【作者】 左永生；

【导师】 胡适耕；

【作者基本信息】 华中科技大学 ， 概率论与数理统计， 2005， 硕士

【摘要】 货币政策对经济增长的影响正日益受到经济学家的重视,本文利用动力系统和随机控制等数学工具建立一组模型,考察了他们两者之间的关系,为方便起见,在不影响分析的前提下,把实际货币存量直接引入代表性消费者的效用函数,讨论代表性消费者在其预算约束下的折现效用最大化问题. 首先考察确定性的情形,此时,经济系统存在唯一的正均衡点,而且是鞍轨稳定的,在均衡状态下,经济增长率、资本—劳动比率和消费水平都与政府名义货币增长率无关.接着讨论随机情形,考虑一个封闭的经济体,假定代表性消费者持有货币与物质资本两种资产,取对数形式的效用函数,将税收内生化,不考虑人口增长的因素,得出了均衡状态下的经济增长率、通货膨胀率和税率,并讨论了货币增长率及其它变量对它们的影响; 继而进行了福利分析,证明了存在唯一的货币增长率使代表性消费者的福利达到最大,这在其它文献中是没有的.最后把上述随机模型进行扩展,假定政府按照一个固定的比率同时发行货币和债券,并给债券持有者一定的利率,得出了均衡状态下各资产的份额、经济增长率、通货膨胀率、消费—资本比率和税率,它们都与债券利率有关,而债券利率则由模型参数和政府政策决定; 接着讨论了模型参数和政府政策对以上均衡值的影响,特别讨论了政府债务政策对经济的影响,这也是其他相关文献没有讨论的; 最后讨论了货币增长率对代表性消费者福利的影响,证明了存在唯一的货币增长率使其达到最大值.更多还原

【Abstract】 The effect of monetary growth on economic performance has been more and more important for economist. In this thesis, we use some mathematical knowledge such as dynamic system and stochastic control theory to make some models, in which optimal monetary policy is investigated, to get it, representative consumer is assumed to maximize his expected lifetime utility, subject to his wealth constrain. Now, it is convenient to assume that he could get utility from his real money stock. At first, a deterministic framework is employed, the system is saddle-path stable, there is a positive steady state, and it is unique. At steady state, economic growth rate, capital-labor ratio and consumption are all independent of money growth rate. Next, we show a stochastic model, in which we investigate a closed economy, it is assumed that representative consumer holds two assets: money and capital, and his utility function is logarithmic function. Then we get the equilibrium value of economic growth rate, inflation rate and tax rate. Unlike the deterministic model, they rely on money growth rate. Besides, we show there is a unique rate of money growth can be choose to optimize representative consumer’s welfare, it has not appeared in literature before. At last, government bonds is introduced, it is assumed that government debt policy is specified in terms of maintaining a fixed bonds to money. Then we get the equilibrium value of portfolio of asset, capital growth rate, inflation rate, consumption-capital ratio and tax rate, they rely on the rate of nominal interest of government bonds, which is determined by parameter and government policy. Given this, we study the effect of model parameter and government policy on these values. Especially we investigate the effect of government debt policy on them, which is not shown in related literature before. In the end, the effect of money growth rate on representative consumer’s welfare is studied and it is proved there is a unique rate of money growth to optimize it.更多还原