In this paper,the endogenous demographic transition function is integrated into the classical Solow model. It is proven that the differential equation which describes the model at least has a nonzero equilibrium. The ...In this paper,the endogenous demographic transition function is integrated into the classical Solow model. It is proven that the differential equation which describes the model at least has a nonzero equilibrium. The differential equation has several equilibria when the technological level or the saving rate is not high enough and undergoes bifurcation at some specified parame-ter values. Therefore,the economy described by the model pre-sents multiple growth paths and ＂Malthusian Poverty Trap＂ when the technological level or the saving rate is low.展开更多
In this paper,under the assumption that the labor force function increases strictly and is bounded and the labor force growth rate function decreases monotonically from a positive value to zero,we obtain an improved S...In this paper,under the assumption that the labor force function increases strictly and is bounded and the labor force growth rate function decreases monotonically from a positive value to zero,we obtain an improved Solow Swan model. We prove that the per capita capital trends stabilitily to the steady state of the classical Solow Swan model with zero the labor force growth rate. Two comparison theorems,a limited theorem and a stability theorem are given. At the end of this paper,we give an example and discuss the economic meaning of this model and the theorems.展开更多
By introducing the logistic-like technology, the classical Solow-Swan model is extended to inquire the technological overflow and catch-up of the developing economy in this paper. The improved model is described by a ...By introducing the logistic-like technology, the classical Solow-Swan model is extended to inquire the technological overflow and catch-up of the developing economy in this paper. The improved model is described by a two-dimensional dynamical system. It is proved that the model has a unique equilibrium which is a sink and the solution of the equation is globally asymptotically stable. And the classical Solow-Swan model is a special case of the model given here. The economic growth patterns are discussed by phase portrait analysis at the end of this paper.展开更多
The aim of this study was to develop an adequate mathematical model for long-term forecasting of technological progress and economic growth in the digital age (2020-2050). In addition, the task was to develop a model ...The aim of this study was to develop an adequate mathematical model for long-term forecasting of technological progress and economic growth in the digital age (2020-2050). In addition, the task was to develop a model for forecast calculations of labor productivity in the symbiosis of “man + intelligent machine”, where an intelligent machine (IM) is understood as a computer or robot equipped with elements of artificial intelligence (AI), as well as in the digital economy as a whole. In the course of the study, it was shown that in order to implement its goals the Schumpeter-Kondratiev innovation and cycle theory on forming long waves (LW) of economic development influenced by a powerful cluster of economic technologies engendered by industrial revolutions is most appropriate for a long-term forecasting of technological progress and economic growth. The Solow neoclassical model of economic growth, synchronized with LW, gives the opportunity to forecast economic dynamics of technologically advanced countries with a greater precision up to 30 years, the time which correlates with the continuation of LW. In the information and digital age, the key role among the main factors of growth (capital, labour and technological progress) is played by the latter. The authors have developed an information model which allows for forecasting technological progress basing on growth rates of endogenous technological information in economics. The main regimes of producing technological information, corresponding to the eras of information and digital economies, are given in the article, as well as the Lagrangians that engender them. The model is verified on the example of the 5<sup>th</sup> information LW for the US economy (1982-2018) and it has had highly accurate approximation for both technological progress and economic growth. A number of new results were obtained using the developed information models for forecasting technological progress. The forecasting trajectory of economic growth of developed countries (on the example of the USA) on the upward stage of the 6<sup>th</sup> LW (2018-2042), engendered by the digital technologies of the 4<sup>th</sup> Industrial Revolution is given. It is also demonstrated that the symbiosis of human and intelligent machine (IM) is the driving force in the digital economy, where man plays the leading role organizing effective and efficient mutual work. Authors suggest a mathematical model for calculating labour productivity in the digital economy, where the symbiosis of “human + IM” is widely used. The calculations carried out with the help of the model show: 1) the symbiosis of “human + IM” from the very beginning lets to realize the possibilities of increasing work performance in the economy with the help of digital technologies;2) the largest labour productivity is achieved in the symbiosis of “human + IM”, where man labour prevails, and the lowest labour productivity is seen where the largest part of the work is performed by IM;3) developed countries may achieve labour productivity of 3% per year by the mid-2020s, which has all the chances to stay up to the 2040s.展开更多
This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h ...This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.展开更多
As a typical tropical agro-forestry ecosystem in Wenchang,Hainan Province,China,rational mechanisms of the rubber-tea-chicken eco-agricultural model were studied with the Solow technological level index,stability indi...As a typical tropical agro-forestry ecosystem in Wenchang,Hainan Province,China,rational mechanisms of the rubber-tea-chicken eco-agricultural model were studied with the Solow technological level index,stability indicator,harmonizing coefficient,grey correlation coefficient and production dominance.This study focused on rational hierarchical structure,the limiting factors and optimal strategies of the model development based on model structure,resource conditions and external market demands.Results showed that rational mechanism of the rubber-tea-chicken ecosystem model mainly included technological contributions,leverage function of dominance component(livestock husbandry),stability of the model structure and harmony of its components,the model dominant product's market demand and government's supporting policies.The contributions of fund,technology,information and talent resources played an important role in improving sustainability and productivity of the agro-forestry model.展开更多
基金Supported by the National Natural Science Foundation of China (70871094)the Humanities and Social Sciences Research Item of Ministry of Education of China (09YJA790155)
文摘In this paper,the endogenous demographic transition function is integrated into the classical Solow model. It is proven that the differential equation which describes the model at least has a nonzero equilibrium. The differential equation has several equilibria when the technological level or the saving rate is not high enough and undergoes bifurcation at some specified parame-ter values. Therefore,the economy described by the model pre-sents multiple growth paths and ＂Malthusian Poverty Trap＂ when the technological level or the saving rate is low.
文摘In this paper,under the assumption that the labor force function increases strictly and is bounded and the labor force growth rate function decreases monotonically from a positive value to zero,we obtain an improved Solow Swan model. We prove that the per capita capital trends stabilitily to the steady state of the classical Solow Swan model with zero the labor force growth rate. Two comparison theorems,a limited theorem and a stability theorem are given. At the end of this paper,we give an example and discuss the economic meaning of this model and the theorems.
基金Supported by the National Natural Science Foundation of China (79970104)
文摘By introducing the logistic-like technology, the classical Solow-Swan model is extended to inquire the technological overflow and catch-up of the developing economy in this paper. The improved model is described by a two-dimensional dynamical system. It is proved that the model has a unique equilibrium which is a sink and the solution of the equation is globally asymptotically stable. And the classical Solow-Swan model is a special case of the model given here. The economic growth patterns are discussed by phase portrait analysis at the end of this paper.
文摘The aim of this study was to develop an adequate mathematical model for long-term forecasting of technological progress and economic growth in the digital age (2020-2050). In addition, the task was to develop a model for forecast calculations of labor productivity in the symbiosis of “man + intelligent machine”, where an intelligent machine (IM) is understood as a computer or robot equipped with elements of artificial intelligence (AI), as well as in the digital economy as a whole. In the course of the study, it was shown that in order to implement its goals the Schumpeter-Kondratiev innovation and cycle theory on forming long waves (LW) of economic development influenced by a powerful cluster of economic technologies engendered by industrial revolutions is most appropriate for a long-term forecasting of technological progress and economic growth. The Solow neoclassical model of economic growth, synchronized with LW, gives the opportunity to forecast economic dynamics of technologically advanced countries with a greater precision up to 30 years, the time which correlates with the continuation of LW. In the information and digital age, the key role among the main factors of growth (capital, labour and technological progress) is played by the latter. The authors have developed an information model which allows for forecasting technological progress basing on growth rates of endogenous technological information in economics. The main regimes of producing technological information, corresponding to the eras of information and digital economies, are given in the article, as well as the Lagrangians that engender them. The model is verified on the example of the 5<sup>th</sup> information LW for the US economy (1982-2018) and it has had highly accurate approximation for both technological progress and economic growth. A number of new results were obtained using the developed information models for forecasting technological progress. The forecasting trajectory of economic growth of developed countries (on the example of the USA) on the upward stage of the 6<sup>th</sup> LW (2018-2042), engendered by the digital technologies of the 4<sup>th</sup> Industrial Revolution is given. It is also demonstrated that the symbiosis of human and intelligent machine (IM) is the driving force in the digital economy, where man plays the leading role organizing effective and efficient mutual work. Authors suggest a mathematical model for calculating labour productivity in the digital economy, where the symbiosis of “human + IM” is widely used. The calculations carried out with the help of the model show: 1) the symbiosis of “human + IM” from the very beginning lets to realize the possibilities of increasing work performance in the economy with the help of digital technologies;2) the largest labour productivity is achieved in the symbiosis of “human + IM”, where man labour prevails, and the lowest labour productivity is seen where the largest part of the work is performed by IM;3) developed countries may achieve labour productivity of 3% per year by the mid-2020s, which has all the chances to stay up to the 2040s.
基金supported by the National Natural Science Foundation of China(7117111370901041)
文摘This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.
基金funded by National Natural Science Foundation of China(Grant No.40971227)International science & Technology Cooperation Program of China (Grant No.2010DFA21880)China Postdoctoral Science Foundation
文摘As a typical tropical agro-forestry ecosystem in Wenchang,Hainan Province,China,rational mechanisms of the rubber-tea-chicken eco-agricultural model were studied with the Solow technological level index,stability indicator,harmonizing coefficient,grey correlation coefficient and production dominance.This study focused on rational hierarchical structure,the limiting factors and optimal strategies of the model development based on model structure,resource conditions and external market demands.Results showed that rational mechanism of the rubber-tea-chicken ecosystem model mainly included technological contributions,leverage function of dominance component(livestock husbandry),stability of the model structure and harmony of its components,the model dominant product's market demand and government's supporting policies.The contributions of fund,technology,information and talent resources played an important role in improving sustainability and productivity of the agro-forestry model.
