical changes in economic environmental employment or other socio economic indicators it is useful to assess the driving forces or determinants that underlie these changes two techniques for decomposing indicator changes at the sector level are structural decomposition analysis sda and index decomposition analysis ida for example sda and ida have been used to analyze changes in indicators such as energy use co2 emissions labor demand and value added the changes in these variables are decomposed into determinants such as technological demand and structural effects sda uses information from input output tables while ida uses aggregate data at the sector level the two methods have developed quite independently which has resulted in each method being characterized by specific unique techniques and approaches this paper has three aims first the similarities and differences between the two approaches are summarized second the possibility of transferring specific techniques and indices is explored finally a numerical example is used to illustrate differences between the two approaches

a complementarity model for the european natural gas market abstract in this paper we present a detailed and comprehensive complementarity model for computing market equilibrium values in the european natural gas system market players include producers and their marketing arms which we call traders pipeline and storage operators marketers lng liquefiers regasifiers tankers and three end use consumption sectors the economic behavior of producers traders pipeline and storage operators liquefiers and regasifiers is modeled via optimization problems whose karush kuhn tucker kkt optimality conditions in combination with market clearing conditions form the complementarity system the lng tankers marketers and consumption sectors are modeled implicitly via appropriate cost functions aggregate demand curves and ex post calculations respectively the model is run on several case studies that highlight its capabilities including a simulation of a disruption of russian supplies via ukraine

the shape of advertising response functions revisited a model of dynamic probabilistic thresholds prior work in marketing has suggested that advertising threshold effects levels beneath which there is essentially no sales response are rarely encountered in practice because advertising policies settle into effective ranges through early trial and error thresholds cannot be observed directly and arguments for their existence must be based primarily on a statistical footprint that is on relative fits of a range of model types to detect possible threshold effects we formulate a switching regression model with two regimes in only one of which advertising is effective mediating the switch between the two regimes is a logistic function of category specific dynamic variables e g order of entry time in market number of competitors and advertising levels nesting a variety of alternative formulations among them both standard concave and s shaped responses a sequence of comparisons among parametrically related models strongly suggests that threshold effects exist that market share response to advertising is not necessarily globally concave that superior fit cannot be attributed to model flexibility alone and that dynamic environmental competitive and brand specific factors can influence advertising effectiveness these effects are evident in two evolving durables categories suvs and minivans although not in the one mature nondurable category liquid detergent studied

european union gas market development abstract the recently announced energy union by the european commission is the most recent step in a series of developments aiming at integrating the european union s eu gas markets in order to increase social welfare and security of gas supply based on simulations with a spatial partial equilibrium model we analyze the changes in consumption prices and social welfare up to 2022 induced by the infrastructure expansions planned for this period for the current market as well as for three hypothetical scenarios a halt of russian gas deliveries to the eu during the winter period ru a simultaneous doubling of available lng lng and for brexit in which the united kingdom market is isolated from the eu in the case of the current market the new infrastructure leads to a slight decrease of wholesale prices moreover the potential of suppliers to exert market power decreases significantly particularly in the baltic states and finland which are the most exposed countries today and consumer surplus increases by 17 4 in the eu in the ru scenario consumer surplus decreases across europe with the largest losses occurring in the baltic states as well as in finland poland and romania in the lng scenario the gains in consumer surplus are primarily found in western europe however the planned infrastructure expansions distribute the gains and losses in consumer surplus more evenly over all eu member states with the exception of romania in the brexit scenario consumer surplus decreases by up to 5 1 in the united kingdom 19 2 in ireland and 3 6 in the other eu countries our results allow us to distinguish three categories of projects i change in gas availability leading to a general increase or decrease of social welfare all over the eu the only project increasing social welfare in all scenarios in most countries is the trans anatolian gas pipeline tanap ii existing gas sources made available to additional countries this leads to an increase of social welfare in the newly connected countries while social welfare drops slightly everywhere else iii projects with a marginal effect on the market most notably the recently announced turkish stream falls into this category our results indicate that if all proposed infrastructure projects are realized the eu s single market will become a reality in 2019 when finland is interconnected to the eu markets however we also find that social welfare can only be increased significantly for the eu as a whole if new gas sources become accessible at the same time efficiency gains albeit decreasing social welfare help to improve the situation of consumers and decrease the dependency of the eu as a whole on external suppliers

a diffusion model incorporating product benefits price income and information we start by assuming that a major benefit of many new durable products such as dishwashers and microwave ovens is time savings others such as vcrs also enhance the value of our leisure time using a household production framework we demonstrate that a utility maximizing individual will have a reservation price for the product which is a function of the product benefits and his wage rate by assuming that the wage rate has an extreme value distribution across the population we are able to derive for the aggregate process an income price dependent logistic adoption equation we then allow for the possibility that certain eligible consumers may delay their purchase of the product because they are unaware that it exists are suspicious of its quality or expect its price to fall unawareness uncertainty and hope for further price declines are assumed to decrease with the increase in the number of previous adopters the resulting diffusion model has the property that the product life cycle phenomenon can be explained jointly or separately by the income price process and the awareness uncertainty expectations process using data on household income on durable penetration within different income classes and on first purchase sales the aggregate diffusion model and its premises are tested and supported it is found that both the income price and awareness uncertainty expectations processes are at work however the dependence of the awareness uncertainty expectations delay process on the number of previous adopters e g word of mouth type effect exists only in certain product categories and is usually relatively weak it is demonstrated that if the word of mouth type effects are weak a price skimming strategy is optimal for a monopolist and also is likely to be implemented by oligopolists the sales forecasting implications of the model also are pursued

china s regional sustainability and diversified resource allocation dea environmental assessment on economic development and air pollution abstract environmental protection including the prevention of air pollution and health hazard materials such as pm2 5 and pm10 is now a very serious policy issue in china after attaining the rapid economic growth and development the pm stands for particular matter indicating the size of both solid particles and liquid droplets found in air unfortunately the economic development has produced a serious healthcare problem in not only china and other surrounding nations to enhance people s healthcare and appeal a good national image to the world china is recently looking for the new industrial and environmental policy direction to attain social sustainability in terms of economic development and environmental prevention to discuss policy implications on the new policy direction this study utilizes data envelopment analysis dea for assessment on its regional performance by incorporating pm2 5 and pm10 as undesirable outputs along with two disposability concepts i e natural disposability and managerial disposability no previous dea study has incorporated the amount of pm2 5 and pm10 in empirical investigation using a simulated data set for the period of 2013 2014 this study measures the efficiency of municipality cities under four different types of regional classifications the empirical results indicate that the chinese government should distribute its economic resources to cities which locate in the northwest region including lanzhou xining yinchuan and urumqi and reinforce more strict regulation on energy consumptions for environmental prevention in major cities e g beijing tianjin shanghai and chongqing the industrial policy change from the economic growth to the environment protection is essential for the future of china which is currently the second largest economic power in the world the environmental protection can enhance the china s image of contributing in economics industry and environmental protection to all other nations it can be envisioned that the new policy effort reduces the regional imbalance and increases the social sustainability in china the empirical findings and policy implications discussed in this study are applicable to not only china but also other industrial and developing nations and those are useful in guiding their industrial and environmental policy development

natural gas corridors between the eu and its main suppliers simulation results with the dynamic gastale model abstract growth in gas demand poses a challenge for european energy consumers and other gas importing countries in terms of an increasing dependency on gas imports and consequently also supply security this paper focuses on interactions among demand supply and investments in natural gas corridors namely pipeline transport lng and storage facilities affecting the european natural gas market over the period 2005 2030 a number of policy scenarios including a business as usual bau scenario are formulated to study the impact of demand uncertainty and delays in investment on the gas transport infrastructure required in the long run in europe the analyses indicate that substantial investments in gas transport corridors are needed to accommodate imports and seasonal demand variations analysis of scenarios of supply interruption in the form of suddenly reduced import capacity for particular pipeline routes indicates that portions of europe could experience price increases of up to 100 in the case of a year long interruption to accommodate import needs and to mitigate possible disruptions pipeline connections running from east to west need to be given special priority

cartelization in gas markets studying the potential for a gas opec natural gas is increasingly important as a fuel for electric power generation as well as other uses due to its environmental advantage over other fossil fuels using the world gas model a large scale energy equilibrium system based on a complementarity formulation this paper analyzes possible future gas cartels and their effects on gas markets in a number of regions across the world in addition scenarios related to lower transport costs and decreased unconventional gas supply in the united states are considered

optimal advertising policies for diffusion models of new product innovation in monopolistic situations this paper deals with the determination of optimal advertising strategies for new product diffusion models we consider the introduction of a new consumer durable in a monopolistic market and the evolution of sales is modelled by a flexible diffusion model repeat sales and possible entry of rivals are disregarded but we allow for discounting of future revenue streams and cost learning curve using standard methods of optimal control theory we characterize qualitatively the structure of an optimal advertising strategy for different versions of the diffusion model

multiplicity of equilibria in conjectural variations models of natural gas markets abstract spatial partial equilibrium models incorporating conjectural variations are widely used to analyze the development of oligopolistic multi agent markets such as international energy and raw material markets although this model type can produce multiple equilibria under commonly used assumptions to the best of our knowledge the consequences for the interpretation of the model results have not yet been explored in detail to this end we derive a linear complementarity model for the gas market and discuss under which assumptions on the model structure a component of the solution is unique in particular we find that the gas flow between a trader and a consumer is unique whenever the trader is modeled to exert market power in the consumer s market we demonstrate our findings by computing the extreme points of the polyhedral solution space and show that erroneous conclusions could be drawn whenever only one arbitrary point in the solution space is picked for interpretation furthermore we discuss whether economically meaningful parameter value changes exist which would enforce uniqueness in all components of the solution

optimal pricing strategy for new products robinson and lakhani 1975 initiated a long research stream in marketing when they used the bass model 1969 to develop optimal pricing path for a new product a careful analysis of the extant literature reveals that the research predominantly suggests that the optimal price path should be largely based on the sales growth pattern however in the real world we rarely find new products that have such pricing pattern we observe either a monotonically declining pricing pattern or an increase decrease pricing pattern that does not seem close to the sales path in this paper we use a variation of the generalized bass model called gbm developed by bass et al 1994 that yields optimal pricing policies that are consistent with empirical data

optimal dynamic advertising policy for new products advertising is one of the key marketing tools managers have at their disposal to influence their customers into purchasing a new product the overall objective of new product advertising is to inform and persuade customers drawing up an advertising plan for a new product that is under the influence of diffusion phenomenon is not an easy task hence research in this area is very limited in our research we use an empirically proven diffusion demand function that explicitly incorporates the advertising component our results suggest that optimal advertising is determined by the advertising effectiveness discount rate and the ratio of advertisement to profits depending upon the interplay among these factors the optimal advertising takes decrease increase increase decrease monotonically increasing or monotonically decreasing shape

china s energy consumption change from 1987 to 2007 a multi regional structural decomposition analysis abstract increasing use of energy has helped to stimulate china s economy despite central planning china has great differences in economic development energy endowment and energy consumption across its regions this paper uses the structural decomposition approach to uncover the regional disparities in energy consumption from 1987 to 2007 we also examine six possible key factors for the change in energy consumption by region we find that final demand change outpaced efficiency improvements to drive up energy use in all regions between 1987 and 2007 more surprisingly from 2002 to 2007 it appears that changes in production structure enhanced energy consumption in most regions china produced more energy intensive goods for capital investment and export we contend that improving the energy efficiency of key energy intensive sectors would lead a significant decline in energy intensity energy directly or indirectly is flowing from northwest central and north china to coastal regions regional specific policies should be designed to promote production structure change and curb energy demand

structural decomposition analysis of physical flows in the economy many environmental problems can be attributedto the extraction and emissions of physicalsubstances increasing our understanding of theeconomic and technological driving forcesbehind these physical flows can contribute tosolving the environmental problems related tothem the input output framework is a usefulsetting in which to integrate detailedinformation about economic structure andphysical flows in this article a specificmethod in input output analysis is reviewed namely structural decomposition analysis sda it is based on comparative static analysis which decomposes historical changes of a policyvariable into determinant effects sda has beenapplied for example to analyze the demand andtechnological driving forces of energy use co2 emissions and various other pollutantsand resources this article examines thetheoretical aspects of structuraldecomposition in particular those concerningphysical flows and environmental issues furthermore the article includes an extensivesurvey of empirical studies

revisiting drivers of energy intensity in china during 1997 2007 a structural decomposition analysis the decline of china s energy intensity slowed since 2000 during 2002 2005 it actually increased reversing the long term trend therefore it is important to identify drivers of the fluctuation of energy intensity we use input output structural decomposition analysis to investigate the contributions of changes in energy mix sectoral energy efficiency production structure final demand structure and final demand category composition to china s energy intensity fluctuation during 1997 2007 we include household energy consumption in the study by closing the input output model with respect to households results show that sectoral energy efficiency improvements contribute the most to the energy intensity decline during 1997 2007 the increase in china s energy intensity during 2002 2007 is instead explained by changes in final demand composition and production structure changes in final demand composition are mainly due to increasing share of exports while changes in production structure mainly arise from the shift of chinese economy to more energy intensive industries changes in energy mix and final demand structure contribute little to china s energy intensity fluctuation from the consumption perspective growing exports of energy intensive products and increasing infrastructure demands explain the majority of energy intensity increase during 2002 2007

endogenous production capacity investment in natural gas market equilibrium models abstract the large scale natural gas equilibrium model applied in egging 2013 combines long term market equilibria and investments in infrastructure while accounting for market power by certain suppliers such models are widely used to simulate market outcomes given different scenarios of demand and supply development environmental regulations and investment options in natural gas and other resource markets however no model has so far combined the logarithmic production cost function commonly used in natural gas models with endogenous investment decisions in production capacity given the importance of capacity constraints in the determination of the natural gas supply this is a serious shortcoming of the current literature this short note provides a proof that combining endogenous investment decisions and a logarithmic cost function yields a convex minimization problem paving the way for an important extension of current state of the art equilibrium models

optimal pricing and advertising policies for new product oligopoly models in this paper our previous work on monopoly and oligopoly new product models is extended by the addition of pricing as well as advertising control variables these models contain bass s demand growth model and the vidale wolfe and ozga advertising models as well as the production learning curve model and an exponential demand function the problem of characterizing an optimal pricing and advertising policy over time is an important question in the field of marketing as well as in the areas of business policy and competitive economics these questions are particularly important during the introductory period of a new product when the effects of the learning curve phenomenon and market saturation are most pronounced we consider first the monopoly case with linear advertising cost exponential demand and three different pricing rules the optimal variable pricing the instantaneous marginal pricing and the optimal constant pricing rules several theoretical results are established for these rules including the facts that the instantaneous marginal pricing rule is a myopic version of the optimal pricing rule and the optimal constant pricing rule is a weighted average over time of the instantaneous marginal pricing rule another surprising result is that after the market is at least half saturated a pulse of advertising must be preceded by a significant drop in price numerical solutions of a number of examples are discussed oligopolistic models are analyzed as nonzero sum differential games in the rest of the paper the state and adjoint equations are easy to write down but impossible to solve in closed form hence we describe how to reformulate these models as discrete differential games and give a numerical algorithm for finding open loop nash solutions the latter was used to solve three triopoly models in each case it was found that optimal prices and advertising rates start high and steadily decline

drivers of provincial so2 emissions in china based on multi regional input output analysis abstract studying the driving factors of pollutant emissions is of great significance for china in the formulation of pollution control strategies existing studies mainly focus on the causes of national aggregate emission changes however considering the large differences among provinces in china and their close economic linkages it is necessary to develop a provincial level analysis to shape provincial policies for emission reduction using the multi regional input output mrio tables of 30 provinces in china and adopting structural decomposition analysis we analyze how changes in the end of pipe treatment cleaner production economic production structure domestic final use domestic exports and international exports drive national and provincial so2 emissions decomposition results show that during 2002 2010 the absolute value of each effect based on the mrio model is higher than that based on the national aggregate input output model which indicates that the existing studies adopting the national average data conceal the variation in the driving factors and underestimate their contributions to so2 emission changes the decomposition results based on mrio model further show that the end of pipe treatment and cleaner production are the major emission reduction factors for all provinces and the effect of the former has noticeably increased during 2007 2010 for the eastern provinces interestingly the economic production structure becomes a major emission reduction factor during the period of 2007 2010 changes in domestic final demand domestic exports and international exports exhibit significantly different contributions among provinces the increased final demand in eastern provinces largely drive so2 emissions for all provinces based on the above findings policy implications that address the so2 emission reduction issues are proposed

recent developments in dynamic advertising research a variety of continuous time differential functions have been developed to investigate dynamic advertising problems in business and economics fields since major dynamic models appearing before 1995 have been reviewed by a few survey papers we provide a comprehensive review of the dynamic advertising models published after 1995 which are classified into six categories i nerlove arrow model and its extensions ii vidale wolfe model and its extensions iii lanchester model and its extensions iv the diffusion models v dynamic advertising competition models with other attributes and vi empirical studies for dynamic advertising problems for each category we first briefly summarize major relevant before 1995 models and then discuss major after 1995 models in details we find that the dynamic models reviewed in this paper have been extensively used to analyze various advertising problems in the monopoly duopoly oligopoly and supply chain systems our review reveals that the diffusion models have not been used to analyze advertising problems in supply chain operations which may be a research direction in the future moreover we learn from our review that very few publications regarding dynamic advertising problems have considered the supply chain competition we also find that very few researchers have used the diffusion model to investigate the dynamic advertising problems with product quality as a decision variable and the pricing decision has not been incorporated into any extant lanchester model the paper ends with a summary of our review and suggestions on possible research directions in the future

oligopoly models for optimal advertising when production costs obey a learning curve business policy questions frequently involve competitive encounters among several different firms oligopoly theory in economics was devised to answer similar questions but its results so far are largely confined to cases of monopoly one firm duopoly two firms and many firms wheat farmers the cases with n firms where 3 n 10 are of great interest to business policy but are rarely treated in the economics literature because of their extreme difficulty the natural mathematical model for studying such questions is the theory of differential games originally devised by r isaacs isaacs r 1975 differential games robert e krieger publishing co huntington new york originally published by john wiley sons new york 1965 for pursuer evader games later it was extended by j case case j h 1979 economics and the competitive process new york university press new york to nonzero sum differential games for application to questions of economic competition the problem of characterizing an optimal advertising policy over time is an important question in the field of marketing it is especially important during the period of the introduction of a new product and it is also during this time that the production learning curve phenomenon is most pronounced in this paper we study oligopoly models which combine elements of bass s demand growth model bass f m 1969 a new product growth model for consumer durables management sci 15 january 215 227 the vidale wolfe vidale m l h b wolfe 1957 an operations research study of sales response to advertising oper res 5 370 381 and ozga ozga s 1960 imperfect markets through lack of knowledge quart j econom 74 29 52 advertising models with linear or quadratic costs and the production learning curve hirschmann w p 1964 profit from the learning curve harvard bus rev 42 january february 125 139 the boston consulting group 1972 perspectives on experience the boston consulting group boston in the monopoly case n 1 the optimal advertising function is derived by applying green s theorem in the duopoly n 2 and triopoly n 3 cases we use discrete differential game models and find nash equilibrium solutions in each of these models the form of the optimal policy is easy to find but because of the complicated nature of the resulting differential equations closed form solutions for the optimal state and control trajectories are impossible to find hence we use a computer to compute these optimal trajectories and plot them for various parameter settings because 13n parameters must be chosen to define a model with n players a complete search of the parameter space is clearly impossible we content ourselves in this paper with presenting computer plots of four different interesting encounters of the triopoly model our methods can be extended to work just as well for competitive encounters among n players where 1 n 10 we believe that in this paper we have opened up the way to studying oligopoly theory with a small number of participants and under widely varying conditions although the lack of closed form solutions may disappoint some readers we feel that the easy availability of graphical solutions is a more than adequate substitute

reexamine so2 emissions embodied in china s exports using multiregional input output analysis previous studies on embodied emission in china s exports focus on the national aggregate analysis while pay little attention to the interregional emission transfer driven by exports we used multiregional input output model of 30 provinces to reexamine the embodied emissions and to capture the interregional linkage in it results in 2002 2007 show that so2 embodied in exports contributes 15 17 22 08 of the total domestic so2 emissions and 74 40 78 14 of the embodiment is in exports from the eastern provinces where over 90 of china s exports occur however only about 70 of the embodied emission in eastern china s exports is discharged in the east an increasing portion 24 to 34 is released in the central and western provinces as a result of interregional production linkage moreover the interregional connection becomes closer during the 2002 2007 period which increases the scale and intensity of embodied emission in china s export given large gaps in emission intensity among regions further analysis on guangdong china s largest export province shows that the so2 emissions per unit of output induced by guangdong s exports are larger than that induced by the province s own exports for most provinces especially the central and western provinces which are restricted in exports and indirectly export by supporting guangdong s exports via interregional economic linkage the results yield important implications for china s export and pollution emission control policy