Resolving Singularities in a Ramsey-type Growth Model

The aim of this paper is to discuss a mathematical solution procedure to solve a Ramsay-type growth model that explains the fundamentals of consumption and capital accumula-tion in a dynamic equilibrium setting. The problem is formulated as a system of recursive equations and studied through some numerical experiments for the time path of the different variables of the model under some alternative assumption for the steady-state equilibrium of the labour market conditioning the possible singularity of the model.     

考虑污染控制、技术进步和人力资本积累下的经济可持续增长

构建一个带有环境污染、污染控制、内生人力资本积累和内生技术进步的动态经济增长模型,并运用最优控制方法探讨经济最优增长路径.研究表明:人力资本积累效率、消费跨期替代弹性和时间贴现率决定着经济最优增长路径.消费跨期替代弹性、时间贴现率、人力资本积累效率、物质产品和技术研发部门的投入产出弹性、污染排放的产出和控制弹性会对稳态中的人均经济增长率、人均污染排放增长率产生影响.     

Capital–labor substitution and long-run growth in a model with physical and human capital

Most of the literature analyzing the growth-substitutability nexus considers models in which long-run growth is exogenous. We study this link in an endogenous growth model with physical and human capital. We show that for two economies differing uniquely in factor substitutability, the one with the higher elasticity of substitution will have higher long-run growth. This is due to the efficiency effect of a higher factor substitution. Furthermore, if the initial ratio of physical to human capital is below (above) its steady-state value, the economy with the higher elasticity of substitution will have a higher (lower) steady-state physical capital income share.     

人力资本、自然资本与最优经济增长要素分析

通过把人力资本、自然资本与社会生产总量联系起来 ,由消费物资多少、获得知识多少及自然资本存量大小这三因素来确定效用 ,提供了物质、人力和自然资本三种重要资产增长的模型框架 ,得到了经济的消费增长率、均衡时各种资本的增长率之间的关系和实现最优经济增长的控制策略 .     

两部门内生增长模型中财政政策的短期分析

在一个两部门内生增长模型中,讨论政府财政政策变化对居民消费,资本积累以及经济增长的长期影响和短期影响.发现在短期内,政府增加资本收入税不仅可以增加居民消费,而且可以刺激人力资本积累,从而刺激短期经济增长.但是政府财政政策改变对长期经济增长不产生影响,而且资本收入税会降低长期的消费水平和资本存量.另外,从经济增长形态和消费者福利两个角度讨论了资本收入税的无效性.     

Stabilizing the Hamiltonian system for constructing optimal trajectories

An infinite-horizon optimal control problem based on an economic growth model is studied. The goal in the problem is to optimize the mechanisms of investment in basic production assets in order to increase the growth rate of the consumption level. The main output variable-the gross domestic product (GDP)-depends on three production factors: capital stock, human capital, and useful work. The first two factors are endogenous variables of the model, and the useful work is an exogenous factor. The dependence of the GDP on the production factors is described by the Cobb-Douglas power-type production function. The economic system under consideration is assumed to be closed, so the GDP is distributed between consumption and investment in the capital stock and human capital. The optimal control problem consists in determining optimal investment strategies that maximize the integral discounted relative consumption index on an infinite time interval. A solution to the problem is constructed on the basis of the Pontryagin maximum principle adapted to infinite-horizon problems. We examine the questions of existence and uniqueness of a solution, verify necessary and sufficient optimality conditions, and perform a qualitative analysis of Hamiltonian systems on the basis of which we propose an algorithm for constructing optimal trajectories. This algorithm uses information on solutions obtained by means of a nonlinear regulator. Finally, we estimate the accuracy of the algorithm with respect to the integral cost functional of the control process.     

Social status and long-run effects of monetary policy in a two-sector monetary economy of endogenous growth

We develop a two-sector monetary economy with human capital accumulation and a cash constraint applied to both consumption and investment to examine the ways in which social status affects the impact of monetary policy on the long-run economic growth rate. Our findings suggest that the formation of human capital is an important determinant to the super-neutrality of money in the growth-rate sense. Within an economy with Lucas-type human capital formation, money is super-neutral; however, within an economy where human capital accumulation formation is more generalized, and in which both physical and human capital are used as inputs, the growth rate in money will have a negative effect on the long-run growth rate of the economy. The existence, uniqueness and saddle-path stability of balanced-growth equilibrium are also examined.     

Unbounded growth in the Neoclassical growth model with non-constant discounting

For a Neoclassical growth model, the literature highlights that exponential discounting is observationally equivalent to quasi-hyperbolic discounting, if the instantaneous discount rate decreases asymptotically towards a positive value. Conversely, in this paper a zero long-run value allows a solution without stagnation. We prove that a less than exponential but unbounded growth can be attained, even without technological progress. The growth rate of consumption decreases asymptotically towards zero, although so slowly that consumption grows unboundedly. The asymptotic convergence towards a non-hyperbolic steady-state which saving rate matches the intertemporal elasticity of substitution and the speed of convergence towards this equilibrium are analyzed.     

Dynamic Game Model of Endogenous Growth with Consumption Externalities

This paper introduces consumption externalities into an endogenous growth model of common capital accumulation and characterizes balanced growth equilibria. Contrary to the standard argument in previous studies, we show that the growth rate in a feedback Nash equilibrium can be higher than that in an open-loop Nash equilibrium if agents strongly admire the consumption of others. This result is irrelevant to whether preferences exhibit “keeping up with the Joneses” or “running away from the Joneses”.     

SOME RESULTS ABOUT RCK MODEL WITH ENDOGENOUSE FERTILITY

1IntroductionTheeconomicgrowthmodelwithendogenousfertilityhasbeengivenmuchattentioninthelit..at.,.[1--4)sincetheBeck'simportantpaperpublished{SJ.ButalmostallpaperinthisfieldfollowsBeck'smethodandusesOLGmodelofdiscretevariabletodealwithit.ItisraretodiscussthisproblembyusingtheRCKmodelofcontinuousvariable.Palivosrecentlygaveapaper[61tohandleitwiththeRCKmodel.FollowingPalivos'ideaandmethodandincorporatingassumptionabouttheutilitywithfertilityinGalor'srecentpaper[2],wegetanimprovedRCKmodel…     

COMBINING SOCIAL CAPITAL AND TECHNOLOGY FOR DROUGHT RESILIENCE IN AGRICULTURE

In water‐scarce regions of the world, water‐saving technology adoption augments farm productivity. But so does social capital. In this paper, the issue of ensuring livelihood for farmers through the combined use of social capital and water‐saving technology is modeled in the context of repeated droughts. The model presented here derives optimal resource conservation and accumulation strategies when the farmer must ensure minimum consumption during a set of repeated drought events in the future. Findings indicate that the path to drought resilience presents a complex trade‐off between accumulating one form of capital over another and is influenced by farmers’ wealth and water endowments, level of risk associated with the repeated droughts and the duration of the repeated drought event that the farmer plans to survive. A higher risk of repeated droughts leads to an increase in groundwater conservation efforts but delays technology adoption. Lower water endowments may also delay adoption and reduce social capital, however, a lower social capital or a slow rate of its growth is not a hindrance to adopting water‐saving technology earlier. Finally, social capital evolves to higher levels when farmer is simultaneously faced with a higher level of risks and a longer span of drought events.     

基于能源消费二重性的经济增长模型

能源作为国民经济生产最基本的物质基础,既是国民经济生产中不可或缺的生产要素,又是人们日常生活中必不可少的消费对象.对能源消费的这种二重性进行了分析,建立了考虑能源消费二重性的经济增长模型.讨论了生产、消费用能源的最优配置条件及资本折旧率、效用贴现率对经济均衡点资本存量的影响.     

Urban public pension, replacement rates and population growth rate in China

This paper uses an overlapping generations model to investigate the urban public pension in China. It examines the effects of the replacement rates and population growth rate on the capital–labor ratio, pension benefits, consumption and utility, and finds the optimal replacement rate. It is shown that raising the individual account benefit replacement rate only induces the increase in the individual account benefits. Raising the social pool benefit replacement rate induces the increase in the social pool benefits and retirement-period consumption, while the decrease in the capital–labor ratio, individual account benefits, working-period consumption and utility. The fall in the population growth rate leads to the increase in the capital–labor ratio, social pool benefits, individual account benefits, working-period consumption and utility, and leads to a decrease in the retirement-period consumption. The optimal social pool benefit replacement rate depends on the individual discount factor, social discount factor, capital share of income and population growth rate, and it decreases in the case of falling population growth rates. It will do more good than harm to raise the individual account benefit replacement rate, reduce the social pool benefit replacement rate and strictly implement China’s population policy.     

具有人力资本和科技进步的经济增长模型研究

通过引入新的变量,将二维非自治动力系统转化为二维自治的动力系统,得到包含教育,实物资本,人口和技术进步的经济增长模型.证明二维自治动力系统存在唯一的平衡点且为结点.对于给定的初始状态,模型描述的经济存在一条增长路径.通过对模型动态性质的讨论,得出维持经济长期增长的关键因素是技术进步.最后,讨论了死亡率、折旧率和对教育的投资对经济增长的影响,得出在相同的生育率的情况下,死亡率越低,经济增长越快;低折旧率对应于高经济增长,加大教育的投入也可有效地促进经济增长.     

APPLICATIONS OF HAMILTONIAN AND LAPLACE TRANSFORM IN AN ECONOMIC MODEL

Since 1928, Ramsey introduced variation to analysis the optimal savings in an intertemproal model. Mathematics becomes an important tool for economists, such as Pontryagin'sMaximal Principle, Bellman Principle, Dynamics etc. These mathematical tools give economya new viewpoint, on the other hand, it also gives mathematicians a good application exaxnple.In this paper, we apply Hamilton system and Laplace transform to analysis the long-run effectsand short-run effects of foreign aid on domes…     

存在人口增长极限下的改进Ramsey模型

在存在人口增长极限的假设下,对标准的Ramsey模型进行了修正,结果表明:首先,与常数人口增长率的Ramsey模型不同,模型的人均消费和人均资本并不一定随时间的推移而递增;其次,人均消费和人均资本不存在平衡增长路径均衡,但是存在渐进平衡增长路径均衡;再次,在外生参数满足一定条件的前提下,人均消费和人均资本渐近于均衡的过程是单调的.     

The Tradeoff between Consumption and Investment in Incomplete Financial Markets

In this paper we are concerned with the tradeoff between long term growth of the expected utility of wealth and consumption. The goal is to find a consumption policy for which the optimal rate of capital growth is zero, i.e. a policy for which balance between consumption and investment is reached. The asymptotic limit of this investment problem when the HARA parameter γ → -∝ is also studied.     

THE C-K MODEL WITH SOLVABLE ENDOGENOUS FERTILITY

§ 1　 IntroductionThe relationship of population and economic growth is one of the most importantproblems in modern economic growth theory.Establishing a mathematical model theoreti-cal to study the interrelation of population and economic growth becomes a fundamentalmethod in this field[1～ 7] .In the papers[8,9] ,we obtain the especial C-K models with solv-able endogenous fertility under the specified strongly additive utility function and Cobb-Douglas production function.In the models,th…     

可解内生生育率的C-K模型

Abstract. In this paper,a C-K model with solvable endogenous fertility under the strongly addi-tive utility function is presented. The discrimination conditions of the existence of the nonzerosteady states are given. Under a kind of utility function and production function,we prove thatthese conditions are satisfied and the economy at least has an optimal growth path. The position-al relationship of the multiple steady states on the plane is discussed when multiple steady statesand multiple growth paths exist. By numerical analysis ,the fertility decreses with the per capitacapital and per capita consumption increasing and increases with the per capita capital and percapita consumption decreasing on the economic growth path are obtained.     

Construction of a regulator for the hamiltonian system in a two-sector economic growth model

We consider an optimal control problem of investment in the capital stock of a country and in the labor efficiency. We start from a model constructed within the classical approaches of economic growth theory and based on three production factors: capital stock, human capital, and useful work. It is assumed that the levels of investment in the capital stock and human capital are endogenous control parameters of the model, while the useful work is an exogenous parameter subject to logistic-type dynamics. The gross domestic product (GDP) of a country is described by a Cobb-Douglas production function. As a utility function, we take the integral consumption index discounted on an infinite time interval. To solve the resulting optimal control problem, we apply dynamic programming methods. We study optimal control regimes and examine the existence of an equilibrium state in each regime. On the boundaries between domains of different control regimes, we check the smoothness and strict concavity of the maximized Hamiltonian. Special focus is placed on a regime of variable control actions. The novelty of the solution proposed consists in constructing a nonlinear stabilizer based on the feedback principle. The properties of the stabilizer allow one to find an approximate solution to the original problem in the neighborhood of an equilibrium state. Solving numerically the stabilized Hamiltonian system, we find the trajectories of the capital of a country and labor efficiency. The solutions obtained allow one to assess the growth rates of the GDP of the country and the level of consumption in the neighborhood of an equilibrium position.