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Monetary policy on economic growth is gaining attention of economists , this paper, power systems and stochastic control and other mathematical tools to create a set of models to study the relationship between them , for convenience , without affecting the analysis premise, the real money stock directly into the consumer's utility function representative to discuss the representation of consumers in their budget constraints discounted utility maximization problem first examine the case of certainty at this time, there is a unique economic system positive equilibrium point is a saddle rails and stable , in equilibrium , economic growth , capital - labor ratio and consumption levels are nominal money growth has nothing to do with the government . then discussed the random case , consider a closed economy , it is assumed on behalf of of consumers hold money and physical capital two assets , logarithmic form of the utility function , the endogenous tax , without regard to population growth factor , obtained equilibrium economic growth, inflation and tax rates , and discussed the monetary growth rates and their impact on other variables ; subsequently conducted a welfare analysis to prove the existence and uniqueness of monetary growth that maximize consumer welfare representative , which in other literature is not. Finally, the above be extended stochastic model , assuming a constant rate according to the Government while issuing currency and bonds , and give bondholders a certain interest rate , obtained equilibrium share of each asset , economic growth, inflation , consumer - capital rates and tax rates , which are related with the bond rate , while the bond rate as the model parameters and government policy decisions ; followed by a discussion of the model parameters and the equilibrium value of government policies on the impact of the above , in particular, discussed the government debt policy impact on the economy , which but also other relevant literature not discussed ; finally discusses monetary growth effects on consumer welfare representative , prove existence and uniqueness of monetary growth to reach the maximum.
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