Money Growth In Stochastic Control Models

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.